Question

The stock of Business Adventures sells for $35 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	$43
Normal economy	2.00	40
Recession	0.85	31

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 = ($43.00 + $2.50 - $35.00) / $35.00
Expected Return = 30.00%

Normal:

Expected Return = (Closing Price + Dividend - Opening Price) / Opening Price
Expected Return = ($40.00 + $2.00 - $35.00) / $35.00
Expected Return = 20.00%

Recession:

Expected Return = (Closing Price + Dividend - Opening Price) / Opening Price
Expected Return = ($31.00 + $0.85 - $35.00) / $35.00
Expected Return = -9.00%

Answer a.

Probability of Boom = 1/3
Probability of Normal = 1/3
Probability of Expansion = 1/3

Expected Return of Stock = (1/3) * 0.30 + (1/3) * 0.20 + (1/3) * (-0.09)
Expected Return of Stock = 0.1367 or 13.67%

Variance of Stock = (1/3) * (0.30 - 0.1367)^2 + (1/3) * (0.20 - 0.1367)^2 + (1/3) * (-0.09 - 0.1367)^2
Variance of Stock = 0.027356

Standard Deviation of Stock = (0.027356)^(1/2)
Standard Deviation of Stock = 0.1654 or 16.54%

Answer b.

Weight of Stock = 0.50
Weight of Treasury Bills = 0.50

Expected Return of Portfolio = Weight of Stock * Expected Return of Stock + Weight of Treasury Bills * Expected Return of Treasury Bills
Expected Return of Portfolio = 0.50 * 0.1367 + 0.50 * 0.03
Expected Return of Portfolio = 0.0834 or 8.34%

Standard Deviation of Portfolio = Weight of Stock * Standard Deviation of Stock
Standard Deviation of Portfolio = 0.50 * 0.1654
Standard Deviation of Portfolio = 0.0827 or 8.27%