ترجیحات و باورهای سرمایه گذار در بازار سهام: تجزیه و تحلیل تسلط تصادفی

This paper analyzes whether the market portfolio is efficiently related to benchmark portfolios formed on size, value, momentum and reversal with various utility theories by using stochastic dominance criteria. The results support the prospect theory including assumption of loss aversion at monthly and yearly horizons, which indicates the market utility is S-shaped, and steeper for losses than for gains. And, the findings do not provide convincing evidence for positive skewness preference. Therefore, it should probe into asset pricing model and financial puzzles by prospect theory preferences. It may thus be difficult for the market to benefit from the asset through its features on skewness or other higher order central moment. We also develop several bootstrap procedures with favorable properties in statistical size and power for testing stochastic dominance efficiency.

The aggregate of investor preferences and beliefs in stock market is the starting point of economics study and finance research, and is a much-debated topic in financial economics. Several asset pricing anomalies suggest that the market portfolio is significantly mean–variance (MV) inefficient relative to the stock portfolios formed on variables such as market capitalization (size), book-to-mark equity ratio (value), price momentum, and price reversal.1 So it should extend or change traditional quadratic form utility to understand the market. Moreover, various risk preferences could be investigated with the pricing model by introducing alternative classes of utilities. This paper uses the implied risk preferences to test three popular and competing utility theories. The first theory is the traditional expected utility theory with the assumption of global risk averse, that is, the utility function is everywhere concave. The second theory is the prospect theory (PT) of Kahneman and Tversky (1979), which assumes an S-shaped utility function that is risk seeking for losses and risk averse for gains. The third theory, named Markowitz utility theory stemming from Markowitz (1952) and Thaler and Johnson (1990), indicates that is contrary to the prospect theory with a reverse S-shaped utility, that is, investors may risk averse for losses and risk seeking for gains. The paper adopts the stochastic dominance (SD) method, introduced by Hadar and Russell (1969), Hanoch and Levy (1969), to identify aggregate risk preferences. It analyzes whether the market portfolio is SD efficient relative to benchmark portfolios formed on size, value, momentum and reversal with various preferences considering anomalies. It finds the bootstrap method of Post and Levy (2005) may easily commit Type I error (rejecting the null when it is true). Therefore, we develop two bootstrap testing procedures for SD efficiency. One procedure adjusts the bootstrap statistic of Post and Levy (2005) corresponding to various significance levels. Another procedure shifts the entire distance between the original estimator of statistic and zero, which is an extended implementation of the method of Linton et al. (2005) for a critical estimation with full-sample bootstrap. However, there is a boundary effect, which may result in inconsistency in the bootstrap statistics. Hence, we also introduce the smoothed bootstrap statistics following the work of Simar and Wilson (1998). The simulation shows the statistics of the new bootstrap procedures have favorable statistical properties for both size and power with large sample size. Even with small sample size, the statistics also have satisfactory statistical size. Moreover, the paper further imposes a restriction of three order derivative on utility function to examine skewness preference. Many empirical evidences imply that the perception of risk is more complex than variance. The phenomena of positive skewness2 and kurtosis preference3 have attracted much attention among scholars. Accounting for the kind of preference, we adopt the SD criterion of Wong and Chan (2008) and extend the empirical examination for the assumption of positive skewness preference. The paper also tests the SD conditions that catch an important aspect of PT, namely, loss aversion as suggested by Benartzi and Thaler, 1995 and Benartzi and Thaler, 1999. Baucells and Heukamp (2006) proposed that the loss aversion play a central role in behavioral decision research in PT. It captures the psychological intuition that losses loom larger than gains, and is a very important explanation for many economic and financial puzzles.4 We incorporate the feature in this study with preference condition introduced by Wakker and Tversky (1993) into the SD criterion of S-shaped utility to analyze investor behavior. The paper investigates the market efficient further not only on monthly data but also on yearly data. Hansson and Persson (2000) considered the recommendation that investors with long investment horizons tilt their portfolios toward stocks is commonplace and an investor can gain from time diversification. Recently, Levy and Duchin (2004) thought that the investors are diverse at their planned investment horizons and the optimal investment decision of an investor may change at different horizons. The study on yearly data will discover the effect of longer horizon on asset equilibrium price and aggregate preferences. The remainder of this paper is organized as follows. Section 2 reviews methods of empirical study on aggregate preferences and the method of SD. Section 3 introduces the SD efficiency criteria. Section 4 investigates the test statistics on bootstrap methodology with newly proposed test procedures. Section 5 presents empirical findings of the aggregate investor preferences of US stock market. Finally, Section 6 gives the conclusions.

The bootstrap procedures of smoothed LAMB, smoothed EDB and standard EDB are proven to be useful for analyzing the SD efficiency. The three statistics also own the best statistical properties for both size and power with large sample size. Even with small sample size, they still have satisfactory statistical size. But, the bootstrap tests of MB may easily commit the Type I error. Many asset pricing anomalies are hard to understand in the context of the expected utility paradigm and globally risk-aversion preference. Under a very general framework of risk preference, this paper investigates the aggregate investor preferences and beliefs of the US stock market by examining enduring puzzles in finance: market size, value, price momentum, and price reversal effects in stock returns. It can be seen that the inferences about the aggregate preferences in our study are not heavily affected by the exact test procedure. Moreover, at monthly and yearly horizon, the findings are consistent. Our results reject SSD efficiency of the market portfolio. We should thus pay particular attention to non-expected utility theories and risk seeking preference for further research. Moreover, our results reject the criterion of MSD and on the contrary, accept the criterion of PSD. Our examination also accepts loss aversion-a vital assumption in the framework of the PT. Therefore, the market is efficient and the prospect theory may be a more prominent non-expected utility theory. It also suggests that the aggregate utility function of the representative investor is in line with the PT, who will adopt different risk attitudes when they face various prospects. The aggregate of investors' preferences is not globally risk-aversion, but risk-aversion for gains and risk-seeking for losses, and more sensitive to losses, i.e., the utility is S-shaped, and steeper for losses than for gains. Therefore, it should probe into asset pricing model and financial anomalies by S-shaped and loss aversion preferences. In fact, the study of Barberis and Huang (2008) show the PT can exactly produce the CAPM formula. Thus, the S-shape risk preference may be suffices to explain many asset pricing anomalies. However, our examination has not convincing evidence for the positive skewness preference. Furthermore, the results also can reject kurtosis preference and higher order preferences. Hence, it may be difficult in the market to benefit from the asset through its features on skewness, kurtosis, or other higher order central moments. It should be noted that our results can only illustrate the general laws of the market, and reveal the aggregate investor preferences of the market rather than the preferences for individuals. Our study can neither decline the expected utility preference, Markowitz utility preference, and MV preference for individual. Our findings also cannot reject the skewness preference, kurtosis preference or higher order preferences for individual. For the researchers in favor of the expected utility preference, Markowitz utility preference, MV preference and high order preferences, our examination may provide a stimulus for further research for differences between the aggregate behavior characteristics and individual behavior features. In the future, it should attach importance to studies on heterogeneous components and emergent behavior, which may result in disappearance of individual preferences in aggregate view. It is still doubtful whether the results are trustworthy because the SD test assumes that return observations are serially identical and independent distributed (IID). But, Sharpe (2007) showed that an investor who holds the market portfolio will satisfy an equilibrium equation31 in the static-state by the analysis of marginal utility and state prices. The equation is consistent with the first-order condition for optimality of our test. Therefore, our results may not be biased by the IID assumption. In addition, there are reasons to doubt the reliability of the findings because we only test with ex-post parameters. Recently, Levy and Roll (2010) found slight variations in parameters, well within estimation error bounds, suffice to make the market proxy MV efficient. Their findings also suggested ex-ante MV efficiency is consistent with the observed parameters. How can our research be reconciled with their study? Firstly, their results mainly infer the efficiency based on the parameters that are “closest” to their observed sample rather than the parameters about the population. Levy and Roll (2010) also considered their research does not constitute a proof of the empirical validity of the CAPM, but it shows that the model cannot be rejected. Secondly, our SD method is testing for the efficiency of a given portfolio with respect to the utility with all possible parameters for one type preference instead of a utility with specific parameters only. Thirdly, the bootstrap procedures inference the efficient statistics in view of the bias with sampling variation, and it is encouraging to see that our results, including descriptive statistics, SD statistics of full sample, and SD statistics of rolling window on different horizon, support each other. Hence, we consider the influence of parameters on our systematic results should be limited.