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Risk-Free Rate and Equity Risk Premium

1. Risk-Free Rate and Equity Risk Premium

Now, let's go through how we are going to obtain the last two components of the CAPM. The risk-free rate and the equity risk premium.

2. Risk-Free Rate

The CAPM requires the risk-free rate as an input. A risk-free security is an asset with zero beta. We can see this from the CAPM. If the asset's beta is 0, then the 2nd term on the right-hand-side of the CAPM, beta times Rm minus Rf, is equal to zero. So the asset's return equals the risk-free return. A common source for the risk-free rate is the yield on long-term US Treasury securities. Long-term can mean 10, 20, or 30 years. The risk-free rate can be obtained from the Federal Reserve Electronic Database or the Federal Reserve H 15 Selected Interest Rates database.

3. Equity Risk Premium

The last component of the CAPM is the Equity Risk Premium or ERP. The Equity Risk Premium measures the extra return that investors demand for putting their money in stocks compared to US Treasuries. The Equity Risk Premium is the market return less the US Treasury return. Since the US Treasury return can be of varying maturities, we should make sure that the term of the Risk-Free Rate is the same for the Rf and the Equity Risk Premium. For example, if we use a Risk-Free Rate of 10 years, we have to make sure the Equity Risk Premium is calculated using a 10-year US Treasury also. To calculate the ERP, we obtain a return series for the S&P 500 Index and, say, the 10-year US Treasury for at least 35 years. We then subtract the US Treasury yield from the S&P 500 Index return each year and average the annual differences. This annual difference is the historical Equity Risk Premium. The typical range of ERP is around 5 to 8 percent.

4. Let's practice!

Let's practice the material we just went through in the following exercise.