Question

You’ve observed the following returns on SkyNet Data Corporation’s stock over the past five years: 19 percent, 24 percent, 11 percent, −9 percent, and 13 percent.

     a.What was the arithmetic average return on the company’s stock over this 5-year period?

     b.What was the variance of the company’s returns over this period? The standard deviation?

Suppose the average inflation rate over this period was 3.6 percent and the average T-bill rate over the period was 4.1 percent.

     c.What was the average real return on the company’s stock?

     d.What was the average nominal risk premium on the company’s stock?

Answer 1

a. Arithmetic average return = (19%+24%+11%-9%+13%)/5 = 11.60%
b. Variance = ((19%-11.60%)^2 + (19%-11.60%)^2 +(19%-11.60%)^2 +(19%-11.60%)^2 +(19%-11.60%)^2)/(5-1) = 1.59%
Standard Deviation = Variance^0.5 =1.59%^0.5 = 12.60%
c. Average Real Return = (1+Average Return )/(1+inflation Rate)-1 = (1+11.60%)/(1+3.6%)-1 = 7.72%
d.Average nominal risk premium = Nominal Return - Risk Free Rate = 11.60%- 4.1% = 7.5%

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