Idiosyncratic Volatility Covariance and Expected Stock Returns

By Peterson, David R.; Smedema, Adam R. | Financial Management, Fall 2013 | Go to article overview

Idiosyncratic Volatility Covariance and Expected Stock Returns


Peterson, David R., Smedema, Adam R., Financial Management


Given that the idiosyncratic volatility (IDVOL) of individual stocks co-varies, we develop a model to determine how aggregate idiosyncratic volatility (AIV) may affect the volatility of a portfolio with a finite number of stocks. In portfolio and cross-sectional tests, we find that stocks whose returns are more correlated with AIV innovations have lower returns than those that are less correlated with AIV innovations. These results are robust to controlling for the stock's own IDVOL and market volatility. We conclude that risk-averse investors pay a premium for stocks that pay well when AIV is high, consistent with our model.

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Previous studies document that aggregate idiosyncratic volatility (AIV) fluctuates substantially over time. This implies that innovations in the idiosyncratic volatility (IDVOL) of individual stocks co-vary rather than cancel each other out. While many studies examine how AIV predicts future market returns, few have investigated the asset pricing implications of the covariance of IDVOL for the cross-section of returns of individual stocks. The purpose of this study is to examine these implications.

The motivation for our empirical hypothesis is straight forward. The variance of a portfolio with a finite number of stocks increases as AIV increases, ceteris paribus. Consequently, a risk-averse investor would prefer to hold stocks that are expected to pay off relatively well when AIV is high. This preference increases the prices of these stocks today, lowering expected future returns. Thus, stocks whose returns are more correlated with innovations in AIV should have lower expected returns than stocks whose returns are less correlated with AIV innovations.

We empirically test this hypothesis by constructing a common empirical measure of AIV and estimating the correlation between an individual stock's returns and innovations in AIV. We call this correlation a stock's "IDVOL beta." We find that portfolios with high IDVOL betas have lower average returns than stocks with low IDVOL betas. Zero investment portfolios that long the highest 20% of IDVOL beta stocks and short lowest 20% of IDVOL beta stocks have abnormal returns of about -0.27% per month. This is an economically and statistically significant amount. The negative correlation is confirmed in cross-sectional regressions. This relationship is robust to a variety of standard control variables, the stock's own IDVOL, and market volatility. These findings are consistent with investors preferring stocks that pay off well when AIV is high.

I. Hypothesis Development

One well documented feature of AIV is that it fluctuates substantially over time. (1) This implies that the IDVOL of individual stocks covaries. While several studies have used AIV to forecast future market returns, we investigate the importance of AIV for the returns of individual assets. (2) To do this, we construct an illustrative model of returns and volatility showing why investors may price innovations in AIV. We begin, following Campbell, Lettau, Malkiel, and Xu (2001), by assuming a simple one-factor model for individual stock returns:

[r.sub.it] = [[beta].sub.i] [r.sub.st] + [u.sub.it], (1)

where [r.sub.it] is the return for stock i at time t, [[beta].sub.i] is its beta that we assume is unity for the average stock, [r.sub.st] is the systematic component of the return, and [u.sub.it] is an idiosyncratic shock to returns that has a mean of zero and a time-varying variance [[sigma].sup.2.sub.it]. Following the basic intuition of traditional asset pricing models, such as the capital asset pricing model, we assume that investors care about the variance of their total portfolio of assets, not just the variance of individual assets. Thus, we form an equal-weighted portfolio p with n assets. Given Equation (1), the time t return of the portfolio, [r.sub.pt], is:

[r.sub.pt] = [bar.[beta]] (n) [r. …

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