You’ve observed the following returns on Doyscher Corporation’s stock over the p

Question

You’ve observed the following returns on Doyscher Corporation’s stock over the past five years: –29.1 percent, 16.4 percent, 35.8 percent, 3.7 percent, and 22.7 percent. The average inflation rate over this period was 3.37 percent and the average T-bill rate over the period was 4.3 percent.

1) 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).)

2) 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).)

You’ve observed the following returns on Doyscher Corporation’s stock over the past five years: –29.1 percent, 16.4 percent, 35.8 percent, 3.7 percent, and 22.7 percent. The average inflation rate over this period was 3.37 percent and the average T-bill rate over the period was 4.3 percent.

1) 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).)

2) 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

Nominal risk-free rate = (1 + risk-free rate) x (1 + rate of inflation) - 1

= ( 1+ 4.3%) * (1+3.37%) -1

= 7.815%

Given a nominal interest rate of 7.815% and an inflation rate of 3.37%, calculate the real interest rate:

The relation between a nominal interest rate (n), inflation (i), and the real rate of interest (r) is shown in the following equation:
1 + n = (1 + i)(1 + r)

Divide each side of the equation by (1 + i):

Solving for r, we get:

  1 + r  =  1.0430008706588

  r  =  1.0430008706588 - 1

  r  =  0.043

Convert Real Interest Rate to a Percentage - Multiply Real rate by 100%:
Real Interest Rate * 100% = 0.043 * 100%

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