Modern Portfolio Theory by Nobel Prize Winner

Harry Markowitz, the winner of 1990 Nobel Prize in Economics, introduced Modern portfolio theory (MPT) in The Journal of Finance on March 1952 (Read more here).  MPT sometimes is called mean-variance portfolio theory because the mathematical models focus on optimizing the risk and return of the portfolio.  This article will focus on using the MPT to construct the portfolios with real world example.  Readers who are interested to understand the underlying concept can google “Modern Portfolio Theory”.

The mathematical model of MPT can be easily constructed by using Excel spreadsheet with Solvers add-ins.  Once the model is ready, users can build the portfolio by keying in the historical returns of the asset classes into the spreadsheet.  It is generally believed that a portfolio shall hold at least 30 stocks in order to enjoy the benefit of diversification (link).  But for the ease of illustration, only ten heaviest weighted stocks that are listed more than 10-years in the FTSE KLCI are chosen for modeling purpose.  Figure 1 is the weightage of 30 stocks in FTSE KLCI as at 17 June 2016 published by FTSE (link).

Figure 1

Table 1 is the 10-years return of the ten selected stocks extracted from MorningStar.com.  The geometry return and standard deviation are calculated using Excel.  Table 2 is the correlation coefficient matrix that is required to calculate the portfolio variance, estimated by Excel as well.  The objective of the model is to find the asset allocations that meet the investors’ risk-return requirement.  Table 3 is the results of the simulation, comparing equally weighted allocation, minimum risk allocation, maximum return allocation and maximum risk-return allocation.

Table 1

Table 2

Table 3

The equally weighted portfolio has the lowest return at 6.02% with highest risk at 23.80%.  The minimum risk portfolio consists of 2.74% CIMB, 54.27% PETGAS, 7.38% KLK and 35.62% MISC.  By holding such portfolio, the risk is greatly reduced to 10.22%, with slightly higher return at 7.14%.  Investors who look for maximum return can always pick the highest return single stock and invest 100% into it.  The MPT model also shows the same result with 100% allocation to PBBANK with 13.52% return at 15.93% risk.  However, the risk of the single stock portfolio is significantly higher than the minimum risk portfolio.  Lastly, by holding 67.06% of PBBANK and 32.94% of PETGAS, investor can reduce the risk to 13.20% yet still enjoying 12.74% return.

As the sample size is small in this model, many stocks in the model with low return and high risk are disqualified during the simulation.  One can increase the sample size to 300 in order to achieve at least 30 stocks allocation.  Another way of doing this is manually pick 30 – 60 stocks that have similar expected return with different risk, and then run the MPT simulation to obtain the optimum allocation.

MPT is often applied on constructing a portfolio that consists of mutual fund, exchange traded fund, bond fund and other funds that are already diversified within its asset class.  As such, the mathematical model can be greatly simplified to holding 3 – 5 well-diversified funds.

Disclaimer:  The above asset allocation calculations do not imply any buy or sell recommendation.   The author disclaims all liabilities arising from any use of the information contained in this article.