Question

The common stock of Nike sells for $28 a share and offers the following payoffs next year:

                            

	Probability	Dividend	Stock Price
Boom	0.35	$1	$19
Normal economy	0.5	$2	$29
Recession	0.15	$6	$37

Calculate the expected return and standard deviation of Nike. (Round your answers to 2 decimal places. Use the minus sign for negative numbers if it is necessary.)

Expected rate of return      %
Standard deviation     %

The common stock of Mandarin, Inc., a restaurant chain, will generate the following payoffs to investors next year:

	Probability	Dividend	Stock Price
Boom	0.35	$8	$198
Normal economy	0.5	$5	$103
Recession	0.15	$1	$3

                    

The stock is selling today for $93.

Calculate the expected return and standard deviation of a portfolio half invested in Nike and half in Mandarin. (Round your answers to 2 decimal places. Use the minus sign for negative numbers if it is necessary.)

Expected return of portfolio       %
Standard deviation of portfolio      %

Why is the portfolio standard deviation lower than for either stock’s individually?

Answer 1

A)    HPR = Stock Price ((End of period value - original value)+Income) / original value) * 100

HPR(boom)= ((19-28)+1)/28 = -28.57%

HPR(Normal)= ((29-28)+2/28 = 10.71%

HPR(Recession)= ((37-28)+6)/28 = 53.57%

Calculation of Expected Return of Nike: (Probability of Boom * Return from Boom) +(Probability of Normal * Return from Normal) +(Probability of Recession * Return from Recession)

=(0.35 x -28.57%) + (0.50 x 10.71%) + (0.15 x 53.57%) = 3.39%

Calculation of Standard deviation Nike:

Variance: [Probability of Boom * (Return from Boom – total expected return)2] + [Probability of Normal * (Return from Normal – total expected return)2] + [Probability of Recession * (Return from Recession – total expected return)2]

= 0.35(-28.57 – (3.39)) 2+ 0.50 (10.71 – (3.39)) 2+ 0.15 (53.57 – (3.39)) 2 = 762.09

Standard Deviation will be Square Root of Variance = 27.61%

B)    HPR = Stock Price ((End of period value - original value)+Income) / original value) * 100

HPR(boom)= ((198-93)+8)/93 = 121.51%

HPR(Normal)= ((103-93)+5/93 = 16.13%

HPR(Recession)= ((3-93)+1)/93 = -95.70%

Calculation of Expected Return of Mandarin: (Probability of Boom * Return from Boom) +(Probability of Normal * Return from Normal) +(Probability of Recession * Return from Recession)

=(0.35 x 121.51%) + (0.50 x 16.13%) + (0.15 x -95.70%) = 36.24%

Calculation of Standard deviation of Mandarin:

Variance: [Probability of Boom * (Return from Boom – total expected return)2] + [Probability of Normal * (Return from Normal – total expected return)2] + [Probability of Recession * (Return from Recession – total expected return)2]

= 0.35(121.51 – (36.24)) 2+ 0.50 (16.13 – (36.24)) 2+ 0.15 (-95.70 – (36.24)) 2 = 5357.972

Standard Deviation of Mandarin will be Square Root of Variance = 73.20%

Calculation of the expected return and standard deviation of a portfolio half invested in Nike and half in Mandarin.

Expected Return of Nike 3.39%

Expected Return of Mandarin 36.24%

Weight of Nike W1 = .50

Weight of Mandarin W2 = .50

Expected Return of portfolio = (.50 * 3.39) + (.50 * 36.24) = 19.81%

Standard deviation of portfolio = (.50 * 27.61) + (.50 * 73.20) = 50.40%

The portfolio standard deviation is lower than for either stock’s individually because the stocks are diversified in different stocks. Diversification leads to the reduction in the risk unless perfect correlation exists between returns on portfolio investments.