Question

You’ve observed the following returns on Yamauchi Corporation’s stock over the past five years: −10 percent, 24 percent, 21 percent, 11 percent, and 8 percent. The average inflation rate over this period was 3.1 percent and the average T-bill rate over the period was 4.1 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

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

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

r = ((1+R) / (1+h)) - 1

r = ((1+4.1%) / (1+3.1%)) - 1

r = (1.041 / 1.031) - 1

r = 1.00969932 - 1

r = 0.009699 or 0.9699%

r = 0.97%

Average real risk free rate = 0.97%

b)
Average return = (-10% + 24% + 21% + 11% + 8%) / 5
= 54% / 5
= 10.8%

Average real risk free revised = ((1+10.8%) / (1+3.1%)) - 1
= (1.108 / 1.031) - 1
= 7.468%

Average real risk premium rate = Average real risk free revised - Average real risk free rate
= 7.468% - 0.97
= 6.50%