Friday, January 1, 2010

Efficient frontier of selected STI stocks

Year 2009 has just come to an end and I am sure there will be some investors who wish to try and fine tune their stocks portfolio for the fresh and coming year. I just completed my tutorials on Modern Portfolio Theory (MPT) so I thought of applying that knowledge into building a minimum variance portfolio consisting of STI stocks. Take note that this post is by no mean an inducement for you to buy such portfolios. It is just an application of a theory that you may or may not find them useful. Personally I don’t use MPT to select my stocks portfolio but I still think MPT deserves a consideration and awareness among investors. After all MPT is one of the highly acclaimed research theories in the study of Finance.

MPT states that one can achieve a minimum variance portfolio from a basket of risky assets. An asset can consist of a stock or a bond. An efficient frontier is plotted for every expected return against lowest portfolio risk (measured by standard deviation) by combining various assets. You can try to read more about this theory to understand MPT better.

Just for the sake of illustration, I try to create a portfolio of stocks consisting of the following bluechips:
Capitaland, Singtel, SIA, Singpost, SGX, Starhub, ST Engg and SIA Engg

In this illustration, I construct a portfolio of only stocks even though it is advisable to include bonds into ones portfolio in order to achieve better diversification. Based on the monthly returns data (from Jan 2005 to Dec 2009) of the above stocks, an efficient frontier is plotted on the following graph.

Efficient Frontier of Selected STI Stocks

There are a few things that one can derive from the above results. First of all, if you are expecting a return of 16% per annum from your portfolio, you should construct a portfolio consisting of 1.19% in Capitaland, 4.44% in Singpost, 19.29% in SGX, 33.42% in Starhub and 41.65% in ST Engg. Secondly you should not include stocks like Singtel, SIA and SIA Engg into your portfolio as you can see that their weightings are zero for every expected return. Of course you can still add them into your portfolio but the portfolio will not be an optimum one. The other thing is that SGX and Capitaland are the two star performers in each year in which both can give higher potential returns. However among the two stocks, SGX is much preferred in ones portfolio because of its lower risk. That is why SGX has a higher weighting than Capitaland for a portfolio with higher expected returns.

Note that the plot of efficient frontier is based on historical data so if returns change going forward, the frontier may change as well. A better plot can be achieved if you have a longer period of data. Also note that the expected returns are high and may not be realistic so a better frontier can be achieved if you add more stocks into the portfolio. Nevertheless I am just try to illustrate the MPT and if you are keen on this theory, you may try to include the other bluechips or even bonds into the computation and plot an efficient frontier for these risky assets. If you want the Excel file as a reference, you can always ask from me.


Anonymous said...

Hi Mike,

There is a lot of analysis on which essentially discredits MPT as a portfolio planning tool.

For your information.



Anonymous said...

Pretty interesting place you've got here. Thanx for it. I like such themes and everything connected to this matter. I would like to read more soon.

Anonymous said...

hi, i'm doing research for MPT, and would like to know where do you get the historical data for STI as a whole?

Karmo said...

You might all want to take a look at

They let you do this kind of portfolio optimization free of charge and without any knowledge of the mathematics of optimization theory. You can also assess sensitivity of the portfolio to a position. Very useful and insightful - especially since they cover so many markets!

There is a tutorial here: