Question

2.the stock of Business Adventures sells for $70 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 $78

Normal economy 1.50 72

Recession 0.50 66

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.)

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.)

Answer 1

Answer a.

Boom:

Holding Period Return = (Ending Price + Dividends - Beginning Price) / Beginning Price
Holding Period Return = ($78.00 + $2.50 - $70.00) / $70.00
Holding Period Return = 0.15

Normal Economy:

Holding Period Return = (Ending Price + Dividends - Beginning Price) / Beginning Price
Holding Period Return = ($72.00 + $1.50 - $70.00) / $70.00
Holding Period Return = 0.05

Recession:

Holding Period Return = (Ending Price + Dividends - Beginning Price) / Beginning Price
Holding Period Return = ($66.00 + $0.50 - $70.00) / $70.00
Holding Period Return = -0.05

Expected Return = (1/3) * 0.15 + (1/3) * 0.05 + (1/3) * (-0.05)
Expected Return = 0.05 or 5.00%

Variance = (1/3) * (0.15 - 0.05)^2 + (1/3) * (0.05 - 0.05)^2 + (1/3) * (-0.05 - 0.05)^2
Variance = 0.00667

Standard Deviation = (0.00667)^(1/2)
Standard Deviation = 0.0816 or 8.16%

Answer b.

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

Expected Return = Weight of Business Adventures * Expected Return of Business Adventures + Weight of Treasury Bills * Expected Return of Treasury Bills
Expected Return = 0.50 * 0.05 + 0.50 * 0.03
Expected Return = 0.04 or 4.00%

Standard Deviation = Weight of Business Adventures * Standard Deviation of Business Adventures
Standard Deviation = 0.50 * 8.16%
Standard Deviation = 4.08%