What is Modern Portfolio Theory (MPT)?
Modern Portfolio Theory (MPT) is an investment theory developed by Harry Markowitz in the 1950s. It provides a framework for building a portfolio of assets to maximize expected return for a given level of risk, or minimize risk for a given level of expected return.
Portfolio theory, originally proposed by Harry Markowitz in the 1950s, was the first formal attempt to quantify the risk of a portfolio and develop a methodology for determining the optimal portfolio. The introduction of modern portfolio theory has led to a mathematical explanation of the expression “don’t put all your eggs in one basket”.
One of the most fundamental conclusions in Markowitz portfolio choice theory is that rational investors should not choose assets only because of their unique properties such as the expected return and variance, but should also consider the co-variation between the different assets. As the number of assets in a portfolio increases, the covariance increasingly makes up a greater part of an individual assets contribution to the total risk of a portfolio.
Basically, what MPT says is that, it is not enough to take only one particular asset’s risk and return under consideration but rather investing in several assets with low correlations towards each other. This will give the portfolio advantages of diversification. He was the first person to show quantitatively why and how diversification reduces risk. Hence, the relevant objective in the MPT concept is to chose the right combination (or proportions) of these assets to the optimal portfolios.
Assumptions of Modern Portfolio Theory
Modern Portfolio Theory relies on the following assumptions and fundamentals that are the key concepts upon which it has been constructed:
- Investors ask for maximizing the expected return of their total wealth.
- All investors have the similar expected single period investment horizon.
- All investors are risk-averse, which means that they only will accept a higher risk if they are compensated with a higher expected return.
- Investors base their entire investment decision on the expected return and risk.
- Investors prefer higher returns to lower returns for a given level of risk.
Some other assumptions:
- For buying and selling securities there are no transaction costs. There is no spread between bidding and asking prices. No tax is paid, its only risk that plays a part in determining which securities an investor will buy.
- An investor has a chance to take any position of any size and in any security. The market liquidity is infinite and no one can move the market. So that nothing can stop the investor from taking positions of any size in any security.
- While making investment decisions the investor does not consider taxes and is indifferent towards receiving dividends or capital gains.
- Investors are generally rational and risk adverse. They are completely aware of all the risk contained in investment and actually take positions based on the risk determination demanding a higher return for accepting greater volatility.
- The risk-return relationships are viewed over the same time horizon. Both long term speculator and short term speculator share the same motivations, profit target and time horizon.
- Investors share identical views on risk measurement. All the investors are provided by information and their sale or purchase depends on an identical assessment of the investment and all have the same expectations from the investment. A seller will be motivated to make a sale only because another security has a level of volatility that corresponds to his desired return. A buyer will buy because this security has a level of risk that corresponds to the return he wants.
- Investors seek to control risk only by the diversification of their holdings.
- In the market all assets can be bought and sold including human capital.
- Politics and investor psychology have no influence on market.
- The risk of portfolio depends directly on the instability of returns from the given portfolio.
- An investor gives preference to the increase of utilization.
- An investor either maximizes his return for the minimum risk or maximizes his portfolio return for a given level of risk.
- Analysis is based on a single period model of investment.
Based on these assumptions, most of which are pretty much common sense, when comparing a single asset or a portfolio of assets, only assets or portfolios with the highest expected return at the same or lower risk level are considered as efficient.
Versijp in 2011 adds the following assumptions for modern portfolio theory to our list.
- Investors prefer more over less (no satiation)
- Investors dislike risk (risk-aversion)
- Traders maximize utility, and do so for 1 period
- Utility is a function of expected return and variance and nothing else
- There is no distortion from inflation
- All information is available at no costs
- All investments are infinitely divisible and last one which should be on our assumption list for proper analysis
- The unit of measurement contains a constant purchasing power.
Of course this list is not the best representation of reality, but allows us to do valuable analysis. Investors are also rational so they will always prefer more to less, i.e. investors will not invest in a portfolio if there consists a second portfolio with a more favorable risk return profile.
Security markets are efficient, as new information enter markets information is quickly reflected in the assets prices. Assets are therefore literally re-priced as soon as new information hit the market. MPT also uses standard deviation (volatility) as a proxy for risk.
Another assumption of the MPT is that there are no limits on the size of positions taken when investing and investors can take any position they want. Investors don’t think about taxes when making investments decisions and are indifferent between receiving dividends or capital gains.
Investors also don’t have to think about transaction costs. Investors as a group also look at the risk-return relationship over the same time horizon. All assets, including human capital can be traded on the market and politics and investor psychology have no effect on the markets. MPT further assumes that returns are normally distributed and that historical average of returns corresponds to expected returns.
Central Concepts of Markowitz’s Modern Portfolio Theory
In 1952, Harry Markowitz presented an essay on “Modern Portfolio Theory” for which he also received a Noble Price in Economics. His findings greatly changed the asset management industry, and his theory is still considered as cutting edge in portfolio management.
There are two main concepts in Modern Portfolio Theory, which are:
- Any investor’s goal is to maximize return for any level of risk
- Risk can be reduced by creating a diversified portfolio of unrelated assets
Maximize Return – Minimize Risk
Return is considered to be the price appreciation of any asset, as in stock price, and also any Capital inflows, such as dividends. In general Standard Deviation is a fair measure of risk as we want a steady increase and not big swings which might possibly end up as loss. Risk is evaluated as the range by which an asset’s price will on average vary, known as Standard Deviation. If an asset’s price has 10% deviation from the mean and an average expected return of 8% you may observe returns between -2% and 18%.
In a practical application of Markowitz Portfolio Theory, let’s assume there are two portfolios of assets both with an average return of 10%, Portfolio A has a risk or standard deviation of 8% and Portfolio B has a risk of 12%. As both portfolios have the same expected return, any investor will choose to invest in portfolio A as it has the same expected earnings as portfolio B but with less risk.
It is important to understand risk; it is a necessary concept, as there would be no expected reward without it. Investors are compensated for bearing risk and, in theory, the higher the Risk, the higher the Return.
Going back to our example above it may be tempting to presume that Portfolio B is more attractive than Portfolio A. As portfolio B has a higher risk at 12%, it may obtain a return of 22%, which is possible but it may also witness a return of -2%. All things being equal it is still preferable to hold the portfolio that has an expected range of returns between +2% and +18%, as it is more likely to help you reach your goals.
Diversified Portfolio & the Efficient Frontier
Risk, as we have seen above, is a welcomed factor when investing as it allows us to reap rewards for taking on the possibility of adverse outcomes. Modern Portfolio Theory, however, shows that a mixture of diverse assets will significantly reduce the overall risk of a portfolio. Risk, therefore, has to be seen as a cumulative factor for the portfolio as a whole and not as a simple addition of single risks.
Assets that are unrelated will also have unrelated risk; this concept is defined as correlation. If two assets are very similar, then their prices will move in a very similar pattern. Two ETFs from the same economic sector and same industry are likely to be affected by the same macroeconomic factors. That is to say, their prices will move in the same direction for any given event or factor. However, two ETFs (Exchange Traded Funds) from different sectors and industries are highly unlikely to be affected by the same factors.
This lack of correlation is what helps a diversified portfolio of assets have a lower total risk, measured by standard deviation than the simple sum of the risks of each asset. Without going into any detail, a bit of math might help to explain why.
Correlation is measured on a scale of -1 to +1, where +1 indicates a total positive correlation, prices will move in the same direction par for par, and -1 indicates the prices of these to stocks will move in opposite directions. If correlation between all ETF pairs is 1, then it would seem reasonable that the total risk of the portfolio is equal to the sum of the weighted standard deviations of each individual ETF. Whereas a portfolio where the correlation of asset pairs is lower than 1 must lead to a total risk that is lower than the simple sum of the weighted standard deviations.
The magic of building different pairs is that by different combination it is possible to achieve basically every risk to return combination, even different from the risk to return level of the single components.
Markowitz Efficient Frontier
The concept of Efficient Frontier was also introduced by Markowitz and is easier to understand than it sounds. It is a graphical representation of all the possible mixtures of risky assets for an optimal level of return given any level of risk, as measured by standard deviation.
Markowitz Efficient Frontier
The chart above shows a hyperbola showing all the outcomes for various portfolio combinations of risky assets, where Standard Deviation is plotted on the X-axis and Return is plotted on the Y-axis.
The Straight Line (Capital Allocation Line) represents a portfolio of all risky assets and the risk-free asset, which is usually a triple-A rated government bond.
Tangency Portfolio is the point where the portfolio of only risky assets meets the combination of risky and risk-free assets. This portfolio maximizes return for the given level of risk.
Portfolio along the lower part of the hyperbole will have lower return and eventually higher risk. Portfolios to the right will have higher returns but also higher risk.
Importance of Modern Portfolio Theory (MPT) for Risk Management
The theory is of vital importance when it comes to financial risk management. It is vastly used by portfolio managers while developing investment diversification strategies. MPT proves to be highly advantageous and highly appreciated among investors, as the results of its implication lead to portfolio optimization with either the same expected return with less risk than before or a higher expected return with the same level of risk.
The theory is an essential tool when it comes to avoiding financial ruin, as traders cannot simply rely on a single investment for financial stability. Through diversifying one’s investments among several asset classes, containing options, bonds, stocks, futures contracts or precious metals, the probability of undergoing financial blow will be reduced even if one or two investments suffer.
Modern Portfolio Theory has played an essential role in the further development of portfolio trading methods, as well as their management as of today. One of the achievements in this sphere that has reached its perfection, providing investors and traders with all the required conditions to get the highest profit with the lowest risk is GeWorko Method. The Method is based on the already well-worked out principles of portfolio theory, meanwhile, representing quite a new approach and range of opportunities in the financial markets.
It is the first in its kind when it comes to opportunities and created conditions for effective trading and risk management. GeWorko Method, based on NetTradeX platform, allows any trader, investor to realize diverse trading strategies, by allowing to combine assets of their choice and create unique personal instruments.
Multiple strategies become possible alongside with investment diversification, through using hundreds of assets of different classes, offered on the platform. It is possible to conduct a thorough retrospective market analysis, as well as use vast technical analysis tools. All these features are oriented towards the investors’ benefits and make it possible to make a profit through minimizing the risk of loss.
Criticism of Modern Portfolio Theory
Being widely and popularly used by investment institutions, Modern Portfolio Theory still has been subjected to various criticisms.
- The assumptions made by Markowitz have been criticized due to research findings in other fields of study, particularly within behavioural economics. The behavioural economists have proven that the assumption on “investors’ acting rationally” is wrong.
- In the same way the studies carried out in the area of behavioural finance, have challenged the idea that all investors have exact idea of potential returns, as normally the expectations of investors are biased.
- The opinion that investors do not need to pay any taxes or transaction costs does not hold true.
- The assumption that investors can buy securities of any size is claimed not to be practical, since some securities have the minimum order sizes, and securities cannot be bought or sold in fractions.
- Besides, investors have a credit limit which does not allow them to lend or borrow unlimited amounts of shares.
- The critics also challenge the idea that the actions of investors do not have an influence on the market; it is claimed incorrect, as great amount of sale and purchase of separate securities has an impact on the price value of the security or related securities.
- Besides, the correlations between assets are never stable and fixed; they tend to change together with the changes in the universal relations, existing between fundamental assets.
- Furthermore, the theory does mathematical calculations on expected values, based on past performance to measure the correlations between risk and return. However, experienced investors consider past performance not to be a guarantee of future performance. Taking into account only past performances leads to overpassing newer circumstances, maybe not having existed during the time when the historical data were compiled.
