Question

9. Calculating Returns and Variability You’ve observed the following returns on Yasmin Corporation’s
stock over the past five years: 19 percent, −13 percent, 7 percent, 25 percent, and 16 percent.
a. What was the arithmetic average return on the company’s stock over this five-year period?
b. What was the variance of the company’s stock returns over this period? The standard deviation?

10. Calculating Real Returns and Risk Premiums In Problem 9, suppose the average inflation rate over
this period was 2.6 percent and the average T-bill rate over the period was 3.25 percent.
a. What was the average real return on the company’s stock?
b. What was the average nominal risk premium on the company’s stock?

Answer 1

9a). E(r) = [Ri / n]

= [19% - 13% + 7% + 25% + 16%] / 5 = 54% / 5 = 10.80%

9b). ² = [{Ri - E(r)}² / (n - 1)]

= [(19% - 10.80%)² + (-13% - 10.80%)² + (7% - 10.80%)² + (25% - 10.80%)² +

(16% - 10.80%)²] / [5 - 1]

= [67.24%² + 566.44%² + 14.44%² + 201.64%² + 27.04%²] / 4 = 876.80%² / 4 = 219.20%²

= [²]^1/2

= [219.20%²]^1/2 = 14.81%

10a). Real Return = [(1 + R_nominal) / (1 + Inflation)] - 1

= [1.1080 / 1.0260] - 1

= 1.0799 - 1 = 0.0799, or 7.99%

10b). Nominal Risk Premium = Nominal Return - Risk Free Rate

= 10.80% - 3.25% = 7.55%