Question

You’ve observed the following returns on Barnett Corporation’s stock over the past five years: –28.5 percent, 16 percent, 35 percent, 3.5 percent, and 22.5 percent. The average inflation rate over this period was 3.35 percent and the average T-bill rate over the period was 4.3 percent.

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.)

Average real risk-free rate             %

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.)

Average real risk premium             %

Answer 1

a) Average Real risk free rate = [ (1 + average nominal T - bill rate) / (1 + average inflation) ] - 1

or, Average real risk free rate = [ (1 + 0.043) / (1 + 0.0335) ] - 1 = 0.009192 or 0.92%

b) First compute the average nominal return and then use the real rate of return formula to compute the real return.

Average Nominal return = (-28.5% + 16% + 35% + 3.5% + 22.5%) / 5 = 9.7%

Average real return on stock = [ (1 + average nominal return on stock) / (1 + inflation) ] - 1

or, Average real return on stock = [ (1 + 0.097) / (1 + 0.0335) ] - 1 = 0.06144 or 6.14%

Average real risk premium = Average real return on stock - Average real risk free rate = 6.14% - 0.92% = 5.22% [ or 5.23%]