Question

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

		Rate of Return
Probability	State of Economy	Stock RST	Stock VVR	Stock BAB
25%	Boom	0%	20%	40%
40%	Normal	6%	12%	15%
35%	Recession	15%	-4%	-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 the standard deviation for each stock

b) Calculate the expected return, expected risk premium and the standard deviation for the portfolio

c) Interpret your answer in (a) and (b) and advise Ravi on his asset allocation plan for the portfolio

d) Compute the expected market risk premium assuming capital asset pricing model holds.

e) Explain whether stock RST or stock VVR is riskier

Answer 1

	Information Provided
	Probability	State of Economy	Stock RST	Stock VVR	Stock BAB
	25%	Boom	0%	20%	40%
	40%	Normal	6%	12%	15%
	35%	Recession	15%	-4%	-26%
	Particulars	Stock RST	Stock VVR	Stock BAB	Total
	Investment Plan	40%	30%	30%	100%
a)	Calculation of expected return and Standard Deviation for each stock.
a	Expected Return
	Formula	=Expected Return X probability %
	Stock RST	=	(0%*25%)+(6%*40%)+(15%*35%)
		=	7.65%
	Stock VVR	=	(20%*25%)+(12%*40%)+(-4%*35%)
		=	8.40%
	Stock BAB	=	(40%*25%)+(15%*40%)+(-26%*35%)
		=	6.90%
b	Standard Deviation
	Formula	=	√Probability X (Given Return-Expected Return)
	Stock RST	=	√ (25% *(0-7.65)^2)+(40% *(6-7.65)^2)+(35%*(15-7.65)^2)
		=	34.63
		=	√34.63
		=	5.88
	Stock VVR	=	√ (25% *(20-8.40)^2)+(40% *(12-8.40)^2)+(35% *(-4-8.40)^2)
		=	92.64
		=	√92.64
		=	9.624
	Stock BAB	=	√ (25% *(40-6.90)^2)+(40%*(15-6.90)^2)+(35%*(-26-6.90))
			288.63
			√288.63
			16.99
c	Interpretation of part a
	Expected Return of RST is highest so major investment should be done in RST and least in BAB as its return is lesser.
	Interpretation of part b
	SD of RST is less hence it is less rikier than other two securities and Stock BAB more riskier hence investment in this securities should be done less.
d	Market Risk Premium by using CAPM
	Expected Return=	Risk free Return+Beta(Market Return-Risk Free Return)
	=
	Expected Return of portfolio=
		Weight in portfolio of security 1X Expected Return of security 1
	Plus	Weight in portfolio of security 2X Expected Return of security 2
	Plus	Weight in portfolio of security 3X Expected Return of security 3
	=	40% X 7.65%
	Plus	30% X 8.40%
	Plus	30% X 6.90%
	=	7.65%
	Risk Free Return	3%
	Assuming Beta is 1 as relevant data not provided.
	Expected Return=	Risk free Return+Beta(Market Return-Risk Free Return)
	7.65	=(3+1*(X-3))
	7.65	=(3+x-3)
	x	=7.65
e	VVR is more riskier as its beta and standard deviation is more than RST.