How Modern Portfolio Theory Works

February 19th, 2015

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This blog post was originally published on the blog by Jin Choi. The website no longer exists, but Jin has graciously allowed us to re-publish his research for the benefit of future investors forever.

Risky business: Modern Portfolio Theory aims to reduce risk in a portfolio without sacrificing returns

At MoneyGeek, we use a variation of Modern Portfolio Theory (MPT) extensively to construct our portfolios. In this article, I will explain what MPT does.

Optimizing A Portfolio Of Two Stocks

Let me explain MPT by way of a hypothetical example. Let's say we have two stocks from corporations ABC and XYZ. Both stocks trade at $10 per share in year 0.

At the end of year 1, ABC goes down by 20%, while XYZ goes up by 50%. In year 2, ABC goes up by 50%, while XYZ goes down by 20%. You can see the price history in the table below.

0 $10 $10
1 $8 $15
2 $12 $12

Now, let's imagine that we have 3 different portfolios.

  • Portfolio 1 invested 100% of its money in ABC in year 0.
  • Portfolio 2 invested 100% of its money in XYZ in year 0.
  • Portfolio 3 invested 50% of its money in ABC, and the other 50% in XYZ in year 0.

Which portfolio gave the highest return by the end of year 2? That's a trick question, because they all performed the same - they all gained 20% in the end.

However, it's easy to see that portfolio 3 had the least risk of all three portfolios. Let me show you a table that tracks the performance of each portfolio.

YearPortfolio 1Portfolio 2Portfolio 3
0 0% 0% 0%
1 -20% +50% +15%
2 +50% -20% +4%
Cumulative 20% 20% 20%

While Portfolios 1 and 2 lurched up and down, Portfolio 3 grew steadily, thanks to diversification. As readers of our free book would know, you can measure this 'steadiness' by a measure called standard deviation. Portfolio 3 has the least standard deviation, making it the safest.

As we said, each portfolio gained 20% in the end. Given the different risk profiles, however, you can see that Portfolio 3 was the 'optimal' portfolio.

Optimizing A Portfolio Of Real World Stocks

In our example, it's easy to see what the best portfolio should be. However, how about in the real world, where the numbers aren't so nice? For example, take a look at the following set of stocks.The chart shows the stock price for each stock for Years 0, 1, and 2.

0 $620 $16.12 $58.99
1 $600 $15.47 $16.72
2 $756 $19.60 $12.92

What's the portfolio mix that would give you the least risk?

Maybe a portfolio that weights 60% towards GOOG, 30% towards YHOO and 10% towards RIM.TO (Blackberry's old symbol) gives you the lowest risk, but perhaps not. Maybe the answer is more like 40%/40%/20%. It's really hard to figure it out by just looking at it.

As you can imagine, the problem gets even more complicated when you throw more stocks or ETFs into the mix.

I don't care how smart you are. You can't find the portfolio with the lowest risk without using some complicated mathematics, and that set of complicated set of mathematics is called 'Modern Portfolio Theory' (MPT).

Using MPT will give you a portfolio mix, such thatthere is minimal fluctuation in the overall portfolio. It does all this without sacrificing potential returns. Some investors say that diversification is the only "free lunch" you'll get in investing - i.e. it's the only way that you can increase your expected returns in relation to your level of risk. MPT maximizes the amount of this free lunch you get.


I've slightly oversimplified things here. There's certainlymore to Modern Portfolio Theory than what I've just described, but those are complicated topics for another time.

At MoneyGeek, we use a set of technologies called 'Post Modern Portfolio Theory' (PMPT), which is the next evolutionary step to Modern Portfolio Theory. There's not a lot of differences between the two theories, and both are used widely by savvy financial professionals (The chances of a financial advisor using it however, are slim because of its complexity).

Although I haven't described how MPT works, I hope that I've adequately explained the point of using it. If you have any further questions, please leave a comment.

This blog post was originally published on the blog by Jin Choi. The website no longer exists, but Jin has graciously allowed us to re-publish his research for the benefit of future investors forever.

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