Question

You’ve observed the following returns on Crash-n-Burn Computer’s stock over the past five years: 8 percent, −15 percent, 19 percent, 31 percent, and 21 percent. Suppose the average inflation rate over this period was 3.1 percent and the average T-bill rate over the period was 3.9 percent.

a.	What was the average real return 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 nominal risk premium over this time period? (Do not round intermediate calculations and enter your answer as a percent rounded to 1 decimal place, e.g., 32.1.)

Answer 1

a. Let the return over last five years be as

R1 = 8%, R2 = -15%, R3 = 19%, R4 = 31% and R5 =21%

Average nominal return over 5 years = (R1 + R2 + R3 + R4 + R5) / 5 = [8% + (-15%) + 19% + 31% + 21%] / 5 = [8% - 15% + 19% + 31% + 21%] / 5 = 64% / 5 = 12.80%

Average inflation = 3.1%

Average real return = (1+Average nominal return over 5 years) / (1+ Average inflation ) - 1 = (1+12.80%) / (1+3.1%) - 1 =(1.1280/1.031) - 1 = 1.094083 - 1 = 0.094083 = 9.4083% = 9.41% (rounded to two decimal places)

Average real return over this time period = 9.41%

b. Average T bill rate = Average risk free rate = 3.9%

Average nominal risk premium = Average nominal return - Average Risk free rate = 12.80% - 3.9% = 8.90% = 8.9%

Average nominal risk premium over this period = 8.9%