Question

(1) Given the following Variance-Covariance Matrix for three securities as well as the percentage of the portfolio that each security comprises, Calculate the portfolios standard deviation?

                                                     Security A                Security B                   Security C

Security A                                        146                           187                                145

Security B                                        187                            854                               104

Security C                                        145                            104                               289

Consider the portfolio given in above table that had proportions XA = 0.2325, XB = 0.4070, XC = 0.3605 respectively (Hint: calculating the standard deviation for a portfolio consisting of N securities involves performing the double sum).                                        

Write short notes on the following.

(a) Role of indifference curves in portfolio selection  

(b) Industry classification adopted by the Colombo Stock Exchange

(c) Fixed income securities  

(d) Initial wealth and terminal wealth in portfolio analysis  

Answer 1

1) The standard deviation is calculated as the square root of the Variance

The standard deviation of a portfolio is given by

Where Wi is the weight of the security i,

is the standard deviation of returns of security i.

and is the correlation coefficient between returns of security i and security j

So, standard deviation of portfolio

=sqrt (0.2325^2*146+0.4070^2*854+0.3605^2*289+2*0.2325*0.4070*187+2*0.2325*0.3605*145+2*0.4070*0.3605*104)

=sqrt(277.1309)

=16.64725