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 9.78 % Standard deviation 17.32 % 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

a.

expected holding returns:

boom = [($50 + $2) - $40] / $40 = 30%

normal = [($44 + $1.40) - $40] / $40 = 13.5%

recession = [($34 + $0.70) - $40] / $40 = -13.25%

expected return = (30% x 1/3) + (13.5% x 1/3) - (13.25% x 1/3) = 0.1 + 0.045 - 0.044 = 0.101 = 10.1%

variance = 1/3(30 - 10.1)² + 1/3(13.5 - 10.1)² + 1/3(-13.25 - 10.1)² = 132 + 3.85 + 181.74 = 317.59

standard deviation = √317.59 = 17.82%

b.

expected holding returns:

boom = [($50 + $2) - $40] / $40 = 30%

normal = [($44 + $1.40) - $40] / $40 = 13.5%

recession = [($34 + $0.70) - $40] / $40 = -13.25%

T-bills = 3%

expected return = (30% x 1/6) + (13.5% x 1/6) - (13.25% x 1/6) + (3% x 1/2) = 0.05 + 0.0225 - 0.022 + 0.015 = 0.0655 = 6.55%

variance = 1/6(30 - 6.55)² + 1/6(13.5 - 6.55)² + 1/6(-13.25 - 6.55)² + 1/2(3 - 6.55)² = 91.65 + 8.05 + 65.34 + 6.30 = 171.35

standard deviation = √171.35 = 13.09%

Step-by-step explanation:

Dividend Stock Price

Boom $2.00 $52

Normal economy $1.40 $44

Recession $0.70 $34