You’ve observed the following returns on Doyscher Corporation’s stock over the p
ID: 2734409 • Letter: Y
Question
You’ve observed the following returns on Doyscher Corporation’s stock over the past five years: –27.9 percent, 15.6 percent, 34.2 percent, 3.3 percent, and 22.3 percent. The average inflation rate over this period was 3.33 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. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).)
What was the average real risk premium? (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: –27.9 percent, 15.6 percent, 34.2 percent, 3.3 percent, and 22.3 percent. The average inflation rate over this period was 3.33 percent and the average T-bill rate over the period was 4.3 percent.
Explanation / Answer
Requirement 1:
The average real risk-free rate can be calculated with the use of Fisher Equation which is given below:
Average Real-Risk Free Rate = (1+T-Bill Rate)/(1+Inflation Rate) - 1
Using the values provided in the question, we get,
Average Real Risk-Free Rate = (1+4.3%)/(1+3.33%) - 1 = .94%
_________
Requirement 2:
The average real risk premium can be calculated with the use of following formula:
Average Real Risk Premium = Average Real Return - Average Real Risk-Free Rate
The average real return can be calculated by taking the arithmetic mean of returns of all the years and using Fisher Equation as follows:
Average Return (Arithmetic Mean) = (Sum of Returns of All Years)/Number of Years = (-27.9% + 15.6% + 34.2% + 3.3% + 22.3%)/5 = 9.50%
Average Real Return = (1+Average Return)/(1+Inflation Rate) - 1 = (1+9.50%)/(1+3.33%) - 1 = 5.97%
______
Now, we can calculate the average real risk premium as follows:
Average Real Risk Premium = 5.97% - .94% = 5.03%
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