Question

Your investment portfolio consists of the following stocks
Investment Portfolio
Name	Price	Beta	# shares
Dow Chemical	$      59.72	1.34	15,000
Walmart	$      69.32	0.19	3,000
Boeing	$   128.00	1.36	8,000
Verizon	$      52.61	0.45	6,000
Consolidated Edison	$      74.00	0.17	3,000
Caterpillar	$      75.00	1.5	13,000
Deutsche bank	$      22.55	1.4	9,000
a)      What is the portfolio beta?
b)      What is the required return on the portfolio if the market return is 11 % and the risk free rate is 3% ?
c)      If you are risk averse (do not like risk), how will you reconstruct your portfolio to reduce the risk or beta in the portfolio you calculated to get a beta between .5 and .6. Show how you will achieve this.
d) If you like risk show how you will reconstruct your portfolio to increase your risk (Beta) level to between 1.4 and 1.5
e) What will happen to your investment if the market goes up 10 % and down 10% for the portfolio beta you calculated in ( c ) and (d)
How much will be your gain and loss in the portfolio you constructed?

Answer 1

We can calculate weights of companies in the portfolio as total protfolio value in dollars divided by value of shares of a company.   

Price/Share Beta Shares Price*Shares Weight (x/3,842,920)

Dow Chemical	$      59.72	1.34	15,000 895,800 0.233
Walmart	$      69.3	0.19	3000 207,960 0.05412
Boeing	$   128.00	1.36	8,000 1,024,000 0.265
Verizon	$      52.61	0.45	6,000 315,660 0.0822
Consolidated Edison	$      74.00	0.17	3,000 222,000 0.0578
Caterpillar	$      75.00	1.5	13,000 975,000 0.2538
Deutsche bank	$      22.55	1.4	9,000 202,500 0.0541 Total Portfolio value=3,842,920 Beta portfolio=beta*weight 1.34*.233+0.19*0.05412+1.36*0.265+.45*.0822+0.17*0.0578+1.5*0.2538+1.4*0.0541 =0.3122+0.0103+0.3604+0.0367+.009826+0.3807+0.07574 BEta value of portfolio=1.186 b)Using CAPM model Rf+beta(market return-Rf) 3%+1.186(11-6) =8.93% C) For risk averse we can decrese the beta by increasing the weights of low beta, and decreasing the weights of high betas so that overall Beta of portfolio is under 0.5 to 0.6 D)We can increase the weights of high betas and decrease the value of low betas so that overall beta lies between 1.4 to 1.5. THis process is called beta adjustment E) For a Beta of 0.5, if market increases by 10%, portfolio value will increase by 5%, if market decreases by 10%, portfolio value decreases by 0.5*10%=5%. For a beta of 1.4, Market up by 10%, we will gain 14% (1.4*10%), if market down by 10% we will lose by 14%.