Featured Story September-October 2013
On the Estimation and Pricing of Correlation

by Ms. Chryssa Markopoulou, Doctoral Candidate

Accurate estimation of correlation is of paramount importance in asset allocation and risk management, particularly in light of existing studies that provide evidence of increased correlation during periods of high volatility. An increase in market wide correlations will increase the aggregate risk borne by investors and affect the risk-return trade-off, thus leading to diminishing diversification benefits when said benefits are most needed.

The importance of correlation as a priced risk factor has been the subject of several recent studies. Pricing of correlation has been examined through the decomposition of index volatility risk premium into individual stocks' volatility risk premium and inter-asset correlation structure. Volatility risk premium has stimulated research interest over past years, with the vast majority focusing on the study of index options. Jackwerth & Rubinstein (1996) and Bakshi & Kapadia (2003a) amongst others, provide evidence of negatively priced volatility risk, suggesting that investors are willing to pay an increased premium for the options, to protect themselves from increased volatility and lower returns in the market.

On the contrary, only a few papers study the pricing of individual equity options. Bakshi & Kapadia (2003b) noted that individual equity option prices embed a negative market volatility risk premium, although much smaller than for the index option. Driessen et al. (2009) and Cosemans (2011) have provided evidence of negatively priced volatility risk premium in index options, whereas no such evidence is found for individual options. They argue that the discrepancy is triggered by the fact that, by definition, index options are exposed to a risk factor lacking in the individual process, namely correlation risk.

In a similar context, Mueller et al. (2012) provide evidence of priced correlation risk in currency markets using option-implied correlations. Krishnan et al. (2009) use historical prices of US stocks and, after controlling for asset volatility, risk factors and higher-order moments, find a significant correlation risk premium tested under different specifications. Pollet & Wilson (2010) examine correlation risk using historical price data and find that differences in exposures to correlation risk justify differences in expected returns, while volatility risk is negatively related or unrelated to the stock market risk premium.

Skintzi & Refenes (2005) use option price data to derive an 'implied correlation index' that measures the average portfolio diversification. Intuitively, index variance is associated with the variances of constituent stocks as well as the pairwise correlations. Implied correlation is, thus, defined as a constant factor that captures any arising difference between the volatility of the index option and the volatility of the portfolio, consisting of the constituent stocks of the index. Historical volatility and correlation estimators rely on the assumption that the time-series dynamics of the series will be replicated in the future. To overcome the ambiguities deriving from the above assumption, stock return moments are inferred from currently traded option prices. Naturally, option prices reflect the current market view of future price movements of the underlying stock. Therefore, the estimation of stock price distribution moments from option prices is widely considered to outperform the estimation based on historical performance in terms of informational efficiency.

Forecasting the dynamics of correlation can be a useful tool in asset pricing and portfolio allocation. Buraschi et al. (2010) investigate the importance of correlation risk in optimal portfolio choice and conclude that correlation risk has a sizeable impact on optimal portfolio weights. Buraschi et al. (2012) show that hedge fund returns and risk are exposed to market-wide correlation risk. From a practical perspective, forecasts of correlation can be used by market participants to form profitable trading strategies. Volatility and correlation trading strategies have stimulated the interest of investors, especially after the dramatic increases in stock market volatilities and correlations following the 2008 financial crisis.


References

Bakshi, G., & Kapadia, N. (2003a). Delta-hedged gains and the negative market volatility risk premium. Review of Financial Studies, 16, 524-566.

Bakshi, G., & Kapadia, N. (2003b). Volatility Risk Premiums Embedded in Individual Equity Options: Some New Insights. Journal of Derivatives, 11, 45-54.

Buraschi, A., Kosowski, R., & Trojani, F. (2012). When there is no place to hide - correlation risk and the cross-section of hedge fund returns, Working paper, National Centre of Competence in Research Financial Valuation and Risk Management.

Buraschi, A., Porchia, P. & Trojani, F. (2010). Correlation risk and optimal portfolio choice. Journal of Finance, 65, 393-420.

Cosemans, M. (2011). The Pricing of Long and Short Run Variance and Correlation Risk in Stock Returns, Working paper, Erasmus University - Rotterdam School of Management

Driessen, J., Maenhout, P.J., & Vilkov, G. (2009). The price of correlation risk: evidence from equity options. Journal of Finance, 64, 1377-1406.

Jackwerth, J. C., & Rubinstein, M. (1996). Recovering probability distributions from option prices. The Journal of Finance, 51(5), 1611-1631.

Krishnan, C.N.V., Petkova, R., and Ritchken, P. (2009). Correlation risk. Journal of Empirical Finance, 16, 353-367.

Mueller, P., Stathopoulos, A., & Vedolin, A. (2013). International correlation risk. Financial Markets Group, The London School of Economics and Political Science.

Pollet, J.M., & Wilson, M. (2010). Average correlation and stock market returns. Journal of Financial Economics, 96, 364-380.

Skintzi, V.D, & Refenes, A. P. N., (2005), Implied correlation index: a new measure of diversification. Journal of Futures Markets, 25, 171-197.

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