You\'ve observed the following returns on Doyscher Corporation\'s stock over the

Question

You've observed the following returns on Doyscher Corporation's stock over the past five years: -25.5 percent, 14.0 percent, 31.0 percent, 2.5 percent, and 21.5 percent. The average inflation rate over this period was 3.25 percent and the average T-bill rate over the period was 4.3 percent. Required: What was the average real return on the stock? (Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).) What was the average nominal risk premium on the stock? (Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).)

Explanation / Answer

(a)

Average real Risk Free Rate ("RFR")

(1+ real rate)(1+ inflation rate) = (1 + nominal rate)
(1+nominal rate) / (1 + inflation rate) = (1 + real rate)
1+ real rate = 1.043 / 1.0325 = 1.0102

Real risk free rate = 1.0102 – 1 = 0.0102 = 0.1.02%

Geometric mean return of stock= {(1 + -0.255)(1.14)(1.31)(1.025)(1.215)}1/5 - 1 = 1.38561/5 - 1 = 1.0674 – 1 = 0.0674 = 6.74%

Mean real return of stock:
(1 + nominal) / (1 + inflation) = (1 + real)
(1+real return) = 1.0674 / 1. 0325 = 1.0338 - 1 = 0.0338 = 3.38%

(b)

Mean real risk premium = Mean real return - Mean real RFR = 0.0338 - 0.0102 = 0.0236 = 2.36%

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