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Modern Portfolio Theory (MPT) - A Useful Tool For Risk Management

How to use Modern Portfolio Theory (MPT) for risk management and asset allocation with real examples and data

Modern Portfolio Theory (MPT) is a financial concept developed by Nobel prize winner Harry Markowitz which describes the relationship between risk and reward within a portfolio. The main assumption of the model is that investor are risk-averse, in other words prefer low risk even if it is a trade off for higher returns. 

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MPT is a powerful tool for investors building portfolios using a quantitative method for asset allocation in which returns would be maximised for any given level of risk.

 

Traditional finance theory used data that the average investor either 1) are not familiar with or 2) are unaware how to find or calculate them; so we are going to break down MPT and show you how construct a portfolio using real company data.

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To start, we need the following information:

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1) Beta

To determine the relationship of two variables within the portfolio we need the beta coefficient 

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2) Expected Return

In order to get an expected return for the portfolio we need to calculate expected return on each asset; we can use CAPM which is a straight forward model to implement by simply inputting figures. The CAPM formula is as follows:

 

Screenshot 2021-04-05 at 21.33.46.png

Expected Return = Risk free rate + Beta * Market Risk Premium

At first glance the formula looks daunting but in reality it's relatively simple once you know how to use it, we have examples below showing demonstrating this application.

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3) Intended Asset Weighting 

As an example lets consider a 5 asset portfolio across different sectors - perhaps (Technology 50%, Energy 20%, Industrials 10%, Utilities 10% and Healthcare 10%), we can use these weightings in the portfolio calculations. A diversification as such shows a good mix of assets utilising the power of correlation and spreading risk between sectors which typically don't perform in the same manner.

Putting It Altogether

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Okay so you want to build a portfolio now and need to gather the data. We have made a sample portfolio of 5 stocks to demonstrate how to implement MPT. 

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STEP 1 - DATA COLLECTION

 

We have selected random stocks across different sectors to use as an example:

PORTFOLIO ASSETS

WEIGHT

E(R)

BETA

Shell (RDSB)

Facebook (FB)

Lloyds (LLOY)

Tesla (TSLA)

Apple (AAPL)

10%

1.6 + {1[15.9 - 1.6]} =

30%

1.6 + {1.3[15.9 - 1.6]} =

25%

1.6 + {1.47[15.9 - 1.6]} =

15%

1.6 + {1.98[15.9 - 1.6]} =

20%

1.6 + {1.2[15.9 - 1.6]} =

15.9%

1

20.19%

1.3

22.62%

1.47

29.91%

1.98

18.76%

1.2

Screenshot 2021-04-05 at 21.33.46.png

CAPM Formula used for expected returns 

DATA 

1) Yahoo finance provided Beta

2) Rf @ 1.6 is current 10YR US Yields

3) E(Rm) @ 15.9%  is 5yr SP500 Average 

STEP 2 - CALCULATIONS 

 

Now we have collected the data and calculated expected returns, we can put it all together to measure the efficiency of the portfolio. To do so, we will measure the portfolio expected returns E(Rp), and risk (Standard Deviation/Beta).

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The standard deviations for risk are comprehensive, also difficult to collect all the data, however it is possible to calculate portfolio beta which will show sensitivity to the market index (SP500). This is a far simpler method however investors need to monitor overall market sentiment/risk then compare with the portfolio beta - unlike with standard deviation which is a individual measure of risk. 

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Portfolio Beta 

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Portfolio beta is a weighted average of each stocks beta

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         So for our example portfolio:

Screenshot 2021-05-31 at 11.36.10.png

Portfolio Beta = 1.3945

Screenshot 2021-05-31 at 11.31.17.png

Portfolio Expected Return 

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Using the same principles of weighted averages we can calculate the expected return on the portfolio 

Portfolio Expected Return = 21.54%

Higher portfolio beta means the portfolio is more responsive to market movements ie: more risky than an index fund. For example, this portfolio has a beta of 1.3945 which means for every 1% move in the underlying market, this portfolio would be expected to move 1.3945% in the same direction. 

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Traditional finance theory states higher risk is a compensation for higher return therefore the higher the beta, the higher the expected return an investor would hope to achieve. 

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As mentioned, for those mathematicians who wish to calculate portfolio standard deviations, this will be a relatively more accurate representation of portfolio risk as it not correlated with an index like beta. However, calculating SD and updating data is a job in itself therefore as an approximate measure, beta is a useful tool to monitor.

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If your portfolio has a beta of 3.5, you would expect a much higher return as a compensation. If you were only achieving the same return as our above example, this would mean your portfolio is less efficient than the current example (higher risk for equal returns). 

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