Question

b) Mr Watson has savings of £12,000. Of this amount he has invested £6,000 in Treasury Bills which currently yield a return of 6%. The remainder has been invested in a portfolio of four different companies’ shares. Details of this portfolio are as follows:

Company	Expected Return	b shares	Worth of share holding
W	7.6%	0.20	£1,200
X	12.4%	0.80	£1,200
Y	15.6%	1.20	£1,200
Z	18.8%	1.60	£2,400

1. Calculate the expected return and beta (b) value of Mr Watson’s savings portfolio.
2. Mr Watson has decided that he wants an expected return of 12% on his savings portfolio. Show how he would achieve this by selling some of his Treasury Bills and investing the proceeds in the market portfolio.                                                                       
3. If Mr Watson were only to invest in Treasury Bills and the market portfolio, what savings portfolio would be required to give him an expected return of 10.32%?

Answer 1

i)

Company	Investment Amount	Weights	Return	Weights*Return	Beta	Weights*Beta
W	1200	0.2	7.60%	1.52%	0.2	0.04
X	1200	0.2	12.40%	2.48%	0.8	0.16
Y	1200	0.2	15.60%	3.12%	1.2	0.24
Z	2400	0.4	18.80%	7.52%	1.6	0.64
	6000	1		14.64%		1.08

Average return = 14.64%

Beta = 1.08

ii)

To achieve an expected return of 12%, Mr Watson needs to readjust his portfolio with x% weight in the Treasury bill and (1-x)% in the market portfolio:

x*(6%) + (1-x)*(14.64%) = 12%

Solving for x, we will get x = 0.3056

So, Mr Watson needs to sell $2332.8 worth of treasury bills and invest this amount in the market portfolio.

iii)

To achieve an expected return of 10.32%, Mr Watson needs to readjust his portfolio with x% weight in the Treasury bill and (1-x)% in the market portfolio:

x*(6%) + (1-x)*(14.64%) = 10.32%

Solving for x, we will get x = 0.5

So, the current portfolio which is 50% amount in Treasury Bills and 50% amount in the market portfolio will give Mr Watson the required return of 10.32%