Abstract
The importance of downside risk cannot be denied. In this study, we have replaced beta in the five-factor model of using downside beta and have added a momentum factor to suggest a new six-factor downside beta capital asset pricing model (CAPM). Two models are tested—a beta- and momentum-based six-factor model and a downside-beta- (proxy of downside risk) and momentum-based six-factor model. Beta and downside beta are highly correlated; therefore, portfolios are double-sorted to disentangle the correlation. Factor loadings, i.e., size, value, momentum, profitability, and investment, are constructed. The standard methodologies are applied. Data for sample stocks from different non-financial sectors listed in the Pakistan Stock Exchange (PSX) are taken from January 2000 to December 2018. The PSX-100 index and three-month T-bills are taken as proxies for market and risk-free returns. The study uses three subsamples for robustness—period of very high volatility, period of stability, and period of stability and growth with volatility. The results show that the value factor is redundant in both models. The momentum factor is rejected in the beta-based six-factor model only. The beta-based six-factor model shows very low R2 in periods of highly volatility. The R2 is high for the other periods. In contrast, the downside beta six-factor model captures the downside trend of the market in an effective manner with a relatively high R2. The risk–return relationship is stronger for the downside beta model. These reasons lead us to believe that, overall, the downside beta six-factor model is a better option for investors as compared to the beta-based six-factor model in the area of asset pricing models.
Highlights
Investors seek to optimize investment decisions by building efficient portfolios in a mean-variance framework [1]
The sample of this study is the Pakistan Stock Exchange (PSX), which was established in 11 January 2016 by merging three stock exchanges—the Karachi Stock Exchange (KSE), the Lahore Stock Exchange (LSE), and the Islamabad Stock Exchange (ISE)
Our results show that the downside-risk-based CAPM (DCAPM) holds better than the capital asset pricing model (CAPM), as in Panel A, HML is rejected for both high downside beta (HH) and LL portfolios and WML is rejected for LL portfolios at the 5% significance level
Summary
Investors seek to optimize investment decisions by building efficient portfolios in a mean-variance framework [1]. The risk–return-based model is linear, and the expected excess returns are dependent on factor loadings These factor loadings are sources of risk that price an asset and define the risk side of mean-variance-based portfolios mimicking these risk factors [2]. The first asset pricing model was presented by [3] and is known as the capital asset pricing model (CAPM) It is generally recognized as the most widely used model [4,5], as it is used by 73.5% of CFOs in the US and 45% of the CFOs in Europe. It marked the birth of asset pricing models and, concurrently, it opened the debate on validity and tests of the CAPM. There are three major perspectives identified in this area [6]
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