Controversy Over Beta

There is no risk-free asset. A risk-free asset is a short-dated asset whose pay-off over some period is known. The CAPM framework assumes that every investor can borrow and lend at the rate of interest of the risk-free asset. Clearly this is unrealistic since there is the possibility that some investors may default on their loans, thus making them no longer risk-free.

However, even in this case a general version of the CAPM will still hold.

A possible explanation for this result was given by the late Fischer Black, whose arguments were based on considering the feasible investment strategies for different types of investors. Suppose that an investor wants to pursue a high-risk investment strategy. In a pure CAPM world he or she

 

could achieve this by either buying high beta stocks or buying low beta stocks and leveraging this position (borrowing at the risk-free rate of interest).

If, however, investors cannot borrow unlimited amounts at the risk-free rate they must buy the high-risk stocks outright. This would imply that investors will bid up the price of high-risk stocks, and consequently the expected return on these assets should be lower than in the pure CAPM world. This result is known as the zero-beta CAPM and states that the reward for beta is lower than in a pure CAPM world.

There is no market portfolio. One of the severest deficiencies of the CAPM was pointed out by Richard Roll of the University of California at Los Angeles in what has become known as the Roll Critique.

He showed that the correct market index for the CAPM was not the stock market but an index of all the risky wealth in the world. The market therefore includes not just all the traded stocks and bonds but also property, human capital and anything else tangible or intangible that adds to the risky wealth of, not just the UK, say, but of all mankind.

The Roll Critique has spawned a large number of novel statistical methods that avoid using the true market index. Although the resulting evidence for beta has been mixed, it is interesting to note that there is some evidence that the CAPM holds when indices that include property and other non-financial assets are used.

The theory does not stack up with reality. The CAPM predicts that a portfolio made up of high beta stocks will outperform a portfolio of low beta stocks. However, the reality seems to indicate investors who purchased high beta stocks have not achieved a higher rate of return than investors who purchased low beta stocks.

Figure 1 shows the evidence for UK stocks for the 10-year period ending December 1995. The figure shows the average return on 10 portfolios grouped by their beta. It can be seen that the relationship between beta and return is essentially flat and that high beta stocks did not on average offer better returns than low beta stocks.

However, a number of authors have argued that 10 years is not sufficient to come to any clear conclusion and that the longer-run evidence is much more favourable for beta. Other authors have argued that beta does actually work in times of large stock market moves