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Statistical tests by Elton, Gruber and Urich[1978] .... Arnott, Robert D. and William A. Copeland, 1985, "The Business Cycle and Security Selection." Financial ...
Phase of the Business Cycle and Portfolio Management

David Nawrocki Professor of Finance Department of Finance College of Commerce and Finance Villanova, PA 19085 USA 610-489-7520 Voice and Fax 610-519-4323 Office and Voice Mail 610-489-0750 Home [email protected] [email protected]

William Carter The QInsight Group San Diego, CA 619-295-9292 Office [email protected]

Preliminary: Do not quote without permission of the authors. The QInsight Group assumes no responsibility for the views or opinions expressed in this paper. The authors bear full responsibility for the views and opinions expressed in this paper. The performance results are provided as part of an academic study and are not to be construed as expectations of future performance.

March 1997

Phase of the Business Cycle and Portfolio Management Abstract The purpose of this paper is to explore the business cycle and to see whether it influences portfolio performance. Hunt[1976] provides the econometric work that serves as the basis for determining the phase of the cycle. The study uses the Standard & Poors industry indexes, individual security data and macroeconomic data to study the business cycle. The tests include a portfolio strategy that switches between industries based on the phase of the economy. The paper concludes that the business cycle influences the performance of stock portfolios and that the phases of the business cycle relate to the phases in Vaga's[1990] Coherent Market Hypothesis.

Introduction The relationship between economic activity and cyclical behavior in the money and capital markets has not received a great deal of attention in the finance literature. Arnott and Copeland[1985] demonstrate that the business cycle has a significant effect on security returns. Chen, Roll and Ross[1986] determine that certain macroeconomic variables (industrial production, changes in the yield curve, and expected inflation) are significant indicators of changes in stock returns. In addition, Moore[1983] explores the relationship between inflation and business cycles. Recently, Peters[1991,1994] using rescaled range (R/S) analysis finds evidence of long term nonperiodic cycles in stock returns that average approximately 48 months in duration. Nawrocki[1995] confirms this result but finds that the cycle is dependent on changes in the money supply and industrial production. Other academic studies focus on the effect that the economic cycle has on the microstructure of the market, (e.g., Abraham and Ikenberry[1994], Liano[1992], Liano and Gup[1989], and Liano, Huang and Gup[1993]). Recently, Bauman and Miller[1995] find that the ranking of investment performance is more consistent over time with complete stock market cycles evaluations rather than market cycle subset evaluations. Bauman and Miller differ from other studies in that they study the peak to peak stock market cycle rather than the peak to peak business cycle as measured by industrial production. Stovall(1996) takes an additional step and breaks the business cycle into five phases. Using the S&P Industry Indexes,

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he is able to demonstrate that different industries dominate (in terms of total return) during each phase. Stovall concludes that an industry sector rotation strategy based on the business cycle will improve investment performance. The major questions to be answered are: Is knowledge of the business cycle necessary in order to manage investment portfolios? Does the stock market rotate into and out of industries in response to changes in the business cycle? The concept of a business cycle is interesting. One position is that it is generated by a time-varying parameter model. As parameters (technology, preferences, rate of financial innovation) of the model change it can experience different states of nature. The changing parameters represent “surprise” to the system which must adapt to the parameters. (The formal definition of information arrival in Shannon and Weaver’s, 1947, information theory is for a message to have information content it must represent “surprise” to the receiver of the message.) If the business cycle can be forecasted, there would be no business cycle. Economic agents anticipating the forecasted parameter changes will make appropriate adjustments to minimize the impact of the changes, hence, no cycle. This view of the economy as constantly evolving over time through different states of nature with time-varying parameters is described in Nawrocki(1984), Anderson, Arrow and Pines(1988) and Vaga(1990, 1994). Vaga[1990,1994], in particular, takes an interesting approach describing the stock market as moving through different types of market behavior. Vaga's market phases include random walk markets, transition markets, coherent markets and chaotic markets. Vaga identifies the statistical properties of each market type. One perspective of this paper is whether Vaga’s market phases relate to the business cycle. Even with this interest in the area of business cycles, Hunt[1976] is the only study that stresses the econometric relationship between macroeconomic variables to detect transition points where the business cycle transitions to new states of nature. Hunt studies macrovariables such as the federal funds rates, capital market yields, business credit demands, unemployment claims, non-farm payroll, inflation, and monetary and reserve aggregates. The relationships between these variables help determine the different phases of the economic cycle. The purpose of Hunt’s work is to identify the change in the business cycle,

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not to forecast it. The first priority of this paper is to see whether Hunt’s methodology is replicable to identify different phases in the economic cycle. Identifying the phases of the economy allows the determination of which industries perform best during individual phases. Therefore, a portfolio strategy that switches between industries will be backtested to see whether the phase information is useful in the construction of portfolios. This paper differs from previous work since it breaks the business cycle into its component phases and uses an industry rotation strategy to take advantage of the individual phases of an economic cycle. Specifically, the study utilizes the 1970-1986 period to identify the phases of the economy and the resulting industry performance. A performance test of the industry rotation strategy then utilizes the 1988-1995 period. (The year 1987 is not in the study since the market crash of 1987 results in highly skewed, leptokurtic distributions for that period. It is realistic that an investment manager in March 1988 would make the same decision after looking at the distributions with and without 1987.) The structure of the study provides a holdout (out of sample) period and avoids the “look ahead” bias that is possible with empirical backtests of investment strategies. The “look ahead” bias includes the problems of “data mining” or “data snooping”. The next section of the paper addresses the methodology used in the study, while the discussion of the empirical results follows. The final section presents the conclusions of the paper.

Methodology The portfolio strategy consists of the following steps: •

Statistical Analysis to Determine Phases of the Business Cycle.

•

The Determination of the Best Industry Performance for each Phase of the Cycle.

•

Portfolio Selection Algorithm to Select 20 Asset Portfolio for Each Phase of the Cycle.

The Data The data include monthly percentage return data for the S&P 500 Composite index as well as for over 100 S&P Industry indexes obtained from Standard & Poors. The data also includes macroeconomic variables from the Citibase/Fame/DRI database. This data is available for the period starting

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in January 1970 and ending in June 1994. The test of the industry rotation model uses weekly relative return data for 1510 stocks for the period March 1988 to February 1995. A screening procedure results in the sample of 1510 stocks. In order to control liquidity costs, stocks with prices under $10 per share and market capitalization under $250 million are not in the sample. To handle any additional implicit trading costs, the transaction fee during portfolio revisions is 0.5% which is higher than the 0.2-0.3% available through discount brokers to larger accounts (such as an investment manager or a mutual fund).

Statistical Analysis The period from 1969 to 1994 is an interesting period. As demonstrated in Table 1, there were three distinct phases in the US economy during this period. The first period is a period of increasing inflation because of the Vietnam War and the failure of the US government to raise taxes to pay for the war. This period is notable for increasing prices particularly fuel prices. To make matters worse, stocks and bonds exhibit very low or negative returns, thus providing negative changes in purchasing power when investing in financial assets. A tangible asset, gold, is the biggest gainer. However, an investor should note that the US drops the gold standard on international payments during this period and allows gold to float with the market prices. The next period is easy to pick because of the Arab-Israeli war in 1973 and the resulting oil embargo. This is the period of the oil crisis with double digit increases in energy prices over the rest of the decade. The stock market rebounds sharply during this period. However, on a real basis, it is only recovering from the 1969-1973 decline. Gold maintains its high real rate of return. After the 1979 oil crisis and the double dip recessions of 1980-82, the US economy entered into its current phase. Factors important in selecting 1983 to start this period include the non-effect of the Iraq-Iran war on fuel prices and the recovery of the US economy from the double-dip recessions. Inflation is below average and approaches the inflation rates of the late 1950s and early 1960s. Inflation in fuel prices is nonexistent. On a real basis, fuel prices decline since 1982. Stocks and bonds provide high real returns during this period while tangible assets like gold lose purchasing power.

Place Table 1 Here

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The Hunt(1976) methodology for determining phases of the economy studies the economic cycle for structural changes. Table 2 provides the definitions of Hunt’s five phases of the economic cycle, and the behavior of macroeconomic variables during these phases and the resulting decision rules used to determine a phase change.

Place Table 2 Here Table 3 presents the results of utilizing Hunt’s methodology for the period from 1970 to 1986. The peaks and troughs are from the NBER’s Survey of Current Business. The NBER does not publish the official peak and trough dates until well after the event. Therefore, an investment strategy cannot be formulated using the NBER announcements. The macroeconomic variables have to be studied in order to identify the phase of the business cycle at the time of the phase change. Hunt’s methodology consists of following macroeconomic statistics that are relatively hard numbers. That is, they are not based on sampling and are usually not subject to revision. Even if the variable is subsequently revised, only the originally announced value is included in this study. The variables consist of money supply, interest rates, and unemployment claims. Sample variables consist of inflation, non-farm payroll, and industrial production. These variables are published on a monthly basis and are rarely revised. Hunt uses econometric relationships, correlations, reversals in variables, and time series analysis to determine when a change in phase has taken place. (It is not possible to describe Hunt’s methodology in a short research paper. Hunt(1976) requires an entire book to develop and explain the methodology.) The method is adaptive, not a proactive forecasting technique. Vaga(1990) also provides statistical tools such as skewness, kurtosis and serial correlations to determine market phases. The easeoff and plunge phases are consistent with the peaks and troughs from the Survey through 1982. (The 11/82 trough is missed by one month.) The easeoff and plunge period noted in 1984 did not meet the NBER’s definition but it did meet Hunt’s macroeconomic conditions. (In addition, the appropriate industry rotation did occur in the stock market.) This is a strong confirmation of Hunt’s methodology since the NBER defined peaks and troughs are not known until months after his methodology indicates the phase change. Knowing the actual dates of the peaks and troughs is not necessary. It is sufficient to know the general phase in which the peak or trough takes place in order to

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benefit from the sector rotation strategy. The economy reaches a peak during the Easeoff phase. At this point the Federal Reserve is following a tight monetary policy that is characterized by large increases in the federal funds rate and decreases in the monetary aggregates. Growth in non-farm payroll slows and there is an increase in initial unemployment claims. Therefore, industrial production reaches a peak and starts to fall. In the meantime, inflation peaks. The economy reaches a trough during the Plunge phase. Industrial production declines as does nonfarm payroll. Initial unemployment claims continue to increase. The Federal Reserve, meanwhile, is increasing monetary aggregates and decreasing the federal funds rate in an attempt to stimulate the economy. Inflation slows to its lowest level during the economic cycle. The stock market exhibits very high returns as it is anticipating the economic revival as a result of the Federal Reserve policy. The early revival (Revival1) starts with large increases in industrial production and increasing federal funds rates. The monetary aggregates continue to grow along with non-farm payroll. Initial unemployment claims drop drastically. Inflation ticks up a bit. Again the stock market exhibits high returns. The transition to the late revival (Revival2) exhibits decreasing stock market returns, slower growth in the monetary aggregates and moderating inflation. Generally, the economy is very stable during this period with stable growth in industrial production and stable prices. The stock market returns while lower are also very stable. An increase in inflation and a restrictive Federal Reserve monetary policy mark the beginning of the Accelerate phase. The federal funds rates increase rapidly, and the growth in the monetary aggregates declines drastically. The overheating economy is evident by the largest gains during the cycle in nonfarm payrolls and large drops in initial unemployment claims. Industrial production is still increasing at a high rate, but is starting to slow because of the restrictive Federal Reserve policy. The stock market starts to decline in anticipation of a future recession. Table 3 also provides the econometric performance during these phases. During the Easeoff period, there is a correlation between the federal funds rate, the monetary base, the employment numbers and industrial production. These same variables along with inflation and the M1 money supply are significant

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relative to industrial production during the Plunge phase. Note that information concerning the transition to a new phase is not available until after the transition. Analysts have to watch for changing correlations as well as changing macroeconomic variables. The federal funds rate, the monetary base, employment numbers and inflation are the important variables to watch during the transition to a Revival 1 phase. The important variables during the revival 2 phase are changes in monetary base, employment numbers and inflation. The federal funds rate is not a factor. The only factor that is significant during the Accelerate phase is the non-farm payroll. The sudden acceleration of the nonfarm payroll as well as slowing growth in the real monetary base signifies a change in the stock market. Each phase lasts for at least six months. This introduces the point that it is not necessary to forecast the phase changes but rather to adapt to changes in economic conditions. There is time in each phase to benefit from the economic conditions of the phase. The adaptation is necessary since most of the macroeconomic data is not available to the markets until weeks after the change in economic conditions.

Place Table 3 Here Vaga’s Stock Market Phases Vaga(1990,1994) proposes that the stock market moves through distinctive phases over time. Vaga describes the phases statistically. Table 4 summarizes Vaga’s four phases of the stock market. Vaga’s descriptions derive from the return, risk, skewness and kurtosis of the stock market returns. As can be seen in Table 4, investors do best in coherent markets and random walk markets. It is best to avoid chaotic markets and transition markets. The statistical properties of the stock market during the different phases of the economy are interesting given Vaga’s work. The random walk exhibits average returns and average risk levels. As is common with random walk conditions, the best strategy is to buy and hold a diversified portfolio. A coherent market by definition is easy to forecast. Diversified portfolios provide high returns and low risk. In addition, investors may utilize forecasting techniques to increase returns. The transition market occurs as the market moves from coherent to chaotic to random. It is a difficult market period for investors depending on the transition. A chaotic market provides the unhappy combination of low returns and high risk.

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Place Table 4 Here Industry Performance Next, using monthly data from January 1970 to December 1986, the risk-return performance ranks the S&P industry indexes for each of the five phases. (December 1986 was the end of a Revival 2 phase. The next phase continued past the simulation starting point of March 1988.) A more sophisticated measure of risk, the reward-to-lower partial moment (R/LPM) ratio, provides a ranking of the industry indexes. Research conducted by Ang and Chua[1979], Nawrocki(1983), and Harlow[1991] support the use of LPM in a portfolio allocation process because of its statistical superiority over the variance measure. For the interested reader, Markowitz[1991, 374-376] provides a comprehensive bibliography of semivariance/lower partial moment research. The n-degree lower partial moment is a measure of downside risk where the semivariance is a special case (n=2). Fishburn(1977) provides the theoretical arguments for using the n-degree lower partial moment. Table 5 lists the top 15 industries as ranked by the R/LPM for each phase.

Place Table 5 Here Portfolio Selection Algorithms Operations research has a long history of using heuristic algorithms because of computational complexity of optimal algorithms. Typically, the heuristic algorithm derives mathematically from the optimal algorithm, thus providing replicable results. The advantage of the heuristic algorithm is usually that it is simpler and less costly to implement. With modern microcomputers, this is not the important factor of twenty-five years ago. Using historical data, an optimal quadratic code will provide a more efficient portfolio set than a heuristic algorithm. However, portfolio management does not take place in the past but rather in the future. Therefore, the question becomes which algorithm, heuristic or optimal, provides the best portfolio management performance. Statistical tests by Elton, Gruber and Urich[1978] and economic tests by Nawrocki[1990] demonstrate that heuristic algorithms provide better ex post performance than optimal algorithms. This study employs the R/LPM heuristic algorithm because of its historic performance and because it is easy to implement with maximum allocation constraints. This simple heuristic algorithm derives from

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Sharpe's[1967] idea that a heuristic algorithm can ignore intercorrelations between securities if the number of securities in the portfolio is sufficiently large (20 or more). Sharpe proposes this algorithm in order to handle maximum investment constraints necessary for mutual fund operations. The resulting algorithm is as follows:

Zi = (Ri-Rf)/(LPMn),

(1)

where Ri is the return on security i, Rf is the riskfree rate of return and LPM n is the n-degree lower partial moment. The allocations represent a weighting according to the R/LPM ratio. The allocations compute as follows:

Xi

= Zi/

k Σ Zj j=1

for all Zj > 0,

(2)

where k is the number of securities where Zi > 0. The portfolio heuristic algorithm in this study uses weekly security relative returns and treasury bill relative returns as the target return. Selecting the parameters of the R/LPM portfolio algorithm is important in order to avoid “data snooping” or “look ahead” bias. A random sample of 150 securities from the CRSP dataset for the period 1958 to 1987 provides a backtest. (The algorithm study ends in 1987 so that the industry rotation study commencing in 1988 avoids the “look ahead” bias.) The R/LPM heuristic algorithm uses 3, 6, 12, 24, 36 and 48 month revision periods to test for the appropriate parameters. An optimal covariance algorithm (Markowitz, 1991)and an optimal cosemivariance algorithm (Hogan & Warren, 1972) are also in the study. A summary of the results is in Table 6. For all revision periods, the LPM heuristic algorithm outperforms the optimal algorithms on a risk-return basis. In addition, the table reports the degree of the LPM that achieves the maximum performance. This paper concerns itself with quarterly revision as the economic data for each quarter becomes available. For three month revisions, a degree of 1.2 provides the best performance for the LPM heuristic.

Place Table 6 Here

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Availability of Economic Data for Determining Phases Determining the phase of the economic cycle is a reactive (adaptive) process. There is a lag in the time from when the economy changes phases to the time when the economic data indicates the change. As a result, the investment strategy is an adaptive strategy rather than a proactive forecasting strategy. Because of the time lag in obtaining economic data, investment decisions that result from this data will not occur at the end of a calendar quarter. There is a lag until the information is available. Therefore, quarterly revision decisions occur in the middle of February, May, August and November. This investment strategy follows a Murphy(1965) Type II adaptive control process. A Type II process consists of a decision vector which is dependent on an environmental vector (current state of nature) and a historical information vector (previous states of nature). The decision is made with a one period lag since the decision cannot be made without the arrival of the new information. This represents a more realistic application of the investment strategy and improves the validity of the backtest.

Investment Strategies The investment strategies employed in this study include: •

S&P500 which is a buy and hold in the S&P 500 composite index during each quarter.

•

No Indust which is a 20 asset R/LPM heuristic algorithm portfolio (equations 1 and 2) selected from the entire database of 1510 stocks. There is no implementation of industry selection by phase.

•

Industry which is a 20 asset R/LPM heuristic algorithm portfolio selected from the 1510 stocks database except the stocks are screened by the appropriate industries for the current economic phase.. If the stock is a member of an appropriate industry for the current phase, then its inclusion into the portfolio is determined by its R/LPM ratio (equations 1 and 2).

All investment strategies are buy-and-hold during the quarter without any implementation of stop loss or other portfolio insurance schemes. Input statistics for the algorithm derive from a historic period of the previous 104 weeks. Backtesting during the 1981-86 period indicates that the 104 week historic period provides the best forecasting performance.

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Empirical Results Quarterly Performance Results Table 7 presents the first set of out-of-sample results from 1988 to 1995. On an aggregate basis, the R/LPM 20 asset portfolios with industry rotation outperform the S&P index over the seven year period both in terms of return and risk-return. The S&P index does provide lower risk than the R/LPM portfolios at the cost of reduced returns and risk-return performance. On an individual quarter basis, the R/LPM 20 asset portfolio outperforms the S&P 500 index during 20 of 28 quarters. This is statistically significant using a binomial test of significance where p=0.5 is the null hypothesis (0.0188). The binomial test uses a normal approximation with a mean, np, and the variance, np(1-p) to compute the appropriate probabilities [Hastings and Peacock, 1975]. The normal approximation applies whenever n>20 and np>5 and n(1-p) >5. The interesting results in Table 7 are the moving 104 week calculations of skewness, kurtosis, and the one week lag serial correlations. During phases 2, 3, and 5 (plunge, early revival, accelerate), the 104 week serial correlations are significantly negative. There are insignificant serial correlations during Phases 1 and 4. The skewness and kurtosis numbers are especially interesting. Phases 1, 2, and 5 exhibit significantly negative skewness and are leptokurtic while phases 3 and 4 have insignificant skewness and kurtosis values close to 3.0. The transition from Easeoff (1) to Plunge(2) is striking. The skewness and kurtosis numbers drop drastically while the serial correlation suddenly becomes significantly negative. The transition from Plunge(2) to Revival 1(3) occurs with skewness values turning insignificant. The transition from Revival 1(3) to Revival 2(4) again is sudden with the serial correlations becoming insignificant. A switch back to significant negative serial correlations marks the beginning of the Accelerate(5) phase. Phase 3, early revival, seems to be a transition period since it has significant negative serial correlation while serial correlations in phase 4, late Revival, are insignificant. Phase 4 provides results close to a random walk, i.e., insignificant serial correlation and distributions that are approximately normal. These results correspond to Vaga's[1990] coherent market hypothesis. Note that in Table 4, leptokurtic

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distributions with significant skewness characterize Vaga's coherent and chaotic markets, while the random walk market is symmetric and mesokurtic (kurtosis = 3.0). The correspondence between the phases determined by Hunt’s methodology and the statistics determining Vaga’s market states is important. It indicates that the statistical stages of Vaga’s coherent market model have an economic (business cycle) foundation.

Place Table 7 Here

Performance Results by Phase To further explore this result, Table 8 presents the aggregate results for the trading strategies in the five phases. The R/LPM portfolio selection employs both industry selection and no industry selection for security screening. Overall, the industry rotation strategy performs better than the other investment strategies (except for Phase 3 - Revival 1). In phase 1, Easeoff, the industry selection using historic 104 week estimates provides the best performance. Significant negative skewness, a high degree of kurtosis and significant serial correlation characterize the first phase. Of the five phases, phase 1 provides the highest returns, which is consistent with the high returns during the 1983-1994 period in Table 1. Phase 1 provides a different result during the last economic cycle than it did during the 1970s and early 1980s with high positive returns during the recent period and negative returns during the 1970-1986 period. While phase 1 does not exhibit the low risk that Vaga identifies with a coherent market, it has the best risk-return performance of the five phases and significant serial correlation. As such it meets the criteria of a Vaga coherent market. Phase 2, Plunge, provides results consistent with a Vaga random walk market: symmetric distributions, kurtosis values close to 3.0 and insignificant serial correlation. The risk-return performance is less than the average for the total period. The industry selected portfolios again provide the best riskreturn performance. A Vaga transition market period characterizes phase 3, Revival 1, because of the kurtosis value for the S&P 500 index is 2.0 (platykurtic). The distributions are symmetric and there is very low serial correlation. The R/LPM heuristic without industry selection provides the best risk-return performance.

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The S&P return does not follow the past history exhibiting losses rather than the large gains available during the 1970-1986 period. Phase 4, Revival 2, is the coherent market period that Vaga speaks so highly about in his work since it exhibits higher than average returns and lower than average risks. There is also the significantly skewed and leptokurtic distributions identified by Vaga. The industry selection provides the best riskreturn performance. Phase 5, Accelerate, is an appropriate time for a portfolio manager to take a vacation. It exhibits the worst risk-return performance as well as the lowest overall returns. This is very interesting result since Hunt(1987) discusses how his investment managers take Caribbean vacations during the Accelerate phase. The distributions are slightly leptokurtic with some serial correlation. Again the industry selection provides the best performance. The pattern of increasing risk and lower return fit Vaga's description of a chaotic market period. All of the phases exhibit the statistical characteristics of the different Vaga market models and they correspond to the phases of the economy that derives from Hunt’s(1976) macroeconomic analysis.

Place Table 8 Here

Summary and Conclusions The economic cycle and its attendant phases have a significant effect on investment performance. The performance of stock portfolios and the S&P 500 varies during the phases. Portfolio construction based on industries selected according to phase provides better overall performance than the no industry rotation strategy. (The industry strategy outperforms the no industry strategy in four of five phases.) The correspondence between Hunt’s[1976,1987] work and the results of this study indicates that the study is successful at replicating Hunt's phases. While the phases originally derive from a macroeconomic top-down approach, it is interesting that a bottom-up analysis using skewness, kurtosis and serial correlations provides confirmation of the phases. Another interesting result is the correspondence between Hunt's phases of the economic cycle and Vaga's[1990] coherent market approach. The popularity of this approach is evident since Hunt[1987], Vaga[1994] and Stovall[1996] have written books on this

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approach targeted at a general audience. All three books espoused switching between different types of investments. Vaga’s switching mechanism depends on the type of market conditions, while Hunt’s and Stovall’s switching mechanism depends on the phase of the economic cycle. The evidence presented in this paper supports a viewpoint that the statistical behavior of the different market periods derives from the general business cycle. In addition, there is strong evidence that the underlying market structure is nonstationary (differing returns during the Easeoff and Revival 1 phases) and that investors have to continually monitor the market conditions for changes in the market structure. This provides additional evidence in support of adaptive management processes rather than static management processes. Finally, does knowledge of the business cycle improve investment performance? Does the market rotate into and out of industries in response to changes in the business cycle? The empirical results obtained in this paper indicate an affirmative answer to both questions.

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References Anderson, P., Arrow, Kenneth, and D. Pines, eds. (1988). Economy as an Evolving Complex System, Addison-Wesley. Ang, James S. and Jess H. Chua, 1979, “Composite Measures for the Evaluation of Investment Performance.” Journal of Financial and Quantitative Analysis, 14, 2, 361-384. Arnott, Robert D. and William A. Copeland, 1985, "The Business Cycle and Security Selection." Financial Analysts Journal, 41, 2, 26-32. Abraham, Abraham and David L. Ikenberry, 1993, "The Individual Investor Around Nontrading Days," Review of Financial Studies, 6, 1, 155-189. Bauman, W. Scott and Robert E. Miller, 1995, "Portfolio Performance Rankings in Stock Market Cycles," Financial Analysts Journal, 51, 2, 79-87. Chen, Nai-Fu, Richard Roll and Stephen Ross, 1986, "Economic Forces and the Stock Market." Journal of Business, 59, 3, 383-404. Elton, Edwin J., Martin J. Gruber and M. Padberg, 1976, "Simple Rules for Optimal Portfolio Selection." Journal of Finance, 31, 5, 1341-1357. Elton, Edwin J., Martin J. Gruber and Thomas J. Urich, 1978, “Are Betas Best?”, Journal of Finance, 33, 5, 1375-1384. Fishburn, Peter C., 1977, “Mean-Risk Analysis with Risk Associated with Below-Target Returns.” American Economic Review, 67, 2, 116-126. Harlow, W.V., 1991, "Asset Allocation in a Downside Risk Framework." Financial Analysts Journal, 47, September/October, 28-40. Hastings, N.A.J. and J.B. Peacock, 1975, Statistical Distributions: A Handbook for Students and Practitioners, Halstead Press, New York: John Wiley and Sons. Hogan, William W. and James M. Warren, 1972, “Computation of the efficient boundary in the E-S Portfolio Selection Model.” Journal of Financial and Quantitative Analysis, 7, 4, 1881-1896. Hunt, Lacy H., 1976, Dynamics of Forecasting Financial Cycles: Theory, Technique and Implementation, JAI Press, Greenwich, CT. Hunt, Lacy H., 1987, A Time to be Rich, Rawson Associates, Macmillan, New York, NY. Liano, Kartono, 1992, "Macroeconomic Events and Seasonality of Risk and Returns," Applied Financial Economics, 2, 4, 205-210. Liano, Kartono, and Benton E. Gup, 1989, "The Day-of-the-Week Effect in Stock Returns," Financial Analyst Journal, 45, 4, 74-77. Liano, Kartono, Gow-Cheng Huang and Benton E. Gup, 1993, "A Twist on the Monday Effect in Stock Returns: A Note," Journal of Economics and Business, 45, 1, 61-67.

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Markowitz, Harry M. 1991, Portfolio Selection: Efficient Diversification of Investments, Second Edition, Basil Blackwell, Cambridge, MA. Moore, Geoffrey H., 1983, Business Cycles, Inflation and Forecasting, NBER Research Studies in Business Cycles, No. 24, Ballinger Publishing, Cambridge, MA. Murphy, Roy E., 1965, Adaptive Processes in Economic Systems. New York: Academic Press. Nawrocki, David N., 1983, "A Comparison of Risk Measures When Used in a Simple Portfolio Selection Heuristic." Journal of Business Finance and Accounting, 10, 2, 183-194. Nawrocki, David N., 1984, “Entropy, Bifurcation and Dynamic Market Disequilibrium.” The Financial Review, 19, 2, 266-284. Nawrocki, David N., 1990, "Tailoring Asset Allocation to the Individual Investor," International Review of Economics and Business, 37, 10-11, 183-194. Nawrocki, David N., 1995, "R/S Analysis and Long Term Dependence in Stock Market Indices." Managerial Finance, 21, 7, 78-91. Peters, Edgar E., 1991, Chaos and Order in the Capital Markets, New York: John Wiley and Sons. Peters, Edgar E., 1994, Fractal Market Analysis: Applying Chaos Theory to Investment and Economics, New York: John Wiley and Sons. Shannon, C.E. and W. Weaver, 1948, The Mathematical Theory of Communications, Urbana, IL: University of Illinois. Sharpe, William F., 1967, "A Linear Programming Algorithm for Mutual Fund Portfolio Selection." Management Science, 14, 3, 499-510. Stovall, Sam, 1996, Standard and Poors Guide to Sector Investing, New York: McGraw-Hill. Vaga, Tonis, 1990, "The Coherent Market Hypothesis." Financial Analysts Journal, 46, 6, 36-49. Vaga, Tonis, 1994, Profiting From Chaos, McGraw Hill, New York, NY.

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Table 1 - Geometrically Linked Annualized Returns and Monthly SemiDeviations for 26 Years (1969-1994) for Various Asset Classes ----------------------------------------------------------------1969 to 1969 to 1974 to 1983 to 1994 1973 1982 1994 Asset Classes Total Period Vietnam Oil Crisis Recovery ----------------------------------------------------------------S&P 500 Stocks 10.17 -2.36 13.73 14.41 (3.00) (3.68) (2.73) (2.81) Mid-Cap Stocks 11.73 -6.56 22.18 14.67 (3.55) (4.65) (3.18) (3.15) Small-Cap Stocks 11.53 -10.50 28.29 12.71 (4.13) (5.29) (3.77) (3.70) LB LT Govt. 7.65 0.04 7.72 11.62 (1.78) (0.98) (2.24) (1.73) LB G/C Intermediate 7.71 1.18 9.52 9.83 (0.78) (0.68) (1.12) (0.56) Gold 9.15 25.03 14.08 -1.16 (3.37) (2.75) (4.18) (3.00) 90 Day T-Bill 7.28 6.22 9.04 6.57 (0.07) (0.11) (0.14) (0.02) CPI - Consumer Prices 5.77 6.49 8.25 3.69 (0.22) (0.21) (0.26) (0.15) CPI - New Cars 3.88 3.02 6.05 2.84 (0.61) (0.99) (0.62) (0.35) CPI - Food & Beverages 5.46 7.80 6.82 3.44 (0.33) (0.36) (0.45) (0.23) CPI - Fuel 6.41 8.98 13.82 0.81 (0.87) (0.30) (0.45) (1.13) Median House Prices 6.79 7.46 8.37 5.41 (2.42) (2.53) (2.00) (2.59)

Data sources include Lehman Brothers bond indexes, CRSP stock datasets, and CITIBASE/Fame/DRI economic database.

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Table 2 - Hunt's Phases of the General Economic Cycle ---------------------------------------------------------------------Phase 1 (EASEOFF) - Economy reaches a peak as defined by the NBER and real GNP starts to decline. The decision rules that indicate the start of this phase include: a 12 month percentage rate of change moving average for industrial production turns negative, initial unemployment claims increase, and nonfarm payrolls decline. Phase 2 (PLUNGE) Real GNP declines as interest rates peak. The economy reaches a trough as defined by the NBER. The decision rules that indicate the start of this phase include: a 12 month rate of change moving average for federal funds rates turns negative and a 6 month rate of change moving average for the real monetary base turns positive. Phase 3 (REVIVAL 1 or Early Revival) - Real GNP starts to increase. The decision rules that indicate the start of this phase include: a 12 month percentage rate of change for industrial production levels off towards a zero percent change, initial unemployment claims decrease, and nonfarm payrolls increase. Phase 4 (REVIVAL 2 or Late Revival) - Real GNP recovers from the recession The decision rules that indicate the start of this phase include: a 12 month percentage rate of change for industrial production becomes positive and nonfarm payrolls increase at a higher rate. Phase 5 (ACCELERATE) - The economy continues to grow at a high rate prompting the Federal Reserve to tighten credit, resulting in decreased consumer spending while business investment continues to increase. The decision rules that indicate the start of this phase include: a 6 month rate of change in consumer prices turns positive, a 12 month rate of change in federal funds rates turns positive, a 6 month rate of change moving average for the real monetary base turns negative, and nonfarm payrolls increase at an even higher rate. Reference: Hunt(1976), The decision rules were determined using Hunt's methodology with data from 1970 to 1986.

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Table 3 - Dates of the US Business Cycle, Percentage Changes and Correlation Coefficients for Macroeconomic Variables During Different Phases of Business Cycle. (Monthly Data - January 1970 to December 1986) -------------------------------------------------------------------------------Easeoff(1) Plunge(2) Revival 1(3) Revival 2(4) Accelerate(5) -------------------------------------------------------------------------------Dates 12/69-4/70P 5/70-12/70T 1/71-5/71 6/71-10/72 11/72-3/73 4/73-9/74P 10/74-5/75T 6/75-12/75 1/72-2/77 3/77-3/79 4/79-4/80P 5/80-7/80T 8/80-12/80 1/81-8/81 9/81-10/81P 11/81-10/82 11/82-4/83T 5/83-10/83 11/83-4/84 5/84-10/84 11/84-8/86 9/86-12/86 -------------------------------------------------------------------------------Annualized Percent Changes S&P -14.59 24.74 22.33 6.34 -0.99 IP -0.92 -5.20 8.96 8.82 7.26 FYFF 22.49 -47.77 35.32 2.69 46.71 FYFF(-12) 44.68 -21.72 -36.61 -7.69 28.12 FMBASE -3.28 3.50 3.62 2.33 1.78 FMBASE(-6) -6.08 5.17 9.42 8.21 6.47 FMFBA -2.47 2.81 3.41 2.08 1.73 FM1DQ -4.95 4.54 2.91 3.18 0.14 LPNAG 1.85 -0.75 2.23 3.05 5.06 LUINC 60.37 7.27 -36.15 -6.05 -12.65 CPI 10.51 4.28 5.54 5.14 6.85 CPI-Energy 23.68 -2.12 4.21 5.77 7.12 -------------------------------------------------------------------------------Correlations S&P IP S&P IP S&P IP S&P IP S&P IP S&P 1.00 .07 1.00 -.03 1.00 -.15 1.00 .34* 1.00 .20 IP .07 1.00 -.03 1.00 -.15 1.00 .34* 1.00 .20 1.00 FYFF -.07 .34* -.22* .42* -.14 .28* -.19* -.13 -.20 .01 FYFF(-12) -.03 .08 -.15 -.04 .01 .19 -.25* -.11 -.05 -.07 FMBASE .07 .22* -.05 .24* .24 -.41* .11 .36* -.23* -.17 FMBASE(-6) .06 .38* -.12 .50* .22 -.23 .02 .23* -.19 .03 FMFBA .17 .07 .06 .31* .25 -.41* .26* .36* .01 -.06 FM1DQ .24* .02 .16 .18* .30* -.18 .20* .05 .16 -.07 LPNAG .10 .51* .06 .76* -.43* .51* .46* .43* .03 .66* LUINC -.30* -.63* .23* -.46* -.22 .31* -.32* -.34* -.13 -.20 CPI -.08 -.03 -.03 -.33* -.05 .56* -.25* -.31* .14 .03 CPI-Energy .11 -.10 .03 -.15 -.21 .05 -.04 -.17 .03 -.03 df 43 53 23 49 35 * indicates significance at 10% -------------------------------------------------------------------------------Citibase/Fame/DRI access codes are used to represent the various macroeconomic variables. All time series are monthly and seasonally adjusted with the exception of the S&P. All data are percentage changes and are nominal amounts except where noted. -------------------------------------------------------------------------------S&P S&P 500 Composite Index FMFBA Real Monetary Base (Fed) IP Industrial Production FM1DQ Real M1 Money Supply FYFF Federal Funds Rate of Change LPNAG Non-Farm Payroll FYFF(-12) Fed Funds 12 Mo. Rate of Change LUINC Initial Unemployment FMBASE Real Monetary Base (St.Louis Fed) CPI Consumer Price Index FMBASE(-6) Real Monetary Base - 6 Mo. ROC CPI-Energy Consumer Energy Prices A NBER defined peak (P) or trough (T) appeared during this period.

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Table 4 - Characteristics of Vaga's Different Types of Market Behavior -------------------------------------------------------------------Market Behavior Skewness Kurtosis Return Risk Mode -------------------------------------------------------------------Chaotic Significant Leptokurtic Low High Bimodal Skewness Coherent

Significant Negative Skewness

Leptokurtic

Transition

Symmetric

Platykurtic

High

Varying

Low

Unimodal

Varying Unimodal

Random Walk Symmetric Mesokurtic Average Average Unimodal --------------------------------------------------------------------Source: Vaga[1990] Leptokurtic - Peaked probability distribution Platykurtic - Flat probability distribution Mesokurtic - Normal distribution ---------------------------------------------------------------------

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Table 5 - 15 Industries Selected by Ranking by R/LPM Ratio for the Five Phases of the Economic Cycle (1970-1986). All R/LPM Ratios are Positive. --------------------------------------------------------------------Easeoff Phase 1 Plunge Phase 2 Revival 1 Phase 3 --------------------------------------------------------------------GOLD MINING UTILITY STOCKS ELECTRIC POWER OIL-GAS DRILLING CONSUMER GOODS FOODS TOBACCO FOODS TEXTILE-APPAREL MFRS CHEM-SPECIALTY BEVERAGES-SOFT DRINK PAPER & FOREST PRODUCTS CHEM-DIVERSIFIED TOBACCO CONTAINERS-PAPER OIL-DOMESTIC PUBLISHING PUBLISHING HOUSEWARES DRUGS PUBLISHING-NEWSPAPERS CONTAINERS-METAL MEDICAL PRODUCTS CHEMICALS ALUMINUM HOUSEHOLD PRODUCTS CHEMICALS-DIVERSIFIED COMMUN.EQUIP.MFR COSMETICS OIL-INTERNATIONAL ELECTRONICS-DEFENSE OIL-INTERNATIONAL SHOES AEROSPACE/DEFENSE SHOES CONTAINERS-METAL&GLASS RAILROADS HOUSEHOLD FURNISHINGS STEEL TRANSPORTATION-MISC AUTO PARTS-AFTERMKT POLLUTION CONTROL TELEPHONE MANUFACTURED HOUSING HOUSEHOLD FURN&APPL ------------------------------------------------------------------Revival 2 Phase 4 Accelerate Phase 5 ------------------------------------------------------------------ELECTRIC POWER CAPITAL GOODS OIL&GAS DRILLING GOLD MINING BEVERAGES-ALCOHOLIC MACHINE TOOLS BEVERAGES-SOFT DRINK OILWELL EQUIP&SERVICE PUBLISHING-NEWSPAPERS OIL&GAS DRILLING HOUSEHOLD PRODUCTS BEVERAGES-SOFT DRINK OILWELL EQUIP&SERVICE TOBACCO MACHINE TOOLS CONTAINERS-PAPER POLLUTION CONTROL DRUGS ELECTRICAL EQUIPMENT HOUSEHOLD PRODUCTS HOUSEHOLD FURN&APPL COSMETICS COMM. EQUIP MFR CHEMICALS-DIVERSIFIED ELECTRONICS-DEFENSE OIL-DOMESTIC AUTOMOBILES OIL-INTERNATIONAL AUTO PARTS-AFTER MKT COMPUTER SYSTEMS -------------------------------------------------------------------

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Table 6 - Historic Performance of R/LPM Heuristic, Covariance Optimization and Cosemivariance Optimization (1958-1987) -------------------------------------------------------------------Revision Best LPM R/LPM Covariance Cosemivariance Period Degree Risk-Return Risk-Return Risk-Return -------------------------------------------------------------------3 1.2 0.2287 0.1536 0.1505 6 1.0 0.2430 0.1636 0.1736 12 1.6 0.2363 0.1494 0.1541 24 1.4 0.2221 0.1383 0.1636 36 2.8 0.2201 0.1230 0.1744 48 4.6 0.2467 0.0842 0.1490 -------------------------------------------------------------------Revision Period indicates that the portfolios were revised every 3, 6, 12, 24, 36, and 48 months. Transaction costs of 1% were assessed during each revision. Best LPM Degree indicates the LPM degree that provided the best riskreturn performance for the particular revision strategy. Risk-Return is measured using the reward to semivariability ratio (R/SV). --------------------------------------------------------------------

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Table 7 - Quarterly Return Values (In Per Cent) for the Period 3/4/1988 to 2/10/1995 Using Portfolios Selected According to Industry and Phase of Economic Cycle. 20 Asset Portfolios Selected Using the R/LPM Heuristic and a Historic 104 Week Period. ------------------------------------------------------------------R/LPM Per Begin EndDate S&P500 20 Asset Skew Kurt Phase TSerCor ------------------------------------------------------------------1 880304 880513 -2.16 5.69 -1.2452* 6.3045 5 1.2575 2 880520 880819 1.35 4.92 -1.2904* 6.4832 5 1.4942* 3 880826 881111 2.95 2.69 -1.2253* 6.4769 5 1.2928* 4 881118 890217 10.77 8.78 -1.1482* 6.6135 1 1.2766 5 890224 890512 5.75 16.71 -1.2241* 6.9247 1 1.1697 6 890519 890818 10.26 18.68 -1.3078* 7.2141 1 1.0979 7 890825 891110 -2.00 5.55 -1.3361* 7.3787 1 1.0071 8 891117 900216 -1.88 -5.42 -.4724* 4.2490 2 -2.7017* 9 900223 900511 5.80 13.78 -.7213* 4.4377 2 -2.8019* 10 900518 900817 -6.87 -1.48 -.6377* 4.3465 2 -2.1705* P 11 900824 901109 -4.30 -4.99 -.7462* 4.0964 2 -1.7145* 12 901116 910215 17.63 21.73 -.6324* 3.6199 2 -2.3073* 13 910222 910510 1.81 2.84 -.3729 3.3695 2 -1.4940* T 14 910517 910802 3.04 6.88 -.3289 3.4657 3 -1.7066* 15 910809 911108 1.48 11.80 -.2441 3.4611 3 -1.6667* 16 911115 920214 4.99 5.53 .0863 2.7983 4 -.6462 17 920221 920508 .87 6.92 .2442 2.7658 4 -.1229 18 920515 920807 .68 8.50 .2675 3.0080 4 -.2968 19 920814 921106 -.31 3.85 .3047 3.2201 4 -.8695 20 921113 930219 3.99 15.74 .6342* 3.4456 4 .1902 21 930226 930507 1.86 2.48 .3824 3.1078 4 -.5334 22 930514 930806 1.44 5.31 .3478 3.1640 4 -.8014 23 930813 931105 2.43 -3.99 .4362 3.6096 4 -.5644 24 931112 940218 1.77 2.87 .4160 3.9379 4 -.3526 25 940218 940506 -4.25 -5.82 -.0480 2.9348 5 -2.3499* 26 940513 940812 3.16 -2.22 -.2545 3.3402 5 -1.3995* 27 940819 941111 .09 4.10 -.6528* 3.8141 5 -1.1435 28 941118 950210 4.13 3.36 -.5194* 3.5421 5 -2.3490* ------------------------------------------------------------------Frequency(R20 > Rm) 20 Binomial Probability 0.0188 (n=28 p=0.5) * - indicates statistical significance for 10% level of significance. ------------------------------------------------------------------Aggregate Statistic S&P 500 R/LPM 20 Asset ------------------------------------------------------------------Weekly Geometric Mean 0.1673% 0.3855% Standard Deviation 1.6917 2.2574 Reward/Variability (R/V) 0.0377 0.1249 Semideviation 1.1958 1.5033 Reward/Semideviation (R/SV) 0.1467 0.2645 Annualized Return 9.0805 22.1486 ------------------------------------------------------------------Per - Period Number P and T are NBER Defined Peaks and Troughs TSerCor - T-statistic for one week lag serial correlation on S&P500 Skew - Skewness Kurt - Kurtosis R20 - 20 Asset R/LPM Portfolio Rm - S&P 500 Return

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Table 8 - Performance Results for the Period March 3, 1988 to February 10, 1995 for Total Period and Different Phases __________________________________________________________________ Total Period - Number of Observations: 363 SerCor Portfolio AnnRet StdDev SemiDev R/SV Skew Kurt T-Test Vaga -----------------------------------------------------------------S&P500 9.08% 1.69% 1.20% .1467 -0.19* 4.02 -2.85* No Indust 18.56 2.51 1.63 .2013 -0.12 3.83 -0.56 Industry 22.15 2.26 1.50 .2645#-0.33* 4.57 -2.35* -----------------------------------------------------------------Phase 1 - Number of Observations: 47 SerCor Portfolio AnnRet StdDev SemiDev R/SV Skew Kurt T-Test Vaga -----------------------------------------------------------------S&P500 26.69% 1.93% 1.40% .3267 -1.49* 6.41 -3.20* Coherent No Indust 39.63 2.21 1.50 .4290 -1.35* 5.65 -0.22 Industry 57.79 2.18 1.29 .6933#-0.72* 3.88 -1.99* -----------------------------------------------------------------Phase 2 - Number of Observations: 79 SerCor Portfolio AnnRet StdDev SemiDev R/SV Skew Kurt T-Test Vaga -----------------------------------------------------------------S&P500 8.61% 2.13% 1.39% .1143 0.08 2.63 -0.19 Random No Indust 19.36 2.88 1.86 .1829 -0.09 3.10 -0.20 Industry 17.83 2.65 1.72 .1837#-0.19 3.90 -0.71 -----------------------------------------------------------------Phase 3 - Number of Observations: 26 SerCor Portfolio AnnRet StdDev SemiDev R/SV Skew Kurt T-Test Vaga -----------------------------------------------------------------S&P500 -7.63% 1.53% 1.13% -.1303 0.14 2.01 -0.62 Transition No Indust 37.12 2.68 1.46 .4173# 0.30 3.20 -0.53 Indust 12.86 2.25 1.32 .1770 0.49 2.85 -0.21 -----------------------------------------------------------------Phase 4 - Number of Observations: 113 SerCor Portfolio AnnRet StdDev SemiDev R/SV Skew Kurt T-Test Vaga -----------------------------------------------------------------S&P500 11.87% 1.24% 0.73% .2968 0.45* 4.32 -0.93 Coherent No Indust 25.71 2.43 1.42 .3096 0.21 4.28 -0.34 Indust 27.35 1.78 1.04 .4481#-0.13 3.92 -0.38 -----------------------------------------------------------------Phase 5 - Number of Observations: 98 SerCor Portfolio AnnRet StdDev SemiDev R/SV Skew Kurt T-Test Vaga ------------------------------------------------------------------S&P500 3.38% 1.69% 1.18% .0540 -0.08 3.61 -1.70* Chaotic No Indust -1.96 2.36 1.75 -.0216 -0.26 3.47 -0.34 Indust 8.27 2.45 1.73 .0881#-0.46* 4.95 -1.93* ------------------------------------------------------------------# - Indicates best risk-return performance. * - Indicates statistical significance for 10% level of significance. AnnRet - Annualized return. StdDev - Monthly standard deviation in per cent. SemiDev - Monthly semideviation (square root of semivariance). R/V - Reward to variability ratio (using standard deviation). R/SV - Reward to semivariability ratio (using semideviation). Skew - Skewness of portfolio returns. Kurt - Kurtosis of portfolio returns. T-Test - T-test of 104 week serial correlations of the S&P 500.

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