Evaluation of the ability to explain unfavorable risk criteria in Tehran Stock Exchange

Master's thesis in the field of financial management

Abstract

In the capital asset pricing model (CAPM), systematic risk or beta is the only factor that explains the difference in asset returns. Beta, as a measure of systematic risk, is the result of an equilibrium state in which investors seek to maximize their utility function based on two parameters, the mean and variance of returns. Return variance as a risk measure is in conflict with the common definition of risk - exposure to risk or potential and calculable loss of investment - for at least the following two reasons. First, return variance can be used as a risk measure when the distribution of asset returns is normal. Second, they do not consider deviations above the average as investment risk.

In this research, the ability to explain unfavorable risk criteria against traditional risk criteria was investigated. The obtained results indicate that Estrada's semi-variance adverse risk measure has a better performance in explaining the risk-return relationship than other systematic risk measures.

Keywords: Conditional model of capital asset pricing; Estrada negative beta; Estrada gamma; systematic risk; Semi-variance. 1-1- Introduction. One of the most important decision-making factors in the field of financial management and investment is risk and proper measurement of this factor, which helps investors in identifying and choosing investment options. Capital asset pricing model [1] (CAPM) is one of the most important and practical pricing models. Despite the strengths of this model, it has faced many criticisms both in the field of practice and in the academic field. Equalizing favorable and unfavorable fluctuations is one of the basic assumptions of this model in measuring investment risk (Strada, 2002).  In the traditional capital asset pricing method (CAPM), beta is the only systematic risk factor that is examined in equilibrium and symmetrical distribution conditions, and investors seek to maximize their utility function according to the two factors of average return and variance of return. Since investors only dislike return values ??lower than the average, and on the other hand, the return distribution of their asset portfolio may not be symmetrical, it is better to use the semi-variance criterion to examine the relationship between risk and return, which examines changes below the average and expresses the concept of risk in both symmetrical and asymmetrical cases. In this research, we aim to replace the three types of unfavorable risk criteria with the traditional risk criteria and examine the relationship between risk and return with a new approach. Fluctuations above the average yield (or any target amount) are desirable yield changes for investors, and only changes below the average (or any target amount) should be considered as risk.

In order to quantify and measure risk, various criteria such as range of changes, interquartile range, variance, standard deviation, absolute deviation from the mean and semi-variance have been presented. One of the most common criteria is variance and beta calculated based on it. In order to calculate the standard deviation, after calculating the average of the data, the deviation of the data from the average is calculated and the average of the sum of the squares of these deviations is presented as a risk measure, but as mentioned, any deviation from the average cannot be considered a risk. To solve this shortcoming, the semi-variance and beta calculated based on it can be used as one of the unfavorable risk criteria.

Using the semi-variance in risk calculation is one of the new approaches that is more suitable with this definition. In the capital asset pricing model (CAPM), if instead of the traditional beta, which is based on variance, an unfavorable beta with a half-variance calculation basis is used, it is possible to better explain the behavior of investors in relation to risk and return (Strada, 2007).

According to the stated cases, the variance of the average return cannot be considered as the only measure of risk.  Because the return variance can be a suitable measure of risk only in a situation where the distribution of return on assets is symmetrical and normal.  On the other hand, in the real world, investors are more sensitive to negative changes compared to positive changes, but variance, as a common measure of risk in traditional pricing models, considers positive and negative changes equally. Another reason is that variance can be directly used as a measure of risk when the asset return distribution is normal. Therefore, if we replace the return variance with the semi-variance as the risk calculation basis, we can overcome the weaknesses of the traditional method. Because in the real world, investors are not avoiding favorable (positive) changes, but only unfavorable (negative) changes. On the other hand, in both symmetric and asymmetric modes of yield distribution, semi-variance can directly express the real concept of risk. In other words, the semi-variance can express the concept of risk at least as much as the variance. For symmetric return distributions, normal beta is the same as unfavorable beta. But for asymmetric return distributions such as logarithmic normal distributions, the results will be different.

1-3- Background and history of the research topic:

Studies conducted by Post and Van Vliet [2] (2006) showed that adverse beta is a more suitable measure to explain risk than traditional beta and they believed that it has a higher explanatory power for value stocks that have a relatively high average return. Estrada [3] (2002) concluded with the research he conducted in emerging markets that adverse risk criteria are significantly superior to traditional risk calculation criteria for explaining changes in returns. A study conducted in the British capital market by Pedersen and Hong [4] (2003) indicated that even if adverse beta can examine part of stock behavior, it does not have such advantages that it can be used as a new model. Consider asset pricing.  

Ang and others [5] (2004) by sampling the American capital market observed that the use of adverse beta has such advantages that neither the traditional beta can explain them nor features such as skewness, size and momentum. Estrada and Serra [6] (2005) with the research they conducted on international stocks in emerging markets, reached results that again showed the superiority of adverse risk measures over other risk measures.

In the research conducted by Galagdra Dan[7] (2007), it was found that the relationship between traditional beta and adverse beta is influenced by factors such as deviation from the standard, skewness, and kurtosis, and the influence of the mentioned factors on the relationships Extracted in the adverse context is significant in terms of importance. The results of Dan's study show that if the distribution of asset returns is not normal, Bava and Lindenberg's beta seems to be a better measure of systematic risk compared to other discussed measures. Also, in markets where the return distribution has more elongation, Harlow and Rao's beta is a good measure of systematic risk compared to other betas. In summary, the results of Dan's study show that there is no standard model that is more acceptable in emerging markets, and this should be the concern of the activists of such markets. The results of Estrada's studies [8] (2007) show that unfavorable risk criteria (especially unfavorable beta) are more reliable based on empirical data compared to traditional risk criteria. In his study, Estrada has used data related to the returns of emerging markets and developed markets. In Estrada studies, unfavorable beta explains 45% of cross-sectional yield changes of the entire sample. Meanwhile, 55% of the cross-sectional return changes of the sample related to emerging markets can be explained through unfavorable beta. Estrada's findings also show that average returns in both emerging and developed markets are highly sensitive to adverse beta changes compared to the same amount of changes in traditional beta.