Conditional asset pricing model

The CAPM of Sharpe and Lintner is an unconditional model, which assumes that the market beta is constant. Their model uses average return and beta risk over the testing period, which neglects to consider variations in the financial market during the testing period. Ferson and Warther (1996) use a simple example to support their argument that

the conditional model is better than the unconditional. The authors assume that the market has a bull and bear state, with each having an equal chance of occurring. They also assume a 20 percent expected return for the S&P 500 in a bull market, and a 10 percent return in a bear market. The risk free return to cash is 5 percent if a mutual fund holds the S&P 500 in a bull and cash in a bear market. For the conditional on a bull market, the beta is 1, while the expected return is 20 percent (the same as with the S&P 500 expected return) and the alpha is zero. Similarly, the alpha of the conditional on a bear market is found to be zero. However, incorrect performance is recorded for the unconditional model, for which the beta is 0.612 and alpha is 0.015. As such, and unlike with the conditional model, the unconditional model reports positive abnormal performance.

There is much literature concerning conditional performance evaluation (CPE). Both risk and market premiums change over time according to the “economic state”, which is measured using public information variables. The earliest CPE studies are from Chen and Knez (1996), Ferson and Schadt (1996) and Ferson and Warther (1996), who all record significant statistic and economic performance under the conditional approach. Hansen and Singleton (1982) find that the conditional CAPM works well when compared with the unconditional CAPM (the market beta is used as the time variance for the conditional CAPM). Merton (1980) notes that, over time, economic conditions affect both expected market excess return and related volatility.

Campbell (1987) finds that time variations in expected stock and bond returns can be explained by using term-structure variables. Likewise, Fama and French (1989) find that expected stock returns and long-term bond returns can be affected by business-cycle patterns and business conditions. Strong economic conditions result in lower expected returns, while a weak economic environment has higher expected returns to induce investment from consumption.

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Ferson and Schadt (1996) find that the unconditional expected returns used in traditional performance methods are unable to observe changes in expected returns and risk over time, and therefore argue that traditional methods are unreliable. The authors duly provide a conditional method, which incorporates instrument variables for controlling time variations that can capture more accurate performance. Time-varying conditional betas are recorded under the conditional model, and the authors report that risk exposure changes according to the availability of public information. In the traditional model, more negative Jensen’s alphas are found than positive, thus indicating poor average performance (Jensen, 1968; and Elton et al, 1992). In contrast, the conditional model provides neutral performance, with the mean of the alphas being almost zero. The evaluation of conditional performance is consistent with the assumption of a semi-strong form of market efficiency. This solves the problem of the dynamic behaviour of returns, something which traditional performance cannot control. Furthermore, the authors also find short term interest rates to be the most important conditional variables (compared with other conditional variables used in the same study).

Several studies argue that the conditional versions of simple asset pricing models are better than traditional models when explaining the cross-section return (including those by Chan and Chen (1988) and Jagannathan and Wang (1996)). Zheng (1999) and Becker et al (1999) both find that mutual funds perform better with conditional alphas than with unconditional alphas. However, Ghysels (1998) and Harvey (2001) find that different instrument variables affect the performance of loading factors.

Furthermore, Fama and French (1997) find estimations of industry cost of equity to be imprecise, with both the CAPM and Fama-French three-factor models returning standard errors of more than 3 percent each year. The same study also finds industry risk loading to vary significantly over time under the CAPM and three-factor models. In order to reduce the volatility of risk loadings, the study employs two different methods. The first method employs rolling regressions by using monthly returns from the previous five years to run the rolling CAPM and three-factor models. As the authors explain: “The idea is that, if the true CAPM and three-factor slopes for industries vary through time, the

time-series variation of the rolling-regression slopes should exceed that implied by estimation error”. The second method is that of conditional regression, which uses instruments to tract risk in order to avoid the weaknesses of unconditional regressions (such as with the CAPM and three-factor models). Both size and book-to-market ratio are used as proxies for the sensitivity of SMB and HML. In the case that one industry is smaller, the SMB loading of that industry is found to increase, while both the book-to- market ratio and HML loading increase if the industry is suffering. With reference to the conditional regression, the authors state that: “Thus, we try to track time-varying sensitivities to SMB and HML with conditional regressions in which an industry’s SMB and HML slopes vary with the average size and book-to-market-equity of firms in the industry”. Finally, they find that the average R square increases when the Ln(ME)SMB and Ln(BE/ME)HML variables are added to the three-factor model. After comparing the performance of the full-period constant-slope regression, conditional regressions and rolling regressions, the authors find that, for a one-month forecast, both the full-period constant-slope regression and rolling regression provide similarly precise forecasts (however, these are still slightly less precise than with the conditional regression). For the long-term forecasts, both the full-period constant-slope regression and conditional regression provide similar forecasts (which are slightly better than the rolling regression for forecasts of more than two years).

3.2.3 Comparison of equally-weighted (EW) and value-weighted (VW) returns