The discount rate determining a stock's sale price in the future—that is, the rate that discounts post-sale cashflows—remains uncertain until the future sale date. As the stock price is a convex function of the discount rate, this discount-rate uncertainty raises the current stock price and thus lowers the stock’s expected return. In this paper, we gauge the economic importance of this discount-rate uncertainty effect. Specifically, we examine whether: (1) there is a negative cross-sectional relation between a stock’s return volatility and its future return, (2) the negative relation is more pronounced among stocks with a shorter holding period, (3) the negative relation is stronger when the per-share price is higher, and (4) the negative relation persists even when investor sentiment is low and even among stocks with low arbitrage costs. The second prediction is on the grounds that the future sale price is more important in stock valuation when the stock is sold in the nearer future. The third prediction stems from the fact that the convexity of a stock’s price is greater when the discount rate is initially low, or equivalently, when the price is initially high. The fourth prediction is due to no role of mispricing or market inefficiency in our hypothesis. Using data from the U.S., we find strong support for all the four predictions. Our hypothesis and empirical results thus offer an efficient market-based resolution for the so-called volatility puzzle that stocks with greater volatility earns a lower return in the future.
Keywords: Discount-rate uncertainty; Convexity; Holding period; Cross-section of stock returns; Volatility puzzle
