Question

The stock of Business Adventures sells for $50 a share. Its likely dividend payout and end-of-year price depend on the state of the economy by the end of the year as follows:

Dividend Stock price
Boom $3.00 $60
Normal economy 1.20 58
Recession . 75 49
a. Calculate the expected holding-period return and standard deviation of the holding-period return. All three scenarios are equally likely. (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Expected return %
Standard deviation %

Answer 1

The expected holding-period return is 55.67% and the standard deviation is 5.35%.

Step-by-step explanation:

To calculate the expected holding-period return, we need to find the weighted average of the returns in each scenario.

The expected return is calculated as follows:

(Boom return * probability) + (Normal return * probability) + (Recession return * probability).

In this case, the expected return is

(60 * 1/3) + (58 * 1/3) + (49 * 1/3) = $55.67.
The standard deviation of the holding-period return is a measure of the volatility of returns. It is calculated as the square root of the weighted average of the squared deviations from the expected return.

In this case, the standard deviation is the square root of

((3 * (60 - 55.67)^2) + (3 * (58 - 55.67)^2) + (3 * (49 - 55.67)^2)) = $5.35.
Therefore, the expected holding-period return is 55.67% and the standard deviation is 5.35%.