Chapter 20, Problem 1SR

To determine

Prove that the expected payoff for the act of purchasing Rim Homes stock is $1,760.

Answer to Problem 1SR

The expected payoff for the act of purchasing Rim Homes stock is $1,760.

Explanation of Solution

From the Table 20-1, the bull market and bear stock for the Rim homes are 2,200 and 1,100, respectively. The corresponding probabilities are 0.60 and 0.40.

The expected payoff for the act of purchasing Rim Homes stock is calculated as follows:

Event	Payoff value	Probability	Expected value
Bull market	2,200	0.60	$2,200\times 0.60=1,320$
Bear market	1,100	0.40	$1,100\times 0.40=440$
			$\begin{array}{c}\text{Total}=1,320+440\\ =1,760\end{array}$

Then, the expected payoff for the act of purchasing Rim Homes stock is obtained by adding the expected values 1,320 and 440. That is, $1,320+440=1,760$.

Thus, the expected payoff for the act of purchasing Rim Homes stock is $1,760.