Asymmetric correlation of stock portfolios: Evidence from the Danish market

Thorben Andresen & Preben Røsvik Hansen

Student thesis: Master thesis


This thesis analyzes asymmetric correlations between stock portfolios and the Danish stock market for the period of 1993-2009. The portfolios are sorted on selected firm and stock characteristics, which are often used by investors to evaluate investment choices. We apply two complementary statistical methods to test and measure the correlation asymmetry. The Hstatistics are used to analyze the difference between the empirical correlation and the correlation implied by a bivariate normal distribution. In addition, the symmetry test is used to analyze if there are any asymmetries in the data at all. We find significant correlation asymmetries between the stock portfolios and the Danish stock market. Our results show that the correlation is higher in periods of falling markets than in periods of rising markets. Furthermore, we find that correlation asymmetries are related to size, book-to-market value and momentum characteristics. The asymmetry increases with a decrease in the size of the company in the portfolio. Portfolios with high book-market value stocks (value stocks) have higher asymmetries than low book-to-market value stocks (growth stocks). For momentum, we find that portfolios of past losers stocks are more asymmetric than portfolios of past winner stocks. These findings are consistent with previous findings from the US stock market. The correlation asymmetries are also analyzed across sub periods in order to evaluate the persistence of the phenomenon. We find that the asymmetries vary over time and are related to the magnitude of unconditional correlation between the stock portfolios and the market. Furthermore, we can find no evidence of correlation asymmetries in the absence of the possibility to sell stocks short. Different approaches to portfolio construction and asset pricing are presented to discuss how investment decisions can be made if correlations are asymmetric. We show that portfolio construction can incorporate downside correlation by optimizing either on downside variance or on the utility of a loss-averse investor. For asset pricing, downside beta or a downside correlation factor can be used to explain variation across stock returns due to correlation asymmetry. We evaluate the impact of different calculation choices on our statistical methods. While these choices have a low impact on the H-statistics, the symmetry test is less robust. The results of the symmetry test should therefore be considered with some criticism.

EducationsMSc in Applied Economics and Finance, (Graduate Programme) Final Thesis
Publication date2010
Number of pages173