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 $50 Normal economy 1.00 43 Recession 0.50 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.) 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 4%.

a. Expected holding-period return = 8.75%; and Standard deviation = 17.88%.

b. Portfolio expected return = 6.38%; and Portfolio standard deviation = 8.94%.

Explanation:

Given:

                              Dividend       Stock Price

Boom                        $2.00                $50

Normal economy      1.00                   43

Recession                 0.50                   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.)

Note: See the attached excel file for the calculation of expected return on standard deviation

The following are used in the excel.

HPY = Holding period yield = (((P1 - P0) + D1)/ P0) * 100

P1 = Year ending price of stock

P0 = Beginning price of stock

D1 = Dividend in each of the scenarios.

Boom = (((50 - 40) + 2)/ 40) * 100 = 30%

Normal = (((43 - 40) + 1)/ 40) * 100 = 10%

Recession = (((34 - 40) + 0.50)/ 40) * 100 = -13.75

From the excel file, we have:

E(X) = Expected holding-period return = 8.75%

Variance = 319.79

SD = Standard deviation = √variance = 17.88%

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 4%.

W1 = Weight of T - Bills = 0.50

W2 = Weight of stock = 0.50

Rf = Return on T - Bill = 4

Rs = Expected return on stock = 8.75

Portfolio expected return = (0.50 * 4) + (0.50 * 8.75) = 6.38%

Portfolio standard deviation = (0.50 * 0) + (0.50 * 17.88) = 8.94%

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