Question

1. Consider a portfolio consisting of the following three stocks:

	Portfolio Weight	Volatility	Correlation with Market Portfolio
HEC Corp	0.26	13%	0.35
Green Midget	0.29	28%	0.52
Alive And Well	0.45	11%	0.54

The volatility of the market portfolio is 10% and it has an expected return of 8%. The risk-free

rate is 3%.

1. Compute the beta and expected return of each stock.
2. Using your answer from part (a), calculate the expected return of the portfolio.
3. What is the beta of the portfolio?
4. Using your answer from part (c), calculate the expected return of the portfolio and verify that it matches your answer to part (b).

Answer 1

Formula				Cor*sd/sdm	rf + (rm-rf)*b
Stock	Portfolio weight (w)	Volatility (sd)	Correlation with market porfolio (cor)	Beta coefficient (b)	Expected return E[r]
HEC Corp.	26%	13%	0.35	0.4550	5.28%
Green Midget	29%	28%	0.52	1.4560	10.28%
Alive and Well	45%	11%	0.54	0.5940	5.97%
Market portfolio	100%	10%		0.8078	7.04%

risk-free rate (rf) = 3%; market return (rm) = 8%; market volatility (sdm) = 10%

a). Beta for a stock = Correlation of the stock with the market (cor)*volatility of the stock (sd)/volatility of the market (sdm)

HEC Corp beta = (0.35*13%/10%) = 0.445

Green Midget beta = (0.52*28%/10%) = 1.4560

Alive and Well beta = (0.54*11%/10%) = 0.5940

Expected return of a stock E[r] = rf + (rm - rf)*beta

E[r] for HEC Corp = 3% + (8%-3%)*0.445 = 5.28%

E[r] for Green Midget = 3% + (8%-3%)*1.4560 = 10.28%

E[r] for Alive and Well = 3% + (8%-3%)*0.5940 = 5.97%

b). Expected portfolio return = sum of weighted returns of all stocks in the portfolio

= (26%*5.28%) + (29%*10.28%) + (45%*5.97%) = 7.04%

c). Beta of the portfolio = sum of weighted beta of all stocks in the portfolio

= (26%*0.4550) + (29%*1.4560) + (45%*0.5940) = 0.8078

d). Using CAPM, expected return of the portfolio = rf + (rm - rf)*portfolio beta

= 3% + (8%-3%)*0.8078 = 7.04%

This is matches the answer computed in part (b).