Chapter 5 Lecture (Part III)

Chapter 5 Lecture (Part III)

Capital Asset Pricing Model

The Capital Asset Pricing Model (CAPM) uses an investment’s beta to determine the required return the investment should have given its systematic risk. The equation for the CAPM is:

Ki = Krf + i(Km – Krf)

Where:

Ki is the required return on asset i

Krf is the risk-free rate

i is the beta of investment i

Km is the required return on the market portfolio

What the CAPM tells us is that for a risky security i, investors want to at minimum get the return on the risk-free asset[1]. But if asset i is any asset other than the risk-free asset, it must compensate investors for the additional risk they assume. Since diversified investors only bear systematic risk, it is this they need to be compensated for bearing. The term after the plus sign, i(Km – Krf) is called the security risk premium. It is the extra compensation investors demand for taking on the additional systematic risk. Notice the security risk premium is a function of the asset’s beta. The higher the asset’s beta the higher the security risk premium will be and the higher the security’s required return will be. The term (Km – Krf) is called the market risk premium. It represents the addition return investors demand from the market portfolio (whose beta is always 1 since the market portfolio always moves perfectly with itself)over the risk-free rate. The market risk premium is a measure of investors’ aversion to risk. When investors are very nervous, as they are now over the credit crisis and oil prices, they will demand a higher risk-premium for bearing risk. When they are less nervous, the market risk will be lower.

Notice the CAPM is a one variable model. The only item on the right-hand side of the equation that changes from one investment to the next is i. At any given point in the risk-free rate and the required return on the market remain the same for all investments.

Notice that if we graph the CAPM equation we will get a straight line since the CAPM is in the form of y = a + b(x). Can you look at the CAPM and determine which of the variables in the equation represents the slope coefficient? Perhaps it would help if I draw a graph of the CAPM:

Now can you figure out which variable in the CAPM represents the slope of the straight line? While you are thinking about this, the graph of the CAPM, the straight line, is called the security market line (SML).

May now you have figured out which of the variables in the CAPM equation represents the slope of the security market line. Did you guess that i is the slope of the SML? If you did, you would be wrong. i is the X axis, so it can’t be the slope. What else could the slope be?

Remember, the slope of a straight line is just the rise over the run. Why don’t we evaluate the SML from a Beta of 0 to a Beta of 1, then see what the rise is:

Rise/Run = (Km - Krf)

1 – 0

What this shows is that the market risk premium is the slope of the security market line.

Effect of Increased Risk Aversion on the SML

What effect would an increase in investor risk aversion have on the security market line? An increase in risk aversion would increase the market risk premium (Km - Krf) and steepen the SML as shown on the graph below:

Effect of a Change in the Expected Inflation Rate on the SML

To determine the effect of a change in the expected inflation rate (notice the word “expected” – nobody cares about past inflation) on the security market line, we need to refer back to its origin, the CAPM equation:

(Includes a premium forexpected inflation)

Ki = Krf + i(Km – Krf)

The expected inflation rate over the life of the investment is reflected in both the return of the risk-free asset (Krf) and the market return (Km). Both of these will change with a change in the expected inflation rate. For example if the expected inflation rate rises by 2 percentage points, then so will the returns on both the risk-free asset and the market. An interesting study is to examine what happens to the market risk-premium (Km – Krf) when there is a change in the expected inflation rate. Again, suppose the expected inflation rate rises by 2 percentage points. Both the market return and the risk-free rate will rise by 2 percentage points. So what happens to the market risk-premium? Nothing. Any increase in Km is exactly offset by the same increase in Krf . Since the market risk premium does not change, the slope of the security market line does not change either. The graphsshown below illustrate the effect a change in the expected inflation rate would have on the SML.

Effect of an Increase in Expected Inflation on the SML

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Effect of a Decrease in Expected Inflation on the SML

[1] The risk-free asset is an asset whose returns are risk-less. Currently, the risk-free asset is given by the 30-year U.S. Treasury bond. Given the $9 trillion (and growing) U.S. national debt, it is arguable that this bond will remain riskless. Incidentally, the Beta of the riskless asset, whatever it is considered to be, is zero.