Markowitz Portfolio Theory. Methodology for the formation of an investment portfolio

2024 Author: Howard Calhoun | [email protected]. Last modified: 2023-12-17 10:16

In this world, the one who chooses the best strategy of behavior wins. This applies to all areas of life. Including investment. But how to choose the best strategy of behavior here? There is no single answer to this. However, there are several techniques that increase the chances of successful activity. One of them is the Markowitz portfolio theory.

General information

This approach is perhaps the most common. It should be noted that the theory of Harry Markowitz presented in the article is designed for people with experience or at least minimal theoretical knowledge in the field of portfolio management. First, some general information. Markowitz Portfolio Theory is a systematic approach based on the analysis of expected averages. This technique is used for the optimal selection of assets with subsequent acquisition according to the established risk / return criterion. The theory also involves a detailed analysis of the variations of random variables. It should be noted that it was developedback in the middle of the last century, and has been the basis for portfolio modeling ever since.

What is its essence?

Markowitz's theory is based on the assertion that it is necessary to minimize the possible risk of a deposit drawdown. To do this, the optimal portfolio of assets is calculated. The yield vector and the covariance matrix are also used. But the main feature of this approach is the probabilistic-theoretic formalization of the concepts of "profitability" and "risk" proposed by Markowitz. So, in particular, a probability distribution is used for this. The expected rate of return, specific to the portfolio, is considered as the average of the profit distribution. And the risk is the standard deviation of this value in mathematical terms. Moreover, all these indicators can be calculated both for the entire portfolio and for its individual elements. At the same time, the condition of recession or economic recovery is taken as a criterion for a possible deviation for profitability.

Let's look at an example…

Building an optimal investment portfolio is no easy task. To consolidate the material already written, let's look at a small example. Suppose that a certain company "Sunflower" issued shares worth one hundred rubles each. We have an equity investment fund. It is planned that this asset will remain in the portfolio for one year. In this case, the return on a share can be estimated as the sum of two components, namely, the growth in the value of securities and dividends. Let's pretend thatthe mathematical expectation (average value) of the share price increase over the past two years was ten percent. And for dividends, the amount of payments per share is four percent. And the expected return is 14% per annum.

What if there are deviations?

Initially, let's look at the table, and then there will be explanations for it.

Economic environment	Expected return	Probability
Rise	42%	0, 2
Neutral	14%	0, 6
Recession	-6%	0, 2

So what does this mean? What are the prospects for our investment portfolio? This table considers the option of an economic recovery, a continuation of the current situation and a recession. The previously calculated values consider a situation where nothing qualitatively changes. At the same time, there is a twenty percent chance that the acquisition of Podsolnukh shares will bring an annual return of 42%. This is if there is a rise in economic activity. If there is a recession, then a loss of six percent is expected. Then we need to calculate the expected return. For this, the following formula is used: E(r)=0, 420, 2+0, 140, 6+(-0, 06)0, 2. It is intuitive, and there should be no problems with its adaptation. The result of the calculations isindex. If for risk-free assets its value is equal to zero (this is observed for Treasury bonds with a fixed coupon), then for all the rest the deviation will be much stronger.

Continue with the example

Someone may already think that this example is not so small, but believe me, when you have to act in real conditions, you will remember the Sunflower company with kindness and affection. So, our equity investment fund, according to the proposals of Markowitz, proposes to diversify the portfolio so that it includes the least correlated assets in terms of risk / return. This will lower the overall standard deviation, optimizing the overall indicator. For example, the portfolio includes agricultural enterprises and companies producing sunflower oil. These enterprises are correlated according to one principle - the price of culture. How? If sunflowers rise in price, then the shares of agricultural enterprises grow, and oil producers fall. And vice versa. Investing in these facilities, in fact, will be a pouring from one jug to another. Thus, the Markowitz theory is based on two key principles: the optimal risk / return ratio and the minimum correlation of assets.

Weak spots

Alas, the Markowitz portfolio is not perfect. It is possible to achieve a minimum risk for investments, but with certain reservations. And in order to fully explore the topic, you need to speak notonly about strengths, but also about weaknesses. First of all, it should be noted that if the market is growing, then the Markowitz theory can significantly simplify the process of activity and achievement of objectives for the investor. But problems appear when it unfolds. In such cases, investment management, built on the principle of "buy and hold", turns into an increase in losses. It is also necessary to mention the specifics of the mathematical expectation, and more specifically, the chosen time interval. The larger it is, the slower the reaction to the emergence of a new series of values.

What other cons are there?

The fact is that the Markowitz theory does not provide tools for determining trade entry/exit points. Because of this, the portfolio has to be recalculated very often and the leaders of the fall must be excluded from it. It should also be noted that the presence of a ban on short transactions means that a falling market has its own specific assessment points. For example, the concept of an efficient portfolio often loses its meaning in such cases. Another problem: certain behavior of specific instruments in the past does not at all guarantee the presence of the same in the future. Therefore, active or combined strategies are gradually gaining popularity as a replacement for Markowitz's theory. In them, portfolio theory interacts with technical analysis, allowing you to more quickly respond to market changes.

Several managerial moments

Every investor who decides where to spend his available funds,must deal with a large number of issues. Depending on the field of activity and the goals set, one should study the forecast of market dynamics, macroeconomic indicators, and evaluate their impact on individual assets and portfolios. At the same time, it is necessary to maximize profitability while maintaining an acceptable level of risk. Also, investment management requires that the following questions be answered:

1. What should you pay attention to - the risk of individual assets or the entire portfolio that is formed from them?
2. How to quantify potential hazards?
3. Is it possible to reduce the risk of a portfolio by changing the weight of assets in it?
4. If so, how can this be achieved while maintaining or even increasing portfolio returns?

A few words about diversification

As previously mentioned, this plays a big role. The special point in this case is that risk must be considered as a property of the entire portfolio, and not of individual assets. Remember earlier about the correlation between different assets? If we imagine that we have invested half of our funds in the cultivation of sunflowers and the same amount in the production of oil from them, then any movement in this market, in other words, will be a zero-sum game. Therefore, there must be no direct links between different assets, as well as taking into account the risk of not individual assets, but the entire portfolio. And yet, let's say certain securities were sold and others acquired. Thus, a new portfolio is formed, ideally,optimal at the moment. But during the acquisition of new assets, the question arises of their optimal ratio. If there are many of them, then the solution of this problem becomes problematic and requires significant computing power. It is difficult to name here a specific approach that is universal and applicable in any situation. It is possible to operate in an extensive way, simply by increasing the capacity. As another option, it is to develop a more advanced technology for solving the problem.

What conclusions can be drawn from this

It should be remembered that any theory benefits only practitioners, and only those who are clearly aware of all the features of its application. So let's sum up all of the above:

1. Mathematical apparatus has been developed, which makes it possible to significantly facilitate the process of forming an investment portfolio. But at the same time, it requires certain knowledge, without which the entire toolkit is worth nothing. For example, a variation of a random variable. What should she be? What to take as basic data? In addition, it should also be noted that the Markowitz theory allows you to visually provide information.
2. It should be remembered that this technique is based on prehistory and does not use forecasting methods. Therefore, the theory is ineffective during a general market decline. It also does not provide entry/exit criteria.
3. Despite the fact that a lot of time has passed since the formation of Markowitz's theory, and many serious scientificmethods of analysis, it is still widely used. But now more like part of the math toolkit.

Using this theory or not is up to you. The main thing is to take a responsible approach to calculations and forecasting.