بهینه سازی سبد سرمایه گذاری تحت ناهنجاری های قیمت گذاری دارایی

Fama and French (1993) find that the SMB and the HML factors explain much of the cross-section stock returns that are unexplained by the CAPM, whereas Daniel and Titman (1997) show that it is the characteristics of the stocks that are responsible rather than the factors. But both arguments are largely based only on expected return comparisons, and little is known about how important each of the two explanations matters to an investor's investment decisions in general and portfolio optimization in particular. In this paper, we show that a mean-variance maximizing investor who exploits the asset pricing anomaly of the CAPM can achieve substantial economic gain than simply holding the market index. Indeed, using monthly Japanese data on the first 50 largest stocks over the period 1980–1997, we find the optimized portfolio constructed from characteristics-based model is the best performing one and has monthly returns more than 0.81 percent (10.16 percent annualized) over the Nikkei 225 index with no greater risk.

There is a growing literature on the major asset pricing anomaly that the realized cross-section stock returns are not consistent with the predictions of the basic capital asset pricing model (CAPM) of Sharpe (1964) and Lintner (1965). Among the competing explanations, Fama and French (1993) find that the anomaly is largely driven by the SMB and the HML portfolios (two zero net investments in which the first is long in small firms and short large ones and the second is long in high book-to-market firms and short low book-to-market ones), whereas Daniel and Titman (1997) show that it is the characteristics of the stocks that are responsible. But both arguments are largely based on expected return comparisons, and little is known about how important each of the two explanations matters to an investor's investment decisions in general and portfolio optimization in particular. Intuitively, if an investor can do much better in terms of profit making by incorporating the true nature of the anomaly into his investment decision, an economic value for the anomaly will be apparent. In other words, if the SMB and the HML portfolios were the true driving sources for the anomaly, it is likely that the investor can do better in his investment by using the SMB and the HML portfolios than by using the characteristics of the stocks. On the other hand, if all the claimed features of an anomaly matter little in both the investor's portfolio decision and the associated results, one may take a somewhat extreme view of Black (1993) that “most of the so-called anomalies that have plagued the literature on investments seems likely to be the result of data-mining.” Hence, a study on how an investor may utilize an anomaly not only provides insights on the economic significance of the anomaly, but also help to identify competing explanations for the anomaly. In this paper, we show how a mean-variance maximizing investor can exploit the asset pricing anomaly of the CAPM to achieve substantial economic gain than simply holding the market index. While many well-known asset pricing anomalies1 may be analyzed in an analogous utility maximizing framework, we choose to study the CAPM anomaly due to its close relation with all the basic asset pricing models and its wide applications in both investments and corporate capital budgeting decisions. The assumption of a mean-variance investor is to simplify the analysis, and the case of a more general utility function may be solved numerically from the first order conditions as reviewed by Duffie (1988). In assessing the economic importance of the anomaly, we analyze two scenarios. The first is where the investor makes his investment decision based on the CAPM. Following Markowitz (1952), Sharpe (1964) and Lintner (1965), it is well-known that the investor should hold a portfolio of a riskless investment and the market portfolio. In the second scenario, the investor exploits the anomaly by making a dynamic portfolio choice decision based on the time-varying investment opportunity set. More specifically, each of the earlier explanations for the anomaly provides a unique way for the investor at each time t to forecast the means and variances of the security returns, and the forecasts are then used to form his optimal portfolio at time t. All mean-variance maximizing investors who exploit the asset pricing anomaly will hold only portfolios of a riskless investment, and the weight on the optimized portfolio depends on their degrees of risk aversion. Hence, it will suffice to show that the optimized portfolio outperforms the market index substantially in order to prove that the anomaly makes a significant economic difference in investors’ investments. Our approach for portfolio optimization and assessing asset pricing anomaly is a special case of the general utility maximizing approach for evaluating the economic importance of a hypothesis which has gained popularity recently. For example, Kandel and Stambaugh (1996) find that a statistically insignificant stock return predictability can actually make an economically significant contribution into an investor's asset allocation decision. But their studies are different from ours as they examine the predictability of the market index and its relation to asset allocation decision. In contrast, we analyze the cross-section of stock return anomaly and its implications for an investor's mean-variance portfolio choice. Another related study is Brennan and Xia (2001) who show how the SMB and the HML factors translate into forecasts for the drift of a diffusion with known variances and how a CRRA investor can use this to improve his asset allocation.2 In contrast, our analysis focuses on portfolio choices with both unknown means and variances, but restricts the investor's utility be of the quadratic type. In terms of variance forecasting methodology, our procedures reply on similar intuitive approaches of Chan et al. (1999). While they are solely interested in the second moments, we are also interested in forecasting the first moments as well in forming optimal portfolios. The rest of the paper is organized as follows. Section 2 describes the methodology and the models, and explains how various factors and portfolios are constructed. Section 3 describes the data and reports the main results. Section 4 examines further on the empirical results. The last section concludes the paper.

This paper takes a new approach to examine the economic importance of asset-pricing models from an investor's portfolio optimization perspective. In contrast to the usual cross-sectional analysis of stock returns which focuses on the comparison of expected returns, our approach examines also the variances and covariances as well as their joint impact on portfolio performance. This approach can be regarded as a hybrid of the realistic practical optimization procedure of Chan et al. (1999) (which focuses on forecasting covariances only) with the emerging literature, such as Kandel and Stambaugh (1996), Brennan and Xia (2001), and Pástor and Stambaugh (2000), on analyzing investment choices from the perspective of a non-representative agent. Our empirical results shed some light on whether the factor or characteristics based models are better at explaining the cross-section of stock returns. Using Japanese data over the period 1980–1997, we find that an investor who believes Fama and French (1993) factor model would have obtained a much higher return than holding the market index, but also with a much higher risk. In contrast, if the investor optimizes his portfolio according to the characteristics-based model of Daniel and Titman (1997) and Daniel et al. (2001), and if the first 50 largest stocks were used, he would have had a monthly return of more than 0.81 percent (10.16 percent annualized) over the Nikkei 225 index with no greater risk. Moreover, this overwhelmingly better performance is also robust to various formations of the portfolio and various estimators of the covariances. In short, our findings seem to support the results of Daniel et al. (2001) in a different direction that, like the US evidence, the Japanese market is better described by using the characteristic-based models than by using the factor models.