Question

Ravi, a fund manager working for a private equity firm, is considering including the following stocks in the firm’s portfolio:

Rate of Return State of Probability Economy Stock RST 0% 6% 15% Stock VVR 25% 40% 35% Boom Normal Recession 20% 12% -4% Stock BAB 40% 15% -26%

He plans to invest 40% of the portfolio funds in stock RST and the balance equally between VVR and BAB. Beta of stock VVR is 0.15 higher than RST.

The firm’s in-house economist anticipates the probability of boom, normal and recession to be 25%, 40% and 35% respectively. The yield on long term government securities is 3% per year.

(a) Calculate the expected return and standard deviation for each stock. (6 marks)

(b) Calculate the expected return, expected risk premium and standard deviation for the portfolio. (4 marks)

(c) Interpret your answer for part (a) and (b) and advise Ravi on his asset allocation plan for the portfolio. (6 marks)

(d) Compute the expected market risk premium assuming capital asset pricing model holds. (4 marks) (e) Explain whether stock RST or stock VVR is riskier. (5 marks)

Answer 1

a)For stock RST

Probability(P)	RST(X)	px	(r-T	$p(x-\bar{x})^{2}$
0.25	0%	0	-7.65	14.63
0.40	6%	2.4	-1.65	1.089
0.35	15%	5.25	7.35	18.91

$\bar{x}$=$\sum$px Variance=$\sum$  $p(x-\bar{x})^{2}$=34.629

= 7.65 S.D=Square root of variance=5.88

Stock VVR

Probability(P)	RST(Y)	pY	$(y-\bar{y})$	$p(y-\bar{y})^{2}$
0.25	20%	5	11.6	33.64
0.40	12%	4.8	3.6	5.18
0.35	-4%	-1.4	-12.4	53.82

     $\bar{y}$=$\sum$py Variance=$\sum$  $p(y-\bar{y})^{2}$=92.64

= 8.4 S.D=Square root of variance=9.62

Stock BAB

Probability(P)	RST(z)	pz	$(z-\bar{z})$	$p(z-\bar{z})^{2}$	$p(x-\bar{x})(y-\bar{y})$	$p(x-\bar{x})(z-\bar{z})$	$p(y-\bar{y})(z-\bar{z})$
0.25	40%	10	33.1	273.90	-22.185	-63.30	96
0.40	15%	6	8.1	26.24	-2.376	-5.346	11.664
0.35	-26%	-9.1	-32.9	378.84	-31.9	-84.63	142.79
				COV-------	-56.461	-153.28	250.454

  $\bar{z}$=$\sum$pz Variance=$\sum$  $p(z-\bar{z})^{2}$=678.98

= 6.9 S.D=Square root of variance=26.06

b)Expected return of portfolio

=$\sum$weight of stock* Expected return of each stock

=0.40*7.65+0.30*8.4+.30*6.9

=7.65

Standard deviation of portfolio=

square root of
2w1wzCov(RAS, BAB)

=8.35

Expected Risk premium

Assuming CAPM hold true

We have two equations =7.65

+(Rm -

=8.4

UTT

Solving this equation simultaneously we get

(Rm-Rf)($\beta ras-\beta vrr$)=-o.75

we know difference of beta is 0.15 given in the sum

Rm -Rf=5

Risk premium is 5

c)Lets calculate coefficient of variation(CV)

(S.D/Mean )*100

RAS=76.86%

VRR=114%

BAB=377.68%

So we see VRR and BAB are very risky as CV is high thus he should allocate more funds to RST and VRR

And also for diversification its better to invest in Rst as it moves in opposite direction diversification mitigates risk

D) Same as answer B) third part risk premium is 5

e)Stock VRR is riskier as its CV is higher than RST

CV is calculated above in answer c)