Ebook Asset Pricing and Mispricing
As Eugene Fama points out, tests of classical asset pricing models such as the CAPM, CCAPM, or ICAPM implicitly rely on an assumption of market efficiency which permits the substitution of realized returns for expected returns. However, there is increasing evidence that common stocks are mispriced relative to these models, although the reasons for the pricing discrepancies remain in dispute. For example, de Bondt and Thaler (1985, 1987) find long run reversals of prior stock price changes which they interpret as corrections of prior over-reactions to news, while Jegadeesh and Titman (1993) among others find positive autocorrelation of individual stock returns at the 6-12 month horizon, which is consistent with the slow adjustment to firm specific news documented in a large number of studies.
Jegadeesh and Titman (1995) also find evidence that stock prices tend to over-react to firm specific information. Lee and Swaminathan (2000) find that low (high) trading volume stocks tend to be under (over-) valued by the market. Pastor and Stambaugh (2003), Acharya and Pedersen (2005) and Sadka (2006) show stock returns are affected by (or at least covary with) the state of stock market liquidity, while Amihud (2002) shows that unanticipated increases in market illiquidity reduce the level of stock prices. Lee et al. (1991) and Swaminathan (1996) (more circumspectly) argue that stock prices are affected by the state of ‘sentiment’.
In this paper we show that, for securities which are subject to stochastic mispricing relative to a given asset pricing model, it is likely that either their prices will fail to be unconditionally rational or their returns will fail to be unconditionally rational, or both. By unconditionally rational prices we mean prices whose unconditional expectations are consistent with the fundamental asset pricing model, and by unconditionally rational returns we mean returns whose unconditional expectations are consistent with the fundamental asset pricing model. Thus a stock that on average trades at 100% of its fundamental value, but whose price fluctuates about the fundamental value, will have a return that is biased up relative to that predicted by the model that determines the fundamental value. This ‘mispricing return bias’ is the focus of this paper.
The basic intuition of our analysis follows immediately from Jensen’s Inequality: price is a non-linear function of expected return, so that if one variable is subject to random error then the expectation of the other variable will be biased. It is of course possible that neither prices nor expected returns are unconditionally rational. The bias in the expected returns due to mispricing is shown to depend on the volatility and first order autocorrelation of the mispricing. Unfortunately, the mispricing is not directly observable, and we must use proxies for the mispricing return bias. Our empirical tests reveal that portfolios formed on the basis of proxies for the mispricing return bias have significantly different returns after adjusting for risk using standard models.
The analysis in this paper has implications for studies that find significant relations between stock returns and variables that may be proxies for the mispricing related return bias we consider. Thus, measures of the cost of transacting such as the bid ask spread or Kyle’s ? are likely to be positively associated with the magnitude of pricing errors since transactions costs impede arbitrage. This suggests that a part of the approximately 7% return differential between high and low liquidity portfolios documented in several studies may be attributable to this mispricing return bias.
Similarly, we show that the sensitivity of stock returns to variables that have common effects on stock prices, such as market liquidity or sentiment, is related to the mispricing return bias, so that a part of the the annual return premium of around 7.5% between high and low liquidity beta portfolios reported by Pastor and Stambaugh (2003) is likely to be attributable at least in part to the mispricing return bias. We also show that it is possible to generate a return premium of the type that Hou and Moskowitz (2005) have found to be associated with slow adjustment to (market-wide) information in a model in which prices are unconditionally rational but adjust slowly to new information and are subject to ‘liquidity shocks’, since these stocks will be subject to the mispricing return bias.
This paper follows an early literature on the implications of security mispricing for measuring rates of return, including Blume and Stambaugh (1983), and Roll (1983), who are concerned with the effects of daily auto-correlations and the bid-ask bounce on measured rates of return. More recently Liu and Strong (2006) analyze the effects of portfolio rebalancing assumptions on reported returns.
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