Learn why the Markowitz Modern Portfolio Theory is still delivering more return than a risk adjusted Portfolio risk management with the Moreira and Muir model


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The Modern Portfolio Theory has been developed in the 1950s by US economist Harry Markowitz, who has been awarded a Nobel Prize for it.

The main point of the theory is, that the investment risk can be reduced by investing with a higher dispersion – that means having a more diverse portfolio.

The whole Modern Portfolio theory by Harry Markowitz is based on this, to put it simply. The US economist developed his “Portfolio Selection Theory” in the 1950s and has even been awarded a Nobel Prize for it.

In contrast, Moreira & Moir are assuming that there’s higher risk in some market phases due to a high volatility, which goes along with low expectations, which should be avoided. They recommend that it’s best to leave the market such phases.

In the following article, we’re explaining and comparing both approaches.

Markowitz’ Modern Portfolio Theory – Minimal risk by diversification

Markowitz‘ goal was finding a method, which allowed measuring the advantages of investing with a wider dispersion. The earning prospects should be put in relation to existing risks and thereby put together an ideal portfolio.

His first premise was that investors are generally shy at high risks. The typical investor is attempting to achieve maximum earnings with little to no risk.

Accordingly, investments needed to be balanced as good as possible in order to give the investor an ideal investing strategy. Diversification is helping to eliminate or reduce – at least part of – the risks, without having to deal with lower rates of return.

Ideally, the risk can be reduced by 25-30% by using the Modern Portfolio theory.

What is the meaning of “risk” in the Modern Portfolio theory?

When Markowitz is talking about risk, he mainly considers it as the amount of yield fluctuations around the expected yield.

This means that the risk is getting higher as the chance of the expected income is getting more insecure. The term for this used in the stock market is “volatility”.

What makes a portfolio efficient?

Two values are being used to find the ideal investment for an investor. Firstly, the earning-capacity value of the yield, and secondly, the volatility. Those two values are put into a coordinate system. The first result will be a cloud of many different points. There’s also an efficiency curve and vertices being put in.


From this graphic, you can now read, which portfolio is efficient. The highest efficiency is the blue line called "efficient frontier", a line towards the portfolios are optimized. The portfolio nearest to the efficient frontier is the best. For example the 15 percent risk portfolio (with 16 percent return, see green dot) and the 20 percent return portfolio (with 24 percent risk) are the best possible portfolios. The goal are highest performance expectations while maintaining an acceptable risk, which is being considered efficient.

    It just as desirable to have a portfolio that nobody else can outperform in the following two variants:

  • No other portfolio has the same profit while maintaining a lower risk
  • No other portfolio has more profit while maintaining the same risk

The superiority of a diverse portfolio over single investments have been clearly proven using the Modern Portfolio theory of Harry Markowitz.

In order for this theory to make sense for the investor, it needs to be viewed from a mathematical point. This theory won’t work as soon as emotional factors are brought in by the investor.

    Emotional factors can be:

  • The investor only wants to buy shares from his own country
  • The investor prefers certain shares
  • The investor brings and other kind of personal preference into the theory

All these factors can lead to a suboptimal portfolio and need to be avoided.

Math over personal preferences

Another important value is the so-called correlation coefficient. It states how big the correlation between the yields of the shares is. The correlation coefficient is located between -1 and 1. Zero would mean that there’s no correlation. If the correlation coefficient is positive, this shows that the performance of the shares is parallel - there’s no risk minimization. A negative correlation coefficient shows that there’s an opposed movement visible: If one share loses value, the other’s value rises. The ideal correlation coefficient value would be -1, the shares are ideal for risk minimization.

However, you can’t forget that risk minimization mostly leads to reduced yield expectations. At a correlation coefficient value of -1, risk and income basically cancel each other out.

Combining as many investment classes with a value between 0 and -1 as possible makes most sense.

If you want high yields, you need to accept a higher risk. The risk is mainly being controlled by your yield expectations.

By adding options to the portfolio, risk can be lowered which improves the portfolio.

Dynamic risk management following Moreira & Muir

The US-American scientists Alan Moreira and Tyler Muir are focusing on dynamic risk management, opposed to the Markowitz theory. The main idea is to make the portfolio more stable in downward swing phases, than the market and higher long-term yields are supposed to earn(find one of the later studies at Alan Moreira und Tyler Muir in Volatility-Managed Portfolios, published in Journal of Finance ). Simply put, this means that high-risk shares are to be sold when the risk rises, while they are to be bought when the risk is sinking.

This may sound way easier than it actually is, since it’s working only if risk management is able to warn early enough if the markets are in danger.

Followers of dynamic risk management claim being able to deliver such warnings. Just not for stock market crashes caused by unpredictable events such as terror attacks, natural catastrophes etc.

A well-known example is the bankruptcy of Lehman Brothers (September 16th 2008). The S&P didn’t collapse instantly; it took approximately two weeks until it crashed massively. By the end of the year, the crash had caused losses of around 16 trillion dollars.

According to the approach of Moreira & Muir, investors should sell high-risk shares and prefer low-risk investments as soon as these warning signals become visible.

While volatility usually appears in clusters, this doesn’t mean that a downward market fluctuation will be followed by another downward fluctuation – it might as well go upward again, in this case the overly-careful investor would’ve sold his shares already and thereby lost yields.

The Moreira & Muir risk adjusted portfolio can adapt to the risk level in case of a volauprise but it will under deliver in profit and performance compared to the Modern Portfolio Theory portfolio. As most volatile and risky markets increase (and not decrease) in the time of higher vola the investor in the Moreira & Muir portfolio will miss the uptrend and end up with less money in his pocket. This effect should be visible after the first risk adjustment of the Moreira & Muir portfolio.

Conclusion: Markowitz vs. Moreira & Moir

    If you directly compare both models to each other, you will note the following:

  • If an investor stays in the market with his shares even though there’s higher volatility, he’s got higher yields than an investor following Moreira & Muir, who’s selling his shares right before the market rises again.
  • In this case, the mathematical risk is higher in the Modern Portfolio theory than it is following Moreira & Muir, however, yields are higher. The risk doesn’t have any effects if it’s a long-term investment.
  • If you’re comparing the Buy-and-hold model (Markowitz) and the volatility model (Moreira & Muir) in the same time frame (since the 1970s), you’ll see the lines are parallel – there’s no practical difference.
  • Especially if the Modern Portfolio theory model is secured with additional options, it’s superior over the Moreira & Muir model.

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