Question

The stock of XYZ sells for $75 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	$2.50	$83
Normal economy	1.30	77
Recession	0.75	65

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.)

Answer 1

The probability of each scenario is 1/3

Holding period return is found using the following equation

The expected holding period return when the economy is in boom

Expected holding period return when economy is in boom = 4.666666667 %

The expected holding period return when the economy is in normal

r = 1.466666667 %

The expected holding period return when the economy is in recession

r = - 4.111111111 %

Expected holding-period return =  4.666666667 % + 1.466666667 % + - 4.111111111 %

Expected holding-period return = 2.02 %

Variance of the expected holding - period return = 1/3 [ 4.666666667 % - 2.02 % ] ² + 1/3 [  1.466666667 %   - 2.02 % ] ² + 1/3 [  - 4.111111111 %   - 2.02 % ] ²

Variance of the expected holding - period return =  0.149731687 %

Standard deviation =

Standard deviation =

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Expected holding-period return = 2.02 %

Standard deviation of the holding-period return = 3.87 %