Finding the True Value of a Security
Noisy Prices and Inference Regarding Returns
Practitioners and academicians seek to understand the determinants of variation in mean returns across assets. The stock prices we observe however contain noise, i.e., we do not observe the true value of a security. This paper assesses the effects of noisy prices on inferences regarding mean returns to individual securities and portfolios, and regarding return premia associated with stock characteristics.
If security prices contain noise, then return premium estimates obtained by comparison of equal-weighted mean returns across portfolios or by ordinary-least squares return regressions are biased estimates of the true return differentials. The bias is relevant, because mean true returns, not mean observed returns, determine the rate of growth across time in expected prices and shareholder value.
The authors assess, by theory and simulation, the properties of a set of possible corrections for noisy security prices, under broader assumptions than allowed for in previous papers, including the possibility that the noise in prices may be serially correlated and/or contain a common component across stocks. They assess the properties of several return-weighting methods, including equal-weighting, prior-gross-return weighting, initial equal-weighting, prior-period-value weighting, and annual-value weighting. They demonstrate that equal-weighting estimates are always biased in the presence of noisy prices. When the noise in prices is autocorrelated and/or contains a common component across stocks, the alternative methods may also be biased, but generally will be less so than the equal-weighting estimates. For plausible parameter estimates the remaining bias in prior-gross-return weighting or prior-firm-value weighting estimates is minimal.
Their analysis gives little reason to prefer prior-gross-return weighting over prior-period-value weighting, or vice versa. However, the former provides a bias-corrected estimate that places equal weight on the information contained in each security, while the latter corrects for bias while weighting large firms more heavily. The choice between prior-gross-return weighting and prior-firm-value weighting methods may therefore depend on the desired weight to be given to the information contained in small versus large capitalization securities.
Comparisons of returns across attribute-sorted decile portfolios as well as univariate cross-sectional regressions reveal statistically significant biases in estimated return premia associated with every attribute considered, including firm size, market-to-book ratio, trading volume, share price, and illiquidity. However, the economic magnitude of the bias varies considerably, and is minimal in the case of the market-to-book ratio. In contrast, the bias attributable to noisy prices in return premia estimates associated with firm size, share price, trading volume and illiquidity can be substantial, equal to 50% or more of the corrected estimate.
The findings reported here indicate that correcting for the effects of noise in prices has significant effects on return premia estimates obtained from monthly return data. The empirical analysis presented here focused on monthly returns, and on five selected firm characteristics. Significant biases may well arise in other empirical applications. Any explanatory variable that is cross-sectionally correlated with the variance of the noise in prices is likely to be susceptible to bias in estimates of associated return premia.
Elena Asparouhova and Hendrik Bessembinder are both with the University of Utah. Ivalina Kalcheva is an assistant professor of finance at the Eller College of Management, University of Arizona.
Forthcoming in The Journal of Finance.