Question

Your friend recently inherited $20,000 from a wealthy relative. His stockbroker has advised him to invest in three particular stocks. Because of the volatility of the market, your friend requires the stockbroker to provide him with historical yearly returns for these stocks over the past four years. This data is shown in the table below. Find the efficient frontier of this portfolio.

Year	Stock A	Stock B	Stock C
1	0.202	0.109	0.153
2	0.024	0.187	0.068
3	0.159	0.098	0.185
4	0.049	0.121	0.057

Answer 1

To calculate the efficient frontier, we need the following things.

Mean- Nothing but average.
Variance- Its the measure of the spread of the returns.
Standard Deviation- Square root of variance. Measure of the risk the stock has.
Covariance- Measure of how the returns vary with each other (if one rises, does the other rise? etc).
Correlation- Normalized covariance Ranges between -1 and 1.

Now, a efficient frontier is basically a curve that tells you at what risk level you will get what return. We caculate it by plotting standard deviation on the X-axis (since its the measure of the risk) and returns on the Y-axis. We will need to use excel for these. There are formulas in excel that easily calculate the parameters such as standard deviation. I will put a link to the excel below. Here I will describe the process. Follow it with excel and it should be very easy to see what I have done.

The idea is that we take difference weightages for the three stocks (lets say 20% of A, 30% of B and 30% of C) and see what return we are getting. Then we change the weightages and see the new return. And so on. Thus we will get a range of returns. Similarly, for each of these ranges, we will also get a standard deviation. Plotting std dev on X-axis and return on Y, we will get an efficient frontier.

The main problem that we face here is that there are 3 different sets of stocks. Since by definition correlation is between 2 variables, we will need to create a correlation matrix here. It will look like below (please see excel for calculation)-

Now that we have the correlations, we can assign different weightages to different stocks (effectively creating different portfolios) and get the standard devication of those portfolios. All we then need to do is to plot the standard deviation and returns. This will give us the following graph (which is the efficient frontier)-

The excel has been uploaded here (please download it and open in excel)- https://drive.google.com/open?id=1PI2EWn4Q7baV8F6vsww8fy1AU_B552Rj