Question

You’ve observed the following returns on Crash-n-Burn Computer’s stock over the past five years: 11 percent, –11 percent, 18 percent, 23 percent, and 10 percent. Suppose the average inflation rate over this period was 2 percent and the average T-bill rate over the period was 3.1 percent.

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

Answer 1

1) (1 + Nominal rate of return) = (1 + Real rate of return)(1 + Inflation rate)

(1 + 0.031) = (1 + Real rate of return)(1 + 0.02)

Real rate of return = [(1 + 0.031) / (1 + 0.02)] - 1

Real rate of return = 0.0108 or 1.08%

2) Average return = Sum all the returns / Number of returns

Average return = (0.11 - 0.11 + 0.18 + 0.23 + 0.10) / 5

Average return = 0.102 or 10.2%

(1 + Nominal rate of return) = (1 + Real rate of return)(1 + Inflation rate)

(1 + 0.102) = (1 + Real rate of return)(1 + 0.027)

Real rate of return = [(1 + 0.102) / (1 + 0.02)] - 1

Real rate of return = 0.0804 or 8.04%

Average real risk premium = Real return - risk free rate

Average real risk premium = 8.04% - 1.08%

Average real risk premium = 6.96%