# 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