7.12 You’ve observed the following returns on Crash-n-Burn Computer’s stock over
ID: 2791022 • Letter: 7
Question
7.12
You’ve observed the following returns on Crash-n-Burn Computer’s stock over the past five years: 4 percent, -12 percent, 22 percent, 14 percent, and 18 percent. The average inflation rate over this period was 3.4 percent and the average T-bill rate was 4.5 percent.
What was the average real return on Crash-n-Burn’s stock? (Do not round intermediate calculations.)
What was the average nominal risk premium on Crash-n-Burn’s stock? (Do not round intermediate calculations.)
You’ve observed the following returns on Crash-n-Burn Computer’s stock over the past five years: 4 percent, -12 percent, 22 percent, 14 percent, and 18 percent. The average inflation rate over this period was 3.4 percent and the average T-bill rate was 4.5 percent.
Explanation / Answer
Returns during past 5 years = 4% -12% 22% 14% 18%
Inflation Rate = 3.4%
Risk-Free Rate =4.5%
a.) Real Returns during past 5 years = (4-3.4)% (-12-3.4)% (22-3.4)% (14-3.4)% (18-3.4)%
= 1.4% -15.4% 18.6% 10.6% 14.6%
To compute the average return over 5 years, we will add 1 in each of above values and then take geometric mean of the arrived numbers i.e.
Product of Returns = {1.0140 x 0.846 x 1.186 x 1.106 x 1.146}(1/5) -1 = 1.2895(1/5) -1 =1.0521 -1 = 0.0521
Hence, average return is 5.21%
b.) Annual Risk Premium = (4-4.5)% (-12-4.5)% (22-4.5)% (14-4.5)% (18-4.5)%
= -0.50% -16.5% 17.5% 9.6% 13.5%
To compute the average return over 5 years, we will add 1 in each of above values and then take geometric mean of the arrived numbers i.e.
Product of Returns = {0.995 x 0.835 x 1.175 x 1.096 x 1.135}(1/5) -1 = 1.21437(1/5) -1 =1.0396 -1 = 0.0396
Hence, average return is 3.96%
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