Question

The stock of Business Adventures sells for $55 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	$2.10	$65
Normal economy	1.40	58
Recession	0.50	49

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

a.	Expected return	6.67	%
	Standard deviation	13.10	%
Working Notes:
	Holding period return (HPR)
	= (Ending price + Dividend per share - Beginning price per share)/Beginning price per share
Boom	=($65 + $2.10 -$55)/$55 = 0.22
Normal economy	=($58 + $1.40 -$55)/$55 = 0.08
Recession	=($49 + $0.50 -$55)/$55 = -0.10
	Each scenarios are equally likely hence probability each scenario (1/3)
	Expected return = Sum of ( Return at each scenario x Probability of each scenario)
	Expected return = 0.22 x (1/3) + 0.08 x (1/3) + (-0.10) x (1/3)
	Expected return = 0.06666667
	Expected return = 6.67%
	Standard deviation of HPR = Square root of ( Sum of (Prob. x (return - expected return )^2))
	Standard deviation of HPR = Square root of ( ((1/3) x (0.22 - 0.0666666 )^2) + ((1/3) x (0.08 - 0.0666666 )^2) + ((1/3) x (-0.10 - 0.0666666 )^2) )
	Standard deviation of HPR = Square root of ( 0.017155556)
	Standard deviation of HPR = ( 0.017155556)^(1/2)
	Standard deviation of HPR = 0.13097922
	Standard deviation of HPR = 13.10%
b.	Expected return	4.83%
	Standard deviation	6.55%
Working Notes:
	1	2
	Business Adventures	Treasury bills
Return	6.66666667%	3%
Weight	0.50	0.50
	half	half
Standard deviation	0.13097922	0
		[risk is zero for treasury]
	Expected return of portfolio = Weighted average expected return of Individual assets
	Expected return of portfolio = W1 x r1 + W2 x r2
	Expected return of portfolio =( 0.50 x 6.66666667%)+ (0.50 x 3%)
	Expected return of portfolio =0.04833333
	Expected return of portfolio =4.83%
	Standard deviation of a portfolio of one risky and one risk free assets
	Standard deviation = W1 x s.d. 1
	Standard deviation = 0.50 x 0.13097922
	Standard deviation = 0.0654896
	Standard deviation =6.55%
Please feel free to ask if anything about above solution in comment section of the question.