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
ASSIGNMENT 2A DUE: January 31, 2019 I REVIEW THE MATRIX SHOWN TO THE RIGHT INPUT DATA...