Question

ASSIGNMENT 2A DUE: January 31, 2019 I REVIEW THE MATRIX SHOWN TO THE RIGHT INPUT DATA Ob 7.5% pbs Rf 0.25 2.5% a What is the term used to describe the matrix? 11.0% 6.0% 18.5% b what is the mix of stock fund and bond fund that will provide a Portfolio weights ERp) Sdevn(p) minimum-variance portfolio [given the data in the matrix]? Ws 0.000 1.000 0.025 0.975 0.0500.950 0.075 0.100 0.125 0.150 0.175 0.200 0.800 0.2250.775 0.250 0.300 0.700 Wb 6.0% 6.1% 6.3% 6.4% 6.5% 6.6% 6.8% 6.9% 7.0% 71% 7.3% 7.500% 7.442% 7.411% 7.407% 7.432% 7.483% 7.562% 7.667% 7.797% 7.950% 8.126% what factors could result in a change in the mix of the minimum- variance portfolio? 0.925 0.900 0.875 0.850 0.825 d calculate the E(Rp) and Sdevn(p) for a mix of 30% in stocks and the remainder in bonds e calculate the E(Rp) and Sdevn(p) for a mix of 30% in stocks and the remainder in a Risk free instrument for a mix of 20% in stocks and 80% in bonds, you are told that a portfolio has a Sdevn 0.750 of 9.585%, what must be the correlation coefficient for this portfolio? s- stock fund, b- bond fund

Answer 1

a            

the matrix lists down the expected return and risk (standard deviation) for different weights of assets (stocks and bonds) in the portfolio. This is called portfolio risk-return matrix or simply portfolio return matrix  

              

b            

out of the listed data in the matrix, the minimum risk (std dev) is 7.407%. The associated weightage of stocks in the portfolio is 7.5% and that of bonds is 92.5%    

              

c            

the minimum variance portfolios is the one where the portfolio has the lowest risk (std dev) for a given level of return            

factors affecting the min var portfolio are-           

change in historical std dev of the portfolio assets            

change in expected returns of the portfolio assets           

change in the correlation between the portfolio assets   

              

d            

E(Rp)= ws*E(Rs)+wb*E(Rb)

Stddev(p)=               (ws^2*stdev(s)^2+wb^2*stdev(b)^2+2*ws*wb*stdev(s)*stdev(b)*correl(sb))^0.5

              

E(Rp) for 30% stock and 70% bonds-       

7.50%    =30%*11%+70%*6%

              

Stddev(p) for 30% stock and 70% bonds-              

8.54%    =(30%^2*18.5%^2+70%^2*7.5%^2+2*30%*70%*18.5%*7.5%*0.25)^0.5

e            

For risk free asset, the formulae remain the same. However, as the name suggests, the std dev (risk) for risk free asset is 0 and the correlation between stock returns and reisk free asset returns is also 0.              

E(Rp)= ws*E(Rs)+wb*E(Rb)

Stddev(p)=               (ws^2*stdev(s)^2+wb^2*stdev(b)^2+2*ws*wb*stdev(s)*stdev(b)*correl(sb))^0.5

              

E(Rp) for 30% stock and 70% risk free asset-        

5.05%    =30%*11%+70%*2.5%

              

Stddev(p) for 30% stock and 70% risk free asset-

5.55%    =(30%^2*18.5%^2+70%^2*0^2+2*30%*70%*18.5%*0*0)^0.5

              

As expected, the risk free asset lowers the portfolio risk and associated portfolio return as compared to any other asset      

              

f             

we have a portfolio std dev for 20-80 mix. To calculate the correlation between the assets, we have to reverse calculate the following equation-             

               9.585%=(20%^2*18.5%^2+80%^2*7.5%^2+2*30%*70%*18.5%*7.5%*C)^0.5

C=          (9.585%^2-(20%^2*18.5%^2+80%^2*7.5%^2))/(2*30%*70%*18.5%*7.5%)

C=          0.72385

Correlation coefficient= 0.72385