Question

Consider 2 scenarios: Boom Economy and Normal Economy. The Boom economy has 30% chance of happening, while Normal economy has 70% chance of happening.

For each scenario (Boom and Normal), stock ABC has a return of 25%, and 4%, respectively; stock XYZ has a return of 10% and 6.5%, respectively; the market portfolio has a return of 12% and 5% respectively.

1) Calculate Expected return, Variance and Standard deviation for stock ABC and XYZ

2) Based on your results in part (1), can you decide which stock to invest?

3) Calculate Beta for stock ABC and XYZ

4) If the T-bill rate is 3%, what does the CAPM say about the fair expected rate of return on the two stocks? How does this result influence your investment decision?

Answer 1

Economy

Probability

R(ABC)

R(XYZ)

R(market)

(R(ABC)-ABC)

(R{(ABC)-ABC)}2

P{(R(ABC)-ABC)}2

(R(XYZ)-XYZ)

{(R(XYZ)-XYZ)}2

P{(R(XYZ)-XYZ)}2

(R(market)-market)

{(R(market)-market)}2

P{(R(market)-market)}2

P(R(ABC)-ABC)(R(market)-market)

P(R(XYZ)-XYZ)(R(market)-market)

Boom

30%

25

10

12

(25-10.3)=14.7

14.72=216.09

216.09*30%= 64.83

(10-7.55)=2.45

2.452=6

6*30%=1.8

12-7.1=4.9

4.92=24.01

24.01*30%=7.20

30%*14.7*4.9= 21.60

30%*2.45*4.9= 3.60

Normal

70%

4

6.5

5

(4-10.3)=-6.3

-6.32=39.69

39.69*70%= 27.78

(6.5-7.55)=-1.05

-1.052=1.10

1.10*70%= 0.77

5-7.1=-2.1

-2.12=4.41

4.41*70%=3.08

70%*-6.3*-2.1= 9.26

70%*-1.05*-2.1= 1.54

92.61

2.57

10.28

30.86

5.14

Answer to Q 1:

Calculation of Expected Return=

Expected return of ABC(ABC)=(25*30%)+(4*70%)=10.3%

Expected return of ABC(XYZ)=(10*30%)+(6.5*70%)=7.55%

Expected return of ABC(market)=(12*30%)+(5*70%)=7.1%

Expected Retun on Market is considered as Rm=7.1%

Answer to Q 1:

Calculation of Standard Deviation=

ABC==9.6234

XYZ==1.6031

market==3.2078

Answer to Q 1:

Calculation of Variance=²

²ABC=92.61

²XYZ=2.57

²Market=10.28

Answer to Q 3:

Calculation of Beta_ABC=P(R(ABC)-ABC)(R(market)-market) / P{(R(market)-market)}²

=30.86 /10.28=

=3

Calculation of BetaXYZ=PP(R(XYZ)-XYZ)(R(market)-market / P{(R(market)-market)}²

=5.14 /10.28

=0.5

Answer to Q 4:

Expected Retun on Market is considered as Rm=7.1%

Calculation of Expected Return using CAPM on ABC =Rf +Beta (Rm-Rf)

=3+3(7.1-3)

=15.3

Calculation of Expected Return using CAPM on XYZ =Rf +Beta (Rm-Rf)

=3+0.5(7.1-3)

=5.05

Answer to Q2: In which stock to Invest

	Expected Return	Standard Deviation
ABC	10.30%	9.6234
XYZ	7.55%	1.6031

In which stock to invest depends upon Investor's attitude towards risk. & return

If investor is risk taker then he would invest in Stock ABC ( Return: 10.30% & risk: 9.62)else he will invest in Stock XYZ ( Return: 7.55% & risk: 1.6031)

Please feel free to reach or comment back if you need further clarity or something is missing