The Curious Investor

Now that we know a few methods of estimating future growth, we will round out the analysis necessary for application in the discounted dividend model with a brief look at the Capital Asset Pricing Model which is often used for estimating required rate of return.

Obviously, when using the discounted dividend approach to valuation, you could just use an assumed required rate of return. For example, maybe you are only willing to invest in a stock priced to allow you to make 10% return. That’s fine. Any evaluation you use with this required rate of return will give you a baseline price with which to buy a stock.

Many times, however, valuations are important in allowing you to get an accurate picture of how the market is pricing a security. And, furthermore, to give you an accurate estimation of “true” value as opposed to your personally preferred value. That’s where the capital asset pricing model comes in. Let’s take a look.

Capital Asset Pricing Model
The Capital Asset Pricing Model (CAPM) is based on the theory that return and risk ought to be positively correlated. In fact, it believes that risk and return have a linear correlation. When we discuss risk, we mean systematic risk or market risk which is risk which cannot be diversified away. Basically, risk due to the market and changes in the economy as opposed to individual event risk such as bankruptcy or accounting scandals.

If you’ve read this blog for a while, you’ll remember that the commonly accepted measure for systematic risk is beta which measures a stock or a portfolio’s volatility relative to the market overall. Please refer to the post on calculating beta for an in depth look at how to calculate it.

CAPM assumes that beta and return are related. To quantify this relationship, we assume that market return would have a beta of 1. And, then we look for the risk free rate which would be return to a portfolio with a beta of 0. CAPM then assumes that one can draw a line between these two points (known as the security market line) and this line would give you the expected return of any portfolio with corresponding beta.

Why would the relationship be linear? The explanation is simple. Assume that you can always buy an index fund to replicate market return with a beta of 1 and you can always buy a treasury bond at a given risk free interest rate. You can always create a portfolio with any beta you want using a combination of these two securities. And thus, any other portfolio with a similar beta would have to have the same return as returns that don’t match the security market line would allow beta-based arbitrage opportunities.

So, let’s try to construct a security market line. The average return of the S&P 500 since 1950 was 8.48%. The average 3-month treasury rate (usually taken as being risk free) since 1958 was 5.16%. This implies that the equity risk premium, the excess return investors demand for taking on market risk, is around 3.32%.

The above graph was created using data on the S&P 500 and the 3-month Treasury return from 1958 till the 2006. The equation on the line is y = 3.32x + 5.16 gives us an equation for expected rate of return given the beta of a security. y is the expected rate of return. x is beta. And, 3.32 is the equity risk premium.

If you’d like to try to crunch your own numbers data for S&P 500 returns can be found here. And, data on many kinds of bond rates can be found here.

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