Portfolio Management - Expected Return and Risk Calculation

Due to most of my friends do not know how to calculate the portfolio risk, so I revisit the variance-covariance matrix construction. Hopefully every body can benefit from it.

Step 1: Data Collection

60 monthly historical prices of a security are collected. You may download the historical price from Yahoo! Finance.

Step 2: Calculate Expected Portfolio Return

E(r,i) = average expected return of 60 monthly data for stock i;

E(r,p) = expected return of a portfolio;

Let us take 3 individual securities for example.

 E(r,p) = 1.09% monthly

  

Step 3: Calculate Portfolio Risk

Calculation of the portfolio risk can be simplified by summing up all the component(s) inside the variance-covariance matrix.

 1) Variance-Covariance matrix for one number of stock, 1^2 = 1 component

2) Variance-Covariance matrix for two number of stocks, 2^2 = 4 components

3) Variance-Covariance matrix for three number of stock, 3^2 = 9 components

4) Variance-Covariance matrix for four number of stocks, 4^2 = 16 components

 5) Variance-Covariance matrix for five number of stocks, 5^2 = 25 components

 6) Variance-Covariance matrix for six number of stocks, 6^2 = 36 components

...ha ha, I have 14 investments in my portfolio, 14^2 = 196 components

Expected Return and Risk of a portfolio which are calculated here will be used to optimize the return-risk of a portfolio via Excel Solver. This optimization had been discussed earlier (see portfolio optimization).