The Performance of Tactical Asset Allocation

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The Performance of Tactical Asset AllocationAuthor(s): Eric J. WeigelSource: Financial Analysts Journal, Vol. 47, No. 5 (Sep. - Oct., 1991), pp. 63-70Published by: CFA InstituteStable URL: http://www.jstor.org/stable/4479472 .

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by Eric J. Weigel

The Performance of Tactical Asset Allocation

Tactical asset allocation (TAA) is the practice of altering asset class exposures in accordance with model-based risk-reward expectations. An analysis of 17 U.S. managers who use TAA to rebalance between large-cap stocks, long-term bonds and cash equivalents reveals that the vast majority provided positive timing ability at a statistically significant level. This holds for both managers' simulated and actual market returns.

The managers' market-timing skills, however, are inversely related to other investment skills. Managers good at timing broad market aggregates appear to be deficient in other investment activities. Transaction costs may partly explain this phenomenon, but the sheer magnitude of the return-diminishing non-market-timing term is too large to be entirely attributable to transaction costs.

Furthermore, the market-timing performances of the managers varied considerably over time. This tendency will probably persist in the future, as managers update their forecasting systems and capital market conditions change.

T HE DYNAMIC adjustment of a portfolio's investment weights across broad asset classes has become a hot topic since

the October 1987 market crash. Of course, investment managers have been altering exposures to different asset classes according to "gut" feeling or subjective risk/reward assess- ments for a long time. What is new now is the thorough application of the principles of mod- ern portfolio theory and econometrics to exam- ine quantitatively the expected risk/reward tradeoffs of major asset classes.

A driving force behind the rush to apply quantitative techniques to dynamic asset allocation strategies has been recent statistical evidence on the predictability of stock and bond market returns. While most of the analyses have focused on forecastability over long horizons, there is evidence that stock and bond market returns are also predictable (but at more modest levels) over shorter intervals.1

From a practical perspective, the result has been the "growth" of money management firms professing to be able to time the movements of

broad market aggregates. Their market-timing activities have been labeled "tactical asset allocation" (TAA). We estimate that there are cur- rently over $42 billion under management in TAA strategies.

Our study attempts to determine quantitatively the market-timing ability of a sample of 17 U.S. TAA managers. All are major firms man- aging substantial amounts of money. They all switch funds between large-company stocks, long-term bonds and cash equivalents-a so- called three-way market-timing strategy.

Because of the relatively short history of the strategy, hence the limited number of market observations, we formed two samples. One combined manager-simulated with actual market returns. The other used only actual market performance.

The measurement methodology we use is taken from Merton and Henriksson and has its origins in option pricing theory.2 The performance attribution methodology decomposes manager returns into three sources-returns to a static asset class mix, returns to market timing and returns to non-market-timing strategies such as security selection, stock index arbitrage 1. Footnotes appear at end of article.

FINANCIAL ANALYSTS JOURNAL / SEPTEMBER-OCTOBER 1991 O 63



and trading execution, all net of transaction costs. Our results led us to the following conclusions.

* In the aggregate, the sample of TAA managers showed significant positive market- timing skill. Timing ability was apparent in actual as well as in manager-simulated returns. This finding is in stark contrast to previous academic research on the timing ability of mutual funds, which has found no ability.3

* Like prior research, we found a negative relation between market-timing skill and other possible sources of ability.4 While transaction costs may partly explain this result, that explanation alone is insufficient. Moreover, return-benchmark misspecification does not appear to account fully for this relationship.

* Some managers exhibited considerable variation in market-timing skill over time. This may reflect either changing capital market conditions or modified investment-decision processes.

Measuring Market-Timing Skill An objective evaluation of market-timing skill is clearly important, given the substantial amount of money committed to TAA strategies, as well as the proliferation of managers claiming market-timing ability. The disaggregation of investment returns into sources of value is also important, as managers may engage simultaneously in a variety of strategies, including market timing, security selection, hedging and derivative- market arbitrage. The primary purpose of this article is to evaluate market-timing ability; we thus break investment returns down into market-timing skill and all other types of skill combined.

One would ideally want to assess timing skill by looking at all the managers' forecasts going back several years. Investment analysts, however, seldom have access to such data; instead, they rely on realized returns to assess investment skill. The drawback is that realized returns are subject to considerable noise, hence it is difficult to separate the contribution of skill from the effects of pure luck. A further complication is that, in order to estimate whether the manager has any skill at market timing, it is necessary to assume the return-generating process for all risky assets. Consequently, ex post tests of

market-timing skill, such as those we perform, are always joint-hypothesis tests of investment ability and the adequacy of the return-generating process.

Method The finance literature has focused a great deal

of attention on evaluating money manager performance. Most of the efforts have concentrated on the "microforecasting," or security selection abilities, of professional investment managers. In recent years, however, there has been an increasing interest in evaluating "macrofore- casting," or market-timing skill.

The methodology we use was originally applied to the case of a risk-free asset in conjunc- tion with a risky asset such as common stock.5 The methodology is, however, easily generalized to three-way market timing. In any case, a clairvoyant market timer will always pick the best performing asset class in his universe. A three-way market timer switching between stocks, bonds and cash equivalents with perfect forecasting skill would have an end-of-period return equal to:

Rp= max[Rf, Rb, RJ], (1)

where Rp corresponds to the return on the portfolio, Rf denotes the return to cash equivalents, Rb the return to long-term bonds and Rs the return on stock.

A clairvoyant three-way market timer will always invest 100 per cent of his or her portfolio in the best performing asset class. An equivalent pattern of returns could be obtained by engag- ing in either of two option strategies-holding a call option plus an investment in cash equivalents, or holding a put option plus an investment in stock.6 More precisely, the pattern of returns to a manager with perfect foresight is analogous to either of the following two strategies.

Call Option Plus Cash: A strategy of investing in cash equivalents and holding a call option on the better performing of the stock or bond market with a strike price equal to the return on cash. This type of call option is referred to as a look-back option, because one does not know the underlying asset (the return on stocks or bonds) until expiration. The portfolio's return consists of the return to cash equivalents plus the maximum of the excess return to stocks or bonds, should cash equivalents not turn out to be the best performing asset class:




Rp= Rf + max[RS-Rf, Rb-Rf, 01 (2)

Should cash equivalents turn out to be the best performing asset class, then the option holder would simply let the option expire unexercised. Should stocks outperform the other two asset classes, then the portfolio's return will equal the return to stocks (Rp = Rf + [Rs - Rf] = Rs). Similarly, the portfolio's return will be equal to the return to bonds should bonds perform best (Rp = Rf + [Rb - Rf] = Rb).

Put Option Plus Stock: A strategy of investing in the stock market and holding a put option on the stock market return with a strike price equal to the better performing of bonds or cash equivalents. Again, only at expiration does one know the appropriate strike price. Under this strategy, the portfolio's return will equal the return on stock plus the payoff to the put option:

Rp = Rs + max[Rf-Rs, Rb-Rs, 0]. (3)

The portfolio's return is always going to be equal to the return on the better performing asset class. Should stocks outperform bonds and cash equivalents, then the option will be left unexercised.

If the right options were available to market participants, anybody could replicate the returns to a market timer with perfect foresight

(before subtracting the cost of the options). The "fair" value of such options can be determined analytically.7 One can thus engage in a dynamic strategy designed to replicate the payoff (before transaction costs) to perfect market timing.8 The value added by successful market timers lies in providing the put or call option on the best performing asset class at less than "fair" market value.

Implementation of the Test Because of the difficulty of obtaining reliable ex ante manager forecast data, we used a regression-based approach (hereafter referred to as the HM approach) that uses a two-factor return- generating process to distill market-timing skill from other types of ability.9 The two factors are an equity index and a bond index. 10 Specifically:

RP - RF= ap + 13b[Rb - Rf] + /s[RS - Rf]

+ E p, (4)

where

atp = excess return, /3b = comovement with the bond market, Ps = comovement with the equity market

and ? p = random zero-mean error term.

The HM test estimates the fraction of the perfect-market-timing option provided by the investment managers.11 The parametric HM test adapted for the three-way market-timing case is a multiple regression that decomposes portfolio returns into three sources-returns to a normal static mix under specific market environments, returns to the look-back market-timing option and returns to all other strategies (security selection, hedging, index arbitrage, transaction costs, etc.)

The intent is to estimate the fraction of the perfect-market-timing option embedded in the manager's process over the time frame of the sample. The specific regression for a manager switching between stocks, bonds and cash is:

Rp - Rf = ap + 1b[Rb- Rf] + Js[Rs - Rf]

+ ypZ + Ep, (5)

where

Z = perfect-market-timing option or, max[R, - Rf, Rb - Rf, 01 and

,yP = fraction of the perfect-timing option embedded in the manager's process.

Glossary Dynamic Asset Allocation: A particular rebalanc-

ing strategy that seeks to replicate the payoff pattern of an option instrument. Portfolio insurance is the most notable example, as investment managers vary the allocation to risk-free and risky assets in a systematic way in order to replicate the payoff patterns of an option.

Tactical Asset Allocation: The process of allocat- ing an investment portfolio, using systematic decision rules, across a set of asset classes according to model-based estimates of risk and return. Most commonly, assets are allocated among an equity index, a long-term bond index and cash equivalents.

Market Observations: Refers to a situation where real money is invested as opposed to a simulated paper portfolio.

Performance Attribution: The practice of decom- posing a manager's return into the sources of performance. Most often, a manager's performance is traced to asset allocation decisions, security selection decisions, currency effects and residual (sometimes called interaction) effects.

FINANCIAL ANALYSTS JOURNAL / SEPTEMBER-OCTOBER 1991 El 65



The coefficient ap measures the return to non- market-timing activities net of transaction costs. Pb and P3. denote the static asset allocation to bonds and stocks when cash equivalents are, ex post, the best performing asset class. yp corresponds to the fraction of the perfect-market- timing option delivered by the manager in each time period. With no net short asset class sales, the value of yp is bounded by (+/-1) and can be interpreted as the ability to exchange the return on cash for a fraction of the better performing of stocks or long-term bonds.

Investment Performance of TAA Managers Our sample comprised 17 money managers. We combined manager-simulated and actual market returns and, to provide an unbiased picture of TAA, we also created a sample containing only the actual market performance figures. This sample contained data on 12 of the original 17 managers (those with at least four years of actual market history).

Data We used quarterly manager return series ob-

tained from the Frank Russell Company. All returns were net of transaction costs, but not of the manager's fee. Simulated manager returns were adjusted to account for transaction costs. 12 For stock, bond and cash returns, we used gross S&P 500 total returns, 20-year U.S. bond total returns and three-month Treasury bill returns, respectively. These return series correspond most closely to the benchmarks used by TAA managers.

The length of each manager's series of returns varied considerably. The longest simulated time series started in the first quarter of 1966. The longest actual return series started in the first quarter of 1980. The last data point for each series corresponds to the fourth quarter of 1989.

Table I presents the empirical distribution of the sample of simulated and actual manager returns. The first three moments of each manager's return distribution are shown. Figures within parentheses correspond to summary measures using actual observations only. For five managers (3, 4, 7, 10 and 16), we possessed only actual market observations.

Table I reveals that the majority of managers possess the right-skewed return distributions associated with successful market-timing activities. It is also interesting to note that those

managers with sufficient market history performed better than their simulated histories. The opposite held for standard deviations (with the exception of one manager). Given the small number of observations for most managers, especially in market situations, these summary measures are quite sensitive to outlier events.

Regression Results Equation (5) presented the ordinary-least-

squares (OLS) regression model used to estimate the asset class weights, the success of non-market-timing activities and the contribution of market-timing skill. It is important to analyze the regression error terms (the ep in Equation (5)) for any systematic patterns. The presence of a systematic pattern in the error terms indicates that the regression model is misspecified and, as a consequence, hypothesis tests may lead to erroneous conclusions.

A number of the manager equations exhibited a statistical problem called heteroscedasticity. That is, the error terms were systematically related to the values of the explanatory variables. Another common phenomenon in time series data is the presence of autocorrelation in the error terms. This means that successive values of the error terms are correlated with each other. Both these statistical problems affect the accuracy of any tests of the regression pa- rameters. To ensure accurate testing, we used a procedure called generalized least squares

Table I Basic Descriptive Statistics (quarterly returns)*

Standard Average Deviation

Manager Return (%) (%) Skewness Obs. 1 4.02 (2.28) 6.28 (0.19) 0.38 (-0.13) 76 (7) 2 4.00 (1.64) 7.19 (3.39) -0.13 (0.04) 48 (6) 3t 4.31 (4.31) 5.60 (5.60) 0.45 (0.45) 26 (26) 4t 4.94 (4.94) 5.93 (5.93) 0.29 (0.29) 32 (32) 5 3.83 (2.76) 5.57 (4.49) 0.83 (0.65) 96 (14) 6t 3.87 (4.30) 6.23 (5.91) 0.35 (0.24) 68 (24) 7t 4.49 (4.49) 6.20 (6.20) -0.02 (-0.02) 29 (29) 8 4.58 (3.06) 5.91 (2.22) 0.45 (0.36) 28 (10) 9t 4.64 (5.13) 6.27 (5.93) 0.23 (0.36) 36 (16)

10t 4.42 (4.42) 6.77 (6.77) 0.45 (0.45) 40 (40) 11t 3.90 (4.67) 6.70 (6.16) 0.53 (1.17) 80 (19) 12 4.09 (3.04) 5.48 (5.47) 0.48 (0.57) 36 (14) l3t 4.00 (4.15) 6.03 (5.77) 0.40 (0.63) 68 (19) 14t 4.50 (5.08) 5.48 (5.29) 0.76 (0.52) 88 (20) 15t 4.20 (4.51) 6.46 (5.88) 0.29 (0.24) 50 (23) 16t 4.34 (4.43) 6.58 (6.89) 0.21 (-0.06) 46 (16) 17t 3.88 (3.88) 5.20 (5.20) -0.63 (-0.63) 16 (16)

* Figures in parentheses correspond to real returns. t Manager is part of real-return sample.

FINANCIAL ANALYSTS JOURNAL / SEPTEMBER-OCTOBER 1991 r 66



Table II Market-Timing Results for Combined Sample*

Manager ap Pb s yp R2

1 -0.40 (0.40) 0.05 (0.07) 0.46 (0.09) 0.31 (0.13) 0.73 2 -0.08 (0.84) 0.10 (0.06) 0.78 (0.06) 0.04 (0.12) 0.89 3 0.49 (0.34) 0.05 (0.04) 0.48 (0.03) 0.30 (0.06) 0.96 4 0.31 (1.22) -0.02 (0.15) 0.42 (0.12) -0.24 (0.23) 0.60 5 -0.44 (0.29) 0.07 (0.05) 0.27 (0.05) 0.46 (0.09) 0.80 6 -0.52 (0.41) 0.18 (0.06) 0.38 (0.07) 0.34 (0.11) 0.82 7 -0.97 (0.39) 0.07 (0.05) 0.55 (0.04) 0.26 (0.07) 0.96 8 -1.81 (0.74) 0.10 (0. 09) 0.27 (0.07) 0.60 (0.14) 0.86 9 0.66 (0.53) 0.43 (0.08) 0.51 (0.08) 0.03 (0.13) 0.88

10 -1.87 (1.15) 0.05 (0.13) 0.23 (0.15) 0.55 (0.24) 0.54 11 -1.01 (0.52) 0.23 (0.08) 0.25 (0.08) 0.49 (0.13) 0.74 12 -1.45 (0.51) -0.14 (0.06) 0.41 (0.05) 0.47 (0.10) 0.87 13 -1.00 (0.49) 0.10 (0.07) 0.26 (0.08) 0.49 (0.12) 0.76 14 -0.68 (0.37) 0.08 (0.05) 0.13 (0.06) 0.63 (0.10) 0.82 15 -0.35 (0.32) 0.29 (0.06) 0.53 (0.08) 0.21 (0.11) 0.86 16 -0.15 (0.23) 0.39 (0.05) 0.47 (0.07) 0.16 (0.09) 0.90 17 0.23 (0.34) 0.17 (0.04) 0.51 (0.03) 0.04 (0.05) 0.97 Average -0.53 0.13 0.40 0.30 0.82

* Figures in parentheses correspond to standard errors.

(GLS) to correct for both these statistical problems. 13

Table II shows the regression estimates for the combined simulated and market sample. Table III aggregates the individual manager results with respect to significance level and signs on the market timing (yp) and non-market-timing (ap) coefficients. Market timing skill and non- market-timing ability are evaluated by one- sided and a two-sided test statistics, respectively. In evaluating market-timing skill, we were interested in testing whether the yp term was greater than zero, which would indicate market-timing skill. For non-market-timing skill, ap, we tested whether the estimate was statistically different from zero.

In the aggregate, our TAA managers exhibit considerable skill at market timing. They delivered an average fraction of 30/100 of the perfect- market-timing option. Investors benefited from the manager's timing skills by obtaining the

equivalent of 0.30 options for free. In addition, for over three-fourths of the managers, we failed to reject the hypothesis (at the 95 per cent confidence level) that the manager's investment process contained no market-timing skill. 14

Only one manager out of 17 showed perverse (negative) timing skill; from a statistical point of view, however, the ap estimate was not reliably different from zero.

The results also show a negative correlation between estimates of the market-timing skill coefficient and the intercept term, implying that managers that are good at market timing are paying for this skill in the form of negative returns to non-market-timing strategies. The average estimate for the intercept term is -0.53 per cent per quarter. Only one of the four managers that exhibited positive intercept terms also showed statistically significant market- timing skill (manager 3). The rest showed negative intercepts; five had results that are reliably different from zero.

While our regression format does not allow us to partition the intercept term into finer subdi- visions, several factors may be causing this negative relation between market-timing skill and non-market-timing returns. The most obvi- ous explanation is transaction costs. Even in the absence of any type of non-market-timing activities, a manager with perfect forecasting skill will incur transaction costs in rebalancing its portfolios, resulting in a negative intercept term. But the magnitude of the intercept terms for our sample of TAA managers is too large for

Table III Market-Timing Aggregate Results for Combined Sample by Significance Level

Type of Skill Coefficient 1% 5% 10% 15% Positive Market 16 10 3 0 0

Timing* Negative Market 1 0 0 0 0

Timing Positive Interceptt 4 0 0 0 0 Negative Intercept 13 1 4 1 2 Total Managers 17

* One-sided test. Two-sided test.




Table IV Market-Timing Results for Real Sample*

Manager ap Pb PS yp R2

3 0.49 (0.34) 0.05 (0.04) 0.48 (0.03) 0.30 (0.06) 0.96 4 0.31 (1.22) -0.02 (0.15) 0.42 (0.12) -0.24 (0.23) 0.60 6 -0.39 (0.44) 0.24 (0.04) 0.61 (0.05) 0.15 (0.08) 0.95 7 -0.97 (0.39) 0.07 (0.05) 0.55 (0.04) 0.26 (0.07) 0.96 9 0.39 (0.41) 0.48 (0.03) 0.33 (0.05) 0.20 (0.07) 0.88

10 -1.87 (1.15) 0.05 (0.13) 0.23 (0.15) 0.55 (0.24) 0.54 11 -2.69 (0.99) 0.03 (0.08) 0.23 (0.12) 0.76 (0.17) 0.83 13 -1.84 (0.92) 0.01 (0.08) 0.46 (0.11) 0.48 (0.16) 0.83 14 -1.94 (0.81) 0.06 (0.07) 0.07 (0.09) 0.74 (0.14) 0.84 15 -0.53 (0.46) 0.22 (0.04) 0.60 (0.05) 0.18 (0.08) 0.93 16 -0.58 (0.82) -0.18 (0.07) 0.87 (0.11) 0.49 (0.15) 0.75 17 0.23 (0.34) 0.17 (0.04) 0.51 (0.03) 0.04 (0.05) 0.97 Average -0.78 0.25 0.29 0.32 0.84

* Figures in parentheses correspond to standard errors.

transaction costs to be the sole culprit. Other return-diminishing factors must be at work.

Possible contributors are hedging activities or option-replication activities undertaken by managers to reduce the volatility of their portfolios and other forms of insurance-type strategies. Several managers use the futures market, not only to alter their asset class exposures, but also to arbitrage with respect to the spot markets. If the futures contract is unfavorably mispriced, or the manager shows poor skill at arbitrage, this may account for part of the negative alpha returns.

Another possible explanation may be benchmark misspecification. Managers could track asset class indexes other than those used in this study. We experimented with a variety of addi- tional stock and bond indexes, however, and the results were qualitatively indistinguishable from those reported here. Moreover, the results of two internal Frank Russell Company studies on U.S. active equity and fixed income managers did not support the benchmark misspecification explanation.

On a theoretical level, the negative relation between the non-market-timing term and the market-timing coefficient could reflect the omis- sion of relevant factors in the assumed return- generating process. Previous studies have noted a negative relation between market-timing skill and other forms of ability, but no consensus has emerged as to the cause of this phenomenon.15

When we restricted our analysis to actual market observations, we reached similar conclusions. Tables IV and V give the individuAal manager and summarized results, respectively. In the aggregate, the average fraction of the

perfect-market-timing option embedded in the managers' investment process increased to 0.32 (out of a maximum of 1.00), but the average intercept term declined to -0.78 per cent per quarter. Eleven of 12 managers in this return sample showed positive market-timing skill. We can reject the hypothesis of no detectable timing skill for 10 of them.

Again, with the exception of two managers, our results indicate negative non-market-timing ability. Because of the small number of actual observations available, these results are sensitive to outlier events.

Variation in Timing Skill Over Time Under the regression format specified in Equa- tion (5), the market-timing coefficient is assumed to be fixed over the sample interval. Under changing capital market conditions, this assumption may not be valid. In addition, TAA managers are constantly updating their predic- tive models. Consequently, one would expect variation over time in managers' market-timing abilities.

Table V Market-Timing Aggregate Results for Real Sam- ple by Significance Level

Type of Skill Coefficient 1% 5% 10% 15% Positive Market 11 7 3 0 0

Timing* Negative Market 1 0 0 0 0

Timing Positive Interceptt 2 0 0 0 0 Negative Intercept 10 1 2 1 0 Total Managers 12

* One-sided test. Two-sided test.




A regression format incorporating such time variation in the coefficients would be a useful way to model changing sensitivity without ex- plicitly including the variables causing such variation. As our study focused on measuring market-timing ability, we only explored variation in the fraction of the "free" option delivered over time (the yep). To model the variation of the market-timing coefficient over time, we used a random walk. In this model, the market- timing coefficient, yp, varies over time in a random fashion, without reverting to a fixed value.16 In terms of the regression format, we assume:

yp(t) = yp(t - 1) + 77p(t), (6)

where the timing coefficient, yp(t), is allowed to change permanently over the course of the historical time period without reverting to a fixed mean, and the error term, 71p(t), has an average value of zero and satisfies the usual ordinary-least-squares assumptions. Under the fixed-parameter specification, the error term, rqp(t), is assumed to be time-invariant or, equiv- alently, its variance is set at zero.

Table VI summarizes the extent of the variation of the market-timing coefficient for each manager, using a combination of actual and simulated returns. Ideally, an investment manager would exhibit consistently high coefficients, without any major up or down movements. In practice, one would expect variability in the market-timing performance of any manager. The standard deviations of the coefficient

estimates provide summary measures of variability in market-timing skills.

The range of outcomes for most managers is quite wide; in three cases, we observe negative lower bounds for the timing coefficient, indicat- ing very poor timing skill. The standard deviation measures the fluctuation in the market- timing coefficient around its mean value and confirms that most managers exhibited substantial period-to-period differences in market- timing skill.

Table VII presents the results for the 12 managers in the actual-return sample. The pattern that emerges is quite similar to that in Table VI. Only one manager had a negative lower bound.

For the seven managers with sufficient simulated and actual data observations, a compari- son of the results in Tables VI and VII does not yield any firm conclusions. Five exhibited higher average market-timing coefficients based on the actual results and, in general, the variability of their coefficients was lower.

Conclusions Our results indicate that U.S. TAA managers displayed market-timing skill over the sample period. Whether this success will continue in the future is hard to assess. As with many new strategies, the innovators in the field are likely to reap most of the rewards. As the field be- comes more crowded, and competition increases, pricing inefficiencies are likely to disap- pear more quickly. As the popularity of TAA strategies increases, one might expect forecasts of asset class returns and associated risks to bear fewer rewards. U

Table VI Time-Varying Market-Timing Coefficients for Combined Sample

Average Standard Manager Coefficient Deviation Maximum Minimum

1 0.26 0.17 0.56 -0.15 2 -0.05 0.29 0.31 -1.00 3 0.20 0.04 0.32 0.13 4 0.18 0.12 0.41 0.02 5 0.43 0.08 0.56 0.22 6 0.32 0.04 0.39 0.25 7 0.24 0.03 0.27 0.16 8 0.59 0.00 0.59 0.59 9 0.02 0.00 0.02 0.02

10 0.46 0.13 0.65 0.23 11 0.49 0.05 0.55 0.36 12 0.46 0.11 0.64 0.30 13 0.44 0.13 0.61 0.11 14 0.64 0.03 0.68 0.57 15 0.16 0.12 0.31 -0.04 16 0.12 0.04 0.17 0.03 17 0.03 0.02 0.05 0.00

Table VII Time-Varying Market-Timing Coefficients for Real Sample

Average Standard Manager Coefficient Deviation Maximum Minimum

3 0.20 0.04 0.32 0.13 4 0.18 0.12 0.41 0.02 6 0.18 0.03 0.22 0.09 7 0.24 0.03 0.27 0.16 9 0.16 0.06 0.22 0.05

11 0.50 0.22 0.79 -0.07 13 0.42 0.08 0.52 0.29 14 0.74 0.00 0.75 0.74 15 0.18 0.00 0.18 0.18 16 0.56 0.00 0.56 0.56 17 0.03 0.02 0.05 0.00

Footnotes 1. For evidence of forecastability at longer horizons,

see three papers by E. F. Fama and K. R. French:




"Permanent and Transitory Components of Stock Prices," Journal of Political Economy 96 (1987), pp. 246-73; "Dividend Yields and Expected Stock Returns," Journal of Financial Economics 22 (1988), pp. 3-25; and "Business Conditions and Ex- pected Returns on Stocks and Bonds," Journal of Financial Economics 25 (1989), pp. 23-49. Also J. A. Poterba and L. M. Summers, "Mean Reversion in Stock Prices: Evidence and Implications," Journal of Financial Economics 22 (1988), pp. 27-59. For evidence of forecastability at short horizons, see R. D. Arnott and J. N. von Germeten, "System- atic Asset Allocation," Financial Analysts Journal, November/December 1983; W. Breen, R. L. Glos- ten and R. Jagannathan, "Economic Significance of Predictable Variations in Stock Index Returns," Journal of Finance, December 1989; J. Y. Campbell, "Stock Returns and the Term Structure," Journal of Financial Economics 18 (1987), pp. 373-99; J. Conrad and G. Kaul, "Mean Reversion in Short- Horizon Expected Returns," Review of Financial Studies 2 (1989), pp. 22540; and D. B. Keim and R. F. Stambaugh, "Predicting Returns in the Stock and Bond Markets," Journal of Financial Economics 17, pp. 357-90.

2. R. C. Merton, "On Market Timing and Invest- ment Performance: An Equilibrium Theory of Value for Market Forecasts," Journal of Business, July 1981, and R. D. Henriksson and R. C. Merton, "On Market Timing and Investment Performance: Statistical Procedures for Evaluat- ing Forecasting Skills," Journal of Business, Octo- ber 1981.

3. See E. C. Chang and W. G. Lewellen, "Market Timing and Mutual Fund Performance," Journal of Business, January 1984; R. D. Henriksson, "Market Timing and Mutual Fund Performance: An Empirical Investigation," Journal of Business, January 1984; M. C. Jensen, "The Performance of Mutual Funds in the Period 1945-1964," Journal of Finance, May 1968; S. F. Kon and F. Jen, "The Investment Performance of Mutual Funds: An Empirical Investigation of Timing, Selectivity, and Market Efficiency," Journal of Business, April 1979; and S. F. Kon, "The Market Timing Perfor- mance of Mutual Fund Managers," Journal of Business, July 1983.

4. See Henriksson, "Market Timing and Mutual Fund Performance," op. cit., and Chang and Lewellen, "Market Timing and Mutual Fund Per- formance," op. cit.

5. The analysis by Merton and Henriksson applied to the case of a risk-free asset such as T-bills and a risky asset such as stock.

6. One of the fundamental arbitrage relations in

option pricing is that of "put-call" parity, which states that an investment in an underlying security plus a put option on the security will equal an investment in a risk-free discount bond and a call option on the security. The terms to maturity and the strike prices of both options have to be the same, and the relationship applies strictly to European options.

7. The analytical solution for the "fair" value of the perfect-market-timing term is in R. M. Stulz, "Options on the Minimum or the Maximum of Two Risky Assets," Journal of Financial Economics 10 (1982), pp. 161-85. Computationally, the main difficulty in solving the value of the option is in evaluating a bivariate normal density function.

8. For an application, see J. A. Tilley and G. D. Latainer, "A Synthetic Option Framework for Asset Allocation," Financial Analysts Journal, May/ June 1985.

9. There is also a nonparametric test for detecting market-timing skill, but it requires the ex ante forecasts of the manager.

10. The return-generating process used here is analogous to that in F. Evnine and R. D. Henriksson, "Asset Allocation and Options," Journal of Portfo- lio Management, Fall 1987.

11. The measure of market-timing skill consists of the fraction of the perfect-market-timing option embedded in the manager's investment process. One full option is necessary for delivering the perfect-market-timing return. Hence, under real- world conditions, it is highly unlikely that managers will have estimates close to one.

12. The adjustment is performed by the managers themselves, not by the author.

13. The procedure for correcting for heteroscedasticity follows the approach of Henriksson and Mer- ton adapted to the case of the three-way market timer. To correct for the autocorrelation in the error terms, we used the Cochrane-Orcutt procedure. See G. S. Maddala, Econometrics, Chapter 12 (New York: McGraw Hill, 1977) for a more detailed explanation.

14. A 95 per cent confidence level means that there is only 5 per cent chance of concluding that the hypothesis of detectable market-timing skill is accepted by chance.

15. Henriksson, "Market Timing and Mutual Fund Performance," op. cit., and Chang and Lewellen, "Market Timing and Mutual Fund Performance," op. cit.

16. G. S. Maddala, Econometrics, Chapter 17, op. cit.




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The Performance of Tactical Asset Allocation