Question

1) You’ve observed the following returns on Crash-n-Burn Computer’s stock over the past five years: 2 percent, -9 percent, 29 percent, 14 percent, and 13 percent. The average inflation rate over this period was 3.2 percent and the average T-bill rate was 4.95 percent. Requirement 1: What was the average real return on Crash-n-Burn’s stock? 13.31% 6.08% 6.72% 7.03% 6.40% Requirement 2: What was the average nominal risk premium on Crash-n-Burn’s stock? 0.64% 4.41% 4.855 3.93% 3.44 2) A stock had returns of 12 percent, 15 percent, 10 percent, -10 percent, 16 percent, and -4 percent over the last six years. a) What is the arithmetic return for the stock? 6.70% 6.50% 6.83% 6.60% 7.80% b)What is the geometric return for the stock? 6.02% 7.26% 6.74% 6.12% 5.82%

Answer 1

Answer to Question 1:

Average Nominal Return = [0.02 + (-0.09) + 0.29 + 0.14 + 0.13] / 5
Average Nominal Return = 0.49 / 5
Average Nominal Return = 0.098 or 9.80%

Average Real Return = [Average Nominal Return - Average Inflation Rate] / [1 + Average Nominal Return]
Average Real Return = [0.0980 - 0.0320] / [1 + 0.0320]
Average Real Return = 0.0660 / 1.0320
Average Real Return = 0.0640 or 6.40%

Average Nominal Risk Premium = Average Nominal Return - Average Risk-free Rate
Average Nominal Risk Premium = 9.80% - 4.95%
Average Nominal Risk Premium = 4.85%

Answer to Question 2:

Arithmetic Return = [0.12 + 0.15 + 0.10 + (-0.10) + 0.16 + (-0.04)] / 6
Arithmetic Return = 0.39 / 6
Arithmetic Return = 0.0650 or 6.50%

Geometric Return = [(1+0.12) * (1+0.15) * (1+0.10) * (1-0.10) * (1+0.16) * (1-0.04)]^(1/6) - 1
Geometric Return = 1.419973632^(1/6) - 1
Geometric Return = 1.0602 - 1
Geometric Return = 0.0602 or 6.02%