Bad Beta, Good Beta

Bad Beta, Good Beta

By: Campbell and Vuolteenaho

            Campbell and Vuolteenaho (C and V) break down the CAPM model into separate betas to hopefully find a new approach to asset pricing than the single beta CAPM.  They break down betas into two categories, one using news of the market’s future cash flows (CF) and the other reflecting news about the market’s discount rate (DR).  Based on ICAPM theory, CF should be the beta with the higher price of risk.  As a metaphor, C and V compare the good and bad beta to good and bad types of cholesterol, and say that not all beta is bad just like not all cholesterol is bad.  After breaking down the betas into these categories, C and V find that small and value stocks have much higher CF beta than large and growth stocks and explains why they have higher returns.

            Robert Merton (1973) suggests that the price of risk for DR beta should be equal to the variance of the market return, while the price of risk for CF beta should be multiplied by gamma to compensate an investor for their risk aversion.  C and V build on this notion using a model that follows Merton’s suggestion.  Using the two-beta model, they find that the two-beta model outperforms the standard CAPM in the modern period from July 1963 to December 2001.  This is due to the fact that growth stocks, with low returns, have high betas, but they are mostly the good beta that comes with low risk prices.  On the contrary, value stocks with higher average returns, have higher bad beta than growth stocks. The single-beta CAPM adequately explained the data from the early period (1929-1963) because during this time, they find that the ratio of good to bad beta remains fairly constant.

In the lower left section of table 3 shows the correlation f shocks to individual state variables with the news terms for CF and DR.  r^e_M is log excess return, TY is the term yield spread, PE is the Price-earnings ratio, and VS is the small-stock value spread.

            Figure 1 shows market cash flows and market discount rate lined up with the occurrence of recession (indicated by the dotted vertical line).  In some cases, a recession occurs when CF decreases (valuation recession).  In other cases, a recession occurs when DR increases (profitability recession).  There are also some that occur as a result of both types (mixed recession).  Combining this with table 3, you can see what changes in state variables could do to CF and DR, and can in turn, do to the market.  For example, a valuation recession is characterized by a declining PE ration, a steepening yield curve, and larger declines in growth stocks than in value stocks.

            Table 5 shows the level of CF beta and DR beta based on size of the company and their measure from growth to value stocks.  The highest level of CF beta is recognized as you move to smaller value stocks.  The highest level of DR beta is when you move toward small growth stocks.

 

This is the equation used to find the results in table 7.  Expected returns are on the left side of the equation. Variance of the beta for Cash Flows and Discount rate are shown on the right, with gamma in front of the Cash flow beta term.  This is due to Merton’s suggestion mentioned above.

Table 7 shows the differences in beta premium between cash flows and discount-rate and follows the overall results talked about above.

            Based on these results, C and V conclude that value stocks and small stocks have higher cash-flow betas than growth stocks and large stocks, and this can explain their higher average returns.  The post-1963 negative CAPM alphas of growth stocks are explained by the fact that their betas are mostly of the good variety.  This model also explains why CAPM betas induced very little spread in the post-1963 period.  It is because the CAPM beta sort induces a post-ranking spread only in the good discount-rate beta, which carries the low premium (because it is the good beta).  For investors, C and V say these results show that risk-averse long-term investors who hold only equities should view the high average returns on value and small stocks as appropriate compensation for risk.  Lower risk-averse investors should overweight these stocks while investors with higher risk aversion should underweight them.