Are Stocks Really Less Volatile in the Long Run?

Abstract

According to conventional wisdom, annualized volatility of stock returns is lower when computed over long horizons than over short horizons, due to mean reversion induced by return predictability. In contrast, we find that stocks are substantially more volatile over long horizons from an investor's perspective. This perspective recognizes that parameters are uncertain, even with two centuries of data, and that observable predictors imperfectly deliver the conditional expected return. Mean reversion contributes strongly to reducing long-horizon variance, but it is more than offset by various uncertainties faced by the investor, especially uncertainty about the expected return. The same uncertainties also make target-date funds undesirable to a class of investors who would otherwise find them appealing.

Predictability of stock returns and asset allocation under structural breaks

“…Our portfolio allocation results lend further credence to the finding in Pastor and Stambaugh (2009) that the long-run risks of stocks can be very high. In a model that allows for imperfect predictors and unknown but stable parameters of the data generating process, Pastor and Stambaugh find that the true perperiod predictive variance of stock returns can be increasing in the investment horizon due to the combined effect of uncertainties about current and future expected returns (and their relationship to observed predictor variables) and estimation risk.…”

“…Long investment horizons make it more likely that breaks to model parameters will occur and some of these breaks could adversely affect the investment opportunity set, thereby significantly increasing investment risks. Asset allocation exercises mostly assume that although the parameters of the return prediction model or the identity of the ''true'' model need not be known to investors, the parameters of the data generating process remained constant through time (e.g., Barberis (2000) and Pastor and Stambaugh (2009)). Studies that have allowed for timevarying model parameters such as Dangl and Halling (2008) and Johannes et al (2009) only consider mean-variance investors with single-period investment horizons.…”

The role of data limitations, seasonality and frequency in asset pricing models

“…Despite its elegance and intuitive appeal, the CAPM has been repeatedly rejected in empirical analysis. The literature in this area includes, but is not limited to, Black et al (1972), Fama and MacBeth (1973), Banz (1981), Bhandari (1988), Stattman (1980), Rosenberg et al (1985), Basu (1983), Fama and French (1992), Jegadeesh and Titman (1993), and Pastor and Stambaugh (2003). There is also indirect evidence against the CAPM, which suggests that idiosyncratic risk appears to be priced in asset returns (see Goyal and Santa-Clara (2003) and Ang et al (2006)).…”

“…Examples of papers, which attempt to correct the first issue by providing a more realistic version of the model, are Fama and French (1993) (adding size and value factors), Carhart (1997) (adding momentum factor), Pastor and Stambaugh (2003) (adding liquidity factor), Merton (1973) (allowing for intertemporal trade offs), and Jagannathan and Wang (1996) (accounting for the influence of past information). Attempts to blame statistical methods used in the CAPM tests include, for instance, Shanken (1992), Jagannathan and Wang (1998), Roll and Ross (1994), Gibbons et al (1989), and, more recently, Connolly and Rendleman (2008) and Grauer and Janmaat (2009).…”

“…The traditional argument against higher frequency data is that such data may contain too much noise. A number of studies have examined the influence of data frequency/investment horizon on portfolio optimization Goetzmann and Edwards (1994), Kim and In (2005), Pastor and Stambaugh (2011)). We find a relationship between the use of limited data and the choice of data frequency.…”