A Bound on Expected Stock Returns

Abstract

We present a sufficient condition under which the prices of options written on a particular stock can be aggregated to calculate a lower bound on the expected returns of that stock. The sufficient condition imposes a restriction on a combination of the stock’s systematic and idiosyncratic risk. The lower bound is forward-looking and can be calculated on a high-frequency basis. We estimate the bound empirically and study its cross-sectional properties. We find that the bound increases with beta and book-to-market ratio and decreases with size and momentum. The bound provides an economically meaningful signal about future stock returns. (JEL G11, G12) Authors have furnished an Internet Appendix, which is available on the Oxford University Press Web site next to the link to the final published paper online.

Volatility, Valuation Ratios, and Bubbles: An Empirical Measure of Market Sentiment

“…This rules out using our approach to detect bubbles in such assets. The situation is more promising in the case of individual stocks: it may be possible to argue that the mNCC holds for stocks with betas sufficiently close to or greater than one, along the lines of Martin and Wagner (2019) and Kadan and Tang (2019), but we leave this extension for future research.…”

What Is the Expected Return on a Stock?

“…Another is to estimate firms' conditional CAPM betas from historical return data and combine the beta estimates with the aforementioned market premium predictions. We also consider firm‐level risk‐neutral variance () as a competitor forecasting variable, motivated by Kadan and Tang (), who show that under certain conditions provides a lower bound on stock i 's risk premium.…”

“…In a more closely related, and contemporaneous, paper, Kadan and Tang () adapt an idea of Martin () to derive a lower bound on expected stock returns. To understand the main differences between their approach and ours, recall that Martin starts from an identity that relates the equity premium to a risk‐neutral variance term and a (real‐world) covariance term.…”

“…If so, the risk‐neutral variance of the market provides a lower bound on the equity premium . Kadan and Tang () modify this approach to derive a lower bound for expected stock returns based on an NCC for individual stocks. But it is trickier to make the argument that the NCC should hold at the individual stock level, so their lower bound applies only for a subset of S&P 500 stocks.…”

Extracting expected stock risk premia from option prices and the information contained in non-parametric-out-of-sample stochastic discount factors

“…Martin (2017) discusses several examples for alternative preference specifications and return distributions, including the traditional CAPM.4 Kadan and Tang (2018) show the conditions under which expression (3) holds for individual stock returns.…”