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 $48 Boom Normal economy Recession $2.80 1.80 0.90 43 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 5%. (Do not round intermediate calculations. Round your answers to 2 decimal places.) Expected return Standard deviation

Answer 1

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 = [ (48 - 40 ) + 2.80 ] / 40 * 100 = 27 %

Normal = [ ( 43 - 40 )+ 1.80 ] / 40 * 100 = 12 %

Recession = [ (34 - 40 ) + 0.90 ] / 40 * 100 = - 12.75 %

Calculation of expected return on standard deviation

X	P	X * P	Dx	Dx2	P*Dx2
27	0.333333	9	18.25	333.0625	111.0208
12	0.333333	4	3.25	10.5625	3.520833
-12.75	0.333333	-4.25	-21.5	462.25	154.0833
	E(X) =	8.75		Variance	268.625
				Standard deviation	16.39

Expected return= E(X)  = 8.75 %

Standard deviation. = square root ( variance ) = square root ( 268.625 )  = 16.39 %

Question - 2

W1 = Weight of T - Bills = 0.50

W2 = Weight of stock = 0.50

Rf = Return on T - Bill = 5

Rs = Expected return on stock = 8.75

Portfolio return = 0.50 * 5 + 0.50 * 8.75 = 6.88 %

Portfolio standard deviation = 0.50 * 0 + 0.50 * 16.39 = 8.20 %