You've observed the following returns on Doyscher Corporation's stock over the past five years:...

Question:

You've observed the following returns on Doyscher Corporation's stock over the past five years: 27.6 percent, 15.4 percent, 33.8 percent, 3.2 percent, and 22.2 percent. The average inflation rate over this period was 3.32 percent and the average T-bill rate over the period was 4.3 percent.

(a) What was the average real return on the stock?

(b) What was the average nominal risk premium on the stock?

Real rate of return

Real rate of return refers to the inflation adjusted return of an asset. It is a return that discounts an increase of consumer price to determine how much is the actual gained of an asset relative to the current purchasing power of the investment.

Question (a)

Formula on calculating the average real return of the stock

{eq}\begin{align*} Average~real~return&=\frac{1+\frac{\sum stock~return}{number~of~periods}}{1+average~inflation~rate}-1\\ &=\frac{1+\frac{.276+.154+.338+.032+.222}{5}}{1+.0332}-1\\ &=\frac{1+\frac{102.2}{5}}{1.0332}-1\\ &=\frac{1.2044}{1.0332}-1\\ &=1.1657-1\\ &=.1657 \end{align*} {/eq}

The average real return of Doyscher Corporation's stock is 16.57 percent

Question (b)

Formula of the average nominal risk premium on the stock

{eq}\begin{align*} Average~nominal~risk~premium&=\frac{\sum stock~return}{number~of~periods}-Average~T-bill~rate\\ &=\frac{.276+.154+.338+.032+.222}{5}-.043\\ &=\frac{102.2}{5}-.043\\ &=.2044-.043\\ &=.1614\\ \end{align*} {/eq}

The average nominal risk premium of Doyscher Corporation stock is 16.14 percent 