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Today we examine the Capital Asset Pricing Model, which value investors tend to be skeptical of.

The CAPM assumes that the risk-return profile of a portfolio can be optimized. According to the theory, an optimal portfolio is one which displays the lowest possible level of risk for its level of return. Additionally, since each additional asset introduced into a portfolio further diversifies the portfolio, the optimal portfolio must comprise every asset, (assuming no trading costs) with each asset value-weighted to achieve the above (assuming that any asset is infinitely divisible). All such optimal portfolios, i.e., one for each level of return, comprise the efficient frontier.

Furthermore, because the unsystematic risk is diversifiable, the total risk of a portfolio can be viewed as beta. When the expected rate of return for any security is deflated by its beta coefficient, the reward-to-risk ratio for any individual security in the market is equal to the market reward-to-risk ratio (see Figure below).

 capm

According to CAPM, beta is the only relevant measure of a stock’s risk. It measures a stock’s relative volatility – that is, it shows how much the price of a particular stock varies relative with how much the stock market as a whole moves. If a share price moves exactly in line with the market, then the stock’s beta is 1. A stock with a beta of 1.5 would rise by 15% if the market rose by 10%, and fall by 15% if the market fell by 10%.

A small and reprobate minority, value investors in the Graham-and-Dodd mould understand the shortcomings of the theory, and disregard both the conventional definition of investment risk and the standard practice of investment risk management.

 

Shortcomings of CAPM

There are two problems we see with the conventional risk-return relationship proposed by CAPM.

The first one is that the expected market rate of return is usually estimated by measuring the geometric average of the historical returns on a market portfolio (i.e. S&P 500). CAPM assumes that expected market return always follows past performance, which is a dubious assumption (as shown in the housing bubble burst of 2008).

The second problem is that the risk free rate of return used for determining the risk premium is usually the arithmetic average of historical risk free rates of return. In a similar fashion as the expected return, the average risk-free rate is somehow dependent on past performance, which is not a sensible assumption to make.

Several other assumptions are:

a) The model assumes that asset returns are (jointly) normally distributed random variables. It is however frequently observed that returns in equity and other markets are not normally distributed. As a result, large swings (3 to 6 standard deviations from the mean) occur in the market more frequently than the normal distribution assumption would expect.

b) The model assumes that the variance of returns is an adequate measurement of risk. This might be justified under the assumption of normally distributed returns, but for general return distributions other risk measures (like coherent risk measures) will likely reflect the investors’ preferences more adequately.

c) The model assumes that all investors have access to the same information and agree about the risk and expected return of all assets (homogeneous expectations assumption).

d) The model assumes that the probability beliefs of investors match the true distribution of returns. A different possibility is that investors’ expectations are biased, causing market prices to be inefficient.

e) The model assumes just two dates, so that there is no opportunity to consume and rebalance portfolios repeatedly over time.

 ValueHuntr Portfolio According to CAPM

We have used CAPM to measure the expected performance of our ValueHuntr Portfolio. The analysis, as shown in the figure below, indicates that our portfolio is one with high risk. CAPM estimates our expected return at nearly 5% due to a volatility of 10% above the market average beta of 1.

 capm_valuehuntr

Obviously, we believe these results do not accurately reflect the prospects of our portfolio, as the volatility of our holdings tells us nothing about risk. Tomorrow, we will introduce a simple relation developed by ValueHuntr to be used as an alternative to CAPM.

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