Modeling Risk: Capital Asset Pricing Model

Modeling Risk: The Capital Asset Pricing Model (CAPM)

Portfolio theory has important implications for how stocks are actually valued. If investors seek to reduce risk in anything like the manner Harry Markowitz described, the stock market will tend to reflect these risk-reducing activities. This brings us to what is called the “capital-asset pricing model”, a creation devised by Stanford professor William Sharpe, the late Harvard professor John Lintner, and others.

We’ve mentioned that the reason diversification cannot usually produce the miracle of risk elimination, as it did in our mythical island economy, is that usually stocks tend to move up and down together. Still, diversification is worthwhile – it can eliminate some risks. What Sharpe an Lintner did was to focus directly on what part of a security’s risk can be eliminated by diversification and what part can’t.

Can you imagine any stockbroker saying, “we can reasonably describe the total risk in any security (or portfolio) as the total variability (variance or standard deviation) of the returns from the security? He’d probably scare away the few individual customers who are left. But we who teach are under no such contraints, and we say such things often. We go on to say the part of total risk or variability may be called the security’s systematic risk and that this arises from the basic variability of stock prices in general and the tendency for all stocks to go along with the general market, at least to some extent. The remaining variability in a stock’s returns is called unsystematic risk and results from factors peculiar to that particular company; for example, a strike, the discovery of a new product, and so on.

Systematic risk, also called market risk, captures the reaction of individual stocks (or portfolios) to general market swings. Some stocks and portfolios tend to be very sensitive to market movements. Others are more stable. This relative volatility or sensitivity to market moves can be estimated on the basis of the past record, and is popularly know by the Greek letter beta.

Modeling risk. Photo by Elena

You are now about to learn all you ever wanted to know about beta but were afraid to ask. Basically, beta is the numerical description of systematic risk. Despite the mathematical manipulations involved, the basic idea behind the beta measurement is one of putting some precise numbers on the subjective feelings money managers have had for years. The beta calculation is essentially a comparison between the movements of an individual stock or portfolio and the movements of the market as a whole.

The calculation begins by assigning a beta of 1 to a broad market index, such as the NYSE index or the S&P 500. If a stock has a beta of 2, then on average it swings twice as far as the market. If the market goes up 10 percent, the stock rises 20 percent. If a stock has a beta of 0.5, it tends to be more stable than the market (it will go up or down 5 percent when the market rises or declines 10 percent). Professionals often call high-beta stocks aggressive investments and label low-beta stocks as defensive.

Now the important thing to realize is that systematic risk cannot be eliminated by diversification. It is precisely because all stocks move more or less in tandem (a large share of their variability is systematic) that even diversified stock portfolios are risky. Indeed, if you diversified perfectly by buying a share in the S&P index (which by definition has a beta of 1) you would still have quite variable (risky) returns because the market as a whole fluctuates widely.

Unsystematic risk is the variability in stock prices (and therefore, in returns from stocks) that results from factors peculiar to an individual company. Receipt of a large new contract, the finding of mineral ressources on the company’s property, labor difficulties, the discovery that the corporation’s treasurer has had his hand in the company till – all can make a stock’s price more independently of the market. The risk associated with such variability is precisely the kind that diversification can reduce. The whole point of portfolio theory is that, to the extent that stocks don’t move in tandem all the time, variations in the returns from any one security will tend to be washed away or smoothed out by complementary variation in the returns from other securities.

Suppose we randomly select securities for our portfolio that tend on average to be just as volatile as the market (the average betas for the securities in our portfolio will always be equal to 1). As we add more and more securities the total risk of our portfolio declines, especially at the start.

When 10 securities are selected for our portfolio, a good deal of the unsystematic risk is eliminated, and additional diversification yields little further risk reduction. By the time 20 well diversified securities are in the portfolio, the unsystematic risk is substantially eliminated and our portfolio (with a beta of 1) will tend to move up and down essentially in tandem with the market. Of course, we could perform the same experiment with stocks whose average beta is 1 ½. Again, we would find that diversification quickly reduced unsystematic risk, but the remaining systematic risk would be larger. A portfolio of 20 or more stocks with an average beta of 1 ½ would tend to be 50 percent more volatile than the market.

Burton G. Malkiel. A Random Walk Down Wall Street, including a life-cycle guide to personal investing. First edition, 1973, by W.W. Norton and company, Inc.