The correlation coefficient between the daily stock return in each portfolio is also calculated and combined with the standard deviations in a covariance matrix to calculate the variance and standard deviation for each portfolio. Sensitivity analysis is also carried out by changing the weights of each stock in the portfolio to see how the performance changes.
The variance and thus the standard deviation are far more difficult to calculate because the variance of a portfolio is not simply a weighted average of the individual variances of the stocks included in the portfolio except for the special case where the individual stock returns are uncorrelated with one another. The variance for a two stock portfolio is given by:
We need to set up a covariance matrix to bordered covariance matrix to be able to calculate the 1variance and standard deviation for a portfolio of more than two stocks. For a three stock portfolio the bordered covariance matrix can be written as follows (Bodie et al., 2002):
The portfolio variance is calculated from the above nine terms by multiplying the bordered weights by the corresponding covariance and then summing the different terms. ...