Question

Q18. Use the following scenario analysis for Stocks X and Y to answer problems. Bear Market Normal Market 0.2 Probability Stock X Bull Market 0.3 50% 10% 0.5 18% 20% -20% -15% Stock Y a) What are the standard deviations of returns on Stocks X and Y? b) Assume that of your $10,000 portfolio, you invest $9,000 in Stock X and $1,000 in Stock Y. What is the expected return on your portfolio?

Answer 1

A) Standard deviations of return on stock X =24.33

Standard deviations of return on stock Y =13.23  

                    

Standard Deviation (SD

                                               

Standard deviations of return on stock X

Economy	Probability (P)	Rate of return (%)	(X - x̅)	P(X - x̅)2
(I)	(II)	(III)	(IV)	(V) = (II) * (IV)2
Bear Market	0.20	-20	-20-20=-40	0.20 * (-40)2 = 320
Normal Market	0.50	18	18-20=-2	0.50* (-2)2 =2
Bull Market	0.30	50	50-20=30	0.30*(30)2=270
Total ( ∑P(X - X̅)2)				592

x̅ = Expected return of the stock X = 0.20*(-20) + 0.50*18+0.30*50

                                                            =20%

x= Return on investment of the stock x

                                                    

Standard Deviation (SD

=                                               

=24.33

Standard deviations of return on stock Y

Standard deviations of return= /P(Y – 7)?

                                               

Standard deviations of return on stock Y

Economy	Probability (P)	Rate of return (%)	(Y - Y̅)	P(Y - Y̅)2
(I)	(II)	(III)	(IV)	(V) = (II) * (IV)2
Bear Market	0.20	-15	-15-10=-25	0.20 * (-25)2 = 125
Normal Market	0.50	20	20-10=10	0.50* (10)2=50
Bull Market	0.30	10	10-10=0	0.30*(0)2=0
Total ( ∑P(Y - Y̅)2)				175

Y̅ = Expected return of the stock Y = 0.20*(-15) + 0.50*20+0.30*10

                                                            =10%

Y= Return on investment of the stock y

                                                           

Standard deviations of return= /P(Y – 7)?

=                                   

=13.23

B) Expected Return on the portfolio when $9000 is invested in stock X and $1000 in stock Y = 19 %

Expected Return on portfolio = (Px * ERx) + (*Py * ERy)

                                                   = (0.90*20) + (0.10*10)

                                                    =19%

Note:

Investment in stock X=9000

Investment in stock Y=1000

Total investment = 9000+1000=10000

Px = Proportion of stock X=9000/10000=0.9 or 90%

Py = Proportion of stock Y=1000/10000=0.10 or 10%

ERx = Expected Return on stock x = 20

ERy = Expected Return on stock y = 10