an empirical investigation

The International Journal of

R

Business and Finance ESEARCH

VOLUME 6

NUMBER 4

2012

CONTENTS Volatility and Compounding Effects on Beta and Returns William J. Trainor Jr Do Small and Medium Sized Enterprises Match their Assets and Liabilities? Evidence from Portugal Jan Bartholdy, Cesario Mateus & Dennis Olson

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13

Convenience Yields in Bulk Commodities: The Case of Thermal Coal Jason West

33

International Evidence on Market Linkages after the 2008 Stock Market Crash Gulser Meric, Christine Lentz, Wayne Smeltz & Ilhan Meric

45

The Price Response to Nikkei 225 Stocks Index Adjustments Chia-Jung Tu

59

The Price of Stocks in Latin American Financial Markets: An Empirical Application of the Ohlson Model Pedro Martínez, Diego Prior & Josep Rialp

73

Forecasting Term Structure of HIBOR Swap Rates Mei-Mei Kuo, Shih-Wen Tai & Bing-Huei Lin

87

Cost Efficiency of French Commercial Banks: Domestic versus Foreign Banks Raoudha Béjaoui Rouissi & Houssam Bouzgarrou

101

Analysis of Extreme Dependence Between Istanbul Stock Exchange and Oil Returns Gözde Ünal & Derya Korman

113

Integration of Key Worldwide Money Market Interest Rates and The Federal Funds Rate: An Empirical Investigation Krishna M. Kasibhatla

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The International Journal of Business and Finance Research Editors Academic Editor Terrance Jalbert

Managing Editor Mercedes Jalbert Editorial Advisory Board Robert J, Boldin Indiana University of Pennsylvania James E. Briley Northeastern State University E.M. Ekanayake Bethune-Cookman University Gary M. Fleischman University of Wyoming Stoyu I. Ivanov San José State University Paul D. Hutchison University of North Texas John S. Jahera Jr. Auburn University Lynda S. Livingston University of Puget Sound

Linda Naimi Purdue University M.T. Naimi Purdue University Petr Polák Swinburne University Eduardo E. Sandoval Universidad de Concepción Jonathan D. Stewart Abilene Christian University Dirk Swagerman University of Groningen Ranjini Thaver Stetson University Gianfranco Vento Regent’s College-London

The International Journal of Business and Finance Research, ISSN: 1931-0269 (print) and ISSN 2157-0698 (online), publishes high-quality articles in all areas of finance, accounting and economics. Theoretical, empirical and applied manuscripts are welcome for publication consideration. The Journal is published quarterly by the Institute for Business and Finance Research, LLC. All papers submitted to the Journal are double-blind reviewed. The Journal is distributed in print, through SSRN and EBSCOhost Publishing, with nation-wide access in more than 70 countries. The Journal is listed in Cabell’s directories and Cabell online. The Journal is also indexed in the American Economic Association’s Econlit, e-JEL,and JEL on CD, Ulrich’s Periodicals Directory, and Colciencia. The views presented in the Journal represent opinions of the respective authors. The views presented do not necessarily reflect the opinion of the editors, editorial board or staff of the Institute for Business and Finance Research, LLC. The Institute actively reviews articles submitted for possible publication. However, the Institute does not warrant the correctness of the information provided in the articles or the suitability of information in the articles for any purpose. This Journal is the result of the collective work of many individuals. The Editors thank the members of the Editorial Board, ad-hoc reviewers and individuals that have submitted their research to the Journal for publication consideration. All Rights Reserved . The Institute for Business and Finance Research, LLC

ISSN : 1931-0269 (print) and ISSN: 2157-0698 (online)

The International Journal of Business and Finance Research ♦ VOLUME 6 ♦ NUMBER 4 ♦ 2012

VOLATILITY AND COMPOUNDING EFFECTS ON BETA AND RETURNS William J. Trainor Jr, East Tennessee State University ABSTRACT Previous research indicates that long-term investors are not compensated for beta or volatility risk. This study shows these two results are at least partly due to the mathematics of compounding exacerbated in high volatility markets. Theoretical beta portfolios defined to perform exactly as the Capital Asset Pricing Model (CAPM) would predict on a monthly basis, show that high beta portfolios dramatically outperform in low volatility environments and underperform in high volatility environments. Empirically sorted beta portfolios confirm the results and show in a low volatility environment, high beta portfolios outperform low beta portfolios by 0.42% a month and underperform by 0.51% in high volatility environments. When combining the two market environments, the inevitable result shows no relationship between beta and return. JEL: G11 KEYWORDS: Beta, Compounding, Volatility INTRODUCTION

T

he single factor market model, and by extension, the capital asset pricing model (CAPM) is one of the most tested models in finance. Originally set forth by Sharpe (1964), Litner (1965) and Mossin (1966), the model concludes with the simplest proposition in finance: greater risk should be compensated with a greater return over time. However, over the last 30+ years, empirical validation of this premise has been stymied. One crucial overlooked factor often referred to as the compounding problem help explains why this has been the case. The problem can be elucidated by considering the following: Assume a 0% risk free rate and an index return that falls 10% in period 1 and increases 12% in period 2. Over both periods, the index has a cumulative return of 0.8%. Now consider a 2.0 beta portfolio. It falls 20% in period 1 and increases 24% in period 2. Over both periods, its cumulative return is -0.8%. A 0.8 beta portfolio actually returns 0.83% over the two periods. Thus, over the two periods, the high beta portfolio underperforms the market and a 0.8 beta portfolio actually outperforms the market despite the overall positive market return. This compounding problem is exacerbated through time the higher the beta and the greater the level of volatility. Now consider the CAPM. Traditional testing of the CAPM first employed by Fama & Macbeth (1973) tests whether the coefficient on a regression running the excess return of the stock against beta is significant and positive. The regression takes the general form of R it − R ft = αt + γt βi + µi

(1)

where Rit - Rft is the return on the ith stock minus the risk-free rate and αt and γt are regression coefficients. Betas (β) are calculated based on time period t-1 returns and the above regression is run to see if beta is significantly related to excess returns in time t, i.e. is γt positive and significantly different from zero.

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W. J. Trainor | IJBFR ♦ Vol. 6 ♦ No. 4 ♦ 2012

The inherent problem with this is that monthly returns are usually used to calculate betas. Thus, empirical betas to some extent are just a measure of relative monthly volatility. The greater the relative volatility for a given stock, the greater its beta and theoretically, it should be associated with higher returns. However, the higher the beta, the greater the compounding problem will be when calculating a return over an extended period. In periods of very little volatility, beta should positively relate to excess returns. In periods of high volatility, the compounding problem will be the deciding factor and higher beta stocks will not demonstrate higher returns even if the index return is positive. The findings of this study reconfirm that low beta portfolios perform just as well and even outperform high beta portfolios over long time horizons. However, in low volatility markets, high beta portfolios significantly outperform low beta portfolios. In contrast, the returns of high beta portfolios are significantly negative in high volatility markets. The compounding problem easily explains this phenomenon. Thus, beta appears to be a relevant risk factor only for short-term and more active investors. Over longer horizons, high beta portfolio’s significant losses during volatile periods offset their outperformance in low volatility environments. These losses cause the long-run beta-return relationship to break down due to the simple mathematics of compounding. The remainder of this paper organizes as follows: A short literature review precedes the derivation of a mathematical model showing how the compounding problem affects higher beta portfolios. A description of the data and methodology follows. Thereafter, the results section demonstrates the magnitude of the compounding problem using "perfect" monthly betas and empirically shows how beta and volatility sorted portfolios perform in both high and low volatility environments. A simple ex ante trading model is also tested. The paper finishes with some concluding comments. LITERATURE REVIEW Although the compounding problem highlighted above seems relatively obvious, the havoc it causes did not garner serious scrutiny until the significance of its effect manifested itself in the recently created leveraged ETF market. With funds creating daily betas up to 3.0, the effects of compounding condensed into a relatively short period. Despite near perfect daily betas, leveraged funds had dismal annual performance regardless of underlying index returns. Several studies expounded on this issue and specifically identified compounding as the singular most important explanation, (Trainor & Baryla, 2008; Carver, 2009; Avellaneda & Zhang, 2009; Lu, Wang, & Zhang, 2009; Cheng & Madhavan, 2009). Although betas discussed in the leveraged ETF market are absolute betas since they multiply the actual index return and not the excess return relative to the risk-free rate, the compounding problem can be just as serious when employing the CAPM. Studies running the gamut from Fama & MacBeth (1973) to Fama & French (1992) conclude that the CAPM does not empirically hold. This even led Hulbert (1992) to exclaim, "Beta is dead." Fama & French (2004) continue to reiterate this conclusion although the debate continues, (Grauer & Janmaat, 2009). These studies do not identify the compounding problem. Although not expressly recognized, Pettengill, Sundaram, & Mathur (1995, 2002) mitigate the compounding issue when they tested beta by separating the market into up and down monthly return periods. Not surprisingly, they show that beta actually explains 70% or more of the deviation across portfolios. Their explanation centered on the difference between ex-ante expectations and ex-post realizations, but unwittingly, they also simultaneously eliminated most of the compounding problem by not combining the up months with the down.

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More recently, it has also been shown that low volatility and low beta stocks outperform high volatility and high beta stocks by more than 1% a month, (Ang, Hodrick, Xing, & Zhang, 2006, 2009; Baker, Bradley & Wurgler, 2011). Once again, this phenomenon appears to have its roots within the compounding problem and Baker, Bradley & Wurgler (2011) even make reference to this issue but do not develop the idea to any extent. Thus, stocks or portfolios may be doing exactly what their betas imply they do given market volatility issues. If one measures beta on a monthly basis, it should not be surprising that its usefulness and relationship to return is also going to be on a short-term basis. Although the market has averaged a positive return over time, both the length of time studied and the underlying volatility has broken the link between beta and long-run returns. The next section demonstrates the theoretical underpinnings of why this is the case. THE COMPOUNDING PROBLEM To demonstrate the compounding problem, assume the market portfolio (M) follows a geometric Brownian motion. From Ito's lemma, it follows that: dM/M = µdt + σdW

(2)

where µ is the mean, σ is volatility, and W is standardized Brownian motion. The continuously compounded return for the market from i =0 to t is: MRt = µt − σ2t /2

(3)

dP/P = βdM/M = βµdt + βσdW

(4)

PRt = βµt − β2 σ2t /2

(5)

PRt − βMRt = − [(β2 − β)/2]σ2t

(6)

PRt − MRt = (β − 1)µt + (1 − β2 )σ2t /2

(7)

Now consider any portfolio with a return perfectly related to the market by beta (B). The return model for this portfolio (P) is:

The cumulative compounded return for this portfolio from i = 0 to t is then:

This simply shows that the return and standard deviation of the return process is some beta multiple of the market portfolio. If the portfolio continuously follows the market relative to its beta, then the relationship between PRt and βMRt is

This shows for any positive variance, that the portfolio will not maintain a return that is beta times the underlying index return. The greater the variance and the higher the beta, the faster this relationship degenerates. In absolute terms, the return difference between the portfolio and the market is:

This states that for any given positive market return, if the volatility is high enough, the cumulative return for a portfolio with β > 1 will be less than the market portfolio.

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Figure 1: Annualized Return Difference

Annual Return Difference

15.00% 10.00% 5.00% 1.5 Beta

0.00%

2.0 Beta

-5.00%

2.5 Beta

-10.00% -15.00%

10%

20%

25%

30%

Annual Standard Deviation This figure shows the difference in returns between beta portfolios and the index for standard deviations ranging from 10 to 30%.

Using Equation (7), Figure 1 shows the difference in returns between portfolios with betas of 1.5, 2.0 and 2.5 relative to the index over a year assuming an 8% cumulative annualized return. As Figure 1 shows, the relationship between beta and return turns negative as volatility levels increase. A 2.5 beta portfolio will underperform the index when volatility exceeds 21% and a 1.5 beta portfolio underperforms when volatility reaches 25%. As a numerical example, if β = 2.0, then equation (7) is equal to µt - 1.5σt2. Thus, when µt = 1.5σt2 there will be no relationship between beta and return and when µt < 1.5σt2, the relationship will actually be negative. To quantify this further, if the annualized market standard deviation is 30%, then 1.5 times the daily volatility is equal to 0.00036 assuming 250 trading days in a year. A daily return of 0.036% gives a cumulative annualized return of 9.4% and under these conditions, a portfolio with a β = 2.0 will have zero excess return relative to the market. Any return less than this will result in a 2.0 beta portfolio underperforming the index. Although the CAPM is by definition a single period model, in reality both beta and a portfolio's return are measured over time. The results above clearly show how the compounding problem causes the expected positive relationship between beta and return to break down as volatility increases or market returns decrease. DATA AND METHODOLOGY Although the long-term empirical relationship between beta and returns appears to be non-existent, part of the reason could be due to beta drift after creating portfolios. To eliminate this issue among others that plague beta sorted portfolios, theoretical beta portfolios ranging from 0.5 to 3.0 are created so that their returns are always equal to exactly what the CAPM would imply on a monthly basis. The actual return each month of the Center for Research in Security Price's (CRSP) value weighted index from January 1926 to December 2009 is used as the market proxy and the 30-day t-bill rate is used for the risk-free rate. Excess returns for each beta portfolio are regressed on the actual beta values using equation (1) described earlier. In addition, market periods are separated into high and low volatility environments based on whether they are above or below the average volatility. For the CRSP value weighted index, the average standard deviation from 1926-2009 is 15.8%. Welch's (1947) t-test for the difference in means between

4


volatility environments is conducted for each beta ranked portfolio. This test is appropriate since the comparison of means occurs between different volatility environments. The actual test statistic is:

𝑡=

x�1 − x�2

(8)

s2 s2 � 1+ 2 n1 n2

where x�1 and x� 2are the sample means and s12 and s22 are the sample variances.

Additionally, the same procedure above is applied to CRSP's NYSE/AMEX Scholes-William sorted beta portfolios and volatility sorted portfolios from 1970 to 2009. The smallest and largest beta and volatility portfolios are not used due to extreme values. RESULTS Theoretical Beta Portfolios Table 1 shows the cumulative value of a $1 investment beginning in 1926 for the various beta portfolios. By December 2009, a $1 investment in the index is worth $2,286. For a 2.0 beta portfolio, this value reaches $12,007. Thus, in theory, seeking out higher beta portfolios could lead to vastly superior returns. However, note that a 2.5 beta portfolio only accumulates to $6,982 and a 3.0 beta portfolio only accumulates to $1,093. Thus, for long-term investors, the compounding issue clearly shows that investing in portfolios with significantly higher betas is not associated with higher returns. This result is robust as it holds for the last 40 years as well. Table 1: Theoretical Beta Returns 1926 -2009 Cum. Value

Beta 0.5 $311

Beta 1.0 $2,286

Beta 1.5 $7,900

Beta 2.0 $12,007

Beta 2.5 $6,982

Beta 3.0 $1,093

1926 -2009 Annual Ret.

7.07%

9.64%

11.28%

11.83%

11.11%

8.69%

1970 -2009 Annual Ret.

8.19%

10.07%

11.28%

11.75%

11.41%

10.15%

This table shows the average cumulative value along with the annualized return for the CRSP Value Weighted index.

On a shorter-term basis, Table 2 shows the rolling annual average returns across these beta portfolios. The results show a monotonically increasing relationship between beta and return. Thus, for yearly time horizons, there is a theoretical positive relationship between beta and returns. However, portfolios with betas of 2.0 and greater are associated with extreme risk as all suffer annual losses on at least one occasion of more than 90%. Despite the fact the overall rolling average annual return increases for higher beta portfolios, the compounding issue over longer time horizons not only mitigates, but also overwhelms the shorter-term higher returns. Because higher levels of volatility exacerbate the compounding problem, it is of note to see what occurs to beta portfolios during periods of above and below average volatility. Table 2 shows the advantage of owning higher beta portfolios during periods of below average volatility. While the index returns 15.83%, a 3.0 beta portfolio returns 46.70%. The results are qualitatively the same for the last 40 years as well.

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Table 2: Theoretical Beta Annual Returns Beta 0.5

Beta 1.0

Beta 1.5

Beta 2.0

Beta 2.5

Beta 3.0

Average Annual Ret.

7.57%

11.71%

16.14%

20.88%

25.90%

31.18%

Min. Annual Ret.

-39.21%

-65.84%

-82.42%

-92.01%

-97.03%

-99.28%

Max. Annual Ret.

68.40%

156.35%

260.22%

372.36%

481.57%

573.90%

Low Vol. Annual Ret.

9.54%

15.83%

22.66%

30.05%

38.05%

46.70%

High Vol. Annual Ret.

2.94%

2.02%

0.86%

-0.64%

-2.62%

-5.22%

t-test for difference between means

3.83***

13.81***

8.32***

8.79***

9.36***

10.06***

Average Annual Ret.

8.31%

10.92%

13.62%

16.40%

19.24%

22.12%

Low Vol. Annual Ret.

9.36%

13.35%

17.60%

22.11%

26.87%

31.90%

High Vol. Annual Ret.

5.93%

5.40%

4.61%

3.48%

1.96%

-0.03%


3.33***

4.17***

4.68***

5.12***

5.55***

5.98***

1926 - 2009

1970 - 2009

This table shows annual rolling returns using the CRSP Value Weighted index for theoretical beta portfolios ranging from 0.5 to 3.0. High volatility periods are defined as periods greater than the average for the entire period while low volatility periods are those periods less than the average. Volatility is defined as the annualized standard deviation of 12 monthly returns. ***Significant at the 1% level.

Conversely, during periods of above average volatility, returns decline monotonically from 2.94% for a 0.5 beta portfolio to -5.22% for a 3.0 beta portfolio. These results also hold over the last 40 years with returns falling from 5.93% to -0.03%. In addition, for every beta portfolio, mean returns are significantly greater during low volatility periods and significantly lower during high volatility periods. Welch's t-test confirms this with t-values ranging from 3.33 to 13.81, all of which are significant at the 1% level. Table 3: Theoretical Beta Regression Results Coefficient Estimate

R-square

1926-2009

Constant

Beta (t-stat)

Avg. Excess Return

-0.0129

0.0945 (44.94)***

99.8

Low Vol. Excess Return

-0.0250

0.1485 (34.53)***

99.6

High Vol. Excess Return

0.0107

-0.0311 (-8.49)***

96.4

1970-2009

Constant

Beta (t-stat)

Avg. Excess Return

-0.0026

0.0553 (110.34)***

99.9


-0.0127

0.0902 (47.74)***

99.9


0.0200

-0.0236 (-8.81)***

95.1

This table shows the regression results based on equation (1) which regresses the excess annual returns derived from theoretical beta portfolios on beta. ***Significant at the 1% level.

Table 3 shows the regression results based on equation (1) relating beta to excess returns. These results statistically confirm beta is positively related to excess returns in low volatility periods and significantly negative during high volatility periods at the 1% level. It is also apparent the overall positive annual relationship is driven solely by the magnitude of the positive relationship during low volatility periods. For the overall period, a 0.1 increase in portfolio beta is associated with a 1.485% increase in excess return during low volatility periods. However, this is offset by a 0.311% decrease in high volatility environments. For long-term investors, these swings in returns and the mathematics of compounding cause the annual positive relationship to disintegrate over time.

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Beta Sorted Portfolios The results above show how even theoretically derived portfolios that produce perfect monthly returns in accordance with the CAPM can still show a negative relationship between beta and returns when volatility is high. Empirically derived beta portfolios suffer from the same compounding issue and are subject to even further error due to beta instability and the unique returns to the component stocks in each portfolio. Table 4 shows the average monthly returns for the CRSP NYSE/AMEX Scholes-William sorted beta portfolios from 1970 to 2009. Portfolios rank from smallest to largest and beta values range from 0.67 to 1.42. Confirming previous research, there is no discernible relationship between beta and returns. The regression results in Table 5 show the coefficient for beta equal to 0.0003 with an insignificant t-stat of 0.57 and an r-square of only 5.1%. It should be noted that due to survivorship bias and the equal weighting used for the components stocks, the monthly returns for all the portfolios are quite high. Table 4: Empirical Beta Sorted Portfolio Monthly Returns Beta 1

Beta 2

Beta 3

Beta 4

Beta 5

Beta 6

Beta 7

Beta 8

Beta

0.67

0.83

0.93

1.03

1.11

1.20

1.28

1.42

Return

1.52%

1.59%

1.63%

1.60%

1.53%

1.57%

1.60%

1.58%

Low Vol.

1.95%

2.14%

2.26%

2.21%

2.24%

2.27%

2.35%

2.37%

High Vol.

0.85%

0.72%

0.64%

0.64%

0.43%

0.47%

0.43%

0.34%


2.56**

2.88***

3.05***

2.77***

3.03***

2.78***

2.79***

2.63***

This table shows monthly average returns from January 1970 to December 2009 for Scholes-William sorted beta portfolios. High volatility periods are defined as periods greater than the average for the entire period while low volatility periods are those less than the average. Volatility is defined as the annualized standard deviation of daily returns within each month. ***Significant at the 1% level;**5% level.

Table 5: Beta Sorted Regression Results Avg. Excess Return

Constant 0.0108

Beta (t-stat) 0.0003 (0.57)

R-square 5.1%


0.0124

0.0050 (5.65)***

93.2%


0.0083

-0.0068 (-9.11)***

91.2%

This table shows the regression results based on equation (1) which regress the average excess monthly returns derived from beta sorted portfolios on beta. ***Significant at the 1% level.

During periods of low volatility, the advantage of owning higher beta portfolios is clear as the lowest beta portfolio returns 1.95% while the highest beta portfolio returns an average of 2.37%. This may not appear economically significant, but on an annual basis, it is 5% greater and the regression results shown in Table 5 confirm beta is significant at the 1% level with a t-stat of 5.65. During high volatility environments, portfolio returns monotonically decrease from 0.85% to 0.34% per month. In this case, beta is negatively statistically significant at the 1% level with a t-stat of -9.1. Both of these regressions show beta explains more than 90% of the difference in excess returns across beta portfolios. This reaffirms the theoretical results in the previous section. In addition, at every beta level, the low volatility return exceeds the high volatility return in both an economic and statistically significant sense at the 1% or 5% level with t-stats ranging from 2.56 to 3.05. Thus, Tables 4 and 5 also show that the relationship between beta and returns is not dead. Volatility Sorted Portfolios The correlation between volatility sorted portfolios and beta is quite high. Table 6 shows as the standard deviation of the portfolios increases from 12.06% to 26.21%, the corresponding beta of these portfolios 7


increases from 0.71 to 1.37. The average monthly return actually shows that higher volatility portfolios are associated with higher returns. Regressing the returns on standard deviations confirms that this relationship is statistically significant at the 1% level with a 6.6 t-stat, (see Table 7). This is interesting in that these portfolios also have higher betas, which suggests a general positive relationship between beta and return. This is contrary to the lack of relationship found between beta and return for portfolios sorted by beta. Reaffirming the results from Table 4, high volatility and by association high beta portfolios, outperform their low volatility/low beta counterparts during periods of low volatility. At every ranked standard deviation portfolio level, low volatility portfolios significantly outperform high volatility portfolios with t-stats ranging from 2.28 to 3.39, all of which are significant at the 5% or 1% level. Comparing returns across ranked standard deviation portfolios in the two volatility environments, Table 7 shows that portfolio returns in high volatility periods are not significantly associated with portfolio standard deviation levels, t-stat of 0.33. During low volatility environments, the relationship is pronounced and significant with a t-stat of 6.39. Table 6: Volatility Sorted Portfolio Monthly Returns St. Dev.

Vol. 1 12.06%

Vol. 2 14.07%

Vol. 3 15.79%

Vol.4 17.27%

Vol.5 18.94%

Vol. 6 20.87%

Vol. 7 23.44%

Vol. 8 26.21%

Beta

0.71

0.86

0.97

1.05

1.12

1.21

1.31

1.37

Return

1.10%

1.20%

1.26%

1.27%

1.36%

1.40%

1.35%

1.61%

Low Vol.

1.58%

1.79%

1.90%

2.01%

2.11%

2.15%

2.08%

2.36%

High Vol.

0.34%

0.28%

0.26%

0.12%

0.18%

0.23%

0.19%

0.43%


3.20***

3.35***

3.25***

3.39***

3.18***

2.87***

2.52**

2.28**

This table shows monthly average returns from January 1970 to December 2009 using CRSP's NYSE/AMEX standard deviation ranked portfolios. High volatility periods are defined as periods greater than the average for the entire period while low volatility periods are those less than the average. Volatility is defined as the annualized standard deviation of daily returns within each month. ***Significant at the 1% level.

Table 7: Volatility Sorted Regression Results Avg. Excess Return

Constant 0.0030

Volatility (t-stat) 0.0299 (6.60)***

R-square 87.8%


0.0067

0.0468 (6.39)***

87.2%


-0.0026

-0.0027 (0.33)

13.2%

This table shows the regression results based on equation (1) which regress the average excess monthly returns derived from volatility sorted portfolios on the standard deviation. ***Significant at the 1% level.

Thus, volatility sorted portfolios do show a positive relationship between volatility and return, although it appears most of this is due to the outperformance of high volatility portfolios during below average volatility periods. This provides additional evidence that the compounding problem is an issue but not to the extent, it is in beta-sorted portfolios. It should also be pointed out that these are average monthly returns and do not necessarily imply that a long-term buy-and-hold strategy of high volatility portfolios will outperform. On the contrary, they are more likely to underperform due to the same compounding issue that plagues beta-sorted portfolios. Ex-Ante Trading The evidence above shows that high beta portfolios payoff during low volatility periods. However, this is based on ex-post volatility measurements. To the extent volatility is persistence (Mandelbrot, 1963; Engle, 1982; Bollerslev, 1986; Kritzman, 2010) and thus predictable, it may be possible to exploit this 8


relationship and find an ex ante reason to hold high beta portfolios. A simple trading rule based on the volatility phenomena is to hold the particular beta ranked portfolio if the previous month's volatility is less than the average volatility over the preceding 5 years. Otherwise, hold the lowest ranked beta portfolio. The risk-free asset is not used so the risk differential between the trading strategy and the buy and hold position is more comparable. Table 8 shows the results for this type of strategy for each beta-sorted portfolio. Unfortunately, this simple trading rule does not suggest moving into high beta portfolios based on ex ante volatility levels will increase returns. There is no statistical difference between using the trading rule and the buy and hold strategy at any beta level. In addition, there is no statistically significant relationship between beta and excess return using the trading rule, t-stat of -1.05 on the beta coefficient using equation (1). It is possible that advanced predictive models of volatility or the use of the Chicago Board Option Exchange’s Volatility Index (VIX) will help. However, the results here suggest long-term investors with no priori expectations on future volatility levels are better off investing in low beta portfolios. Table 8: Volatility Based Trading Returns Beta

Beta 1 0.67

Beta 2 0.83

Beta 3 0.93

Beta 4 1.03

Beta 5 1.11

Beta 6 1.20

Beta 7 1.28

Beta 8 1.42

Buy and Hold

1.52%

1.59%

1.63%

1.60%

1.53%

1.57%

1.60%

1.58%

Trading Rule

1.52%

1.60%

1.61%

1.56%

1.52%

1.52%

1.53%

1.53%


0.00

0.03

0.06

0.12

0.03

0.14

0.18

0.12

This table shows average monthly returns from 1970 to 2009 that compare a buy-and-hold strategy to a trading rule that involves holding the particular beta sorted portfolio when the previous month's volatility is less than the preceding 60-month average, else hold the lowest beta sorted portfolio.

CONCLUDING COMMENTS The evidence against a positive relationship between long-run returns and beta is substantial. This study demonstrates that even theoretically derived beta portfolios that explain 100% of the deviation in returns on a monthly basis will not show a positive relationship between beta and return over longer horizons due to the mathematics of compounding. Based on historical returns and volatility, portfolios with betas greater than two appear doomed to underperform over extended holding periods. However, for shorter investment horizons and especially within low volatility environments, there is a rationale for holding higher beta portfolios. Theoretically, there is a pronounced positive relationship between beta and return in low volatility environments where the effects of compounding are mitigated. From 1926 to 2009, the annualized return in low volatility environments for a 3.0 beta portfolio is 46.7% compared to -5.3% in above average volatility environments. This relationship remains over the last 40 years, and the last 20 as well. Empirically sorted beta portfolios show the same qualitative type of outperformance in low volatility environments and significant underperformance in high volatility environments. Compounding is clearly an issue in explaining the breakdown between beta and return over longer periods. For portfolios sorted by volatility, the results are not as clear. However, the outperformance of high volatility portfolios appears to be contained within below average volatility environments reinforcing the idea that the compounding problem is a major issue. Thus, it is the contention of this study that using beta to estimate the risk of a portfolio does have merit. In highly volatile markets when the cost of holding risky portfolios is high, high beta portfolio values fall. However, during low volatility environments, high beta portfolios do realize excess returns. 9


Unfortunately, a simple trading rule based on ex-ante volatility levels does not appear able to exploit this relationship. More advanced models to predict volatility may be more successful. This study is unable to demonstrate any ex ante rationale for long-term investors to hold high beta portfolios. For those with specific volatility forecasts and short-term horizons, the beta values of portfolios are relevant. If an investor is convinced volatility levels will remain low, investing in high beta portfolios should be associated with higher returns. Although this study shows the compounding problem is an issue for cumulative returns, it is unable to explain why the monthly average returns of higher beta portfolios are not associated with higher returns. Thus, other factors still plague the empirical results regarding the CAPM. In addition, the return calculations used in this study ignore transaction costs and both CRSP's beta and volatility-sorted portfolios suffer from serious survival bias. Moving forward, the effects of compounding in other markets remain unexplored. This issue is especially relevant for ETFs that have specialized in narrower markets that are more volatile. In addition, to the extent, the return degradation due to the compounding effect over any horizon can be isolated, a more enlightened answer may be forthcoming as to why size and book-to-market effects are so pronounced. Are these effects consistent regardless of the volatility environment? Finally, future research that controls for the compounding effect along with the use of the CAPM may improve portfolio performance evaluation and give a more accurate measure of manager derived excess return. REFERENCES Ang, Andrew, R. Hodrick, Y. Xing, & X. Zhang (2006) “The Cross-Section of Volatility and Expected Returns,” Journal of Finance, 61, pp. 259-299 Ang, Andrew, R. Hodrick, Y. Xing, & X. Zhang (2009) “High Idiosyncratic Volatility and Low Returns: International and Further U.S. Evidence,” Journal of Financial Economics, 91, 1, pp. 1-23 Avellaneda, M. & S. Zhang (2009), "Path-dependence of leveraged ETF returns," Available at SSRN: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1404708, 19 May. Baker, Malcolm, Brendan Bradley, & J. Wurgler (2011) "Benchmarks as Limits to Arbitrage: Understanding the Low Volatility Anomaly," Financial Analysts Journal, 67, No. 1, pp. 40-54 Bollerslev, T. (1986) "Generalized Autoregressive Conditional Heteroskedasticity," Journal of Econometrics, 31, pp. 307-27 Carver, A. (2009) "Do Leveraged and Inverse ETFs Converge to Zero," Institutional Investor Journals, ETFs and Indexing, 1, pp. 144-149. Cheng, Minder, & A. Madhavan (2009) "The Dynamics of Leveraged and Inverse Exchange-Traded Funds" Journal of Investment Management, Vol. 7, No 4 (2009), pp. 43-62. Engle, R. (1982) "Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica 50, pp. 987-1007 Fama, Eugene & K. French (1992) "The Cross Section of Expected Stock Returns," Journal of Finance 67, pp. 427-465

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Fama, Eugene & K. French (2004) "The Capital Asset Pricing Model: Theory and Evidence," Journal of Econcomic Perspectives, 18, No, 3, pp. 25-46 Fama, Eugene F. & J. Macbeth (1973) “Risk, Return, and Equilibrium: Empirical Tests,” Journal of Political Economy, 81 pp. 607-636 Grauer, Robert R. & J. Janmaat (2009) “On the Power of Cross-Sectional and Multivariate Tests of the CAPM,” Journal of Banking and Finance, Vol. 33, No. 5, pp. 775-787 Hulbert, Mark (1992) “Beta is Dead,” Forbes, June 22 Kritzman, Mark (2010) "Skulls, Financial Turbulence, and Risk Management," Financial Analysts Journal, Vol. 66, No. 5, pp. 30-41 Lintner, John (1965) "The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets," Review of Economics and Statistics, Vol. 47, No. 1, pp. 13-37 Lu, L., Jun W., & Z. Ge (2009) "Long term performance of leveraged ETFs," Available at SSRN: http://ssrn.com/abstract=1344133, 15 February. Mandelbrot, Benoit (1963) "The Variation of Certain Speculative Prices," Journal of Business, 36, pp. 394-419 Mossin, Jan (1966) "Equibrium in a Capital Asset Market," Econometrica, 34, pp. 768-783 Pettengill, G., Sundaram, S. & I. Mathur (1995) "The Conditional Relation between Beta and Returns," Journal of Financial and Quantitative Analysis, 30, pp. 101-116 Pettengill, G., Sundaram, S. & I. Mathur (2002) "Payment For Risk: Constant Beta vs Dual-Beta Models, Financial Review, Vol. 37, No. 2, pp 123-135 Sharpe, William (1964) "Capital Asset Prices: A Theory of Market Equilibrium," Journal of Finance, Vol. 19, No. 3, pp. 425-442 Trainor, W. & E. Baryla (2008) "Leveraged ETFs: A Risky Double that Doesn’t Multiply by Two," Journal of Financial Planning, 21, pp. 48-55. Welch, B. L. (1947) "The Generalization of "Student's" Problem When Several Different Population Variances are Involved," Biometricka, 34, pp. 28-35. BIOGRAPHY William Trainor is an associate professor at East Tennessee State University and a CFA Charterholder. He has written more than 30 papers on investments including publications in the Journal of Investing, Financial Services Review, Journal of Financial Planning, Journal of Personal Finance, and Financial Review. He can be reached at ETSU, Dept. of Economics and Finance, Box 70686, Johnson City, TN, 37614-1709, [email protected].

11


DO SMALL AND MEDIUM SIZED ENTERPRISES MATCH THEIR ASSETS AND LIABILITIES? EVIDENCE FROM PORTUGAL Jan Bartholdy, University of Aarhus Cesario Mateus, University of Greenwich Dennis Olson, American University of Sharjah ABSTRACT For small and medium-sized enterprises, various types of debt are not identical. There are specific costs and benefits associated with each funding source. We argue that the asset and liability sides of the balance sheet are interrelated. Specifically, we hypothesize that firms match specific assets with a specific set of liabilities. We test our theory using a unique sample of Portuguese firms for the years 1990-2000. Our data set identifies various short-term and long-term funding sources, as well as the uses of these funds to purchase various assets. Our results reject independence between the two sides of the balance sheet—suggesting that small and medium-sized firms in Portugal do indeed match specific assets with specific liabilities. The implication for financial theory is that each asset or project may have a different weighted average cost of capital. That is, there is no single weighted average cost of capital for a typical small to medium-sized firm. JEL: G32, M40 KEYWORDS: Asset-liability matching, SMEs, capital structure, sources and uses of funds INTRODUCTION

M

ost of the literature on capital structure has implicitly assumed that the choice between debt and equity depends solely on firm characteristics, or the firm’s demand for debt. For example, Rajan and Zingales (1995) and Booth et al (2001) focus on the demand side of capital structure for large listed firms. However, Faulkender and Petersen (2005, p. 46) have shown that a firm’s debtequity structure depends “not only on the determinants of its preferred leverage (the demand side) but also the variables that measure the constraints on a firm’s ability to increase its leverage (the supply side).” Also, as noted by Stowe, Watson, and Robertson (1980, p. 973), “the actual balance sheets of modern corporations do not exhibit an independence between the two sides of the balance sheet.”

Although the finance literature has recognized the interrelationship between the two sides of the balance sheet, the implications have received little attention. It means the cost of capital can vary between assets, so that a firm need not have a single weighted average cost of capital (WACC). While asset and liability interdependence may not be so important for large corporations, capital constraints and differential costs between the sources of debt capital can have a major impact on small and medium enterprises (SMEs). For SMEs, the cost of funds may vary on a project-by-project basis depending on project size, riskiness, and time horizon. Each source of debt conveys its own particular set of costs and benefits and a firm may choose a different mix of funding sources for each asset it purchases. In this paper, we propose that the two sides of the balance sheet of SMEs are interdependent causing them to match specific assets with specific liabilities. The firm’s optimal capital structure then depends on the assets they purchase. We empirically test our theory of asset and liability matching using a unique sample of 1416 Portuguese industrial SMEs over the years 1990-2000. This data set provides detailed information about sources of SME funding—including internal equity, bank loans, trade credits, non-bank loans, leasing, and other 13

J. Bartholdy et al | IJBFR ♦ Vol. 6 ♦ No. 4 ♦ 2012

short-term debt. For these SMEs, we test for independence between sources of funding and the uses of funds to purchase various assets. Our tests reject independence, suggesting the asset and liability sides of the balance sheets are interrelated. Each asset class has its own unique mix of financing sources. Our results suggest that all types of debt are important for SMEs and that empirical work in finance should distinguish between various types of debt. Thus, a firm does not have a unique average weighted cost of capital and decisions about capital structure become more complicated than in traditional analysis. The debt portion of the debt-equity ratio depends upon the type of debt a firm uses. The remainder of the paper proceeds as follows. The next section provides a brief literature review, the third section describes the data sample, and section 4 discusses sources and uses of funding. The fifth section shows how we distinguished between cheap and expensive trade credits, section 6 presents the empirical results, and section 7 concludes the study. LITERATURE REVIEW In a world of frictionless capital markets with no asymmetric information or agency costs, even small firms can fund all of their positive net present value projects. However, the presence of asymmetric information, as stated by Fama (1985), James (1987), and Carey, Post, and Sharpe (1998), means that the firm knows more about the quality of their own projects than outside lenders. As discussed by Leland and Pyle (1977), Diamond (1984), Ramakrishnan and Thakor (1984), Fama (1985), Haubrich (1989), and Diamond (1991), this problem has encouraged the development of specialized or differentiated financial markets and institutions. Different institutions specialize in extending credit to various firms and banks have some clear advantages in solving the asymmetric information problem for small firms. Mester, Nakamura, and Renault (2001) mention that banks involved in the payment function often know cash inflows before the firms do. Hoshi, Kashyap, and Scharfstein (1990a, 1990b), Petersen and Rajan (1994, 1995) and Berger and Udell (1998) have documented the importance of such relationships between lenders and borrowers and the impact on the cost of borrowing. The advantages of banking relationships are more important for small firms than for large firms. More information is public for large firms, they often have more than one banking relationship, and many of these firms have access to bond financing. Since bonds come with high fixed costs and lower interest rates than bank loans, Faulkender and Petersen (2006) state that large firms are more likely to borrow from financial markets than from financial institutions. Financial institutions also have advantages in solving moral hazard problems (ex-post contractual problems). By offering both short-term lines of credit and long-term loans, banks can withdraw funds and/or renegotiate the conditions and interest rates if the firm engages in “moral hazard” actions (risk shifting etc.). Creditors in financial markets, on the other hand, have to rely on covenants negotiated ex-ante since it is nearly impossible to renegotiate the terms of corporate bonds ex-post. To the extent that banks are successful ex-post monitors and reduce the moral hazard problems, then bank debt becomes the preferred source of external capital for small firms. Rajan (1992), Bolton and Scharfstein (1996), and Bolton and Freixas (2000) noted that different institutions have comparative advantages in resolving financial distress, including the restructuring of firms. Leasing companies are a particular efficient way of minimizing the costs of financial distress. If the firm misses payments, the leasing company simply repossesses the asset. Based on work by Cassar and Holmes (2003), Michaelas and Chittenden (1999), and Daskalakis and Psillaki (2008), some observations can be made about the demand for debt versus equity for SMEs. First, different types of loans and/or institutions finance different types of assets, and secondly, a single external source or type of funding is rarely sufficient to fund most projects. Thus, Iturralde, Maseda, and San-Jose (2010) suggest that Spanish SMEs benefit from multiple bank relationships and multiple funding sources. Garcia-Teruel 14


and Martinez-Solano (2010) argue the debt maturity structure for SMEs conveys information to lenders— meaning that debt is not homogeneous. Similarly, Scherr and Hulbert (2001) and Aivazian, Ge and Qui (2005) show the maturity of assets affects the maturity of liabilities. This finding shows the two sides of the balance sheet are not independent. Most of the capital structure literature has focused on homogeneous debt and the general debt-equity trade-off. An exception is Bolton and Freixas (2000) who examine the choice between bonds, bank loans, and equity. In addition, Berger and Udell (1998) have shown that different capital structures are optimal during different stages in the growth cycle of a firm. Taking this argument a step further, we suggest that different capital structures are optimal for funding different assets, even at a given point in time. Some funding sources are better for financing certain assets and each financing source may have its own collateral (which may only be the future earnings of the firm). The finance literature somewhat recognizes that financing for SMEs is different from financing for large firms and that debt is not homogeneous. Our hypothesis of asset and liability matching builds most specifically upon two pieces of research. First, Faulkender and Peterson (2005) have shown the importance of the supply, or the availability of debt, in determining firms a firm’s capital structure. Second, Stowe, Watson, and Robertson (1980) have specifically stated that the asset and liability sides of the balance are interrelated for most firms. This lack of independence means the investing decision is not separate from the financing decision for most assets or projects. DATA AND METHODOLOGY The primary data source for this study is the Bank of Portugal Statistical Departments database. This database contains balance sheet and income statement data on 1,811 non-listed firms with 11,359 noncontinuous firm year observations. We imposed several selection criteria to obtain a more homogeneous and usable sample. Only manufacturing firms for the period 1990-2000 with more than 100 employees for at least one year are included. This restriction minimizes the number of cases where the owner or the owner’s family uses their personal wealth to guarantee loans of the firm. Firms with negative net worth and less than three continuous data years are not included in the sample. We also deleted companies with observations lying in either tail (0.5%) of the distribution. The final sample consists of 1416 firms and 7546 firm year observations. As shown in Table 1, 271 firms have data for the entire sample and about 200 firms have data for one or two years only. The analysis that follows uses 10 years of data because one year is lost in calculating changes in assets and liabilities. Around 100 firms have consecutive data for 4 to 9 years. Thus, the dataset over weights firms with only a few years of observations and firms with data for the entire 10-year period. The Portuguese government collected this SME data annually during the 1990s, but unfortunately quit collecting such detailed data after the year 2000. As shown in Table 2, the data include six industry groups: Food and drinks, Textiles and clothes, Wood and paper past, Chemical products, Heavy industry, and Machinery and equipment. The total number of observations varies between 699 and 798 per year and each industry group includes a similar number of firms each year. An examination of the Bank of Portugal Statistical Department’s database indicates that our sample is representative of the structure of the Portuguese economy. Looking at the distribution of observations across industries, “Textiles and clothes” includes about a third of the total observations, whereas “Heavy industry” and “Wood and paper paste” each only contain about 15% of total observations.

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J. Bartholdy et al | IJBFR ♦ Vol. 6 ♦ No. 4 ♦ 2012

Table 1: Number of Firms with Consecutive Years of Data Consecutive Years of Data Number of Firms 1 196 2 200 3 149 4 123 5 108 6 100 7 90 8 90 9 89 10 271 Total 1416 The table shows the number of firms in the sample and the number of years for which they have consecutive annual data. For example, only 271 of the 1416 total firms included in the sample have data for all 10 years. The sample is an unbalanced panel because many companies have less than 10 years of data.

Table 2: Number of Observations by Years and Industry Year

1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 Total

Industry Food And Drinks

Textiles And Clothes

102 114 107 105 109 108 106 113 111 97 1072

236 278 272 274 274 270 272 282 277 232 2667

Wood And Paper Paste 56 61 63 59 67 71 70 67 70 59 643

Total

Chemical Products

Heavy Industry

125 119 121 120 130 130 132 133 133 133 1276

53 49 48 50 51 51 56 63 61 65 547

Machinery and Equipment 127 139 128 133 137 134 128 140 138 137 1341

699 760 739 741 768 764 764 798 790 723 7546

This table shows the number of observations in the sample for each industry for each year from 1991 to 2000. Annual totals across the six industries are shown in the right-most column. The bottom row shows the total number of observations for each industry for the entire 10-year period.

Sources and Uses of Funds for Portuguese Firms In Table 3, the owners of the Portuguese firms provide nearly half (46-49%) of their firm’s required capital as equity. The common size balance sheet in Tables 4 and 5 show that Portuguese firms have close to 50% equity, which is similar to levels reported by Berger and Udell (1998) for SMEs in the US. In contrast, Rajan and Zingales (1995) report that large listed firms in the G7 countries have equity percentages ranging from 28% in Germany to 42% in the UK. After internal equity, our data categorizes the liabilities on the balance sheet by three sources of external funding: (1) Other firms (Trade Credits), (2) Banks, and (3) Other Institutions and Miscellaneous providers of finance (e.g., leasing). Trade credits from suppliers constitute from 10% to 14% of SME funds. This compares to 26% for French, 22% for Spanish, and 11% for Swedish manufacturing SMEs, as reported by Garcia-Teruel and Martinez-Solano (2010) over the period 1996-2002. Banks provide 1620% of SME funds, and as shown in Table 4, about half of the bank loans are long-term and half are short-term. Most firms use a variety of sources of debt—meaning the debt-equity trade-off involves nonhomogeneous debt.

16


Table 3: Sources of Funds for Portuguese (Industrial) SMEs

Equity Creditors (trade credit) Banks Other institutions and miscellaneous providers of credit Provisions and accrued expenses

1990

1994

49 10 20 15 6

46 12 19 16 7

1998 % of total funds provided by 49 12 16 15 8

2000 46 14 18 14 8

This table indicates the % of Portuguese SME funds provided in four different representative years by five broad categories of financing sources.

Other institutions (including leasing and factoring) account for 14 -16% of funds, while the remaining 6% to 8% of funding comes from provisions and accrued expenses. Funds from this last category eventually probably belong to one of the preceding categories of equity or debt. For example, provisions probably are part of internal equity. Accrued expenses are short-term liabilities recognized currently for expenses that will occur next year (e.g., vacation subsidies, social expenses, and rent). Any funding source can pay such expenses. Table 4: Average Liabilities and Equity of Portuguese (Industrial) SMEs 1990

1992

1994

1996

1998

2000

Shareholder’s Funds 0.49 0.47 0.46 0.48 0.49 0.46 Capital 0.22 0.21 0.25 0.25 0.24 0.20 Reserves 0.23 0.25 0.19 0.21 0.22 0.21 Net Income of the Year 0.04 0.01 0.02 0.02 0.03 0.05 Provisions 0.02 0.01 0.01 0.01 0.01 0.01 Liabilities 0.49 0.52 0.53 0.51 0.50 0.53 Non-Current Liabilities 0.16 0.15 0.14 0.15 0.13 0.13 Long-Term Debt 0.13 0.12 0.09 0.11 0.09 0.10 Bank Loans 0.10 0.10 0.07 0.09 0.08 0.09 Other 0.03 0.02 0.02 0.02 0.01 0.01 Other Non-Current 0.03 0.03 0.05 0.04 0.04 0.03 Liabilities Current Liabilities 0.33 0.37 0.39 0.36 0.37 0.40 Loans 0.10 0.13 0.12 0.08 0.08 0.09 Bank Loans 0.10 0.13 0.10 0.08 0.08 0.09 Others 0. Complete dependence is obtained when α → 0 and total independence is when α = 1.Dependence of extreme returns between oil and ISE 100 index is identified by the (Chi) statistic of Coles et al. (1999) work. (3) Perfect dependence is denoted by -statistic getting closer to 0.

-statistic getting closer to 1 and independent variables denoted by

EMPIRICAL RESULT Threshold levels of 10th and 90th quantiles of oil returns and ISE 100 returns indicates there are 287 highest and 287 lowest extreme events exceeding selected thresholds out of 2865 daily returns for each phase. The corresponding quantiles, taken as thresholds for the analysis of extreme ISE returns, are 3.41% for the left tail and 3.71% for the right tail in the first phase. In the second phase, the thresholds are -3.29% and 3.21% for the left and right tails, respectively. For Brent returns, 10th and 90th quantiles are 2.38% and 2.29% in the first phase and -2.88% and 2.75% in the second period. For example, if there is a daily loss greater than 3.41% in the first phase studied, the observation is considered to exceed the threshold and is incorporated in the estimation of the GPD model for the left tail. Similarly, if there is a daily return higher than 3.71% in the first phase, the observation is included in the estimation of the model for the right tail. Table 3 shows bivariate EVT model results for ISE100 and Brent oil extreme returns. Independence assumption suggests that 28.6 events coincide on the same day at 10th and 90th quantiles. Between 1988 and 1999, our results show that 30 of the 287 highest returns and 31 of the lowest 287 returns happen on the same day. However, between 2000 and 2011, higher numbers of joint exceedances occurred, as 45 highest returns and 55 lowest returns happen on the same day. In other words, there are 55 days when ISE lost more than 3.29% and Brent oil lost more than 2.88% concurrently. Table 3 also shows us figures for computing conditional probabilities to investigate oil price latency effect to stock markets by setting a 3-day margin. Under total independence assumption, for each consecutive day 28.6 extreme observations, or a total of 85.8 extreme observations over the next three days is expected. This study shows that 92 of the 287 highest returns (32%) and 85 of the lowest 287 returns (30%) happen within the 3 days at the first phase, while 118 of the 287 highest returns (41%) and 130 of the lowest 287 returns (45%) happens within the 3 days at the second phase respectively. The numbers in parentheses imply conditional probabilities of having an extreme daily stock market return in the coming next three days when today is an extreme day for oil returns. Given that oil loses more than 2.88% one day in the second subperiod, there is 45% probability that in the next three days ISE experiences a daily loss greater than 3.29%. Table 4 shows the estimated parameters and their standard errors of the GPD models that are fit to our exceedance data over selected thresholds. Except for the second shape parameters for right and left tails in 120


the phase 1, all estimated parameters are significant. The alpha parameters of all four models estimated (for both sub periods and for both right and left tails) are close to one, which imply independence in extreme observations. These results are in line with chi-statistic values reported in Table 3, which also imply independence with close to zero values. Table 3: Bivariate Extreme Model Results for ISE100 and Brent Returns Phase 1 (1988 -1999) Right Tail

Phase 2 (1999 - 2011) Right Tail

Left Tail

0.017

Left Tail 0.008

0.06

0.103

Deviance

331

412

196

344

Marginal Number Above

287

287

287

287

Joint Number Above

30

31

45

55

Chi-Statistic

Joint Number Above (3days) 92 85 118 130 This table shows the results of the bivariate extreme value models forecasted for Brent oil and ISE 100 extreme returns. The right and the left tail models show results for extreme high returns and extreme high losses returns at 90th quantile respectively. The analysis is carried for two subperiods, where phase 1 corresponds to the period between 1988 and 1999 and phase 2 to the period between 2000 and 2011.

Table 4: Bivariate Extreme Model Estimates for ISE100 and Brent Returns Phase 1 (1988 - 1999) Right Tail Scale1 Shape1 Scale2 Shape2

Left Tail

0.0153

(0.0013)

0.1401

(0.0606)

0.2253

0.0212

(0.0016)

-0.0238

(0.0499)

Phase 2 (1999 - 2011)

0.0131

(0.0011)

Right Tail

Left Tail

0.0123

(0.0011)

0.0140

(0.0012)

(0.0637)

0.1701

(0.0672)

0.1944

(0.0662)

0.0242

(0.0020)

0.0152

(0.0014)

0.0204

(0.0018)

0.0548

(0.0557)

0.3026

(0.0755)

0.1462

(0.0686)

Alpha

0.9880 (0.0105) 0.9942 (0.0118) 0.9560 (0.0159) 0.9238 (0.0174) This table shows the estimated parameters of the GPD models fit using bivariate data series ISE 100 and Brent oil returns at 90th quantile. The numbers in parentheses gives standard errors of the estimated parameters. The analysis is carried for two subperiods, where phase 1 corresponds to 1998 and 1999 and phase 2 to the period between 2000 and 2011.

In general, it is not possible to speak of a dependency relationship between oil and ISE index. Bivariate extreme dependence analysis indicates that oil and ISE 100 returns have higher dependence at the second phase, in the years from 2000 to 2011. Joint number of days exceeding selected thresholds at second phase is increased by 50 percent for the positive tail and by 77 percent for the negative tail compared to the first phase. Chi-statistics at the second phase is 3.5 times greater for the positive tail and 12.9 times greater for the negative tail, compared to the first phase. In the light of model results, increase in the oil and ISE 100 returns extreme dependence during the second phase is clearly mentioned. Negative returns for oil and ISE 100 index have higher dependence value compared to the positive returns at the second phase. It is possible to refer that negative oil price movements affect ISE 100 index more commonly compared to positive movements at the second phase. CONCLUSION This paper examines extreme dependence between oil prices and the Turkish stock index. The data used for dependence analysis consist of daily log returns on Brent oil prices and ISE 100 index for the period 121

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between 1988 and 2011. Turkey supplies nearly half of its energy requirement from crude oil. Oil is one of the major commodities for Turkey’s total imports. Expanding emerging countries need oil as a source of energy for their growing industries. Their exposure to oil price fluctuations is directly compared to developed nations. The main motive of this study is to show an oil price effect on an oil dependent emerging country. Researches that investigate oil price and stock market relationship in the literature, mainly focus on analyzing central observations. This paper is first to study the dependency relationship of stock exchange and oil returns by exploring the extreme observations employing bivariate EVT models. Results of this study reveal an asymptotic independence between oil prices and ISE 100 index returns in extreme observations. Bivariate extreme dependence analysis applied to the data set by dividing data into two phases, where phase 1 and phase 2 cover the periods from 1988 to 1999 and from 2000 to 2011. In the first phase studied, the chi-statistics are very close to zero (0.008 and 0.017 for the left and right tails respectively), implying no dependence at all. In the second phase, the extreme observations chi-statistics are somewhat higher but still very close to zero (0.103 and 0.060 for the left and right tails respectively). Extreme dependence analysis indicates that oil and ISE 100 returns have higher dependence at the second phase. It is also observed that negative oil price movements affect ISE 100 index more commonly compared to positive movements at the second phase. Oil price effect latency to stock markets is also examined within the study by setting a 3-day margin. Yet, the number of observed joint exceedances is quite close to the expected values under complete independence assumption. Findings of this study, which indicates absence of extreme dependence between oil and stock markets, may help portfolio managers and investors identify better diversification opportunities. However, considering higher dependence of stock markets for negative oil price movements especially in the last decade, diversification opportunities must be used with caution in the times of crisis. REFERENCES Al-Fayoumi, N. A. (2009). Oil Prices and Stock Market Returns in Oil Importing Countries: The Case of Turkey, Tunisia and Jordan. European Journal of Economics, Finance and Administrative Sciences, 16, 84-98. Basher, S. A. and Sadorsky, P. (2006). Oil price risk and emerging stock markets. Global Finance Journal, 17(2), 224-251. Bhar, R. and Nikolova, B. (2010). Global oil prices, oil industry and equity returns: Russian experience. Scottish Journal of Political Economy, 57(2), 169-186. Choi, K. and Hammoudeh, S. (2010). Volatility behavior of oil, industrial commodity and stock markets in a regime-switching environment. Energy Policy, 38(8), 4388-4399. Elsevier B.V. Coles, S., Heffernan, J. and Tawn, J. (1999). Dependence Measures for Extreme Value Analyses. Extremes, 2(4), 339-365. Constantinos, K., Ektor, L. A. and Dimitrios, M. (2010). Oil Price And Stock Market Linkages In A Small And Oil Dependent Economy: The Case Of Greece. Journal of Applied Business Research, 26(4), 55-64. Eryigit, M. (2009). Effects of Oil Price Changes on the Sector Indices of Istanbul Stock Exchange. International Research Journal of Finance and Economics, 25, 209-216.

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Faff. R. W. and Brailsford, T. J. (1999). Oil price risk and the Australian stock market. Journal of Energy Finance & Development, 4(1), 69-87. Elsevier B.V. Filis, G. (2010). Macro economy, stock market and oil prices: Do meaningful relationships exist among their cyclical fluctuations? Energy Economics, 32(4), 877-886. Elsevier B.V. Filis, G., Degiannakis, S. and Floros, C. (2011). Dynamic correlation between stock market and oil prices: The case of oil-importing and oil-exporting countries. International Review of Financial Analysis, 20(3), 152-164. Elsevier B.V. Gisser, M. and H Goodwin, T. (1986). Crude Oil and the Macroeconomy: Tests of Some Popular Notions: Note. Journal of Money, Credit and Banking, 18(1), 95-103. Ohio State University Press. Hamilton, J. D. (1983). Oil and the Macroeconomy since World War II. Journal of Political Economy, 91(2), 228. Hammoudeh, S. and Li, H. (2005). Oil sensitivity and systematic risk in oil-sensitive stock indices. Journal of Economics and Business, 57(1), 1-21. Hammoudeh, S. and Choi, K. (2006). Behavior of GCC stock markets and impacts of US oil and financial markets. Research in International Business and Finance, 20(1), 22-44. Hearn, B. and Man, S. Y. (2010). An Examination of Price Integration Between Stock Market and International Crude Oil Indices: Evidence from China. Applied Economics Letters, Forthcoming. Available at SSRN: http://ssrn.com/abstract=1724303 Huang, R. D., Masulis, R. W. and Stoll, H. R. (1996). Energy shocks and financial markets. Journal of Futures Markets, 16(1), 1-27. John Wiley & Sons. Hyndman, R. J. (2011). A users guide to the ‘forecast’ package, (Version 3.11), http://cran.rproject.org/web/packages/forecast/index.html Jones, C. M. and Kaul, G. (1996). Oil and the Stock Markets. Journal of Finance, 51(2), 463. Klüppelberg, C. and May, A. (2006) Bivariate extreme value distributions based on polynomial dependence functions. Mathematical Methods in the Applied Sciences, 29, 1467–1480. Laopodis, N. T. (2011). Equity prices and macroeconomic fundamentals: International evidence. Journal of International Financial Markets Institutions and Money, 21(2), 247-276. Elsevier. Ledford, A. W. and Tawn, J. A. (1996). Statistics for near independence in multivariate extreme values. Biometrika, 83(1), 169-187. Lee, Y.-H. and Chiou, J.-S. (2011). Oil sensitivity and its asymmetric impact on the stock market. Energy, 36(1), 168-174. Elsevier Ltd. Loungani, P. (1986). Oil price shocks and the dispersion hypothesis. The Review of Economics and Statistics, 68(3), 536–539. JSTOR.

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Maghyereh, A. (2004). Oil price shocks and emerging stock markets: A generalized VAR approach. International Journal of Applied Econometrics and Quantitative Studies, 1(2), 27–40. Euro-American Association of Economic Development. Malik, F. and Hammoudeh, S. (2007). Shock and volatility transmission in the oil, US and Gulf equity markets. International Review of Economics Finance, 16(3), 357-368. Mendes, B. and Moretti A. R. (2002). Improving Financial Risk Assessment through Dependency. Statistical Modelling, 2, 103-122. Mohanty, S., Nandha, M. and Bota, G. (2010). Oil shocks and stock returns: The case of the Central and Eastern European (CEE) oil and gas sectors. Emerging Markets Review, 11(4), 358-372. Elsevier B.V. Mork, K. A. (1989). Oil and the Macroeconomy When Prices Go Up and Down: An Extension of Hamiltonʼs Results. Journal of Political Economy, 97(3), 740-744. The University of Chicago Press. Narayan, P. K. and Narayan, S. (2010). Modelling the impact of oil prices on Vietnam’s stock prices. Applied Energy, 87(1), 356-361. Onay, C. and Ünal, G. (2011) Cointegration and Extreme Value Analyses of Bovespa and Istanbul Stock Exchanges. Czech Journal of Economics and Finance, Forthcoming. Available at SSRN: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1636183 Park, J. and Ratti, R. (2008). Oil price shocks and stock markets in the U.S. and 13 European countries. Energy Economics, 30(5), 2587-2608. Papapetrou, E. (2001). Oil price shocks, stock market, economic activity and employment in Greece. Energy Economics, 23(5), 511-532. Elsevier. Ribatet, M. (2009). A user's guide to the POT package, (Version 1.1-0), http://cran.rproject.org/web/packages/POT/index.html Sadorsky, P. (1999). Oil price shocks and stock market activity. Energy Economics, 21(5), 449-469. Zhu, H., Li, S. and Yu, K. (2011). Crude oil shocks and stock markets: A panel threshold cointegration approach. Energy Economics, 33(5), 987-994. Elsevier B.V. ACKNOWLEDGEMENT This research is supported by Bogazici University Research Fund (D6300). BIOGRAPHY Gözde Ünal is an Instructor of Finance at Boğaziçi University, Istanbul. Prior to her academic career she also worked in the Corporate Finance field. Her research appears in journals such as Journal of Risk Model Validation, Finance a úvěr (Czech Journal of Economics and Finance). She can be reached at Boğaziçi University, Bebek 34342 Istanbul/Turkey, [email protected] Derya Korman is graduate student in International Trade Management at Bogazici University. He is also works as a trade coordinator at Derin Shipping, Transport and Trading Ltd., Istanbul. He can be reached at Boğaziçi University, Bebek 34342 Istanbul/Turkey, [email protected], [email protected]. 124


INTEGRATION OF KEY WORLDWIDE MONEY MARKET INTEREST RATES AND THE FEDERAL FUNDS RATE: AN EMPIRICAL INVESTIGATION Krishna M. Kasibhatla, North Carolina A&T State University ABSTRACT This study investigates whether there is an increased integration of U.S. domestic money market interest rates and the Eurodollar market interest rates following two important changes that the U.S Federal Reserve (the Fed) implemented. First, elimination of reserve requirements on Eurodollar bank deposits in the early 1990s. Second, change in the operating procedure for conducting monetary policy in early 1992 from borrowed reserves targeting to federal funds rate targeting. The money market interest rates are three and six month Eurodollar London Interbank Offered Rates (Libor), three and six month U.S. Treasury bill (T-bill) rates, and the effective federal funds rate. Cointegration and error-correction methodology of Johansen and Juselius (1990,1992) is employed for this empirical study. Results indicate that integration of the five interest rates increased following the two changes by the Fed. It is the effective fed funds rate and the three-month T-bill rate that participate in the adjustment process back to their equilibrium path following an external shock to the system. Granger causality tests produced different and somewhat conflicting results when the error-correction model is estimated with and without the federal funds rate in the system. This finding requires further study and investigation. JEL: C32, C58, E43, G15 KEYWORDS: Libor, Unit Root, Cointegration, Granger Causality INTRODUCTION

T

he primary objective of this study is to examine whether there is an increase in the integration of U.S. domestic money market interest rates and the offshore Eurodollar London interbank offered rates (Libor) since 1990 following two important changes made by the U.S. Federal Reserve (the Fed). First, a regulatory change eliminating reserve requirements on Eurodollar liabilities of offshore banks in early 1990, and second, change in the Fed’s operating procedure for conducting monetary policy switching from borrowed reserve targeting to federal (fed) funds rate targeting in early February, 1992. The money market interest rates used in this study are the three and six month U. S. Treasury bill (T-bill) rates, effective fed funds rate, and the offshore three and six-month Libor. To my knowledge there is no published study that exclusively investigated the relationship between the domestic and offshore rates after the monetary policy regime change to fed funds targeting in early 1992. The relationship between U.S. T-bill yields including the effective fed funds rate and the Libor of different maturities is examined employing cointegration and error correction methodology developed by Johansen and Juselius (JJ) (1990, 1992). The choice of methodology to examine the relationships is supported by several similar studies summarized in Hall, Anderson, and Granger (1992). These money market rates play a very important role in influencing various other interest rates. For instance the three month T-bill rate is a prominent default-risk-free rate in the U.S. and often used as a proxy for a risk-free asset as well as a benchmark lending rate. Likewise, according to some estimates, the value of financial contracts linked to the Libor is over $3 trillion. The Eurodollar market and the fed funds market are located in different places but the currency in both the markets is the U.S. dollar. The volume of transactions in the Eurodollar interbank market is larger than the U.S. fed funds market. Further, 125

K.M. Kasibhatla | IJBFR ♦ Vol. 6 ♦ No. 4 ♦ 2012

according to Baba et al (2009) European banks had substantially increased their U.S. dollar asset positions from about $2 trillion to over $8 trillion by mid-2007. The effective federal funds rate is considered a ‘bellwether’ rate leading all short-term rates. The effective fed funds rate is the weighted average of the funds rates that prevailed during the day. The weights are the amounts of funds traded at different rates during the day. During the financial and banking crises in the U.S. from late 2007 to mid-2009 the international money markets, especially, the interbank Eurodollar market, ran into serious trouble due to shortage of U.S. dollars. According to McAndrews et al (2008) the volume of transactions in the interbank market sharply declined and banks reportedly could not borrow funds at the posted rates. These interbank loan rates rose to very high levels, and spreads between the three-month Libor and the effective fed funds rate suddenly jumped to over 90 basis points, from an average of 20 basis points. The increased spread was mainly attributed to increased liquidity and credit risks of banks. Banks sustained huge losses due to the collapse of the mortgage market in the U.S. McAndrews et al (2008) reported that on December 12, 2007, the Fed responded to the shortage of term funds for banks by introducing the ‘Term Auction Facility’ (TAF) that provided term funding to eligible banks through periodic auctions. According to Taylor and Williams (2008) as many private loans are linked to Libor rates, the sharp increase in these spreads raised the cost of borrowing and interfered with monetary policy. The widening spreads became a major focus of the Federal Reserve which took several actions including the TAF. The foreign-currency exposures of European banks had grown significantly over the decade preceding the crisis, with dollar exposures accounting for half of the growth in European banks’ foreign exposures over the period from 2000 to 2007 (McGuire and von Peter 2009a). European Union, United Kingdom, and Swiss banks’ on-balance sheet dollar exposures were estimated to exceed $8 trillion in 2008.While there was severe shortage of term funds for banks, there was a lot of concern about the alleged manipulation of Libor in 2008, and according to the financial press reports several participating banks were accused of conspiring to artificially keep the Libor rates low. If these accusations are proven to be valid, then we cannot expect the key rates to maintain an equilibrium relationship if Libor manipulated rather than market determined. An understanding of the relationship among these key market rates and rates targeted by central banks is of great importance for market participants as well as the monetary authorities in implementing monetary policy. To my knowledge, there is no study which examined all the five rates simultaneously. The results of this study provide much needed insight into the interactions between monetary policy and key money market rates in the U.S. and Eurodollar market. The remainder of this paper is organized as follows. The following section contains literature review. Section two presents the data and an overview of the methodology. Section three contains the estimated results and discussion. Section four contains summary and concluding remarks. LITERATURE REVIEW The literature on the integration of key domestic and international market interest rates is extensive. This literature review includes a select group of studies widely cited. These studies are divided into two categories. The first category of studies, which I refer to as early studies, mainly focused on testing for causal links among the domestic and foreign interest rates. The second category of studies was mainly interested in testing the ‘expectations hypothesis’ of the term structure of interest rates, besides examining their short-term dynamics. Expectations hypothesis is that long-term interest rate is the average of the current short-term rates and expected future short-term rates plus a constant term premium. The following studies by Hartman (1984), Swanson (1987, 1988), Fung and Isberg (1992), Mougoue and Wagster (1997) belong to the first category, that tested for temporal causality between U.S. domestic 126


interest rates Eurodollar rates. All of these studies used U.S. domestic certificate of deposit (CD) rates, weekly or daily frequency, and either one month or three month Eurodollar deposit rates in their studies, except Kaen and Hachey (1983), whose study involves the relationship between Eurodollar rates and the Euro-sterling rates. The sample period of Hartman’s (1984) study ranges from 1971-1978, divided into two sub-periods, 1970-1974 and 1975-1978. The study reported unidirectional causality running from the U.S. domestic CD rates to the 3-month Eurodollar rates for the 1970-1974 period, and bidirectional or mutual causality for the 1975-1978 period. Swanson (1987, 1988) used daily CD rates to test for Granger causality for the sample period from mid-1973 to December 1984, split the sample into three sub-periods. For the first sub-period (1974-1980) she reported unidirectional causality (note, Hartman study reported bidirectional causality for this period). And for the sub-period 1981-1982 her study reported bidirectional causality, and for the sub-period 1982-1983 the finding was reverse unidirectional causality, from the Eurodollar rates to the CD rates. The study by Fung and Isberg ( 1992) used daily CD rates and employed vector error correction model to test for the causal links for the sample period 1981-1988. For the sub-period 1981-1983 they found unidirectional causality from the U.S. CD rates to the Eurodollar rate. Note, for the same period Swanson study reported reverse unidirectional causality. For the 1984-1988 sub-period they reported bidirectional causality. The study by Mougoue and Wagster (1997) employed daily CD rates and 3-month Eurodollar deposit rates for the sample period from mid-1973 to mid-1993. They argued that the correct way to measure and test for the relationship between the rates should recognize the difference in trading times of these two markets. They did account for this difference in trading times. They divided the sample into three sub-periods, coinciding with the three different monetary policy operating regimes of the U.S. Federal Reserve. Mougoue and Wagster (1997) identified three different monetary policy regimes the Fed had followed, first, the Fed targeted federal funds rate targeting from July 16, 1973 to October 5, 1979, second, nonborrowed reserve targeting from October 9, 1979 to October 7, 1982, and the third, targeting borrowed reserves from October 8, 1982 to February 7, 1992, in conducting monetary policy. For the three different regimes Mougoue and Wagster (1997) study reported three different causal relations. For the fed funds targeting regime their finding was bidirectional causality, for the non-borrowed reserve targeting causality was reverse unidirectional, from the Eurodollar market to the U.S. domestic market, and for the borrowed reserve targeting causality was unidirectional from the U.S. domestic rates to the Eurodollar rates. The study by Kaen and Hachey (1983) used Eurodollar rates and Euro-sterling rates to test for causality and reported unidirectional causality from the U.S. dollar to the Euro-sterling rate for their entire sample period ranging from 1974 to 1981. We can clearly see the conflicting and contradictory results reported in the above studies. However, one common finding in these studies is that these rates are integrated. Some of the influential studies in the second category include Engle and Granger (1987), Stock and Watson (1988), Campbell and Shiller (1991), Hall et al (1992), Engsted and Tanggaard (1994), Campbell et al (1997), and Thornton (2002). Empirical support for the ‘expectations hypothesis’ reported in these studies is generally weak. In spite of that all these studies reported that the U.S. and Eurodollar rates comove in the long-run. However, there is no agreement as to the causal links between the rates examined. Most recent studies include Clinebell et al (2000), Sarno and Thornton (2003), and Zhou (2007). Clinebell et al (2000) went a step further besides testing whether the financial markets integration increased and examined the changing monetary policy regimes and its impact on Granger causality. That is whether the conflicting results were due to changes in the Fed’s monetary policy targets. The study found strong financial market integration under fed funds rate targeting phase relative to the nonborrowed reserve targeting. Their findings were contradicted by the results reported in the Sarno and Thornton (2003) study. Employing a non-linear error-correction model they reported no change in longrun equilibrium relationship and short-run dynamics between the interest rates irrespective of different 127


monetary policy regimes. The study by Zhou (2007) differs from the earlier studies in one respect, namely, in the selection of interest rates. Zhou(2007) chose the federal funds rate and the Eurodollar rates of different maturities. The cointegration tests conducted in this study are bi-variate, not multivariate, even though the number of rates involved are four. Each pair of interest rates are reported to be cointegrated. The interesting aspect of this study is the results of the error-correction model. Specifically, it is the federal funds rate that plays a major role in the adjustment process of the system when it is out of equilibrium following a shock. This is also one of the key findings of this study. This study differs from the earlier studies, reviewed above, in three important ways. First, this study explicitly includes the effective fed funds rate along with three and six-month Libor and the two domestic three and six-month T-bill rates. One or two of earlier studies included the fed funds target rate, which is not the interbank lending rate, but it is the Federal Reserve’s monetary policy target rate. Second, the sample period in this study is the longest, from January 6, 1986 to September 14, 2009, close to 6,000 daily observations. Time series models estimated using high frequency data as well as a long time periods are expected to perform well in providing more reliable cointegrating rank and coefficient estimates. Finally, this study estimated multivariate cointegration models rather than bi-variate cointegration model as many of the earlier studies. As such, there is very little discussion on the number of identified cointegrating vectors, perhaps, the focus of those studies was testing for the causal linkages between the market interest rates. This study fills the gap by emphasizing the long-run equilibrium relationship rather than just testing for temporal Granger causality. The results of this study provide much needed insight into the interactions between monetary policy and key money market rates in the U.S. and Eurodollar market. The results of this study provide a better understanding of the interactions between monetary policy and key money market rates. METHODOLOGY Data The sample data are the three and six month daily (5-day week) three and six-month T-bill yields, three and six month Eurodollar Libor interbank lending rate, and the effective federal funds rates, for the periods January 6, 1986 to September 14, 2009. The Eurodollar rates are computed by Thomason Reuters for the British Bankers Association. A department of the British Bankers Association (BBA) averages the inter-bank interest rates being offered by its membership. Libor is calculated for periods as short as overnight and as long as one year. Libor daily data series are from the BBA (www.bba.org.uk). The three and six month T-bill rates are the secondary market rates data, and are from the Federal Reserve Bank of St. Louis website (www.stlouisfed.org). Summary statistics of the five interest rate series are presented in Table 1. The first four moments of the five money market interest rates are provided in Table 1. The effective federal funds rate for the sample period averaged about 44 basis points over 3-month T-bill rate and about 27 basis points over the average 6-month T-bill rate. Average effective fed funds rate is below the 3-month and 6-month Eurodollar rates by 38 and almost 50 basis points, respectively. One explanation for the fed funds rate being higher than the U.S T-bill rates is that the two markets are partially segmented according to Campbell et al (1997). This is contrary to the belief that the fed funds rate affects all other short-term interest rates. Another explanation may be due to the fact that the T-bill rates have no liquidity risk and are default risk free, and may have some tax advantages while fed funds rate is not free of default and liquidity risks, according to Sarno and Thornton(2003). Based on the standard deviations of the rates, the fed funds rate is slightly more variable than the T-bill and the Eurodollar rates. The third and fourth moments show positive skewness and high kurtosis, which is an indication that the underlying distributions of these rates are nonnormal. This is confirmed by the Jarque-Bera test for normality (bottom row of Table 1).

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Table 1: Summary Statistics: tb3m, tb6m, lbr3, lbr6m, and ffr tbm3m

tb6m

lbr3m

lbr6m

Ffr

Mean

5.3150

5.4848

6.1454

6.2359

5.7581

Median

5.1800

5.3300

5.9375

5.9883

5.5700

Maximum

9.0900

9.1200

10.625

11.000

16.170

Minimum

2.6100

2.7500

3.1250

3.1250

2.5800

Std. Dev.

1.4253

1.3757

1.6352

1.6201

1.7672

Skewness

0.3047

0.2150

0.2194

0.2335

0.3529

Kurtosis

2.7232

2.6859

2.7038

2.7462

3.0938

Jarque-Bera

70.9281

44.9055

44.3878

44.7289

80.2814

Probability

0.0000

0.0000

0.0000

0.0000

0.0000

The first four moments of the five money market sample interest rate series are provided in Table 1. The average effective federal funds rate for the sample period was 44 basis points over the mean 3-month T-bill rate and 27 basis points over the mean 6-month T-bill rate. The mean federal funds rate is below 38 basis points of 3-month average Libor and nearly 50 basis points below 6-month Libor. The rates exhibit positive skewness and a relatively high kurtosis. The distribution of the market interest rates appears to be non-normal.

Model The relationship between T-bill yields (tb3m and tb6m) and Libor (lbrm3m and lbrm6m) and effective federal funds rate (ffr) is studied within the framework of cointegration and error-correction methodology employing the JJ procedure and the error correction model for examining the short-run dynamics. JJ methodology uses an asymptotically fully efficient maximum likelihood technique for the estimation of cointegrating vectors. The general form of the time series model underlying the empirical estimation is stated as a k-order Gaussian vector autoregressive (VAR) model for X as: k

X t = µ + ∑ Ai X t −i + ε t i =1

(1)

where, Xt is a n×1 column vector of observations on the variables of the model, µ is a vector of constants, Ai are n×n matrices of autoregressive coefficients (that do not contain any zero elements), εt is a vector of n non-observable random errors usually assumed to be contemporaneously correlated but not autocorrelated, and k is the number of lags on the variables in the system. If the variables in Xt are integrated of, say, order one, I(1), and are also found to be cointegrated, that cointegration restriction has to be incorporated in the VAR in (1). The Granger Representation Theorem (Engle and Granger, 1987) states that variables, individually driven by permanent shocks are cointegrated if and only if there exists a vector error correction representation of the time series data. A VAR model, with this restriction embedded is referred to as the vector error-correction (VEC) model. Variables in the VEC model enter the equation in their first differences, and the error correction terms are added to the model. The VEC has cointegration relation built into the specification so that it restricts the long-run behavior of the endogenous variables to converge to their long-run relationship while allowing for shortrun dynamics. Deviations from long-run equilibrium are corrected through a series of partial short-run adjustments per unit of time. The VEC representation of the VAR in (1), following JJ is: k

∆X t = µ + ∑ Γi ∆X t −i + ΠX t −1 + ξ t

(2)

i =1

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where Xt is a n×1 vector of I(1) variables, Γi is a n×n matrix of coefficients of the short-run dynamic effects, Π is a n×n matrix of coefficients of long run effects, and ξt is a vector white noise process. If the rank of Π in equation (2) is r, where r ≼ n-1, then Π can be decomposed into two n×r matrices, α and β, such that Π = αβ′. The matrix β is the cointegrating matrix of r cointegrating vectors, β1, β2, …, βr. The β vector represents the estimate of the long-run cointegrating relationship among the variables in the system. The error-correction terms, β′Xt-1, are the mean-reverting weighted sums of cointegrating vectors. The matrix α is the matrix of error correction coefficients, the so called ‘speed of adjustment’ coefficients that measure the speed at which the variables adjust to their long-run equilibrium values. If the rank of Π in equation (2) is found to be r ≼ n-1, the above model can be expressed in the first differences of Xt, augmented by the error correction terms, αβ′Xt–1, as shown below:

∆X t = µ + ∑ Γi ∆X t −i + αβ ′X t −1 + ξ t

(3)

The JJ technique provides maximum likelihood estimates of α and β′. In our model, Xt is a 2×1 vector consisting of T-bill yields, two Libor, and fed funds rate of different maturities. The cointegrating relationship, r, is determined by the trace eigenvalue statistic and the maximum eigenvalue statistic of the stochastic matrix and the maximum likelihood estimates of the cointegrating vectors (β) in equation (3). The standard estimation process has three-steps. First, unit root tests of each of the interest rate series in levels for their degree of integration. If two or more time series are integrated of the same order and are found to be cointegrated, then, according to the Granger Representation theorem (Engle-Granger, 1987), there must be ‘Granger causation’ at least in one direction. Further, such cointegrated series must be modeled within an ‘error correction’ framework as per Engle and Granger (1987). If the interest rate time series are found to be integrated of the same order in the first step, then, in the second step we have to test for cointegration of the time series to see if there is a long-run equilibrium relationship between the variables concerned. If cointegration is found in the levels of the series, then, the interest rate series should be modeled in the framework of vector error correction procedure described in (3). In all of the above estimation procedures, we use the Schwarz (1978) information criterion (SIC) to determine the lag structure for the unit root tests, cointegration tests, and for estimating the vector error-correction model. The initial step in the estimation involves the determination of the time series proprieties of each variable individually by conducting two of the popular unit root tests, namely, the augmented Dicky Fuller (ADF) (1979), and the KPSS (Kwiatkowski, Phillips, Schmidt, and Shin, (1992) test. For the KPSS unit root tests the Bartlett kernel spectral estimation and Newey-West (1994) bandwidth selection methods were used. The ADF test involves running one of the following regressions: Yt = α Xt-1 + Σdi ∆Xt-I

(4)

Yt = µ + α Xt-1 + Σdi ∆Xt-I

(5)

Yt = µ + βT+ αXt-1 + Σdi ∆Xt-I

(6)

The KPSS test differs from the ADF unit root test. In the KPSS test, each e series, Xt, is assumed to be trend- stationary under the null hypothesis. The KPSS statistic is based on the residuals from the OLS regression of Xt on the exogenous variables, Xt: (Xt = Zt′δ + ut). The null hypothesis is different for the ADF and KPSS tests. The null hypothesis for the ADF test is H0: I(1), but for the KPSS test is H0: I(0). For the ADF test the correct specification of the equation is determined based on the data generating process (DGP). If it is determined that the DGP is a random walk without a drift and a mean, then the unit 130


root test is based on equation (4). If the DGP is a random walk with a drift and zero mean, then we have to use equation (5). Equation (6) is appropriate if the series has a non-zero drift and non-zero mean. RESULTS AND DISCUSSION The unit root test results for each series, in log levels and in log first differences, are presented in Table 2. The ADF tests, involving each of the time series in log levels, the null of ‘unit root,’ [H0: I(1)], could not be rejected, while the null of ‘no unit root’ [H0 : I(0)], for the KPSS test was rejected. Then, the series are tested in their log first differences. In all the cases, the ADF test rejected the null of ‘unit root,’ in log first differences, and in the KPSS tests, the null of ‘no unit root’ could not be rejected in log first differences of the series (note, the null of the KPSS test is the opposite of ADF test). According to the ADF tests, the five time series are stationary in their log first differences. The KPSS test results confirm the ADF test conclusion. The finding that each one of the interest rates is I(1) is consistent with the results of the studies by Stock and Watson (1988, 1999). Since the unit root tests indicated that each of the interest rate series is integrated of the same order, I(1), we conducted the cointegration tests on the series employing the JJ procedure. Three multivariate cointegration tests of the interest rates are performed. First, a cointegrating rank test among all the five market interest rate series: ltb3m, ltb6m, llbr3m, llbr6m, and lffr. Then, a cointegration test among the four series: ltb3m, ltb6m, llbr3m,and llbr6m. Finally, a cointegration test between ltb3m, ltb6m, and lffr, the U.S.domestic interest rates. All cointegration tests are performed in log levels of the interest rate series and the equations are normalized on the ltb3m. Test results are presented in Table 3, panels (a), (b) and (c), respectively. In the case of the five interest rate series, panel (a) of Table 3, the trace test identified two cointegrating vectors but the maximum eigenvalue tests identified three cointegrating vectors. Since there is no agreement between the trace and maximum eigenvalue tests, I followed the convention of choosing the trace test results of two cointegrating vectors as more appropriate. Among the five interest rate series I conclude that there are two cointegrating vectors. For the four interest rate series without the fed funds rate, panel (b), Table 3, both trace and maximum eigenvalue tests identified two cointegrating vectors. For the three U.S. domestic rates, panel (c), Table 3, both the trace and maximum eigenvalue tests indicated one cointegrating vector. Tests of residuals from the estimated cointegrating equations indicate that the residuals are stationary in all cases. However, we cannot conclude that the estimated coefficients of the cointegrating equations are structural parameters. Results of the cointegration test between ltb3m, ltb6m, and lffr , bottom part of panel (c) of Table 3, indicate one cointegrating vector. There is no one-to-one relationship between ltb3m and lffr. The finding of two cointegrating vectors in the bottom panel (a) of Table 3 imply that there are two ways the five interest rate series can be stable and two ways the series can deviate from each other. In general, more cointegrating vectors means more ways the system will be stable. So, there is strong evidence that the two money markets are more integrated during the sample period for this study. Studies in the late 1980s and early 1990s reported one cointegrating vector between fed funds rate and the T-bill rates, between three month T-bill rate and three month Libor, and between one month CD rate and the three month Libor deposit rate. The studies by Clinebell et al (2000) and Sarno and Thornton (2003) also reported one cointegrating vector. However, Clinebell et al (2000) did report any increased integration of the two markets. Their conclusion is exclusively based on no finding of mutual causation between T-bill rates and Libor. Clinebell et al (2000) state that ‘increased integration and more rapid movement of dollar flows should promote bi-directional Granger causality between T-bills and LIBOR’. The study by Zhou (2007) used bivariate cointegration tests among three different sets of interest series and reported one cointegrating vector in all the three cases. There can only be one cointegrating vector between two variables integrated of the same order, say, I(1). The finding of two cointegrating vectors among the five interest rate series in this study is a strong indication that integration of U.S. domestic and 131


Eurodollar market rates has substantially increased during the sample period under investigation. Since we cannot directly infer that the increased integration is due to the elimination of reserve requirements on Eurodollar deposits in 1990 and also due to the switch to fed funds rate targeting in the conduct of monetary policy by the Fed in 1992. However, the increased integration of the two markets may be in large part attributed to the two changes, the regulatory and monetary policy operating procedure. Table 2: Augmented Dickey-Fuller & KPSS Unit Root Tests ADF Test1

KPSS Test2

Variable

Test Statistic in levels2

Test Statistic in first diff

ltb3m ltb6m llbor3m

-1.1367 0.5242 -0.9965

-20.288*** -4.6543*** -61.757***

4.1011 4.2729 4.3312

0.2914*** 0.5434*** 0.5264***

llbor6m

-0.2018

-25.934***

4.3312

0.3401***

Lffr

-1.0489

-31.989***

4.7371

0.3553***

LM Test Stat in levels

LM Test Stat in first diff

The equation estimated is Yt = µ + α Xt-1 + Σδi ∆Xt-i for the ADF test. ADF and KPSS unit rate test results indicate that all the interest rate series in their log levels are I(1), and are stationary in their log first differences. 1 1 % critical value for ADF test with intercept is -3.4313, 5% critical value with intercept is -2.8618, 1%. Critical value with intercept and trend it is -3.9595, and for 5% it is -3.4105. 2 1% critical value for KPSS LM statistic with intercept is 0.739 and 5% value is 0.463, and with intercept and trend the critical values are 0.216 and 0.146, respectively. *** indicates significance at 1% level.

In the four variable system of ltb3m, ltb6m, llb3m, and llb6m, shown in column (b) of Table 3, the maximum number of cointegrating vectors is three. The finding of two cointegration vectors means that there are two ways these rates can be stable. In the case of one cointegrating vector among ltb3m, ltb6m, and lffr, displayed in column (c), there is only one way the system is stable. The time period from late 2007 to late 2009 is characterized by severe financial crisis in the U.S. During that period there were accusations that the Libor was being manipulated by some of the large participating banks in the Eurodollar market. I used the time period from January 2, 2007 to September 14, 2009 to test whether the accusation of manipulation of Libor had any impact on the cointegrating relationship among the five interest rates. The estimated results indicated two cointegrating vectors among the five interest rate series. For want of space the results are not presented in this paper but are available to anyone interested in these results. However, as the sample period of less than three years is too short to estimate a cointegrating relationship I do not want to conclude that the U.S. financial crisis did not disrupted the degree of integration of the two markets. Instead, I would prefer to examine this issue when the sample period is over five or six years. For examining the short-run dynamics of the interest rates, two VEC models (equation 3) are estimated, one with all the five rates in their log first differences, and the other with the four money market interest rates (i.e. without the lffr) in their log first differences. Based on the estimated results of the VEC models presented in Table 4, panels (a) and (b), we can draw some key inferences about the adjustment mechanism of the interest rates to their long run equilibrium path following an external shock to the system of interest rates. The magnitudes and signs of the estimated error-correction coefficients reported in panels (a) and (b) of Table 4 provide information as to how the equilibrium is restored, the direction and magnitude, following an external shock. Results in panel (a) of Table 4 show that the error-correction coefficients of two equations, Δlffr and Δltb3m, are statistically significant. However, the error correction coefficients in the remaining equations are not statistically significant at the conventional levels, which implies that ltb3m and lffr do participate in the adjustment process, but their participation is not statistically significant. 132


Table 3: Cointegration Test Results H0: r = 0, Ha =1 Trace statistic Critical Value Max. Eigen Stat Critical Value

Panel

(a)

Panel (b)

Panel (c )

893.66*** 85.336 786.91*** 40.295

866.50*** 61.195 778.52*** 33.733

252.05*** 41.195 234.69*** 27.068

106.75*** 61.267 77.029*** 33.733

87.981*** 41.195 74.405*** 27.068

17.353 25.078 15.329 20.161

29.717 41.195 27.067*** 15.759

13.576 25.078 12.268 20.161

15

15

15

Panel (b)

Panel (c)

H0: r ≤ 1, Ha = 2 Trace statistic Critical Value Max. Eigen Stat. Critical Value H0: r ≤ 2, Ha =3 Trace statistic Critical Value Max. Eigen Stat. Critical Value Lags

Normalized cointegrating equations. Normalized on ltb3m Panel (a) ltb3m

1.0000

1.0000

1.0000

ltb6m

-1.0622*** (0.01372)

-1.0658*** (0.0138)

1.0527*** (0.0121)

llbr3m

-0.7239*** (0.0397)

-0.7171*** (0.0384)

llbr6m

0.7688*** (0.0405)

0.7653*** (0.0398)

Lffr

-0.0013 (0.0049)

Constant

0.0419 (0.0111)

0.0293** (00112) 0.0429 (0.0093)

0.1619 (0.0207)

Log likelihood 76,056.44 65,475.04 33,726.65 Estimated system of equations: Xt = µ + Σ Ai Xt - + єt Upper half of the Table 3, Panels (a), (b), and (c) contain hypotheses tests of three cointegrationg equations. In Panels (a) and (b) the inference is two cointegrating vectors and one in Panel (c). Panels (a), (b), and (c) in the lower part of Table 3 contain the normalized cointegrating vectors. Standard errors are in parentheses. ***, ** Significance at 1% and 5% levels.

The magnitude of the error-correction coefficient of Δlffr is much larger, over four times larger, than the coefficient of Δltb3m. Following a positive shock the system is pushed above its equilibrium path. Both lffr and ltb3m react to gradually restore long-run equilibrium relationship between these rates. The negative signs of the error-correction coefficients indicate the direction of that adjustment to equilibrium. Additionally, it appears that the fed funds rate, the focus of monetary policy, reacts significantly in restoring equilibrium. This finding is consistent with the reported results of the studies by Sarno et al (2003) and Zhou (2007). According to Sarno et al (2003) study, ‘the more surprising result was the finding that that the fed funds rate adjusts more rapidly than the three-month T-bill rate’. Likewise, the study by Zhou (2007), that examined the dynamic relationship between the fed funds rate and the Eurodollar rate, reported that, in the post-1994 period the fed fund rate bears the burden of the adjustment toward equilibrium. In general, the belief is that the fed funds rate is the bellwether rate and all other

133


short-term rates follow it. That general belief appears to be in contrast with the findings of this study and also the studies by Sarno et al (2003) and Zhou (2007). Table 4: VECM Estimated Results Panel (a) Error-correction Coeff. (λi) Sums of lagged first differences: ΣΔlffrt-i Sums of lagged first differences: ΣΔltb3mt-i Sums of lagged first differences : ΣΔltb6mt-i Sums of lagged first differences: ΣΔllbr3mt-i Sums of lagged first differences: ΣΔllbr6mt-i Panel (b) Error-correction Coeff. (λi) Sums of lagged first differences: ΣΔltb3mt-i Sums of lagged first differences: ΣΔltb6mt-i

Δlffr -0.0867*** (-8.1021) 0.0204 (0.3980) 0.0876 (1.2247) 0.1196 (1.6542) 0.9463 (1.1223)

Δltb3m 0.0095*** (0.0035) 0.0544*** (3.9040) 0.1031 (1.4321) -0.1273 (1.4634) 0.0671 (1.6454) -0.1367*** (-16.797)

Δltb6m -0.0038 (1.5746) 0.0019 (0.8990) -0.0109 (0.8674) 0.0326 (1.2237) -0.0295 (1.2895) -0.0123*** (-4.4635) -0.1006*** (2.6524)

0.0625*** (3.5424) Sums of lagged first differences : ΣΔllbr3mt-i 0.0329*** -0.0143 (3.6687) (-2.1580) Sums of lagged first differences: ΣΔllbr6mt-i 0.0303 -0.0009 (0.9009) (-1.1057) This table shows VECM Estimated Results. III indicates significance at the one percent level.

Δllbr3m 0.0034 (1.2029) -0.0763 (-1.0971) 0.1996*** (7.5241) 0.1363 (1.4926) 0.3068 (1.0722) -0.0048*** (-3.5403) 0.3670 (2.6948) -0.0480 (-1.0145) 0.4552*** (4.7224)

Δllbr6m 0.0012 (0.4032) -0.0082 (1.5244) 0.2133*** (7.2210) -0.0534 (-0.9327) -0.1358*** (-2.9050)

-0.0041*** (-2.5986) 0.0741 (1.0212) -0.0044 (-0.0875) -0.0585*** (-2.5431)

The short-run dynamics can be inferred from the reported coefficients of the sums of the log differenced and lagged variables in each equation. The reported results in Table 4 panel (a) in the Δltb3m equation, the coefficient of ΣΔlffrt-i is statistically significant while the coefficient of ΣΔltb3mt-i is not significant in the Δlffr equation. The inference is that Granger causality runs from the federal funds rate to the threemonth T-bill rate. Next, one-way Granger causation can be inferred in the short-run between three-month T-bill rate to both three-month and six-month Libor, because in the two equations, Δllbr3m and Δllbr6m, the coefficients of ΣΔltb3mt-i, are significant, columns 5 and 6, panel (a). Finally, none of the variables is causally linked to the six-month T-bill rate because none of coefficients in that equation is statistically significant. Now, let us take a look at the reported results of the error-correction model in panel (b) of Table 4. This model is estimated without the fed funds rate as part of the system. These results are different compared to the reported results in panel (a) of Table 4. First, in panel (a), only the three-month T-bill rate and fed funds rate participate in the adjustment process when the system is out of equilibrium, whereas the results in panel (b) of Table 4 imply that all the four market rates participate significantly in the adjustment process. Secondly, the short-run dynamics among the variables also differ from the results in panel (a) of Table 4. First, in the Δltb3m equation six-month T-bill rate along with the three-month Libor rate cause the three-month T-bill rate. And the three-month T-bill rate causes the three-month Libor. Further, threemonth Libor and six-month Libor are mutually causal. In sum, three-month T-bill rate and three-month Libor are mutually causal, three-month T-bill rate and six-month T-bill rate are mutually causal, and the three-month and six-month Libor are mutually causal. These results are not consistent with the results reported in panel (a) of Table 4. The key difference between the two estimated results is the finding of mutual causation among the four rates. The interpretation of the finding of causality running both directions is not very clear. Some of the studies reviewed above argued that a finding of mutual causation of these rates would imply increased integration of the two markets. Results of this study, reported in 134


Table 4 panel (b) do indicate mutual causation of these rates. If it is assumed that a finding of mutual causation is evidence of increased integration then, this study supports that contention. Instead of basing the inference of increased market integration on a finding of mutual causation of variables, I would argue that the real support for increased market integration has to be based on the number of ways a system can be stable, that is, the number of cointegrating vectors in the system. More ways a system is be stable, that is, the more cointegrating vectors there are, the more integrated the system is. Dickey et al (1991) argued that cointegrating vectors can be thought of as representing constraints that an economic system imposes on the movement or co-movement of the variables in the system in the long-run. Dickey et al (1991) further assert that the more cointegrating vectors there are the more stable the system. Other things being the same, it is desirable for an economic system to be stationary in as many directions as possible. In this paper the inference of increased integration of the markets is based on the finding of two cointegrating vectors among the five interest rate series. Further, there is some controversy regarding the interpretation of the finding of mutual causation between variables. Economists Hess and Schweitzer (2000) raised objection to the interpretation of mutual causation as the two variables concerned cause each other. They argued that two variables may ‘Grangercause one another’, in which case one can conclude only that both economic series are determined simultaneously; hence, a researcher cannot conclude that one series has an independent causal effect on the other’. A second interpretation may be that the two variables involved are caused by a third variable. The finding of conflicting causal linkages in this study may be due to the omission of the fed funds rate in the estimated results of the VEC model presented in Table 4 panel (b). Perhaps, the fed funds rate is an essential part of the system. However, this issue needs further investigation and will be explored in more detail in future research. CONCLUDING REMARKS This empirical study tests whether there is an increase in the degree of integration among the U.S. effective fed funds rate, three and six-month T-bill rates and three and six-month Libor following two key changes. First, in 1990s the Fed dropped the reserve requirement on Eurodollar bank deposits. Second, the Fed switched from borrowed reserve targeting to targeting fed funds rates in conducting monetary policy. To examine this aspect, multivariate cointegrating equations are estimated to test for long-run equilibrium relationship among these rates, and for the short-run dynamics among these rates, two VEC models are estimated. The data used in this study are daily (5-day) series, and the sample period ranges from January 6, 1986 to September 14, 2009. Each of the interest rate series is tested for the degree of integration using ADF and KPSS tests. All the five series in log levels are found to be I(1). The series are stationary in their log first differences. As all the rates are integrated on the same order multivariate JJ cointegration tests are conducted. The tests identified two cointegrating vectors among the U.S. domestic and offshore Libor rates, which implies that the degree of integration among these rates has increased since the 1990s. No published study reported more than one cointegrating relationship between the U.S. domestic rates and the Eurodollar rates. The inference of increased integration between the U.S. domestic and offshore Eurodollar markets is based more on the finding of two cointegration vectors rather than the finding of mutual causation of the interest rates involved. If mutual causation is accepted as proof of increased integration, then, that finding of mutual causation in this study, should reinforce increased integration. One important policy implication of increased integration is that U.S. monetary policy, fed funds targeting, can be expected to be more effective in closely linked markets. In order to examine the short run dynamics among the key interest rates two VEC models are estimated, one with all the five interest rates and the other without the fed funds rate. The results of the two VEC models are different. This is somewhat intriguing as there is little agreement between the estimated results of the two VEC models. For instance temporal Granger causality runs from the three-month T-bill rate to 135


the three-month Libor in the VEC model with the fed funds rate included in the system. The results of the VEC model estimated without the fed funds rate showed bi-directional Granger causality between the three-month T-bill rate and the three-month Libor. These conflicting results will be further investigated as part of further research of this paper. REFERENCES Baba, N., McCauley, R., & Ramaswamy, S. (2009), U. S. dollar money market funds and non-U.S. banks, Bank of International Settlements (BIS), Quarterly (March), p. 65-81. Campbell, J.Y., & Shiller, R. J. (1997), Yield spreads and interest rate movements: A bird’s eye view, Review of Economic Studies, vol. 58, p. 495-514. Dickey, D. A., & Fuller, W. A. (1979), Distribution of the estimators for autoregressive time series with unit root, Journal of the American Statistical Association, vol. 74, p. 427-431. Dickey, D. A., & Fuller, W. A. (1981), Likelihood Ratio Statistics for Autoregressive time series with a unit root, Econometrica, vol. 49, p. 1057-1072. Enders, W. & Granger, C.W.J. (1998), Unit-root tests and asymmetric adjustment with an example using the term structure of interest rates, Journal of Business and Economic Studies, vol. 16, p. 304-311. Engle, R.F. & Granger, C. W. J. (1987), Co-integration and error correction representation, estimation and testing, Econometrica, vol. 55, p. 251-276. Engsted, T. & Tanggaard, C. (1994), Cointegration and U.S. term structure, Journal of Banking and Finance, vol. 18, p. 167-181. Fung, H. G., & S. C. Isberg. (1992), The international transmission of Eurodollar and U. S. Interest rates: A cointegration analysis, Journal of Banking and Finance, vol. 16 (4), p. 757-769. Goldberg, L. S., Kennedy, C., & Min, J. (2010), Central bank dollar swap lines and overseas dollar funding costs, Staff Report No. 429, Federal Reserve Bank of New York. Hall, A.D., Anderson, H.M., & Granger C.W.J. (1992), A cointegration analysis of treasury bill yields, Review of Economics and Statistics, vol. 74, p. 116-126. Hartman, D. G. (1984), The international financial market and U. S. interest rates, Journal if International Money and Finance, vol. 3, p. 91-103. Hess G. D., & Schweitzer, S. M. (2000), Does wage inflation cause price inflation, Policy Discussion paper, Federal Reserve Bank of Cleveland. Johansen, S. & Juselius, K. (1990), Maximum likelihood estimation and inference on cointegrationwith applications to the demand for money, Oxford Bulletin of Economics and Statistics, vol. 53 (1), p. 169-210. Johansen, S. & Juselius, K. (1992), Testing structural hypotheses in a multivariate cointegration analysis of PPP and UIP for U.K., Journal of Econometrics, vol. 53 (1-3), p. 211-244.

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Zhou, S. (2003), Interest rate linkages within the European monetary system: new evidence incorporating long-run trends, Journal of International Money and Finance, vol. 22, p. 571-590. Zhou, S. (2007), The dynamic relationship between the federal funds rate and the Eurodollar rates under interest rate targeting, Journal of Economic Studies, vol. 34, p. 90-102. ACKNOWLEDGEMENTS

I would like to thank the two anonymous referees and the editor of the journal for their valuable suggestions for the improvement of this paper. Also, I would like to thank Dr. Hal Snarr, my colleague at North Carolina A&T State University, for helping me in making the necessary changes to the manuscript to comply with the journal’s guidelines. BIOGRAPHY

Krishna M. Kasibhatla is Associate Professor of Economics, Department of Economics and Finance, School of Business and Economics at North Carolina A&T State University (AACSB accredited). His research appeared, either as lead author, sole author, or co-author of the papers published in Empirical Economics, Economic systems, International Journal of Finance, American Economist, International Advances in Economic Research, American Business Review, Indian Journal of Business and Economics, Journal of Economic and Business Studies . He can be reached at 1601 E. Market Street, Greensboro, NC 27411, [email protected]

138

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Yen-Hsien Lee, Department of Finance, Chung Yuan Christian University

Tatsiana N. Rybak, Belarusian State Economic University

YingChou Lin, Missouri University of Science and Technology Shulin Lin, Hsiuping University of Science and Technology Melissa Lotter, Tshwane University of Technology Xin (Robert) Luo, Virginia State University Andy Lynch, Southern New Hampshire University Eduardo Macias-Negrete, Instituto Tecnologico de Ciudad Juarez Abeer Mahrous, Cairo university Gladys Marquez-Navarro, Saint Louis University Jesús Apolinar Martínez Puebla, Universidad Autónoma De Tamaulipas Cheryl G. Max, IBM Aurora Irma Maynez Guaderrama, Universidad Autonoma de Ciudad Juarez Romilda Mazzotta, University of Calabria Mary Beth McCabe, National University Avi Messica, Holon Institute of Technology Cameron Montgomery, Delta State University Sandip Mukherji, Howard University Tony Mutsue, Iowa Wesleyan College Cheedradevi Narayanasamy, Graduate School of Business, National University of Malaysia Erwin Eduardo Navarrete Andrade, Universidad Central de Chile Dennis Olson, Thompson Rivers University Godwin Onyeaso, Shorter University Bilge Kagan Ozdemir, Anadolu University Dawn H. Pearcy, Eastern Michigan University Eloisa Perez, MacEwan University Pina Puntillo, University of Calabria (Italy) Rahim Quazi, Prairie View A&M University Anitha Ramachander, New Horizon College of Engineering Charles Rambo, University of Nairobi, Kenya

Rafiu Oyesola Salawu, Obafemi Awolowo University Paul Allen Salisbury, York College, City University of New York Leire San Jose, University of Basque Country Celsa G. Sánchez, CETYS Universidad I Putu Sugiartha Sanjaya, Atma Jaya Yogyakarta University, Indonesia Sunando Sengupta, Bowie State University Brian W. Sloboda, University of Phoenix Adriana Patricia Soto Aguilar, Benemerita Universidad Autonoma De Puebla Smita Mayuresh Sovani, Pune University Alexandru Stancu, University of Geneva and IATA (International Air Transport Association) Jiří Strouhal, University of Economics-Prague Qian Sun, Kutztown University Diah Suryaningrum, Universitas Pembangunan Nasional Veteran Jatim James Tanoos, Saint Mary-of-the-Woods College Jeannemarie Thorpe, Southern NH University Ramona Toma, Lucian Blaga University of Sibiu-Romania Jorge Torres-Zorrilla, Pontificia Universidad Católica del Perú Md Hamid Uddin, University Of Sharjah Ozge Uygur, Rowan University K.W. VanVuren, The University of Tennessee – Martin Vijay Vishwakarma, St. Francis Xavier University Ya-Fang Wang, Providence University Richard Zhe Wang, Eastern Illinois University Jon Webber, University of Phoenix Jason West, Griffith University Wannapa Wichitchanya, Burapha University Veronda Willis, The University of Texas at San Antonio Bingqing Yin, University of Kansas Junye Yu, Louisiana State University

REVIEWERS

The IBFR would like to thank the following members of the academic community and industry for their much appreciated contribution as reviewers.

Haydeé Aguilar, Universidad Autónoma de Aguascalientes

Ana Ma. Guillén Jiménez, Universidad Autónoma de Baja California

María Antonieta Andrade Vallejo, Instituto Politécnico Nacional

Ana Ma. Guillén Jiménez, Universidad Autónoma de Baja California

Olga Lucía Anzola Morales, Universidad Externado de Colombia

Araceli Gutierrez, Universidad Autonoma De Aguascalientes

Hector Luis Avila Baray, Instituto Tecnologico De Cd. Cuauhtemoc

Andreina Hernandez, Universidad Central de Venezuela

Graciela Ayala Jiménez, Universidad Autónoma de Querétaro Carlos Alberto Cano Plata, Universidad De Bogotá Jorge Tadeo Lozano Edyamira Cardozo, Universidad Nacional Experimental De Guayana Sheila Nora Katia Carrillo Incháustegui, Universidad Peruana Cayetano Heredia emma casas medina, Centro de Estudios Superiores del Estado de Sonora Benjamín Castillo Osorio, Universidad Cooperativa De Colombia y Universidad De Córdoba Benjamin Castillo Osorio, Universidad del Sinú-Sede Monteria María Antonia Cervilla de Olivieri, Universidad Simón Bolívar Cipriano Domigo Coronado García, Universidad Autónoma de Baja California Semei Leopoldo Coronado Ramírez, Universidad de Guadalajara

Arturo Hernández, Universidad Tecnológica Centroamericana Alejandro Hernández Trasobares, Universidad de Zaragoza Alma Delia Inda, Universidad Autonoma Del Estado De Baja California Terrance Jalbert, The IBFR Gaspar Alonso Jiménez Rentería, Instituto Tecnológico de Chihuahua Lourdes Jordán Sales, Universidad de Las Palmas de Gran Canaria Santiago León Ch., Universidad Marítima del Caribe Graciela López Méndez, Universidad de GuadalajaraJalisco Virginia Guadalupe López Torres, Universidad Autónoma de Baja California Angel Machorro Rodríguez, Instituto Tecnológico de Orizaba Cruz Elda Macias Teran, Universidad Autónoma de Baja California Aracely Madrid, ITESM, Campus Chihuahua

Esther Eduviges Corral Quintero, Universidad Autónoma de Baja California

Deneb Magaña Medina, Universidad Juárez Autónoma de Tabasco

Dorie Cruz Ramirez, Universidad Autonoma Del Estado De Hidalgo /Esc. Superior De Cd. Sahagún

Carlos Manosalvas, Universidad Estatal Amazónica

Edna Isabel De La Garza Martinez, Universidad Autónoma De Coahuila Javier de León Ledesma, Universidad de Las Palmas de Gran Canaria - Campus Universitario de Tafira Hilario Díaz Guzmán, Universidad Popular Autónoma del Estado de Puebla Cesar Amador Díaz Pelayo, Universidad de Guadalajara, Centro Universitario Costa Sur Elizabeth Avilés , CICESE Ernesto Geovani Figueroa González, Universidad Juárez del Estado de Durango

Gladys Yaneth Mariño Becerra, Universidad Pedagogica y Tecnológica de Colombia Omaira Cecilia Martínez Moreno, Universidad Autónoma de Baja California-México Jesus Carlos Martinez Ruiz, Universidad Autonoma De Chihuahua Alaitz Mendizabal, Universidad Del País Vasco Alaitz Mendizabal Zubeldia, Universidad del País Vasco/ Euskal Herriko Unibertsitatea Fidel Antonio Mendoza Shaw, Universidad Estatal De Sonora

Ana Karen Fraire, Universidad De Gualdalajara

Juan Nicolás Montoya Monsalve, Universidad Nacional de Colombia-Manizales

Teresa García López, Universidad Veracruzana

Jennifer Mul Encalada, Universidad Autónoma De Yucatán

Helbert Eli Gazca Santos, Instituto Tecnológico De Mérida

Alberto Elías Muñoz Santiago, Fundación Universidad del Norte

Erika Olivas, Universidad Estatal de Sonora Erick Orozco, Universidad Simon Bolivar José Manuel Osorio Atondo, Centro de Estudios Superiores del Estado de Sonora Luz Stella Pemberthy Gallo, Universidad del Cauca Andres Pereyra Chan, Instituto Tecnologico De Merida Adolfo León Plazas Tenorio, Universidad del Cauca

Pol Santandreu i Gràcia, Universitat de Barcelona, Santandreu Consultors Victor Gustavo Sarasqueta, Universidad Argentina de la Empresa UADE Jaime Andrés Sarmiento Espinel, Universidad Militar de Nueva Granada Jesus Otoniel Sosa Rodriguez, Universidad De Colima

Hector Priego Huertas, Universidad De Colima

Edith Georgina Surdez Pérez, Universidad Juárez Autónoma de Tabasco

Juan Carlos Robledo Fernández, Universidad EAFITMedellin/Universidad Tecnologica de Bolivar-Cartagena

Jesús María Martín Terán Gastélum, Centro de Estudios Superiores del Estado de Sonora

Humberto Rosso, Universidad Mayor de San Andres

Jesús María Martín Terán Gastélum, Centro de Estudios Superiores del Estado de Sonora

José Gabriel Ruiz Andrade, Universidad Autónoma de Baja California-México Antonio Salas, Universidad Autonoma De Chihuahua Claudia Nora Salcido, Facultad de Economía Contaduría y Administración Universidad Juarez del Estado de Durango Juan Manuel San Martín Reyna, Universidad Autónoma de Tamaulipas-México Francisco Sanches Tomé, Instituto Politécnico da Guarda Edelmira Sánchez, Universidad Autónoma de Ciudad Juárez Deycy Janeth Sánchez Preciado, Universidad del Cauca María Cristina Sánchez Romero, Instituto Tecnológico de Orizaba María Dolores Sánchez-Fernández, Universidade da Coruña Luis Eduardo Sandoval Garrido, Universidad Militar de Nueva Granada

Jesus María Martín Terán Terán Gastélum, Centro de Estudios Superiores del Estado de Sonora Maria De La Paz Toldos Romero, Tecnologico De Monterrey, Campus Guadalajara Abraham Vásquez Cruz, Universidad Veracruzana Lorena Vélez García, Universidad Autónoma de Baja California Alejandro Villafañez Zamudio, Instituto Tecnologico de Matamoros Hector Rosendo Villanueva Zamora, Universidad Mesoamericana Oskar Villarreal Larrinaga, Universidad del País Vasco/Euskal Herriko Universitatea Delimiro Alberto Visbal Cadavid, Universidad del Magdalena

HOW TO PUBLISH Submission Instructions The Journal welcomes submissions for publication consideration. Authors wishing to submit papers for publication consideration should visit our website at www.theibfr.com/journal.htm, under “How to Submit a Paper.” Complete directions for manuscript submission are available at the Journal website www.theIBFR. com/journal.htm. Papers may be submitted for initial review in any format. However, authors should take special care to address spelling and grammar issues prior to submission. Authors of accepted papers are required to precisely format their document according to the guidelines of the journal. There is no charge for paper reviews. The normal review time for submissions is 90-120 days. However, authors desiring a quicker review may elect to pay an expedited review fee. Authors of accepted papers are required to pay a publication fee based on the length of the manuscript. Please see our website for current publication and expedited review rates. Authors submitting a manuscript for publication consideration must guarantee that the document contains the original work of the authors, has not been published elsewhere, and is not under publication consideration elsewhere. In addition, submission of a manuscript implies that the author is prepared to pay the publication fee should the manuscript be accepted.

Subscriptions Individual and library subscriptions to the Journal are available. Please contact us by mail or by email to: [email protected] for updated information.

Contact Information Mercedes Jalbert, Managing Editor The IBFR P.O. Box 4908 Hilo, HI 96720 [email protected]

Website www.theIBFR.org or www.theIBFR.com

PUBLICATION OPPORTUNITIES

Business Education

E BA

& Accreditation

Review of Business & Finance Studies

Business Education and Acreditation (BEA)

Review of Business & Finance Studies (ISSN: 21503338 print and 2156-8081 online) publishes high-quality studies in all areas of business, finance and related fields. Empirical, and theoretical papers as well as case studies are welcome. Cases can be based on real-world or hypothetical situations.

Business Education & Accreditation publishes high-quality articles in all areas of business education, curriculum, educational methods, educational administration, advances in educational technology and accreditation. Theoretical, empirical and applied manuscripts are welcome for publication consideration.

All papers submitted to the Journal are double-blind reviewed. The Journal is distributed in print and through SSRN and EBSCOhost Publishing, with nation-wide access in more than 70 countries. The Journal is listed in Cabell’s directory.

All papers submitted to the Journal are double-blind reviewed. BEA is is listed in Cabell’s and Ulrich’s Periodicals Directory. The Journal is distributed in print, through SSRN and EBSCOHost publishing, with presence in over 70 countries.

The journal accept rate is between 15 and 25 percent

The journal acceptance rate is between 15 and 25 percent.

Accounting A T & Taxation Accounting and Taxation (AT) Accounting and Taxation (AT) publishes high-quality articles in all areas of accounting, auditing, taxation and related areas. Theoretical, empirical and applied manuscripts are welcome for publication consideration. All papers submitted to the Journal are double-blind reviewed. AT is listed in Cabell’s and Ulrich’s Periodicals Directory. The Journal is distributed in print, through SSRN and EBSCOHost publishing, with presence in over 70 countries. The journal acceptance rate is between 5 and 15 percent.

PUBLICATION OPPORTUNITIES The International Journal of

R

Business and Finance ESEARCH The International Journal of Business and

IJMMR

INTERNATIONAL JOURNAL OF MANAGEMENT AND MARKETING RESEARCH

Finance Research ISSN 1931-0269

International Journal of Management and Marketing Research ISSN 1933-3153

The International Journal of Business and Finance Research (IJBFR) publishes high-quality articles in all areas of finance, accounting and economics. Theoretical, empirical and applied manuscripts are welcome for publication consideration.

The International Journal of Management and Marketing Research (IJMMR) publishes high-quality articles in all areas of management and marketing. Theoretical, empirical and applied manuscripts are welcome for publication consideration.

All papers submitted to the Journal are double-blind reviewed. The IJBFR is listed in Cabell’s, Ulrich’s Periodicals Directory and The American Economic Association’s Econlit, e-JEL and JEL on CD. The Journal is distributed in print, through SSRN and EBSCOHost publishing, with presence in over 70 countries.

All papers submitted to the Journal are double-blind reviewed. The IJMMR is listed in Cabell’s and Ulrich’s Periodicals Directory. The Journal is distributed in print, through SSRN and EBSCOHost publishing, with presence in over 70 countries.

The IJBFR acceptance rate is between 5 and 10 percent.

The IJMMR acceptance rate is between 5 and 10 percent.

Global Journal of

Research Business

RIAF

Revista Internacional

ADMINISTRACION &

FINANZAS

Global Journal of Business Research ISSN 1931-0277

Revista Internacional Administración y Finanzas ISSN 1933-608X

The Global Journal of Business Research (GJBR) publishes high-quality articles in all areas of business. Theoretical, empirical and applied manuscripts are welcome for publication consideration.

Revista Internacional Administracion y Finanzas (RIAF), a Spanish language Journal, publishes high-quality articles in all areas of business. Theoretical, empirical and applied manuscripts are welcome for publication consideration.

All papers submitted to the Journal are double-blind reviewed. The GJBR is listed in Cabell’s, The American Economic Association’s Econlit, e-JEL and JEL on CD, and Ulrich’s Periodicals Directory. The Journal is distributed in print, through SSRN and EBSCOHost publishing, with presence in over 70 countries. The GJBR acceptance rate is 20 percent.

All papers submitted to the Journal are double-blind reviewed. RIAF is listed in The American Economic Association’s Econlit, e-JEL and JEL on CD, and Ulrich’s Periodicals Directory. The Journal is distributed in print, through SSRN and EBSCOHost publishing, with presence in over 70 countries. The Journal acceptance rate is between 5 and 15 percent.

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