Forecasting ability of the investor sentiment endurance index: The ...

Energy Economics 47 (2015) 121–128

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Forecasting ability of the investor sentiment endurance index: The case of oil service stock returns and crude oil prices Ling T. He 1, K.M. Casey ⁎ Department of Economics and Finance, University of Central Arkansas, Conway, AR 72035, United States

a r t i c l e

i n f o

Article history: Received 19 March 2014 Accepted 4 November 2014 Available online 15 November 2014 JEL Codes: C51 C53 C58 G12 G17 M21

a b s t r a c t Using a binomial probability distribution model this paper creates an endurance index of oil service investor sentiment. The index reflects the probability of the high or low stock price being the close price for the PHLX Oil Service Sector Index. Results of this study reveal the substantial forecasting ability of the sentiment endurance index. Monthly and quarterly rolling forecasts of returns of oil service stocks have an overall accuracy as high as 52% to 57%. In addition, the index shows decent forecasting ability on changes in crude oil prices, especially, WTI prices. The accuracy of 6-quarter rolling forecasts is 55%. The sentiment endurance index, along with the procedure of true forecasting and accuracy ratio, applied in this study provides investors and analysts of oil service sector stocks and crude oil prices as well as energy policy-makers with effective analytical tools. © 2014 Elsevier B.V. All rights reserved.

Keywords: Endurance index of oil service investor sentiment Forecasting ability Rolling forecast Accuracy ratio

“But how do we know when irrational exuberance has unduly escalated asset values, which then become subject to unexpected and prolonged contractions as they have in Japan over the past decade?”— Alan Greenspan, from a speech entitled “The Challenge of Central Banking in a Democratic Society,” delivered at the Annual Dinner and Francis Boyer Lecture of The American Enterprise Institute for Public Policy Research, Washington, D.C.—December 5, 1996 1. Introduction The presence of numerous market anomalies and asset pricing inconsistencies leads most modern finance theorists to concede that investors behaving irrationally can and do temporarily impact asset prices. In fact, much of the relatively new field of behavioral finance attempts to model those behaviors and predict their impact on asset prices. One such behavior that is widely believed to impact markets is investor sentiment. From a logical perspective it seems clear that optimistic investors are more likely to buy assets and drive prices higher while pessimistic investors are more likely to sell assets and drive prices ⁎ Corresponding author. Tel.: +1 501 852 0877. E-mail addresses: [email protected] (L.T. He), [email protected] (K.M. Casey). 1 Tel.: +1 501 450 5334.

http://dx.doi.org/10.1016/j.eneco.2014.11.005 0140-9883/© 2014 Elsevier B.V. All rights reserved.

lower. However, at some point this optimism or pessimism can push values far higher or lower than traditional valuation models predict. In other words, a seemingly rational behavior crosses over into irrationality at some point. Former Federal Reserve Chairman Alan Greenspan's famous 1996 quote from a speech made at The American Institute for Public Policy Research refers to this condition of extreme optimism as “irrational exuberance.” As Greenspan clearly states asset prices are impacted by investor sentiment. However, problems exist in measuring and forecasting investor sentiment with enough consistency to forecast asset prices and make profitable trades based on those forecasts. Numerous studies including Barberis et al. (1998), Baker and Wurgler (2006) and Sayim et al. (2013), attempt to identify realistic proxies for investor sentiment and use those proxies in asset pricing models. Each study has varying degrees of success. One problematic issue for researchers is the fact that not all investors react to the same exogenous environmental variables in the same manner. Some investors may be pessimistic with respect to current conditions while other investors may be optimistic to those same conditions. That fact, coupled with the continuous flow of information that must be reviewed and digested by each investor to form everchanging valuation opinions, makes investor sentiment a moving target that can also rapidly switch directions. Therefore the net effect of those

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L.T. He, K.M. Casey / Energy Economics 47 (2015) 121–128

opposing time-varying sentiments will impact asset prices and most measures of investor sentiment fail to capture these dynamics. However, one model of investor sentiment, developed by He (2012), assumes those often conflicting sentiments are captured in the closing stock prices. This method uses readily available information to construct a sentiment endurance index (SE) that is not dependent on the type of news or the ability to predict whether that news will be considered positive or negative by investors. The net effect of the investor sentiment is instead embedded in the closing stock price. In this paper we provide additional evidence that this method can be used to forecast asset prices. To test the model's reliability in volatile markets with available data we use the model to forecast the price of crude oil and various oil service stocks using the Philadelphia Stock Exchange Oil Service Sector Index (OSX) as a proxy. 2. Literature review Investors acting in efficient markets constantly react to new information and adjust their asset positions accordingly. New information, by definition, has not been available to investors prior to its release to be factored into their buy and sell decisions. Upon release the net effect of relevant information is to move asset prices higher or lower. Some information impacts all stocks and their returns as modeled by Fama and French in several studies (1993, 1996, 1997). Still other information is more firm-specific and impacts the returns of select stocks or funds (Daniel and Titman, 1997). In addition to the vast amount of stock specific information and macroeconomic information investor sentiment can also be impacted by non-economic factors such as the weather. For example Kamstra et al. (2003) find that market returns are lower during the fall and winter when the weather is gloomy. They attribute this finding to a specific behavioral disorder associated with declining daylight hours. Given the complexity of human behavior there is no consensus of the type of information that will impact asset prices. Investors, in their quest for excess returns, respond to all information and can respond in different directions to the same set of information. A seminal paper by Delong (DeLong et al., 1990) develops the underpinnings for this line of research. The DSSW paper maintains that investors are subject to sentiment which is defined as a belief about a firm's future cash flows and level of risk that is not supported by current facts. In addition these sentiment beliefs can persist for extended periods of time resulting in asset prices that differ from their intrinsic value. The asset prices can be higher, which is a result of investor overreaction, or lower due to investor underreaction (Barberis et al., 1998). In any case investor sentiment is considered to be one driver of observed asset pricing irregularities. Given that investor sentiment has been identified as a driver of asset mispricing there are a significant number of researchers that focus on ways to measure investor sentiment. This effort is justified since a consistent model that predicts investor sentiment could generate excess returns for investors. A study by Fisher and Statman (2000) is based on the premise that investor sophistication dictates investor sentiment. They divide investors into three groups based on portfolio size and utilize different sentiment proxies for each group. Each sentiment proxy uses survey based data that is currently collected and published. Their findings are interesting since they determine the three investors groups do not move in unison. The sentiment of large investors had almost no correlation with the sentiment of the other two groups. This finding highlights the problem of determining the net impact of investor sentiment on asset prices at any given time. Brown and Cliff (2004) conduct a comprehensive study of measures of investor sentiment and their impact on future stock returns. While they find that aggregate measures of sentiment levels are highly correlated with contemporaneous market returns their model is incapable of consistently forecasting future stock returns. However, their research does support that institutional sentiment is strongly related to large stock returns which further supports that different groups or classes of

investors can engage in trading activities that cancel their respective impacts. Other examples of investor sentiment are identified by Swaminathan (1996) and Neal and Wheatley (1998) that both find that closed-end fund discounts can be a useful proxy for investor sentiment. Neal and Wheatley (1998) also determine that net mutual fund redemptions can aid in forecasting the size of the mispricing. Baker and Wurgler (2007) provide a laundry list of proxies for investor sentiment. These proxies include the aggregate forecasts of newsletter writers identified by Brown and Cliff (2005), changes in consumer confidence (Lemmon and Portniaguina, 2006), and trading volume (Scheinkman and Xiong, 2003). In addition they list other proxies such as mutual fund flows, dividend premium, opinion implied volatility, IPO first-day returns, IPO volume, equity issues over total new issues, and insider trading. All of these investor sentiment indexes and their lagged terms are used as predictors for stock market returns or portfolio returns (Baker and Wurgler, 2006). A few studies have identified industry-specific differences that are useful to review for the purpose of this paper. For example Sayim et al. (2013) find that investor sentiment does indeed positively impact stock returns in several industries including the oil industry. The impact is near term and rapidly disappears as one would expect. Their paper uses fundamental market data to generate a forecast of investor sentiment and finds that about one-third of investor sentiment can be linked to market factors. The market factors include such data as U.S. business conditions and short-term interest rates. Two other studies look at futures markets for various commodities. Spyrou (2006) finds that investors in the IBE Crude Oil Futures are more likely to overreact to positive price shocks in the oil market. He concludes it is possible for a trader to generate significant abnormal profits by exploiting these price inefficiencies. Wang (2001) finds similar inefficiencies in six agricultural commodity futures markets. This sparse list of studies shows the need for additional research on the impact of investor sentiment on oil prices and oil stocks given the importance of this market. Also, as you can see there is no clear measure of investor sentiment found in the finance literature. Few of these proxies perform well when used to forecast future returns. Part of this poor performance is likely due to the fact that investor sentiment is adaptive and continuously reacts to the release of new relevant information. For this reason surveys and other discrete proxies of investor sentiment cannot reflect this new information that investors receive and react to every minute. Given the unpredictability of the release of new information, and the uncertainty surrounding investor reactions to this information, an effective model must rapidly adapt to be useful in forecasting asset prices. Fortunately one data point does incorporate this information and it is the asset's price. An asset's closing price has all of this often-conflicting information and conflicting investor reaction embedded within. While some investors respond positively and other negatively throughout the day the closing price will still be the net effect of the day's transmission of new information and investor sentiment. Although many prices between the high and low prices are going to cancel out each other during a trading day, some of them can form a lasting force that drives stock prices and the overall market. This dynamic process reveals not only investor sentiment, but also resilience or endurance of sentiment. It is only longlasting resilient sentiment that can be built into the closing price. It means that the only feasible way to use investor sentiment contained in stock prices to forecast future stock prices is to detach resilient investor sentiment from stock prices and construct an index of endurance of investor sentiment. In order to improve forecasting quality, this study uses a comprehensive measure of investor reactions to all sorts of relevant information, macro or firm-specific, to predict changes in oil prices and the Philadelphia Stock Exchange Oil Service Sector Index (OSX). The premise of this paper is that the overall impact of investor sentiment


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Table 1 Descriptive statistics and regression coefficients of sentiment endurance index. Monthly data (1997.05–2012.12)

WTI BRENT Return SE SEL

Quarterly data (1997.Q4–2012.Q4)

N

Mean

St. deviation

N

Mean

St. deviation

188 188 188 188 188

0.0117 0.0140 0.0095 0.0120 0.0116

0.0851 0.0913 0.0838 0.0831 0.0832

61 61 61 61 61

0.0362 0.0416 0.0248 0.0098 0.0107

0.1461 0.1487 0.1543 0.0524 0.0529

1.0000 SEL

1.0000 0.9622 0.6853 0.2764 0.3989 WTI

1.0000 0.6997 0.2832 0.4082 BRENT

Coefficients of correlation WTI BRENT Return SE SEL

1.0000 0.9302 0.5346 0.2027 0.3190 WTI

1.0000 0.5286 0.2142 0.3301 BRENT

1.0000 0.5724 0.4696 Return

1.0000 0.1308 SE

1.0000 0.5283 0.4683 Return

1.0000 0.2936 SE

1.0000 SEL

Monthly coefficient estimates of model (3) Dependent variable

SE

SEL

Constant

R2

WTI

0.1678 (2.365)** 0.1911 (2.528)** 0.5242 (9.778)***

0.3045 (4.298)*** 0.3372 (4.465)*** 0.4045 (7.553)***

0.0061

0.1281

0.0078 (1.238) −0.0015 (−0.345)

0.1387

Dependent variable

SE

SEL

Constant

R2

WTI

0.4862 (1.408) 0.5076 (1.451) 1.2602 (3.975)***

0.9599 (2.807)*** 0.9999 (2.888)*** 0.9997 (3.186)***

0.0212 (1.201) 0.0260 (1.455) 0.0018 (0.110)

0.1869

BRENT Return

0.4861

Quarterly coefficient estimates of model (3)

BRENT Return

0.1959 0.3865

WTI = percentage changes in OK WTI Cushing Spot Price FOB (dollars per barrel). BRENT = percentage changes in Europe Brent Spot Price FOB (dollars per barrel). Return = percentage changes of the PHLX Oil Service Sector Indexes. SE = sentiment endurance index from Eqs. (1) and (2). SEL = one-term lagged SE. N = number of observations used in calculations. The first observation is excluded from calculations because of the use of SEL, the lagged SE. t-values are in parentheses and all of them are significant at the one percent level. ** and *** represent the 5% and 1% significant level, respectively.

will be reflected in an asset's price and enduring investor sentiment will dictate the closing price. 3. Methodology and data A promising method to determine investor sentiment that captures the net effect of all information is He's (2012) sentiment endurance index. This index measures the probabilities of the most optimistic and pessimistic sentiments, quantified by the high and low prices, respectively, being the closing price. The following binomial probability distribution model describes this process: P t H t þ ð1−P t Þ Lt ¼ C t ;

ð1Þ

where Pt represents the probability of the high price (Ht) being the closing price (Ct) and takes a value of zero to unity; and (1 − Pt) is the probability of the low price (Lt) being the closing price. When Pt = 0.5, the overall investor sentiment is neutral; if Pt N 0.5, the overall sentiment is considered optimistic; while Pt b 0.5 indicates the overall pessimistic sentiment. Therefore, the index of investor sentiment endurance (SE) at time t is revealed in;

SEt ¼ ðP t −0:5Þ:

ð2Þ

A positive SE indicates a positive sentiment toward the closing price; while a negative SE represents a higher probability of the low price being the closing price. This SE index can effectively quantify investors' continuous reactions to all relevant news. The persistence or endurance of these reactions, implied in closing prices, largely shape the dynamics of stock market returns. The primary data set used in this study is the Philadelphia Stock Exchange (PHLX) Oil Service Sector Index (OSX) which is a price return index comprised of 15 oil service companies. The index has the potential to track the strength of the crude oil market such as oil production and oil prices. The index began on December 31, 1996 at a base value of 75. Data availability dictates that this study covers a period of March 1997 through December 2012. The index numbers include high, low, and closing prices. The daily indexes are averaged into monthly and quarterly series. The monthly and quarterly SE indexes are constructed based on Eqs. (1) and (2). The monthly and quarterly SE indexes, and the lag terms of the SE indexes, are then used to explain changes in monthly and quarterly oil service stock returns represented by percentage changes in the PHLX Oil Service Sector Index. The regression results indicate that only the current term and one-period lagged term of SE have significant influence on oil service stock returns. Other research conducted by Sayim et al. (2013) find similar near-term forecasting ability. In addition He (2012) reports that both the SE and lagged SE can explain a significant portion of variation in the stock market represented by the S&P 500

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Stock Index and Baker and Wurgler (2006) find that their lagged sentiment index has a negative impact on returns of some stock portfolios. The process begins with applying different rolling periods to estimate coefficients of the following regression model: Rt ¼ at þ bt SEt þ ct SEt−1 þ et ;

ð3Þ

where Rt represents stock returns at time t. The rolling coefficient estimates of SE and one-period lagged SE, together with the rolling constant terms, are used to forecast oil service stock returns based on different forecasting methods. First, the in-sample forecasting which uses rolling coefficients at time t to predict oil service stock returns at time t, or contemporaneous returns. The sole purpose of the in-sample forecasting is to test for the goodness of fit. The second step is to generate out-of-sample forecasting using oneperiod lagged rolling coefficients and constant terms to predict changes in the oil service stocks. The out-of-sample forecasting demonstrates some forecasting ability of rolling coefficients. However to overcome the problem of using current period SE to predict current period returns we utilize a forecasting model using only lagged variables. This model, which is a true forecasting model, is shown in Eq. (4). F t ¼ at−1 þ ðbt−1 SEt−1 Þ þ ðct−1 SEt−1 Þ:

ð4Þ

In Eq. (4) the one-period lagged term of SE substitutes SE and multiplies with the one-period lagged coefficient of b. Eq. (4) is not completely consistent with the rolling regression model, Eq. (3), in which the coefficient of b represents sensitivity of oil service stock returns to SE not the one-period lagged SE. However, if SE is stable at times t and t − 1, that may warrant the feasibility of Eq. (4). A simple equality test can then be used to assess the quality of the previous rolling forecasts. This paper uses the t-test without the assumption of equal variances between the two series in analysis of variance (ANOVA) to determine whether the averages of the rolling forecasts are statistically different from the actual oil service stock returns. An insignificant test statistic indicates that the forecasts, on average, do not deviate from the actual oil service stock returns, and therefore are statistically accurate. As He (2012) points out there is a potential flaw involved in this approach, that is, extremely positive and negative inaccurate forecasts may cancel out each other and result in an average of forecasts close to the mean of actual oil service stock returns. The procedure of calculating the accuracy ratio developed by He (2012) can effectively eliminate the potentially unreliable and misleading equality test results. The accuracy ratio procedure starts with computing the forecast errors by subtracting the actual returns from the forecast return. These errors are then sorted in ascending order (smallest to largest). Negative errors indicate the actual return was greater than the forecast return so they are under-forecasts. Conversely positive errors represent overforecasts which are all placed in a separate sample file. The remaining observations with negative forecast errors are now in a sequence of the smallest (most inaccurate) to the largest (most accurate). The equality test for the forecasts and corresponding real stock returns is performed repeatedly in a loop that begins with all under-forecasts and corresponding stock returns. If the statistic of the first test is significant, observation one of both variables is removed. If the second test statistic remains significant, observation two is removed. As more inaccurate forecasts are thrown out, the significance level of the test statistic keeps going down, from the 1%, 5%, to 10%. When the test statistic is not significant at the 10% level, that is, the null hypothesis of equal means of the forecasts and relevant stock returns cannot be rejected at the 10% level, the loop stops. The remaining under-forecasts are considered accurate. The previous process is repeated using forecast errors from the data set containing the over-forecasts. The number of accurate over-forecasts plus the number of accurate under-forecasts from the previous process

Table 2 Monthly OLS coefficients of SE and its lag terms (1997.03–2012.12). Dependent variables

SE SE-1 SE-2 SE-3 SE-4 SE-5 SE-6 Constant term SUM (COEFS) F-statistic R2 (%)

WTI

BRENT

Return

0.1595 (2.170)** 0.3160 (4.269)*** 0.0124 (0.169) 0.0635 (0.858) 0.0181 (0.247) −0.0004 (−0.005) −0.0645 (−0.875) 0.0061 (0.986) 0.5046 (3.34)*** 4.10*** 14.02

0.1822 (2.330)** 0.3541 (4.498)*** −0.0047 (−0.061) 0.0759 (0.964) 0.0175 (0.225) −0.0202 (−0.258) −0.0704 (−0.897) 0.0080 (1.203) 0.5344 (3.33)*** 4.52*** 15.23

0.5340 (10.01)*** 0.4343 (8.096)*** −0.0145 (−0.272) −0.0062 (−0.116) −0.1078 (−2.028)** −0.0636 (−1.188) −0.1303 (−2.439)** 0.0001 (0.029) 0.6458 (5.90)*** 27.3*** 52.21

WTI = percentage changes in OK WTI Cushing Spot Price FOB (dollars per barrel). BRENT = percentage changes in Europe Brent Spot Price FOB (dollars per barrel). Return = percentage changes of the PHLX Oil Service Sector Indexes. SE = sentiment endurance index from Eqs. (1) and (2). t-values are in parentheses. ** and *** represent the 5% and 1% significant level, respectively.

equals the total number of accurate forecasts. The total number of accurate forecasts is then divided by the total number of forecasts to get the accuracy ratio. Computing the ratio in this manner removes the problem of cancelation between under-forecasts and over-forecasts. 4. Results The sample period (1997–2012) in this study covers the two most recent economic recessions. The minor recession occurred in March 2001 to November 2001 and caused a 0.3% drop in GDP. The other recession, now known as the Great Recession, lasted from December 2007 to June 2009 and resulting in a 4.3% plunge in GDP. Given the volatile economic conditions, overall investor sentiment remained optimistic, as evidenced with positive investor sentiment endurance index (SE) and its one-period lagged term (SEL) in Table 1. Consistent with the optimistic investor sentiment, oil service stocks result in a monthly appreciation rate of 0.95% and a quarterly rate of Table 3 Quarterly OLS coefficients of SE and its lag terms (1997.Q3–2012.Q4). Dependent variables

SE SE-1 SE-2 Constant term SUM (COEFS) F-statistic R2 (%)

WTI

BRENT

Return

0.4560 (1.284) 1.0833 (2.958)*** −0.3183 (−0.913) 0.0243 (1.344) 1.2210 (2.54)** 4.69*** 20.09

0.4768 (1.321) 1.0979 (2.95)*** −0.2300 (−0.649) 0.0286 (1.553) 1.3447 (2.76)*** 4.79*** 20.40

1.3230 (4.133)*** 1.0702 (3.241)*** −0.4515 (−1.436) 0.0028 (0.171) 1.9416 (4.49)*** 13.2*** 41.41

WTI = percentage changes in OK WTI Cushing Spot Price FOB (dollars per barrel). BRENT = percentage changes in Europe Brent Spot Price FOB (dollars per barrel). Return = percentage changes of the PHLX Oil Service Sector Indexes. SE = sentiment endurance index from Eqs. (1) and (2). t-values are in parentheses. ** and *** represent the 5% and 1% significant level, respectively.


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Table 4 Monthly results of Granger causality test (1997.04–2012.12). Granger causality tests

Lag length = 1

Null hypothesis

F-stat

P-value

F-Stat

P-Value

F-Stat

P-value

SE does not Granger cause WTI WTI does not Granger cause SE SE does not Granger cause BRENT BRENT does not Granger cause SE Return does not Granger cause WTI WTI does not Granger cause return Return does not Granger cause BRENT BRENT does not Granger cause return SE does not Granger cause return Return does not Granger cause SE

16.866 0.1154 19.470 0.1541 6.8835 0.5534 10.667 0.6787 29.646 0.0468

0.0000 0.7344 0.0000 0.6951 0.0094 0.4579 0.0013 0.4111 0.0000 0.8289

8.7718 0.2049 9.7426 0.6103 5.4949 0.5041 8.0101 0.5203 18.480 0.1253

0.0002 0.8150 0.0001 0.5443 0.0048 0.6049 0.0005 0.5952 0.0000 0.8823

5.9945 1.1566 7.0659 1.2715 3.5872 0.3542 5.0834 0.2090 12.528 0.9032

0.0006 0.3278 0.0002 0.2856 0.0149 0.7862 0.0021 0.8901 0.0000 0.4408

Granger causality tests

Lag length = 4

Null hypothesis

F-stat


Lag length = 2

Lag length = 5 P-value

4.9656 0.8818 5.6025 0.9523 3.9191 0.4129 4.3818 0.2192 9.2715 0.7768

Lag length = 3

F-Stat

0.0008 0.4761 0.0003 0.4352 0.0045 0.7992 0.0021 0.9275 0.0000 0.5416

3.9597 1.3136 4.4386 0.9963 3.4226 0.7931 3.7023 0.3902 7.6571 1.0077

Lag length = 6 P-Value

F-Stat

0.0020 0.2604 0.0008 0.4216 0.0056 0.5560 0.0033 0.8551 0.0000 0.4147

P-Value

3.2049 1.1362 3.9210 0.7868 2.7292 0.7457 3.0687 0.5576 6.7144 1.0492

0.0052 0.3434 0.0011 0.5814 0.0148 0.6136 0.0071 0.7635 0.0000 0.3953

SE = sentiment endurance index from Eqs. (1) and (2). Return = percentage changes of the PHLX Oil Service Sector Indexes. WTI = percentage changes in OK WTI Cushing Spot Price FOB (dollars per barrel). BRENT = percentage changes in Europe Brent Spot Price FOB (dollars per barrel).

2.48%, and oil prices (WTI and Brent) record even higher percentage increase, about 1.2% on a monthly basis and 4% on a quarterly basis (Table 1). Correlations among the sentiment endurance index, stock returns, and oil prices suggest meaningful positive relationships shared by the three factors. The monthly data indicates a strong correlation (about 57%) between stock returns and the sentiment endurance index. However, the correlations between the index and oil prices are weaker, ranged from about 20% to 32% (SEL) on a monthly basis and about 20% to 40% (SEL) on a quarterly basis. Apparently, the correlations between oil prices and SEL are much stronger than the correlations between oil prices and SE. Nonetheless, the strongest correlation lies between oil prices and stock returns, as suggested by two quarterly coefficients of correlation of about 69%. On average, quarterly correlation coefficients are 25% higher than monthly numbers.

Regression results suggest that it is the investor sentiment endurance index that significantly affects changes in oil stock returns and prices. Monthly results indicate that both SE and SEL have significant explanatory power over stock returns and oil prices (Table 1). In contrast, quarterly variations in oil prices are only sensitive to SEL, although stock returns are still sensitive to both SE and SEL. The results suggest that the sentiment endurance index may take longer time to influence oil prices. It is consistent with the higher correlation between oil prices and SEL, compared with SE. When more lag-terms of SE are included in regressions, results basically verify the previous regression results. That is, all additional variables from 2-month to 6-month lag terms of SE have virtually no explanatory power over oil price changes (Table 2). The only exception is stock returns which show sensitivities to two additional lagged SEs,

Table 5 Quarterly results of Granger causality test (1997.Q3–2012.Q4). Granger causality tests

Lag length = 1

Null hypothesis

F-stat

P-value

Lag length = 2 F-Stat

P-Value

F-Stat

P-Value

F-Stat

P-Value


8.2900 0.0206 8.4949 0.1261 4.5853 0.0177 4.6289 0.1594 14.283 5.6656

0.0056 0.8864 0.0051 0.7238 0.0365 0.8945 0.0365 0.6912 0.0004 0.0206

5.1238 0.7067 4.7460 0.2238 4.5342 0.3215 4.3263 0.6164 5.6431 4.0469

0.0091 0.4977 0.0125 0.8002 0.0150 0.7264 0.0180 0.5436 0.0059 0.0229

3.0339 0.4453 2.7241 0.1504 2.7102 0.3602 2.7689 0.4967 4.4800 2.3870

0.0373 0.7216 0.0535 0.9290 0.0544 0.7820 0.0508 0.6862 0.0072 0.0795

2.2362 0.3693 1.9681 0.2755 2.1476 0.5360 2.2616 0.6439 3.5340 1.5168

0.0786 0.8294 0.1141 0.8924 0.0889 0.7099 0.0759 0.6338 0.0130 0.2119

SE = sentiment endurance index from Eqs. (1) and (2). Return = percentage changes of the PHLX Oil Service Sector Indexes. WTI = percentage changes in OK WTI Cushing Spot Price FOB (dollars per barrel). BRENT = percentage changes in Europe Brent Spot Price FOB (dollars per barrel).

Lag length = 3

Lag length = 4

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Table 6 Accuracy ratios for different rolling true forecasts of oil stock returns.

Under forecasts (UF) Retained UF Accuracy ratio Average error Over forecasts (OF) Retained OF Accuracy ratio Average error Retained UF&OF Total forecasts Accuracy ratio MAFE

6-month

12-month

4-quarter

6-quarter

8-quarter

89 46 0.5169 −0.0231 94 45 0.4787 0.0251 91 183 0.4973 0.0241

88 50 0.5682 −0.0233 89 42 0.4719 0.0248 92 177 0.5198 0.0240

27 15 0.5556 −0.0771 31 18 0.5806 0.0867 33 58 0.5690 0.0823

26 14 0.5385 −0.0691 30 13 0.4333 0.0618 27 56 0.4821 0.0656

24 14 0.5833 −0.0640 30 11 0.3667 0.0597 25 54 0.4630 0.0621

True forecasting = constantt − 1 + [(coefficient of SE)t − 1 × SEL] + [(coefficient of SEL)t − 1 × SEL]. Under forecasts (UF) = number of forecasts that are smaller than actual returns. Over forecasts (OF) = number of forecasts that are greater than actual returns. Retained UF = number of under forecasts that are statistically indifferent from actual returns, after excluding large under forecasts at the 10% significance level. Retained OF = number of over forecasts that are statistically indifferent from actual returns, after excluding large over forecasts at the 10% significance level. UF retain ratio = retained UF/UF. OF retain ratio = retained OF/OF. Accuracy ratio = ratio of retained UF or OF to the number of forecasts. Average error = average of (forecast-return) for retained UF or retained OF. MAFE = mean absolute forecast error.

SE-4 and SE-6 with negative coefficients (significant at the 5% level). Quarterly results in Table 3 affirm the significant sensitivity of stock returns to SE and SEL and significant sensitivities of WTI and BRENT only to SEL. The persistent investor sentiment measured by SE not only plays an import role in explaining variations in oil stock returns and oil prices, but also trigger or Granger cause those changes. Table 4 displays results of the Granger causality test based on one- to six-month lags. The following one-direction causal relationships about SE versus oil prices and stock returns are identified: 1) SE → WTI; 2) SE → BRENT; and 3) SE → Return. All results are significant at the 1% level. On the other hand, causality test results completely fail to reject null hypotheses that WTI/BRENT/Return does not Granger cause SE. Additional substantial one-direction causal relationships are running from stock returns to WTI and BRENT. They are mostly significant at the 1% level, except for the relationship running from stock returns to WTI at the 3-month and 6-month lags, with p-values of 0.0149 and

0.0148, respectively. All causal relationships running form WTI/BRENT to stock returns are statistically trivial. Overall, the results suggest that the lasting investor sentiment is a major driving force of oil prices and stock returns. The one-direction causal relationship running from the sentiment endurance index to oil prices is confirmed with quarterly results (Table 5). The quarterly results also indicate that oil stock returns Granger cause changes in oil prices and not the other way around. All one-direction causal relationships suggest that changes in the sentiment endurance index and stock returns lead changes in oil prices up to four quarters, except for the causality from SE to BRENT based on a 4-quarter lag length, which is not statistically significant. Overall, strong causal relationships are based on 1-quarter and 2-quarter lag lengths. Compared with the monthly results in Table 4, the quarterly results present a more complicated causal relationship between the sentiment endurance index and stock returns. The quarterly results confirm the strong causality running from the sentiment endurance index to stock

Table 7 Accuracy ratios for rolling true forecasts of changes in WTI.


6-month

12-month

4-quarter

6-quarter

8-quarter

97 31 0.3196 −0.0231 86 36 0.4186 0.0248 67 183 0.3631 0.0240

93 29 0.3118 −0.0164 84 36 0.4286 0.0207 65 177 0.3672 0.0188

28 11 0.6087 −0.0486 30 17 0.5806 0.0604 28 58 0.4828 0.0558

23 14 0.5385 −0.0714 33 17 0.5152 0.0408 31 56 0.5536 0.0546

25 16 0.6400 −0.0582 29 12 0.4138 0.0539 28 54 0.5185 0.0564

True forecasting = constantt − 1 + [(coefficient of SE)t − 1 × SEL] + [(coefficient of SEL)t − 1 × SEL]. WTI = percentage changes in OK WTI Cushing Spot Price FOB (dollars per barrel). Under forecasts (UF) = number of forecasts that are smaller than actual returns. Over forecasts (OF) = number of forecasts that are greater than actual returns. Retained UF = number of under forecasts that are statistically indifferent from actual returns, after excluding large under forecasts at the 10% significance level. Retained OF = number of over forecasts that are statistically indifferent from actual returns, after excluding large over forecasts at the 10% significance level. UF retain ratio = retained UF/UF. OF retain ratio = retained OF/OF. Accuracy ratio = ratio of retained UF or OF to the number of forecasts. Average error = average of (forecast-return) for retained UF or retained OF. MAFE = mean absolute forecast error.


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Table 8 Accuracy ratios for rolling true forecasts of changes in BRENT.


6-month

12-month

4-quarter

6-quarter

8-quarter

93 31 0.3333 −0.0217 90 39 0.4333 0.0245 70 183 0.3825

93 33 0.3584 −0.0172 84 29 0.2452 0.0223 62 177 0.3503 0.0233

31 17 0.5484 −0.0592 27 7 0.2593 0.0448 24 58 0.4138 0.0196

28 14 0.5000 −0.0506 28 10 0.3571 0.0402 24 56 0.4286 0.0550

27 15 0.5556 −0.0441 27 8 0.2963 0.0409 23 54 0.4259 0.0463

True forecasting = constantt − 1 + [(coefficient of SE)t − 1 × SEL] + [(coefficient of SEL)t − 1 × SEL]. BRENT = percentage changes in Europe Brent Spot Price FOB (dollars per barrel). Under forecasts (UF) = number of forecasts that are smaller than actual returns. Over forecasts (OF) = number of forecasts that are greater than actual returns. Retained UF = number of under forecasts that are statistically indifferent from actual returns, after excluding large under forecasts at the 10% significance level. Retained OF = number of over forecasts that are statistically indifferent from actual returns, after excluding large over forecasts at the 10% significance level. UF retain ratio = retained UF/UF. OF retain ratio = retained OF/OF. Accuracy ratio = ratio of retained UF or OF to the number of forecasts. Average error = average of (forecast-return) for retained UF or retained OF. MAFE = mean absolute forecast error.

returns up to four quarters and also suggest a meaningful causal relationship from Stock to SE up to three quarters. Once again, the quarterly results verify that the lasting investor sentiment Granger causes changes in both oil prices and stock returns. The significant causality implies that the sentiment endurance index may have decent ability to forecast oil stock returns and oil prices. Table 6 reports assessments of rolling true forecasts of oil stock returns. The rolling true forecasts are derived from one-term lagged coefficient estimates of Eq. (3) and one-term lagged sentiment endurance index (SEL) based on various rolling estimation periods. There are two kinds of forecasts, under-forecasts with negative forecast errors and over-forecasts with positive forecast errors. In each set of forecasts, either over-forecasts or under-forecasts, the accurate forecasts are those with an average value close to that of actual returns as suggested by the equality test. For example, the total number of 6-month rolling true forecasts is 183 in which 89 are under-forecasts and 94 overforecasts (Table 6). After large under-forecasts and over-forecasts are rejected by the equality test at the 10% significance level in separate testing loops, there are 46 retained under-forecasts (UF) and 45 retained over-forecasts (OF). Those retained UF and OF are statistically indifferent from the actual oil stock returns. Therefore, the accuracy ratio for UF is 51.69% (46/89) and for OF is 47.87% (45/94). The overall accuracy ratio for the combination of UF and OF is 0.4973 (91/183). In contrast, the 12-month rolling true forecasts generate higher UF accuracy (56.82%) and lower OF accuracy (47.19%), as a result, the overall accuracy is higher (51.98%). In addition, the higher overall accuracy ratio for 12-month rolling does not result in higher forecast errors. The mean absolute forecast error (MAFE) for 12-month rolling forecasts is 2.40%, compared with 2.41% for 6-month rolling forecasts. Fama and French (1997) report about 2.98% and 2.77% for the average monthly rolling forecast errors for 48 industries based on the CAPM and their 3-factor model, respectively. An MAFE of 2.40% is about 14%–20% lower than that. Quarterly forecasts show a mixed picture. The 4-quarter rolling forecasts have the highest accuracy ratio of 56.90%, while the quarterly MAFE is also highest, 8.23%. It is equivalent to a monthly MAFE of 2.743%. Both 6- and 8-quarter rolling forecasts have a lower MAFE, 6.56% and 6.21%, respectively. They are equivalent to a monthly MAFE of 2.19% and 2.07%, respectively. However, the overall accuracy ratio for 6- and 8-quarter rolling forecasts is lower, 48.21% and 46.30%,

respectively. Both forecasts enjoy noticeably higher accuracy for over-forecasts than under-forecasts. In general, the sentiment endurance index does a better job in forecasting oil service stock returns, a sector portfolio, than forecasting changes in the overall stock market (proxied with the S&P 500 stock index) reported by He (2012). The average accuracy ratio of monthly rolling forecasts is about 31% and the overall accuracy ratio for 3 quarterly rolling forecasts ranging from 37% to 44.15% (He, 2012). Compared with the rolling forecasts of oil stock returns, rolling forecasts of WTI indicate that quarterly forecasts are clearly superior to monthly forecasts (Table 7). Both 6-month and 12-month rolling forecasts have an overall accuracy ratio of about 36%. However, the MAFE for the 12-month rolling forecasts is 1.88% and much lower than that (2.40%) for the 6-month rolling forecasts. In contrast, the overall accuracy ratio for the 4-, 6-, and 8-quarter rolling forecasts is 48.28%, 55.36%, and 51.85%, respectively. The average of these ratios (51.83%) is about 40% higher than the overall accuracy ratio (36%) for the monthly forecasts. When the MAFE are converted into the monthly equivalent, the quarterly forecasts have an MAFE of 1.88%, the same as the lower MAFE for the monthly forecasts. Therefore, the results evidently suggest that the quarterly forecasts, especially the 6-quarter rolling forecast, are a better predictor of WTI. The quality of monthly rolling forecasts of BRENT (Table 8) is similar to monthly forecasts of WTI. The 6-month rolling forecasts of BRENT have an overall accuracy ratio of 38.25% and an MAFE of 2.33%; while the overall accuracy ratio of 12-month forecasts is 35.03% and the MAFE is 1.96%. Once again, the quarterly rolling forecasts are more accurate than monthly forecasts. The overall accuracy ratio for 4-, 6-, and 8-quarter rolling forecasts is 41.38%, 42.86%, and 42.59%, respectively. The equivalent of monthly MAFE for the three quarterly forecasts is 1.83%, 1.54%, and 1.43%, respectively. Nevertheless, the quality of forecasts of BRENT is not as good as that of WTI. 5. Concluding comments This study creates a binomial probability distribution-based endurance index of crude oil service investor sentiment by using the Philadelphia Stock Exchange (PHLX) Oil Service Sector Index (OSX). This SE index is then used to measure the probability of the high or low oil service stock price being the closing price. In efficient markets investor

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reactions to all relevant news are incorporated into stock price and the investor sentiment endurance index uses that fact to forecast investor sentiment. Empirical results in this study suggest that the sentiment endurance index plays a significant role in explaining variations in oil prices and oil service stock returns and Granger causes changes in crude oil prices and returns of oil service stocks. The sentiment endurance index is able to serve as a decent predictor of crude oil prices and returns of oil service stocks. Perhaps even more important is that using the investor sentiment endurance index eliminates the need to determine a suitable proxy for investor sentiment that impacts all investors in the same manner. As you can see from the literature most proxies of investor sentiment are only useful for a subset of investors. In contrast the SE index captures the net effect of all investors reacting to all relevant information. Following the forecasting and forecast-quality assessing methods developed by He (2012), this study uses all lagged independent variables to forecast returns of oil service stocks and crude oil prices and utilizes a rigorous procedure that excludes offsetting biases resulting from extreme over-forecasts and under-forecasts to assess the quality of forecasting. Results of the assessment indicate the following: 1. Compared with the 6-month rolling forecasts of returns of oil service stocks, the 12-month rolling forecasts are more accurate, evidenced with a higher overall accuracy ratio of 52% versus 50% for the 6-month rolling forecasts. The mean of absolute forecast error (2.4% and 2.41%) is almost identical to both. 2. Quarterly forecasts of stock returns are comparable to the monthly forecasts. The 4-quarter rolling forecasts have the highest accuracy ratio of almost 57%, but the mean forecast error is also highest. Although the 6- and 8-quarter rolling forecasts have the lowest forecasts errors, their accuracy ratios are below 49%. 3. The quarterly sentiment endurance index demonstrates decent forecasting ability on crude oil prices. The accuracy ratio of 6-quarter rolling forecasts for WTI prices is over 55% with a quarterly forecast error of 5.45%, equivalent to a monthly figure of 1.88%. The quality is much superior to monthly forecasts. 4. The forecasting quality of Brent prices is lower than that of WTI prices. The average accuracy ratio of all quarterly rolling forecasts is about 42%, although the average quarterly forecast error is about 4.8%. Findings of this study suggest that the investor sentiment endurance index can be used to predict future changes in returns of oil service stocks on a monthly or quarterly basis, as well as quarterly changes in

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