Question

The stock of Business Adventures sells for $40 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	$2.00	$52
Normal economy	1.40	44
Recession	.70	34

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	%

b. Calculate the expected return and standard deviation of a portfolio invested half in Business Adventures and half in Treasury bills. The return on bills is 3%. (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Expected return	%
Standard deviation	%

Answer 1

Boom:

Expected Return = (Closing Price + Dividend - Opening Price) / Opening Price
Expected Return = ($52.00 + $2.00 - $40.00) / $40.00
Expected Return = $14.00 / $40.00
Expected Return = 35.00%

Normal:

Expected Return = (Closing Price + Dividend - Opening Price) / Opening Price
Expected Return = ($44.00 + $1.40 - $40.00) / $40.00
Expected Return = $5.40 / $40.00
Expected Return = 13.50%

Recession:

Expected Return = (Closing Price + Dividend - Opening Price) / Opening Price
Expected Return = ($34.00 + $0.70 - $40.00) / $40.00
Expected Return = -$5.30 / $40.00
Expected Return = -13.25%

Answer a.

Weight of Boom = 1/3
Weight of Normal = 1/3
Weight of Recession = 1/3

Expected Return of Business Adventures = (1/3) * 0.3500 + (1/3) * 0.1350 + (1/3) * (-0.1325)
Expected Return of Business Adventures = 0.1175 or 11.75%

Variance of Business Adventures = (1/3) * (0.3500 - 0.1175)^2 + (1/3) * (0.1350 - 0.1175)^2 + (1/3) * (-0.1325 - 0.1175)^2
Variance of Business Adventures = 0.038954167

Standard Deviation of Business Adventures = (0.038954167)^(1/2)
Standard Deviation of Business Adventures = 0.1974 or 19.74%

Answer b.

Weight of Business Adventures = 0.50
Weight of Treasury Bills = 0.50

Expected Return of Portfolio = Weight of Business Adventures * Expected Return of Business Adventures + Weight of Treasury Bills * Expected Return of Treasury Bills
Expected Return of Portfolio = 0.50 * 0.1175 + 0.50 * 0.0300
Expected Return of Portfolio = 0.0738 or 7.38%

Standard Deviation of Portfolio = Weight of Business Adventures * Standard Deviation of Business Adventures + Weight of Treasury Bills * Standard Deviation of Treasury Bills
Standard Deviation of Portfolio = 0.50 * 0.1974 + 0.50 * 0.0000
Standard Deviation of Portfolio = 0.0987 or 9.87%