Financial Management

Problems graded on effort

2.   (a)  Expected return of Portfolio 1= (0.5*12) + (0.5*8) = 10% 

       Expected return of Portfolio 2= (0.25*12) + (0.75*8) = 9% 

       Expected return of Portfolio 3= (0.75*12) + (0.25*8) = 11% 

      Variance (Portfolio 1)= (0.52*0.082) + (0.52*0.052) + 2(0.5*0.5*0.2*0.08*0.05) =21/8000

      Standard deviation (Portfolio 1) = (21/8000)0.5 = 0.0512 = 5.12% 

      Variance (Portfolio 2) = (0.252*0.082) + (0.752*0.052) + 2(0.25*0.75*0.2*0.08*0.05)

                                          = 2.10625 x 10-3

      Standard deviation (Portfolio 2) = (2.10625 x 10-3)0.5 = 0.04589 = 4.59%

      Variance (Portfolio 3) = (0.752*0.082) + (0.252*0.052) + 2(0.25*0.75*0.2*0.08*0.05)    

                                          = 4.05625 x 10-3

         Standard deviation (Portfolio 3) = (4.05625 x 10-3)0.5 = 0.06369 = 6.37%  

     (b)

[pic 1]

(c) Given that Mr Harrywitz can lend at 5% interest rate, this loan can be taken as a risk-free asset. By combining this risk-free asset with the set of portfolios, we are able to get the tangency portfolio as denoted in the graph below. Therefore, the efficient market portfolio as denoted by the graph is Portfolio 1. He should invest 50% of his portfolio in X and 50% in Y.  

[pic 2][pic 3]

Chapter 9 Problem 11

1. The required return on Okefenokee stoke is

r = rf+beta(rm-rf)

r = 0.04+1.5*0.06

r= 13%

1. Cost of capital :

[pic 4]

= 0.04*4/10+0.13*6/10

=9.4%

1. The discount rate is 9.4% if the risk of the project is similar to the risk of the average of other asset

1. r = rf+beta(rm-rf)

r = 0.04+1.2*0.06

r= 11.2%

[pic 5]

= 0.04*4/10+0.112*6/10

=8.32%

Graded Problem 2

1. Assume Percival’s portfolio comprises x% of index fund, (100-x)% of T-bills.

Given that T-bills are taken to be a risk-free asset, its standard deviation is assumed to be zero. Therefore, Percival’s portfolio variance = variance of index fund = [(x/100)2 * 0.162] 

(x/100)2 * 0.162 =0.12 (Given that variance = square root of standard deviation)

Solving for x, value of x = 62.5

Therefore, to maintain a similar portfolio risk, Pervical’s new portfolio will have to comprise of 62.5% index fund and 100-62.5= 37.5% of T-bills.