PII: 1057-0810(93)90004-A FINANCIAL SERVICES REVIEW, 3(l): 29-43 Copyright (9 1993 by JAI Press Inc. ISSN: 1057-0810 All rights of reproduction in any fom mserved. Market Timing for the Individual Investor: Using the Predictability of Long-Horizon Stock Returns to Enhance Portfolio Performance Steven P. Rich William Reichenstein Recent research indicates that dividend yield and earnings-price ratio can partially predict long-horizon stock returns. We examine whether individual investors can successfidly construct timing portfolios based on either of these variables or a measure of the expected market risk premium. The out-of-sample tests in this study require that investors rely only on information that was available at the time of the ~r~t-t~~g decision. Timing portfblios based on the market risk premix show the strongest ab~i~ to rime the market. We present an eco~mic ra~o~e for the results that is consistent with @scent ~~~. I. INTRODUCTION Several studies by leading financial economists conclude that long-horizon stock returns are partially predictable (e.g., Campbell & Shiller, 1988; Fama & French, 1988a,b, 1989; and Fama, 1991). These studies suggest that up to 25% of the variation in long-horizon returns on large (e.g., S&P) stocks is predictable. A larger portion of long-horizon small stock returns appears predictable. This study investigates the impli~tions of the market ~~ic~bili~ literature for market timing by individu~ investors. Can the individual investor construct timing portfolios that outperform nontiming benchmark portfolios where the timing portfolios are based on variables that show a consistent relation with long-horizon stock returns? We address this question by constructing timing portfolios that combine the S&P Index and Treasury bills and, separately, portfolios that combine Steven P. Rieb l Hankamer School of Business, Baylor University, Waco, TX 76798-8004. William Reiekenstein l Baylor University, Waco, TX 76798-8~. 30 FINANCIAL slmv1cEs REVIJZW, 3(l) 1993 small stocks and Treasury bills. We then calculate several measures of portfolio performance, including raw return and risk-adjusted return. By every criterion, timing portfolios based on a measure of the expected market risk premium outperform S&P benchmark portfolios. Of the small-stock timing portfolios, those based on the expected market risk premium perform best, but portfolios based on dividend yield and earning-price ratios also show some ability to time small stock returns. Finally, we discuss the limitations of this study and their implica~ons for individ~ investors that plan to follow a market timing strategy. II. REVIEW OF bERATURE Several financial studies indicate that long-horizon stock returns are partially predictable. Many economists argue that this predictability reflects the action of a rationally priced stock market with a time-varying market risk premium. Simply put, average stock returns tend to be generous when the market is priced to offer a generous risk premium. Nobel-la~~tc William Sharpe, who sells market timing advice based on a relative market risk premium, expresses this view, “This is not a story that the market is screwed up. This is a story of how investors behave when their wealth changes. Say I tell you the relative risk premium is 120-you’ll get 120% of the normal expected return for bearing risk. If that was the only thing I told you, you’d say, ‘Let’s buy stocks.’ But what if I also told you the reason for that is we’re in a recession and someone in your family is out of work. If you’re average, you’ll say, ‘I guess these are offsetting. I’ll stay with what I’ve got.’ In fact, that’s what has to happen in an efficient market. The risk premium has to adjust to where the average investor doesn’t want to do anything” (Berss, 1990, p. 78). Fama and French also support this view. They conclude that the market risk p~~urn is highly autocorrelated, but slowly mean reverting’; that is, when the risk premium is large it tends to remain large for several quarters while slowly reverting to its historic mean, and vice-versa. This produces a predictable component of stock returns that increases roughly proportionately with the return horizon out to one or two years. We offer the following illustration of their story. Let P represent the price of an index of stocks. For simplicity, we assume the zero growth model with projected year-ahead dividends D, equal to projected earnings E,. That is, D, = E, . In this model, where the required rate of return K = r + MRP, r denotes the risk-free interest rate, and MRP denotes the unobservable market risk premium. It follows that Market Timing for the Zndividual Znvestor 31 D,/P = E,IP = r + MRP. UB) As equation 1B shows, both dividend-price and earnings-price ratios perfectly reflect shocks to the market risk premium that are independent of dividend and earningsforecasts. These ratios are not important per se, but only to the degree that they reflect movement in the unobservable market risk premium. Thus theory suggests that the predictive content of historic dividend-price and earnings-price ratios reflects their tendency to proxy for the unobservable market risk premium. Suppose the risk-free interest rate is 5% and the market risk premium is 8%, its historic average. A shock raises the premium to 9.3%. The rise in the market premium drives the current stock price from $7.7D to $7D. If the premium followed a random walk then stocks would now offer a permanently higher expected return. However, the market premium slowly reverts to its mean. During the reversion, the expected risk premium exceeds its historic mean. After the reversion, the market risk premium is again 8% and the stock price $7.7D. This economic story can explain the evidence supporting the predictability of long-horizon stock returns. 1. Model 1B explains why dividend yield and earnings-price ratio can predict stock returns. More generally, any variables that move with the time-vary- ing market risk premium should be able to predict long-horizon stock returns. 2. McQueen and Thorley (199 1) found that a bad year in the stock market tends to follow two good calendar years and a good year tends to follow two bad years. This pattern is expected if movements in the market risk premium strongly influence individual year stock returns. 3. There appears to be a transitory, and thus predictable, component of stock price. In the example above, the shock to the market risk premium produced a transitory drop in stock price that is eventually offset by subsequent gains. Equivalently, the mean-reverting market risk premium gives rise to negative autocorrelations in distant stock returns; the rise in the market risk premium produces a current period loss that is offset by higher subsequent returns. III. CONSTRUCTION OF TIMING PORTFOLIOS Prediction Variables In this study, we examine whether individual investors can successfully construct timing portfolios using three variables shown to predict stock returns. The first of the variables is the end-of-quarter earnings-price ratio on the Standard and Poor’s Composite Index, EP. The second is the median year-ahead dividend yield as published by Value Line, YIELD. 32 FECAL SERVICES AVOW, 3(l) 1993 RP S&P 0.4 0.8 0.35 0.6 0.3 0.4 025 0.2 02 0 0.15 9.2 0.1 0.05 9.4 0 -0.6 66 6B 70 71 72 73 74 75 76 77 78 73 80 61 62 63 84 85 86 87 8B 0.4 0.35 0.3 0.25 0.2 0.15 0.t 0.05 0 RP I- J 0.E - 0.6 ” 0.4 - 0.2 - 0 - -0.2 - -0.4 - -0.6 “.” 66 68 70 71 72 73 74 75 76 77 76 79 80 61 62 63 64 65 86 87 69 Figure I. Relationship Between RP and Cumulative Six-Quarters-Ahead Excess Returns on S&P and Small Stock Indexes The third predictor is a direct measure of the expected market risk premium: RP = (YZELZ3 + CapGains) - R. Cap~i~s denotes the median ammal capital gain return and is calculated (1 + APPR~~“.*5 -1 where APPREC is the median three-to-five year price appreciation potential as forecast by VaZue Line. The variable R denotes the bond-equivalent yield on three-month Treasury bills. Value Market Timing for the Individual Investor 33 Line’s “Summary and Index” highlights YIELD and APPREC weekly on the cover page. Figure 1 shows the close relationships between RP and cumulative six-quarters-ahead excess returns on both the S&P and small stock indexes. The RP frequently hit a peak immediately prior to a strong six-quarter return. For example, RP reached a peak at the end-of-September 1974. This correctly predicted the peak excess S&P return from October 1, 1974, through March 3 1, 1976. The RP offers a number of important advantages compared to the ratio of past-four-quarters dividends to current stock price, the ratio most prevalent in prior studies of stock predictability. 1. It is a direct measure of the unobservable market risk premium, the alleged source of predictive content. 2. It uses forecasts of dividends and returns instead of historic information, and, not surprisingly, forecasts provide a better measure of expectations. 3. Value Line forecasts are generally accessible to the individual investor. In a recent study, Reichenstein and Rich (1992) examined the ability of EP, YIELD, and RP to explain S&P and small stock returns for 1968-1988 and for two equal subperiods. The market risk premium RP is the only candidate to show a consistent in-sample relation with S&P returns. The risk premium RP, earnings- price ratio EP, and dividend-price ratio YIELD all show consistent in-sample relations with long-horizon small stock returns. The next section describes the timing strategies considered in this study. Market Timing Strategies Each quarter from the third quarter of 1978 (1978.3) through the fourth quarter of 1988 (1988.4) we form out-of-sample timing portfolios based on the three prediction variables. Since RP is the only candidate to show a consistent in-sample relation to S&P stock returns, we determine whether it can enhance large (i.e., S&P) stock returns in out-of-sample tests. Since all three show a consistent relation to in-sample small stock returns, we determine whether any of them can enhance small stock returns in out-of-sample tests. We examine two basic timing strategies, the first, the all-or-nothing strategy, calls for a portfolio that each quarter is either 100% in stocks or 100% in Treasury bills. Each quarter a regression of 1968.2-to-date stock returns on the prediction variable determines whether the timing portfolio invests in stocks or bills.2 Consider the general regression: r(t,t+n-l)=a+b*X(t-l)+e(t), (2) where r(t, t + it - 1) is the n-quarters-ahead market risk premium (market return less Treasury bill return), X(t - 1) is the time t-l value of the prediction variable, and 34 FINANCIAL SERVICES REVIEW, 3(l) 1993 e(t) is the regression residual. If the fitted value 2 + &X(t - 1) is positive, the all-or-nothing portfolio consists of stocks; if negative, it consists of Treasury bills. For example, the 1968.2-1977.1 regression of six-quarter small stock excess returns on the Value Line market risk premium is:3 r(b, t+5) =-O-2717 + 1.83RP(b- 1). If the end-of-June 1978 value of RP exceeds 0.148 (0.2717/1.83), then the fitted value is positive and the timing portfolio invests in small stocks for the 1978.3 quarter. If less than 0.134, then it invests in bills. We update the regressions every four quarters.4 The forecast horizon in (2) is set at six quarters for RP and eight quarters for the other candidates.5 We compare all-or-nothing portfolio returns to that on a buy-and-hold benchmark portfolio that always allocates 100% to stocks. The second timing strategy, the variable-weights strategy, better reflects timing strategies in practice in that it allows portfolio weights of stocks and bills to vary according to market prospects, but it does not require either the 100% stocks or 100% bills extremes. This strategy calls for the timing portfolio to contain 25% stock when the market predictor signals “poor” stock prospects, 50% stock when it signals “average” prospects, and 75% when it signals “good” prospects. The balance of the portfolio is invested in T-bills. The benchmark portfolio begins each quarter with bill-stock weights of 50% each. Stock prospects depend upon whether the prediction variable is high, average, or low by historic standards. Poor and good stock prospects occur when the variable falls in, respectively, the bottom and top fourth of its 1968.1”to-date distribution. Average stock prospects occur when the variable falls in the middle 50% of its distribution. Distributions are updated every four quarters. Table 1 suites the 1%8.1-1988.3 ~st~butions of the predictive vari- ables and the 1968.2-1988.4 (continuously compounded) quarterly risk premiums on the S&P and small stocks. It provides historic perspective for individual investors who wish to use the variables. TABLE 1. Summary Statistics: 19684988 Variable Mean RP 13.74% EP 8.77% YIELD 4.07% S&P 2.40% Small Stock 3.07% St. Dev 6.34% 2.80% 1.04% 8.82% 13.62% 1st Q 10.10% 6.08% 3.2% -2.61% -5.02% Median 12.72% 8.37% 4.1% 3.05% 1.82% 3dQ 16.91% 11.09% 4.9% 8.31% 12.19% Note: RF’, EP, and YIELD refer to the Value Line estimates of the market risk premium, earnings-price ratio on S&P 500, and Value Line estimate of median year-ahead dividend yield. S&P and Small Stock show the distribution of quarterly risk pnxniuzn-total returns less Treasury bill returns. Market Timing for the Individual Investor 35 S&P Index RP Benchmark Equity Weights of Timing Portjolios All-or-Nothing Variable Weights 0 or 100% stock 25,50 or 75% stock 100% stock 50% stock Small stocks All-or-Nothing Variable Weights RP 0 or 100% stock 25,50, or 75% stock EP 0 or 100% stock 25,50, or 75% stock YIELD 0 or 100% stock 25,50, or 75% stock Benchmark 100% stock 50% stock Each portfolio contains stocks and/or Treasury bills. The figure shows the equity weights. Figure 2. Outline of Timing Strategies The average annual risk premium (RP) of 13.74% equals a continuously compounded quarterly return of 3.22%. This exceeds both the average small stock premium 3.07% and average large stock premium 2.40%. We attribute this upward bias to the optimistic nature of investment advisory services. Nevertheless, the results of this study suggest that movements in RP mirror movements in the unobservable expected market risk premium. Figure 2 summarizes the market timing andbenchmark portfolios. For the S&P Index, we compare returns on two RP-based portfolios with returns on their benchmark portfolios. The all-or-nothing portfolio contains either 0% or 100% stock. Its returns are compared to the returns on a buy-and-hold 100% stock portfolio. The variable-weights timing portfolio contains 25%, SO%, or 75% stock. Its returns are compared to the returns on a constant-weights 50% debt-50% stock portfolio. For small stocks, we examine separately the market timing ability of RP, EP, and YIELD. IV. OVERVIEW OF TESTS In this section we examine whether RP can be used to enhance portfolio returns using large (i.e., S&P) stocks and whether RP, EP, or YIELD can be used to enhance portfolio returns using small stocks.6 The 1978.3-1988.4 out-of-sample perform- ance of each timing portfolio is compared to the performance of a benchmark portfolio. We use five performance criteria to determine whether RP, EP, or YIELD can be used to time the market. The criteria include raw return, risk-adjusted return, and three CAPM-based regressions of timing ability. 36 FINANCIAL SERVICES REVIEW, 3(l) 1993 S&P Index RP Benchmark Small Stock Index RP EP Yield Benchmark AN or Nothing 1.49% 38.1% 1.38% 100.0% AN or Nothing 2.22% 54.8% 1.63% 76.2% 1.62% 45.2% 1.74% 100.0% Variable Weights 1.04% 47.0% 0.69% 50.0% Variable Weights 1.43% 47.0% 1.12% 55.4% 1.35% 42.3% 0.87% 50.0% Note: All returns are continuously compounded. Thus mean returns are geometric means. Mean quarterly risk premium equals the average of portfolio returns minus the return on T-Bills. All-or-nothing timing portfolio has either 100% stock or 100% Treasury bills. Its benchmark is a buy-and-hold stock portfolio. Variable- weights timing portfolio has weights of 75%. 50%. or 25% on stocks and the rest in Treasury bills. Its benchmark portfolio always maintains a 5C50 stock-bills mix. Raw Return Table 2 presents the raw (unadjusted for risk) returns on timing and benchmark portfolios. The mean quarterly risk premium denotes the average of the portfolio return less the return on Treasury bills. S&P Index, Both the RP-based all-or-nothing and variable-weights timing port- folios earned higher raw returns than their benchmark portfolios. The mean risk premium for the all-or-nothing timing portfolio was 1.49%. Its benchmark portfolio earned 1.38%. The mean risk premium on the variable-weights timing portfolio (1.04%) also exceeds its benchmark portfolio (0.69%). The all-or-nothing portfolio managed to earn a higher raw return than the buy-and-hold benchmark, despite being out of the market 62% of the time. Small Stocks. Among the all-or-nothing timing portfolios, only the RP-based portfolio earned more (2.22%) than the benchmark (1.74%). It earned higher returns despite being out of the market about half of the time. The EP-based (1.63%) and YIELD-based (1.62%) all-or-nothing portfolios failed to match the benchmark. All of the variable-weights timing portfolios earned more than the benchmark. With the exception of the EP-based portfolio, the timing portfolios earned higher return despite a lower average exposure to stocks. The RP-based portfolio earned the highest return (1.43%). Figure 3 shows that the higher raw returns on the timing portfolios produce substantial long-run wealth implications. For example, $10,000 invested in the variable-weights S&P benchmark portfolio (i.e., 50% S&P and 50% T-bills) at the beginning of the third quarter of 1978 would have grown to $33,303 by the end of 38 FINANCIAL SERVICES REVIEW, 3(l) 1993 1988. However, had the $10,000 been invested in the RP-based variable-weights timing portfolio instead, it would have grown to $38,711. The results from timing with small stocks are even more impressive. The benchmark portfolio would have grown to $34,454 while the RP-based variable-weights portfolio would have grown to $43,722. As Figure 3 shows, the gains from timing accrued slowly but steadily over the entire period. Risk-Adjusted Return Valid performance comparisons across portfolios should consider differences in portfolio risk. The Sharpe (1966) ratio incorporates these differences by dividing the mean quarterly risk premium by its standard deviation, thus providing a measure of return per unit of risk. Table 3 presents the Sharpe ratios for the timing and benchmark portfolios. S&P Index. Both RP-based timing portfolios outperform their benchmark. The all-or-nothing portfolio earned twice as much return per unit of risk as the bench- mark, 0.328 versus 0.163. The variable-weights portfolio earned 60% more return per unit of risk, 0.266 versus 0.163. Small stock. All of the timing portfolios earned higher risk-adjusted returns than their benchmark portfolios. However, the RP portfolio (0.3 19) earned much larger risk-adjusted returns than the YIELD portfolio (0.180), its nearest competitor. Among the variable-weights portfolios, RP again performed best (0.244) followed TABLE 3. Risk-Adjusted Returns: Sharpe Ratios Portfolio AN or Nothing Variable Weights S&P Index RP 0.328 0.266 Benchmark 0.163 0.163 Small Stock Index RP 0.319 0.244 EP 0.165 0.160 YIELD 0.180 0.234 Benchmark 0.143 0.143 Note: All returns are continuously compounded. Thus mean returns are geomet- ric means. The Sharpe ratio reflects return per unit of risk and is defined as the ratio of mean-to-standard deviation of quarterly excess return. All-or-nothing timing portfolio has either 100% stock or 100% Treasury bills. Its benchmark is a buy-and-hold stock portfolio. Variable-weights timing portfolio has weights of 75%,50%, or 25% on stocks and the rest in Treasury bills. Its benchmark portfolio always maintains a S&50 stock-bills mix. Market ISming for the Individual Investor 39 closely by YIELD (0.234). Both RP portfolios earned at least 70% more return per unit of risk than the benchmark portfolios. Regression Tests of Timing Ability One weakness of the Sharpe ratio is that it cannot test the statistical signifi- cance of the performance differences between timing and benchmark portfolios. The three regressions presented here provide such tests. Estimates of Jensen (1968) regressions take the following form: rpt - r--t = a + b(r,, - r-ff) + e, where rpt denotes the portfolio return, and rPt - rrt is the quarterly risk premium earned by the timing portfolio, r,,,, - rfr is the market risk premium, e, is the error term, and a and b are regression coefficients. A positive intercept, a, indicates that the timing portfolio beats the benchmark portfolio on a risk-adjusted basis. A negative intercept indicates inferior performance. In general, a positive intercept can result from consistent selection of undervalued stocks, successful market timing, or both. For the portfolios considered here, a positive intercept indicates successful market timing since no individual stocks are selected. Estimation of Quadratic and Dummy regressions provide direct tests of timing ability. They take the forms: rpt - rrt = a + b(r,, - rrt> + c(rti - r-,t)’ + e, (Quadratic) and rp, - r-f, = a + b(r,, - rfr) + c[W, - rrt)l + e, (Dummy) where D, = 0 if r, > rr, and -1 if r,,,, < rrt. In both regressions a positive “c” coefficient indicates successful timing ability.’ Table 4 presents the results. S&P Index. The regressions indicate superior timing for the BP-based all-or-noth- ing portfolio. The Jensen intercept of 1.09% (based on a quarterly-returns regres- sion) indicates a compound annual return advantage of 4.43%. The positive “c” in the Quadratic regression indicates a tendency for the timing portfolio’s beta to rise with the market return. The positive “c” in the Dummy regression indicates that the average beta in an up market (i.e., r, > rfr) was 0.46 more than the average beta in a down market. This indicates that the timing portfolio tended to invest in stocks during an up market and in bills during a down market. Both “c” coefficients imply timing ability at significance levels better than 10%. The regressions lend even stronger support to the claim of timing ability in the variable-weights portfolio. The “c” coefficients in the Quadratic and Dummy regressions show significance beyond the 1% level. The Jensen intercept of 0.45% indicates an annual premium of 1.8%. FlNANCIALSERVICESREVIEW,3(1) 1993 TABLE4. Regression Tests of Timing Strategies All or Nothing Variable Weights Portjxo aorc t-statistic aorc t-statistic S&P Index RP Jensen 1.09% 1.80* 0.45% 1.93* Quad. 1.01 2.11* 2.93 4.65*** Dummy 0.46 2.01* 0.62 3.94*** Small Stock In&x RP Jensen 1.65% 1.85* 0.65% 1.97* Quad. 1.44 3.99*** 2.73 5.93*** Dummy 0.77 3.72*** 0.68 4.80*** EP Jensen 0.48% 0.53 0.19% 0.47 Quad. 0.36 3.29*** 1.73 2.41** Dummy 0.50 2.12** 0.27 1.29 YIELD Jensen 0.68% 0.71 0.59% 1.73* Quad. 0.50 1.71; 1.69 2X5*** Dummy 0.22 0.83 0.37 2.15** Notes: * Significant at 10% level. **Significant at 5% level. *** Significant at 1% level Jensen’s Regression: rpl - rfr = a + b(rm - rfr) + et Quadratic Regression: rpr - rfr = a + b(r,,,t - r@ + c(rmr - r@2 + et Dummy Variable Regression: rp - rfr = a + b(rm - ry) + c[Dl(rm - r@] + e, All returns am continuously compounded. Thus mean returns am geometric means. All-or-nothing timing portfolio has either 100% stock or 100% Treasury bills. Its benchmark is a buy-and-hold stock portfolio. Variable-weights timing portfolio has weights of 7546, 5046, or 25% on stocks and the rest in Treasury bills. Its benchmark portfolio always maintains a 50-50 stock-bills mix. Small stock. Each of the all-or-nothing timing portfolios demonstrates statisti- cally significant timing ability at the 10% level or better at least once. However, the RP-based portfolio produced the strongest evidence of timing ability for each regression type. It produced a Jensen intercept of 1.65% (6.76% annually) and “c” coefficients of 1.44 and 0.77 in the Quadratic and Dummy regressions. These are at least 42% larger than the nearest competitor. Only the RP portfolio shows significant timing ability at the 10% level or better across all regressions. A similar story prevails for the variable-weights portfolios. All of these portfolios show significant timing ability at the 10% level at least once. Both RP and YIELD show significant timing ability across all regression types. However, the RP portfolio consistently produces the strongest results. V. SUMMARYAND~MPLICATIONS Long-horizon stock returns are partially predictable. The $100,000 per year charged by William Sharpe for his asset allocation advice suggests that pension funds can Market Timing for the Individual Investor 41 exploit this predictability (Berss, 1990). But can the individual investor use market predictability to effectively time the market? The evidence presented here suggests that they can. The results imply that individual investors who specialize in large (i.e., S&P) stocks can successfully time the market with RP-an estimate of the expected market risk premium based on Value Line forecasts. The all-or-nothing timing portfolio beat the buy-and-hold S&P benchmark by every criterion. It earned higher raw returns, twice the risk-adjusted return, and it generated evidence of significant timing ability at the 10% level in all three regression tests. Similarly, the RP-based variables-weights portfolio beats its S&P benchmark by every criterion. All of the regression tests support the claim of timing ability at the 10% level and two of the three tests were significant at the 1% level. The results also imply that investors can use RP to successfully time small stock returns. Among the all-or-nothing strategies, the RP portfolio outperformed by every criterion the small stock benchmark portfolio. It also outperformed timing portfolios based on dividend yield (YIELD) and earnings-price ratio (EP). Among variable-weights strategies, the RP portfolio performed best by every criterion. Compared to the nontiming benchmark portfolio, it earned a 2.3% larger annual raw return and 70% larger risk-adjusted return. The RP portfolio also showed significant timing ability at the 1% level in two of the three tests and at the 10% level on the remaining test. YIELD beats the benchmark by every criterion, and EP beats it by most criteria. They all demonstrate significant timing ability at the 5% level in at least one regression test. Why did RP, and to a lesser extent YIELD and EP, succeed in enhancing portfolio returns? More important, are they likely to do so in the future? We believe that the literature review on the predictability of long-horizon stock returns provides the answer. If the market risk premium varies through time, long-horizon stock returns should be predictable. These variables should move with the unobservable market risk premium and continue to predict long-horizon stock returns. Will RP continue to predict as well in the future? Possibly. In 1990, we noticed that Value Line’s prediction of median three to five year appreciation potential hit a low in August, 1987, shortly before the crash. This drew our attention, encouraged the development of the RP model, and later we saw how the model fit into the stock predictability literature. As we are all aware, a model usually performs better in the period in which its predictive content is “discovered” than in later periods. However, we believe, that RP will continue to predict returns better than dividend yield and earnings-price ratio because it is a direct measure (although possibly biased) of the unobservable market risk premium. Finally, how could an individual implement an RP-based strategy? One approach would be to calculate RP, perhaps every three months, and to compare its current value to its historic distribution as presented in Table 1. If RP is well below average, perhaps below the first-quartile value of 10.1 %, then the portfolio’s equity 42 FINANCIAL SERVICES REVIEW, 3(l) 1993 weight can be reduced below the investor’s long-run target equity weight. If RP is well above average, perhaps above the third-quartile value of 16.9%, then equity weight can be increased. This type of strategy would allow an individual to increase equity exposure when the rewards to bearing stock market risk appear above average and to lower exposure when the rewards appear below average. In so doing, we believe that an investor will likely increase the portfolio’s long-run return without increasing the average risk exposure. We caution, however, against an all-or-nothing timing strategy and other timing strategies that require sharp swings in the portfolio’s equity position. To illustrate why, suppose an individual investor who maintains constant portfolio weights of 50% stock-50% debt. The stock predictability literature encourages varying the equity weight around 50%. But how far should the investor allow the weights to vary? The answer requires balancing the benefits of diversification across assets against the benefits of market timing. Nobel-laureate Paul Samuelson (1990) recommends a modest range for the equity weights of perhaps 40% to 60% around the 50% long-run target weight. In essence, he argues that the benefits of diversifi- cation across assets are more certain than the benefits of market timing. Other economists would encourage a wider range. In summary, the stock predictability literature suggests that the individual investor might benefit from varying the equity weight around the long-run target weight based on market conditions, but the investor should probably exercise moderation in establishing the acceptable range of equity weights. Acknowledgments: We acknowledge the helpful comments of an anonymous referee, Frank L. Page, and other participants at the Academy of Financial Services 1992 annual meeting. NOTES 1. They conclude that nominal, real, and excess stock returns are highly autocorrelated, but slowly mean reverting. Excess returns (returns less Treasury bill returns) prove most useful for market timing purposes. See Fama and French (1988a). 2. Value Line forecasts began at the end-of-quarter 1968.1. The 1968.1 value of X forecasts 1968.2 and later returns. Value Line did not publish median appreciation potential for a few weeks surrounding the 1972.3 quarter. Thus RP has one missing observation. 3. The last observation for the dependent variable covers 1977.1-1978.2. The last observation for RP reflects the end-of-December 1976 value. 4. The regression results for 1968.2-1987.1 yield a critical value of 0.1037 (0.1819/1.7545). 5. These forecast horizons are set to maximize 1968.2-1978.2 predictive content. See Reichenstein and Rich (1992). 6. The small stock portfolio data came from Ibbotson Associates (1992). 7. For a discussion of the quadratic regression methodology see Treynor and Mazuy (1966) and Admati, Bhattacharya, Pffeider, and Ross (1986). For a discussion of the dummy variable regression methodology see Henriksson and Merton ( 198 1). Market Timing for the Individual Investor 43 ItJWJZRENCES Admati, Anat R., Sudipto Bhattacharya, Paul Pfleider, and Stephen A. Ross. 1986. “On Timing and Selectivity,” Journal ofFinance, 41:715-730. Berss, M. R. 1990. “Modem Portfolio Timing,” Forbes, December 2476-78. Campbell, John Y., and Robert J. Shiller. 1988. “Stock Prices, Earnings and Expected Dividends,” Journal of Finance, 43~661676. Fama, Eugene F. 1991. “Efficient Capital Markets: II,” Journal of Finance, 46:1575-1617. Fama, Eugene F., and Kenneth R. French. 1989. “Business Conditions and Expected Returns on Stocks and Bonds,” Journal of Financial Economics, 25:3-49. Fama, Eugene F., and Kenneth R. 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