1 Capial make line Assume at ihe expecred ate of reurn on th

1. (Capial make line) Assume at ihe expecred ate of reurn on the market poIlolio is 23% und the rate of return on T-bills (the risk-free lae) is 7% The standard deviajon ol lle market is 32% Assume that he markel portfolio is efficient (a) What is he eqaion o he cap narke line? (b) (i) If an expected FUtuin of 39% is desired, what is the standard deviation of his posiion? (ii) Ii you have $1,000 above position? ives how should you allocale i o achieve the (c) I you invesi $300 n the risk-free asset and $700 in he market portfolio, how nuch money should yon expect lo have at the end o ihe yuar?

Solution

1.=(market return-risk free)/standard deviation of market portfolio=(23%-7%)/32%=0.5

2. 39%=7%+0.5*standard deviation of portfolio

=>standard deviation of portfolio=64%

Let w be the weight of risk free and 1-w weight of market portfolio

=>Standard deviation of portfolio=w*0+(1-w)*32%

=>w*0+(1-w)*32%=64%

=>w=-1 and 1-w=2

So, borrow 1000 and invest 2000 in market portfolio

3.=300/1000*7%+700/1000*23%=18.2%