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Expected Correlation and Future Market Returns
Research / 18. Dezember 2018
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Professor of Finance
Grigory Vilkov is the Professor in the Department of Finance at Frankfurt School of Finance & Management. Grigory's preferred topic so far has been the use of derivative instruments and option-implied information in asset pricing and portfolio management, and general equilibrium modeling with frictions.

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Option prices, by construction, reflect investors’ expectations about future price movements, and, hence, measures of risk extracted from index options are natural candidates for predicting future market returns. However, empirical evidence also suggests that information about the comovement of individual stocks, jointly extracted from index options and the cross-section of individual stock options, can be used to predict future market returns.

Our objective is to improve the understanding of the predictive power and the information content of options-based measures of stock comovement and to study the underlying economic sources explaining their return predictability. In particular, we carefully analyze the implied correlation and the correlation risk premium, and we contrast their ability to predict future market excess returns with that of variables exclusively based on the marginal distribution of the aggregate stock market (i.e., inferred solely from index options).

 

Figure 1: Time-series dynamics of option-implied variables. The figure shows the time series of the implied correlation (Panel A), the time series of the implied variance (IV) and the upside and downside implied semivariances (Panel B), the risk premiums for variance and semivariances (Panel C), and the correlation risk premium (Panel D). The sample period spans from January 1996 to December 2017, with variables being computed from 1-month options and sampled daily.

Figure 1: Time-series dynamics of option-implied variables. The figure shows the time series of the implied correlation (Panel A), the time series of the implied variance (IV) and the upside and downside implied semivariances (Panel B), the risk premiums for variance and semivariances (Panel C), and the correlation risk premium (Panel D). The sample period spans from January 1996 to December 2017, with variables being computed from 1-month options and sampled daily.

In-sample Market Return Predictability

We find that both the implied correlation and the correlation risk premium significantly predict future market excess returns for horizons of up to 1 year and that this predictability mostly can be attributed to the forward-looking information encapsulated in option prices. Moreover, their information content is incremental to that of variables exclusively extracted from index options known to forecast future market returns. Even out-of-sample, we document a significant predictive power for future market excess returns for horizons of up to 1 year; in particular so when using our novel extension of the contemporaneous-beta approach that combines high- frequency increments in option-implied variables with the respective risk premiums.

This strong and incremental return predictability is rather surprising. The implied correlation reflects the relative pricing of individual and index options and, hence, is a function of individual stocks’ expected variances and the expected market variance. However, there exists hardly any empirical evidence supporting market excess return predictability by expected market variance. Moreover, because the predictive power of implied correlation persists even after controlling for index-options-based variables, the implied correlation does not simply act as a proxy for these variables. Hence, the predictability must be related to information contained in individual stocks’ expected variances.

In particular, in contrast to measures of risk exclusively based on the marginal distribution of the market, the expected correlation is intimately linked to idiosyncratic risk and the cross- sectional dispersion in systematic risk. Consequently, we hypothesize that temporal variations in the amount of (priced) idiosyncratic risk and the cross-sectional dispersion in systematic risk are largely responsible for the incremental return predictability by the expected correlation. That is, if idiosyncratic risk is priced or the equity risk premium is affected by the cross-sectional dispersion in systematic risk, the implied correlation will be able to capture fluctuations in future market excess returns resulting from variations in these variables, whereas purely market- based measures will not.

We provide substantial empirical evidence in favor of this hypothesis. First, we carefully document the in-sample predictive power of the implied correlation. In univariate regressions, we find that the implied correlation, extracted from options data, can predict future market excess returns for horizons of up to 1 year. Its regression coefficient is always highly significantly positive (with t-statistics consistently above 2), and its predictive power, measured in terms of R2, is increasing from about 3.5% at the monthly horizon to around 5%–6% for 9- and 12-month horizons. Indeed, excluding short horizons of up to one quarter, the implied correlation delivers the strongest predictive power; dominating index-based variables, such as the implied (semi)variances and their risk premiums. Moreover, even after controlling for these index-based variables in multivariate regressions, the implied correlation significantly predicts future market excess returns, with a consistently positive sign. We also relate the predictive power of the implied correlation to the forward-looking information encapsulated in option prices; that is, the predictive power of the historical realized correlation is much weaker.

 

Figure 2: In-sample return predictability. The figure depicts the results of the in-sample market excess return predictability analysis for horizons from 1 to 12 months. Panels A and B show the adjusted R2 and the regressors' t-statistics for univariate regressions of (2), respectively. Panel C shows the univariate R2s corrected for the autocorrelation of the regressors. Finally, Panel D reports the t-statistic for the implied correlation in multivariate regressions. The standard errors are corrected for autocorrelation using Newey and West (1987), with the red dotted lines indicating 1:96 bounds around zero.

Figure 2: In-sample return predictability. The figure depicts the results of the in-sample market excess return predictability analysis for horizons from 1 to 12 months. Panels A and B show the adjusted R2 and the regressors‘ t-statistics for univariate regressions of (2), respectively. Panel C shows the univariate R2s corrected for the autocorrelation of the regressors. Finally, Panel D reports the t-statistic for the implied correlation in multivariate regressions. The standard errors are corrected for autocorrelation using Newey and West (1987), with the red dotted lines indicating 1:96 bounds around zero.

Economic Rationale for Predictability Results

We then provide a conceptual framework for interpreting the documented return predictability by implied correlation. Using a stylized model for individual stock returns, we study the determinants of the average expected correlation and illustrate its relation to idiosyncratic risk and the cross-sectional dispersion in systematic risk. Variations in the expected correlation can be summarized in terms of (1) the amount of aggregate risk, (2) the amount of idiosyncratic risk, and (3) the cross-sectional dispersion in systematic risk. Intuitively, an increase in aggregate risk implies stronger comovement among the individual stocks, because it strengthens the importance of aggregate shocks. Conversely, when idiosyncratic risk increases, the expected correlation declines, because stock-specific shocks are, to a larger extent, responsible for fluctuations in individual stock returns. Finally, we show that the expected correlation falls as the cross-sectional dispersion in systematic risk rises. We then empirically study the relation between the implied correlation and measures of the amount of future idiosyncratic risk and the future cross-sectional dispersion in systematic risk. Consistent with our stylized framework, we find that the implied correlation negatively predicts future idiosyncratic volatility and the future cross-sectional dispersion in market betas. Importantly, the empirical evidence indicates that these predictions are distinctly different from those of the implied (semi)variances.

Out-of-sample Market Return Predictability

Lastly, we study out-of-sample return predictability. The implied correlation, the down- side semivariance risk premium, and the correlation risk premium show similar out-of-sample predictability for short horizons of up to one quarter, but only the implied correlation can predict future market excess returns at longer horizons of up to 1 year. However, we also find that traditional out-of-sample regression techniques cannot fully exploit the predictive power of many variables, because they require a long historical estimation window for the regression coefficients. For example, in our applications, the out-of-sample predictability evaporates when the estimation window is shortened to 5 years or less. In lieu of this evidence, we propose a novel out-of-sample predictability approach that extends the contemporaneous-beta approach (see, e.g., Cutler, Poterba, and Summers (1989) and Roll (1988)). This approach combines high- frequency increments in option-implied variables with the variables’ risk premiums to predict future market excess returns. For predictions based on correlation and downside semivariance risk, the approach leads to out-of-sample R2s of around 8% for horizons of 3 to 6 months and of about 7% for 12 months. Consistent with our initial motivation, we link the better performance of our new approach to its stable and up-to-date regression coefficients.

Figure 5: Out-of-sample return predictability. This figure shows the out-of-sample R2 from (8) for various model specifications, forecasting horizons, and predictability approaches. The results depicted in Panels A and B are based on the traditional approach with a 10-year estimation window. The results shown in Panels C and D are based on the traditional approach with a 3-year estimation window. Finally, the results in Panels E and F are based on the contemporaneous-beta approach with a 3-year estimation window. The left panels show the statistics for the univariate specifications, and the right panels show the statistics for the multivariate ones. In all cases, predictions are made at a monthly frequency. 28

Figure 5: Out-of-sample return predictability. This figure shows the out-of-sample R2 from (8) for various model specifications, forecasting horizons, and predictability approaches. The results depicted in Panels A and B are based on the traditional approach with a 10-year estimation window. The results shown in Panels C and D are based on the traditional approach with a 3-year estimation window. Finally, the results in Panels E and F are based on the contemporaneous-beta approach with a 3-year estimation window. The left panels show the statistics for the univariate specfications, and the right panels show the statistics for the multivariate ones. In all cases, predictions are made at a monthly frequency.

You can read the whole paper here.

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