Question

Mr Brown is the manager of a portfolio consisting of stocks as shown below. the market risk premium is 8% and the risk free-rate is 3%

Stock	Investment	Beta
X	$2 m	1.4
Y	$3 m	1.0
Z	$5 m	-0.2

i) Calculate the beta and expected return of the portfolio

ii) Appraise & discuss why Mr Brown included stock Z in the portfolio

iii) Mr Brown strongly believe that the stock market would rise in the next one year. Discuss one possible way that he could use to increase the performance of the portfolio if the stock market were to rise.

Answer 1

i)	Calculation of beta and expected return of the portfolio.
	The beta of the portfolio is the weighted average beta of all stocks in the portfolio.
	therefore beta of the portfolio is
	Stock	Beta	Investment	Weight	Weighted beta
	a	b	c	d=c/10	e=d*b
	X	1.4	2	0.2	0.28
	Y	1	3	0.3	0.3
	Z	-0.2	5	0.5	-0.1
			10	1	0.48
	Therefore Beta of portfolio = 0.48
	Expected return of the portfolio = Rf + beta(Rm-Rf)
		Where,
		Rf = Risk-Free Return
		Rm - Rf= Market risk premium
		= 3% + 0.48 * (8%)
		=6.84%
ii)	Stock Z has a negative beta that means stock Z will give return which is less than the risk-free return.
	The of stock Z half of the portfolio stocks, therefore, the changes in returns in stock will significantly
	affect the portfolio return.
	Mr. Brown included stock Z in the portfolio to reduce overall portfolio risk through diversification.
iii)	If Mr. Brown strongly believe that the stock market would rise in the next year he may
	reduce investment in Z and increase investment in X and Y which will give him higher returns.