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Markowitz Modern Portfolio Theory

Modern Portfolio Theory (MPT) of Harry M. Markowitz deals with the questions related to asset allocation.

Markowitz developed this world-famous modern portfolio theory in 1952 from his considerations in this regard.

He was later honoured with the Nobel Prize for Economics.

Markowitz successfully demonstrated that investing in an uncertain future can be best done with portfolio diversification.

He successfully demonstrated that every investor's goal is to maximize returns for any level of risk.

The risk can be reduced by diversifying the portfolio of unrelated assets, rather than investing in a single asset. Putting all the eggs in the same basket.

About Harry M. Markowitz

Harry Max Markowitz was born on August 24, 1927. He worked at "The Rady School of Management" at the University of California, San Diego (UCSD) as a Professor.

He was also a member of the Advisory Panel at Research Affiliates (an investment management firm) and at Index Funds Advisors.

His scientific contributions greatly changed the Wealth Management industry, and his theory is still considered as cutting edge in portfolio management.

Based on these studies, he developed a theory that has become widely known as the Modern Portfolio Theory.

In 1990, Markowitz together with his colleagues Merton H. Miller and William F. Sharpe was awarded the Nobel Prize for Economics.

The Subject of Modern Portfolio Theory

According to Markowitz MPT, individual investments should be assessed in terms of their impact on the entire portfolio. And not in terms of isolation.

He managed to prove this fact mathematically.

Where he uses three parameters, which can indicate the contribution of the individual investor to the result of the entire portfolio:

  1. Future Return on each investment

  2. The breadth of fluctuation of the returns of each investment expressing the risk. This is measured as Standard Deviation or Variance

  3. The development of the individual plants in relation to each other, which is measured as a Correlation

Portfolio Diversification

The risk is always a welcomed factor when investing. It allows us to reap rewards for taking on the possibility of adverse outcomes.

MPT shows that the overall risk of a portfolio can be significantly reduced by having a mixture of diverse assets.

The risk is seen as a cumulative factor for the overall portfolio and not by simple addition of single risks.

This clever combination is called portfolio diversification.

Portfolio Optimization

Now the portfolio should not only be diversified, but this diversification should, of course, bring optimal results. This is called portfolio optimization.

There are two types of optimization. Optimizing the portfolio means that you will have a better return with the same risk. Or you can get the same return at a much lower risk.

According to Harry Markowitz, the return-risk ratio of a diversified portfolio is always superior to single asset investment.

He proved that mathematically with his Modern Portfolio Theory.

One of the Markowitz assumptions is that the average investors' goal is to get maximum returns. Avoiding the risks at all costs.

A professional investor would not do that. Because a certain value of fluctuation over a longer period of time is completely normal and is practically unavoidable.

On the other hand, the private investor finds his optimal portfolio by taking the risk. Which he previously classified as unacceptable, if the best possible returns were achieved. In technical jargon, this is also referred to as an efficient portfolio.

What are Efficient Portfolios and Efficient Edge?

The explanation given above makes it clear that there can be no universally valid Efficient Portfolio. But rather, there is an efficient portfolio for every risk.

If all the possible portfolios are mapped together with their corresponding risks, we get the so-called efficient edge. (blue line in the diagram)


He successfully demonstrated that every investor wants to build an efficient portfolio. Which can be done by combining different individual investments in a single investment portfolio.

The investor can see all the return options and in return also gets the development of his overall portfolio. In this context, only the above-mentioned correlation comes into play.


In order to minimize the fluctuations in the value of the individual investments and the overall portfolio. Investment under no circumstances should lead to an equivalent reaction in another investment.

Two plans should, therefore, have a correlation < 1, the ideal case being a correlation = 1.

This expresses a total independence of both systems from each other.

Perhaps a negative correlation (correlation > -1) is even better. This also means that the price decline of one brings with it an increase in the price of the other.

So far the theory, but what does the practice look like?

The Actual Diversification Effect - Theory vs. Theory Practice

Firstly, it can be said very clearly that the risk can only be reduced up to a certain extent. Otherwise, that would be too good to be true and all the world would only invest in the stock market.

Overall, certain authors speak of a risk reduction of a quarter to a third.

In addition, one can observe a much higher correlation in global crises than assumed by Markowitz and his supporters. Because once a really black mood prevails on the stock exchanges, virtually everything goes down in the shared cellar.

Exactly when one needs the blessing of diversification the most, he shows his curse or weaknesses.

Of course, the diversification generally works well and may even reduce the catastrophic consequences in the time of crisis.

But it's not a panacea and has its limits. Absolute guarantees on the stock market are not possible anyway because of their nature.

However with the diversification made according to the Modern Portfolio Theory, one can certainly achieve better results with it.

And the future is always uncertain unless you have insider information that you obviously can not use legally.

Optimal diversification of the portfolio as a mathematical process

Optimizing portfolio for diversification using Markowitz Portfolio Theory is no longer a skilful assessment (including Markowitz Portfolio Selection).

Based on the financial advisors experience it is nothing but a pure mathematical rational process that is understandable.

He uses the above-mentioned key figures, to remind you:

  • Yield

  • Fluctuation of returns

  • Correlation of the return development

Thus, there is no room for personal likes or dislikes with regard to certain asset classes. Only the correlation between risk and return decides.

Efficient portfolios of low-risk and riskier investment

The facts can be illustrated by means of the diagram inserted above,

The blue line is determined by two endpoints A and B.

Point B represents a portfolio that contains only secured bonds. Which are extremely safe investment with minimum risk and also will yield the lowest returns.

On the other hand, point A is a portfolio of 100% Stocks. It, therefore, has the highest risk, but can also get the best returns.

Point M is a clever mix of different assets with the smallest value fluctuations. Experts call this type of portfolio also as Minimum Variance Portfolio. This portfolio has the lowest risk of all.

All portfolios on the M-A line can be considered as efficient portfolios.

Conversely, the portfolio between the M and B points cannot be described as the efficient portfolio.

There is a portfolio with better returns for each of the defined risks. These can be found between M and Q. Because here the risk is reduced with increasing returns.

To achieve this, small parts of riskier investments are mixed into a safe investment, which should not be fully correlated.

All portfolios to the right of side ‘S’ have very high returns, but at the same time, the risk increases disproportionately.

If profit is expected without much risk, you should refrain from these portfolios.

In practice, most real-world portfolios are only sub-optimal.

In the figure, you will find portfolios marked with X. These are well below the efficiency line.

The reasons for this can be both high administrative costs, but the investment might not have been sufficiently diversified.

For example, small private investors often prefer shares of their home country, although in many cases foreign stocks may be superior.

Experts speak of a home bias in this context.

A similar effect has the preference for certain asset classes because so a so-called lump risk is generated.

Ideally, a diversified portfolio should include investments of all or at least several asset classes from different countries and regions. Of course, the administrative costs should be reduced as much as possible. If all this is given, the return increases or the risk decreases.

However, the realistic and accurate estimation of the real risk is by no means a simple undertaking.

The portfolio theory offers various options here.

However, it must be noted that not every measure can be implemented by a small private investor.

Portfolio Theory - The Separation Theorem to Tobin

Already relatively early - more precisely in 1958 - Tobin had already introduced the so-called 'separation theorem'. This states that it is best to have two funds. This involves a risky investment and is called Tangential portfolio. By contrast, the second fund consists of secure investments.

Of course, there are now a lot of possible combinations of both funds.

The following graphic illustrates the idea.


The possible combinations of the high-risk tangential portfolio (T) and secure investments are typically shown as straight lines.

With the exception of the tangential point T, these are always above the so-called efficient edge. (see above)

In common language, the investors will always achieve an optimal investment result with the separation theorem. However, that is actually the theory, because in practice this is unfortunately not always the case.

The problem lies in the fact that, ultimately everything here is based on an estimate, not on a calculation.

For example, the underlying expected returns on all the risky asset classes are estimated. Hence it would be an unbelievable coincidence that the estimated earnings can be met - i.e., the perfect tangential portfolio.

For this obvious dilemma, the financial theory seems to offer a possible solution.

Portfolio Theory - Sharpe's Market Portfolio

William Sharpe found an apparent solution to the problem of estimating, with CAPM (Capital Asset Pricing Model) in 1964.

A higher return for a given level of risk can be expected from the investment with the higher modified Sharpe Ratio. An investment may seem to yield higher returns, making it more desirable. However, the investment may be unstable and simply reflecting a high-risk result.

For example, if equities represent 50% of all global assets, then the corresponding portfolio should contain 50% of equities.

As a basis, Sharpe takes a perfect capital market, which represents the investment preferences of all investors through its value.

In this way, estimates and speculations on a future development are unnecessary.

Thus, the problem of splitting, which Tobin identified, seems to be the same for all investors.

Criticism from a private investor's point of view of Separation Theorem and the Market Portfolio

As often, the big theories are geared more towards the big investors. Rather than the private investors next door, who just want to invest their savings.

Of course, the reality of the private investor differs fundamentally from that of the major investors.

Here are some aspects that should be considered:

  • If he pays higher interest for the loan, then there is no straight line, but rather a down-turned line. Which in the worst case can even fall below the efficient margin.

  • Namely, when the interest rate of the debt exceeds the return of the risky portfolio (tangential portfolio). Of course, you should never do stock deals on credit.

  • In principle, "safe" investment is not existent- more precisely since 2008. Because interest rates on the bonds are now below the inflation rate. Above all, a broad diversification of the risk, ie good diversification, is certain. The goal is a low-fluctuation portfolio, which yields a return close to or slightly above the inflation rate.

  • Theoretically, all asset classes should be considered in proportion to their assets, this is not really the case in practice. As most of the optimally composed portfolios are stock heavy and are on the efficient margin relatively far to the right. When this portfolio is mixed with a secure portfolio, the combined performance is usually below the efficient margin. Thus, the investment result is usually sub-optimal.

Optimization procedures seldom lead to the optimal portfolio.

It can, therefore, be stated that optimization methods as described above rarely lead to optimal portfolios in practice.

It's simply not possible to predict future returns without errors. Even experienced traders and wealth managers have difficulty predicting how an investment will perform in the next 6-12 months.

So it is unlikely that medium-term developments of entire asset classes can simply be foreseen as error-free. As a result, it is realistic to expect sub-optimal portfolios as a rule.

However, the described procedures make it possible to come relatively close to an optimized portfolio with good returns.

Passive portfolio management as an answer

So, if you do without complex forecasts and estimates, you'll be back in passive portfolio management. Simple, unweighted portfolios, in which each asset class is equally weighted, typically perform surprisingly well.

Nevertheless, one can take advantage of significant insights of the investment portfolio theory, keeping them in mind:

  • Diversification leads to an optimized investment result.

  • Diversification is based on asset classes (not individual stocks).

  • The asset classes used, which are combined with each other, should not be completely correlated.

  • In the efficient portfolios, there is a higher return with a higher risk.

  • The investor determines how much return he wants to achieve and thus decides on the risk. The risk tolerance of the investor determines the maximum achievable return.

  • Nobody knows today the 'optimal portfolio' of tomorrow. Only dubious people claim that.

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