Question

1.  Your cousin Vigny is trying to take advantage of the recent changes in stock market.  However, he

      would like to invest in just two stocks, stock X and stock Y.  He calls you asking for help, he knows you    

     are a UPRRP MBA candidate.

The following information has been provided by Miguelito-Investments, Vigny’s broker:

Expected returns of X= E(RX)=20%; Expected Returns of Y=E(RY)=15%.  In addition, you find out that the expected product of the returns of RX times the return of RY, or E(RX.RY)=3%; the Standard Deviation of the returns of X=STD(RX)=29.5% and the standard deviation of the returns of Y=STD(RY)=18.20%.

Vigny has $ 2,000,000 that would like to invest, in both X and Y; 50% of that amount will go to X.  

Required:

            a.  What return does Vigny expect to generate on this portfolio?

            b.  What is the risk of the portfolio?

            c.  Determine the correlation between X and Y.

            d.  Does this portfolio provides a favorable reward to risk relation attractive?  

                          Note: you must support your argument with numbers.

            e.  What is the minimum variance portfolio?

Answer 1

a) The return from portfolio would simply be weighted average of returns from two assets

Rp= WxRx + WyRy​​​​​ = (20*50%) + (15*50%) = 17.5%

b) Risk of portfolio =

σp =

where cov(x,y) = E[X,Y] - E[X].E[Y] = 3%- (15%*20%) =0

RISK OF PORTFOLIO = Sq.rt ( (50%* 29.52) + (50%* 18.22)+0 =Sq.rt(600.745) =24.51

c) Corelation between x, y = Covariance (x,y)/σyσx

Since covariance is 0 , therefore, correlation =0

d) Reward / Risk = 17.5/24.51= .0.71399: 1

It means that Vigny is willing to risk 1 in order to get reward of 0.71399 . This is not a favourable situation

e) Minimum variance portfolio indicates a well diversed portfolio. A well diversed portfolio results in minimization of risk It leverages risk of each individual asset with an offsetting investment. The risk of one investment is minimised by investing in other offsetting asset