The authors demonstrate that value stocks (i.e., stocks with high book-to-mark ratios) tend to have annual returns that are correlated with the performance of fixed-income securities. This finding is peculiar because equity securities are viewed as a hedge against fixed-income securities. Furthermore, value stocks appear to generate excess return beyond what should be the appropriate risk-adjusted return based on the capital asset pricing model (CAPM). This excess return is called the "value premium."

To address why the value premium exists, the authors posit that value stocks may not be appropriately compared with an all-equity market index (via the CAPM) given that value stocks exhibit return characteristics similar to those of fixed-income securities. Furthermore, if investors treat downside risk differently from upside risk, then the mean–variance (MV) framework of the CAPM is possibly misspecified. The authors offer a mean–semivariance (MS) framework to generate CAPM-like betas that can capture downside risk aversion.

For downside risk, MS betas are generally higher than MV betas for value stocks, which implies that part of the value premium is the result of not accounting for downside risk aversion within value stocks. In addition, when fixed-income securities are introduced into an all-equity market index, the value premium tends to dissipate because fixed-income securities receive proportionately more representation within the index. These effects appear to be separate from each other.

For investment horizons other than one year, the reduction of the value premium based on greater representation of fixed-income securities in the market index appears to only be effective annually within the MV framework. But within the MS framework, the value premium–reduction effect appears in time horizons that vary between 0.5 and 1.5 years.

Practitioners can benefit from the finding that when using an annual time horizon, value stocks are not an effective hedge for fixed-income securities, despite being equity securities. Furthermore, the idea that an MS framework might price risk better than the traditional MV framework because of downside risk aversion is worth noting.

The authors use annual data from 1963 to 2007. Annual data are chosen based on a realistic time horizon and because the data should not suffer from either heteroscedasticity or serial correlation. They separate equities gathered from CRSP into 10 portfolios based on the book-to-market ratio, for which "high" means "value" and "low" means "growth." The CRSP value-weighted index serves as the all-equity market index, and the authors generate a bond index by taking the average of three existing bond indices: the long-term government bond index, long-term corporate bond index, and intermediate-term government bond index.

CAPM-type regressions produce alphas for each of the portfolios. The authors calculate a measure based on the alphas that is the average of the top two "value" portfolio measures minus the average of the bottom two "growth" portfolio measures (value minus growth, or VMG). The VMG-alpha decreases as the bond index becomes proportionately larger within the market index under the MV framework for calculating beta. Under an MS framework, the reduction in the VMG-alpha measure becomes much more pronounced (almost to zero) as the bond index becomes proportionately larger within the market index.

The results are robust to different measures of value (the ratios of earnings to price and cash flow to price) and to different interactions with value based on size, institutional ownership, and idiosyncratic volatility. The last two measures have been given as reasons for the existence of a value premium.

The results do change depending on the time frequency of the data (month-long, quarter-long, semiannual, 18-month-long, and biannual horizons). Under the MV framework, the results are achieved only when using an annual horizon. Under the MS framework, the results are achieved when the horizon varies between 6 and 18 months.

Additional testing that considers time-series effects on monthly data and bond index changes supports the idea that the MS framework provides a better fit for the data and that including the bond index appears to be prudent when considering value stocks.

I find the analysis interesting and, at a minimum, believe that value stocks are somehow related to fixed-income returns. But I wonder why there is a connection. Downside risk aversion appears to be a plausible, but not complete, explanation.