Question

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%?

ii and iii?

Answer 1

Ans i )

Here :

Weight in Portfolio = Worth of Share Holding / Savings Portfolio Total Value =  Worth of Share Holding / 12,000

Weighted Beta = Weight in Portfolio *  Beta of Shares

Now for Treasury Bills Beta will be Zero. As risk associated in T Bill considered as almost Nil.

Weighted Expected Return = Weight in Portfolio * Expected Return

Beta of Portfolio = Sum of ( Weighted Beta )

Expected Return of Portfolio = Sum of ( Weighted Expected Return )

Ans :

Beta of Portfolio = 0.54

Expected Return of Portfolio = 10.32%

Ans ii )

To achieve expected return of 12% Mr. Watson decided to sell Some of his Treasury Bills Holding and Investing in Market Portfolio.

Assume Weight of W he invested in Market Portfolio. So the Same amount of Weight will reduce from T Bill.

For Market Portfolio Beta will Be always = 01

Expected Return = Risk free Rate + Market Risk Premium  

Market Risk Premium = Excess Market Return / Beta of that Stock

For Company W

Market Risk Premium = Excess Market Return / Beta of that Stock =  Expected Return - Risk Free Rate  / Beta of that Stock = (7.60% - 6.00%) / 0.2 = 8.00%

Market Risk Premium = 8.00%

Expected Return for Market Portfolio = Risk free Rate + Market Risk Premium = 6.00% + 8.00% = 14.00%

Now

Expected Return for the portfolio :

Expected Return of Portfolio = Sum of ( Weighted Expected Return )

12.00 % = 0.1 * 7.60% + 0.1 * 12.40% +  0.1 * 15.60% + 0.2 * 18.80% + ( 0.5 - W) * 6.00% + W * 14.00%

12.00% = 10.32% + W * 14.00% - W * 6.00%

8.000% * W = 1.68%

W = 0.21

Now Value of The T-Bill he should Sold = Portfolio Value * Weight = 12,000 * 0.21 = 2520 (Ans)

Extra Amount to be Invested in Market Portfolio = Portfolio Value * Weight = 12,000 * 0.13125 = 2520 (Ans)

Ans iii )

Investing Only in Treasury Bills and the market portfolio

the expected return of portfolio 10.32%

Expected Return of T Bill = 6.00%

Expected Return for Market Portfolio = 14.00%

Amount Invested in T Bill = 6000

Amount   Invested in  Market Portfolio = X

Weigh of T Bill = 6000/ (6000 + X) [ Invested in Particular Asset / Total Investment ]

Weigh of Market Portfolio = X / (6000 + X)  [ Invested in Particular Asset / Total Investment ]

Weighted Expected Return of TBill = Weigh of T Bill * Expected Return = 6000/ (6000 + X) *  6.00%

Weighted Expected Return of Market Portfolio   = Weigh of Market Portfolio * Expected Return = X/ (6000 + X) * 14.00%  

Expected Return OF Portfolio = Weighted Expected Return of TBill + Weighted Expected Return of Market Portfolio

10.32% = 6000/ (6000 + X) * 6.00% + X/ (6000 + X) * 14.00%

(36,000 + 14X) /   (6000 + X) = 10.32

14X - 10.32X = 10.32*6000 - 36000

X = 25,920 / 73.68 = 7043.48

So he should invest in Market Portfolio = 7043.48 Amount

Saving Portfolio Value = X + 6000 = 7043.48 + 6000 = 13043.48 (Ans)