Question

You’ve observed the following returns on Crash-n-Burn Computer’s stock over the past five years: 20 percent, –12 percent, 17 percent, 20 percent, and 10 percent. Suppose the average inflation rate over this period was 1.7 percent and the average T-bill rate over the period was 4.6 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

%

Answer 1

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)

(1 + 4.6%) = (1 + 1.7%) * (1 + r)

r = 1.046/ 1.017 - 1

r = 2.85%

Part B

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

Arithmetic average return = (20% - 12% + 17% + 20% + 10%)/ 5

Arithmetic average return = 11%

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

(1 + R) = (1 + r) * (1 + h)

(1 + 11%) = (1 + 1.7%) * (1 + r)

r = 1.11/ 1.017 - 1

r = 9.14%

Average real risk premium = 9.14% - 2.85%

Average real risk premium = 6.29%