Question

The stock of ABC sells for $50 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

Good economy                            1.5                                46                                

Normal economy                         1.00                              43

Recession                                   .50                                34

a. Calculate the expected holding-period return and standard deviation of the holding period

return. All four scenarios are equally likely.

b. Calculate the expected return and standard deviation of a portfolio invested 60% in

ABC and 40% in Treasury bills. The return on bills is 3%.

Answer 1

Sol a. The workings are as under:-

Stock Price Now	50	P0	Expected Return = HPR * Probability = 4.00%*0.25 in Boom and the same follows for others
Stock Price End of Boom year	50	P1
Stock Price End of Good year	46	P1
Stock Price End of Normal year	43	P1
Stock Price End of Recession year	34	P1
Dividend Rec at the end of Boom Year	2	D1
Dividend Rec at the end of Good Year	1.5	D1
Dividend Rec at the end of Normal Year	1	D1
Dividend Rec at the end of Recession Year	0.5	D1
Holding Period Return (HPR) Formula = (P1-P0 +D1) / P0
Type of Economy	HPR	Probability	ER 1st Step	2nd Step HPR - ER	3rd Step (HPR-ER)^2	4th Step is Variance = [(HPR-ER)^2] * Probability
Boom	4.00%	0.25	1.00%	0.0300	0.0009	0.0002
Good	-5.00%	0.25	-1.25%	-0.0375	0.0014	0.0004
Normal	-12.00%	0.25	-3.00%	-0.0900	0.0081	0.0020
Recession	-31.00%	0.25	-7.75%	-0.2325	0.0541	0.0135
	Total Expected HPR		-11.00%	Variance of Expected HPR is		0.0161
				Standard Deviation is the Square Root of Variance		0.1269

Sol (b) We have assumed that economy is in boom and the workings are as under:-

Stock Price Now	50	P0	Expected Return = HPR * Weight in Portfolio = 4.00%* 0.60 in Boom and for Treasury it is 3.00%*0.40
Stock Price End of Boom year	50	P1
Dividend Rec at the end of Boom Year	2	D1
Holding Period Return (HPR) Formula = (P1-P0 +D1) / P0
Type of Economy	HPR	Weight in Portfolio	ER 1st Step	2nd Step HPR - ER	3rd Step (HPR-ER)^2	4th Step is Variance = [(HPR-ER)^2] * Weight
Boom (Invested in ABC)	4.00%	0.6	2.40%	0.0160	0.0003	0.0002
Invested in Treasury Bills	3.00%	0.4	1.20%	0.0180	0.0003	0.0001
	Total Expected HPR		3.60%	Variance of Expected HPR is		0.0003
				Standard Deviation is the Square Root of Variance		0.0168