You’ve observed the following returns on Crash-n-Burn Computer’s stock over the past five years: 18 percent, –14 percent, 20 percent, 22 percent, and 10 percent. Suppose the average inflation rate over this period was 3.1 percent and the average T-bill rate over the period was 4.4 percent.

Problem 12-11 Calculating Real Rates [LO1]

You’ve observed the following returns on Crash-n-Burn Computer’s stock over the past five years: 18 percent, –14 percent, 20 percent, 22 percent, and 10 percent. Suppose the average inflation rate over this period was 3.1 percent and the average T-bill rate over the period was 4.4 percent.

What was the average real risk-free rate over this time period? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Average real risk-free rate

%

What was the average real risk premium? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Average real risk premium

%

 

Explanation:

We can find the average real risk-free rate using the Fisher equation. The average real risk-free rate was:

(1 + R) = (1 + r)(1 + h)

f = (1.044 / 1.031) – 1

f = .0126, or 1.26%

To find the average return, we sum all the returns and divide by the number of returns, so:

Average return = (.18 – .14 + .20 + .22 + .10) / 5

Average return = .112, or 11.2%

To calculate the average real return, we can use the average return of the asset, and the average inflation in the Fisher equation. Doing so, we find:

(1 + R) = (1 + r)(1 + h)

= (1.112 / 1.031) – 1

= .0786, or 7.86%

And to calculate the average real risk premium, we can subtract the average risk-free rate from the average real return. So, the average real risk premium was:

Average real risk premium = Average real return – Average risk-free rate

Average real risk premium = 7.86% – 1.26%

Average real risk premium = 6.60%