# Asymmetric Correlations in Financial Markets

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2013

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## Abstract

This dissertation consists of three essays on asymmetric correlations in financial markets. In the first essay, I have two main contributions. First, I show that dividend growth rates have symmetric correlations. Second, I show that asymmetric correlations are different than correlations being counter-cyclical. The correlation asymmetry I study in this dissertation should not be confused with correlations being counter-cyclical, i.e. being higher during recessions than during booms. I show that while counter-cyclical correlations can simply be explained by counter-cyclical aggregate market volatility, the correlation asymmetry with respect to joint upside and downside movements of returns are not just due to the heightened market volatility during those times.

In the second essay I present a model in order to explain the correlation asymmetry observed in the data. This is the first paper to offer an explanation for observed correlation asymmetry. I formalize the explanation using an equilibrium model. The model is useful to understand both the cross-section and time-series of correlation asymmetry. By the means of my model, we can answer questions about why some stocks have higher correlation asymmetry, and why the correlation asymmetry was higher during 1990s? In the model asset prices respond the realization of dividends and news about the future. However, price responses to news are asymmetric and this asymmetry is endogenous. Price responses are endogenously stronger conditional on bad news than conditional on good news. This asymmetry also generates the observed correlation asymmetry. The price responses are asymmetric due to the ambiguity about the news quality. Information about the quality of the signal is incomplete in the sense that the exact precision of the signal is unknown; it is only known to be in an interval, which makes the representative agent treat news as ambiguous. To model ambiguity aversion, I use Gilboa and Schmeidler (1989)'s max-min expected utility representation. The agent has a set of beliefs about the quality of signals, and the ambiguity-averse agent behaves as if she maximizes expected utility under a worst-case scenario. This incomplete information about the news quality, together with ambiguity-averse agents, generates an asymmetric response to news. Endogenous worst-case scenarios differ depending on the realization of news. When observing ``bad" news, the worst-case scenario is that the news is reliable and the prices of trees decrease strongly. On the other hand, when ``good news" is observed, under the worst-case scenario the news is evaluated as less reliable, and thus the price increases are mild. Therefore, price responses are stronger conditional on a negative signal and this asymmetry creates a higher correlation conditional on a negative signal than conditional on a positive signal. I also show that the results are robust to the smooth ambiguity aversion representation.

Motivated by the model, I uncover a new empirical regularity that is unknown in the literature. I show that correlation asymmetry is related to idiosyncratic volatility: the higher the idiosyncratic volatility, the higher the correlation asymmetry. This novel empirical finding is also useful to understand the time-series and cross-sectional variation in correlation asymmetry. Stocks with smaller market capitalizations have greater correlation asymmetry compared to stocks with higher market capitalization. However, an explanation for this finding has been lacking. According to the explanation offered in this paper, smaller size stocks have greater correlation asymmetry compared to bigger size stocks because small size stocks tend to have higher idiosyncratic volatilities compared to bigger size stocks. In the time-series, correlation asymmetry shows quite significant variation as well. The average correlation asymmetry is especially high for the 1990s and decreases significantly at the beginning of the 2000s. This pattern in times-series can also be explained in terms of the time-series behavior of idiosyncratic volatilities. Several papers including Brandt et al. (2010), document higher idiosyncratic volatilities during 1990s while the aggregate volatility stays fairly stable. Basically, the high idiosyncratic volatilities during the 1990s also caused greater correlation asymmetry.

In the third essay, I study the correlation of returns in government bond markets. Similar to the findings in equity markets, I show that there is some evidence for asymmetric correlations in government bond markets. First, I show that the maturity structure matters for correlation asymmetry in bonds markets: Unlike long-maturity bonds, shorter-maturity bonds tend to have asymmetric correlations. Second, I show that the correlation asymmetry observed in European bond markets disappears with the formation of a common currency area. Lastly, I study the correlation between equity and bond returns in different countries. For long-maturity bonds, correlations with the domestic equity returns are asymmetric for half of the countries in the sample, including the U.S. These findings show that results on asymmetric correlations from equity markets can generalize, at least to some extent, to other financial markets.

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Ozsoy, Sati Mehmet (2013). *Asymmetric Correlations in Financial Markets*. Dissertation, Duke University. Retrieved from https://hdl.handle.net/10161/7267.

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