Modern Portfolio Theory Re-visited

Poor Harry Markowitz. Every time investors get whipped in the financial markets, they take it out on his Modern Portfolio Theory – Joan Warner

Wide diversification is only required when investors do not understand what they are doing – Warren Buffett

Introduction

I first heard of Modern Portfolio theory during a Corporate Finance class back in the mid 90s. MPT was introduced to myself and my fellow students as a non-emotional and rational way to build an investment portfolio – that is probably because the course was part of an MBA. Like many I grasped on MPT as a neat way to explain the concepts of risk, efficient frontier, and diversification. Since around 2008 I have increasingly heard more and more people question the very foundation of MPT. Its relevance as modern is called into question – it has been around for 59 years after all. Furthermore the core principles and underlying assumptions are often criticized. And when I speak with the more vehement they state that MPT has been proved wrong.

Consider this comment taken from Money Morning on 17 November 2011:

“The point we’re making is this: the mainstream view is that diversifying your investments across many investments within an asset class and across different asset classes is the best way to create wealth. In fact the opposite is the case. Sure. If you’re lazy… or you just don’t care… Or you figure the government will pay you a wage in retirement, then go ahead, diversify.”

There are a few blogs questioning the veracity of MPT. Check out just two of them here:

Is Modern Portfolio Theory Wrong?  and  Rethinking Modern Portfolio Theory

In this paper I want to simply revisit some of the basic principles of MPT. I would like to consider Risk and the Efficient Frontier from MPT viewpoint, and finally I would like to highlight some of the underlying assumptions implicit in MPT. Having done that I would like to invite you to draw your own conclusions about whether MPT is still a valid theory of investment portfolio construction.

Modern Portfolio Theory

Modern Portfolio Theory (MPT) was introduced by Harry Markowitz in the 1952 Journal of Finance published under the title “Portfolio Selection”. MPT is one of the most important and influential economic theories dealing with finance and investment. Prior to Markowitz’s work, investors focused on assessing the risks and rewards of each security in constructing their portfolios. Standard investment advice was to find securities that offered the best opportunities for gain with the least risk and then build a portfolio from these. MPT says that it is not enough to look at the expected risk and return of one particular stock. By investing in more than one stock, an investor can reap the benefits of diversification – chief among them, a reduction in the riskiness of the portfolio. MPT is essentially a broad theory for portfolio choice drawing on a mathematical interpretation of diversification. Markowitz proposed that investors focus on selecting portfolios based on their overall risk-reward characteristics instead of merely compiling portfolios from securities that each individually has attractive risk-reward characteristics. In a nutshell, inventors should select portfolios not each security.

Investopedia defines MPT as “A theory on how risk-averse investors can construct portfolios to optimize or maximize expected return based on a given level of market risk, emphasizing that risk is an inherent part of higher reward.”

In summary MPT:

• Is a theory of investment;
• Which attempts to maximize portfolio expected return for a given amount of portfolio risk or equivalently lower risk for a given level of expected return;
• By carefully choosing the proportions of various assets;
• Based on a mathematical formulation of the concept of diversification in investing; and which
• Aims to select a collection of investment assets that has collectively lower risk than any individual asset.

Risk

Investment risk refers to the possibility that an investment will give a return which is lower than the expected return. Modern portfolio theory states that the risk for individual stock returns has two components, namely systematic risk and unsystematic risk.

• Systematic Risk refers to the risk inherent in all securities in the market. These include interest rates, recessions and wars. Systematic risk cannot be diversified away (within one market).
• Unsystematic Risk is risk associated with specific individual stocks. Also known as “specific risk” it refers to the specific risk that is inherent in each investment and can be diversified away as you increase the number of stocks in your portfolio.

For most investors, the risk they take when they buy a stock is that the return will be lower than expected. In other words, it is the deviation from the average return. Each stock has its own standard deviation from the mean. The volatility of the asset, and its correlation with the market portfolio, are historically observed and are given. MPT defines risk as the standard deviation of return, and models a portfolio as a weighted combination of assets so that the return of a portfolio is the weighted combination of the assets’ returns. By combining different assets whose returns are not perfectly positively correlated, MPT seeks to reduce the total variance of the portfolio return.

The risk in a portfolio of diverse stocks will be less than the risk inherent in holding any one of the individual stocks (provided the risks of the various stocks are not directly related). MPT demonstrates that portfolio diversification can reduce investment risk. In fact, modern money managers routinely follow its precepts. The fundamental concept behind it is that the assets in an investment portfolio should not be selected individually, each on their own merits. Rather, it is important to consider how each asset changes in price relative to how every other asset in the portfolio changes in price. In other words, Markowitz showed that investment is not just about picking stocks, but about choosing the right combination of stocks among which to distribute one’s nest egg.

The Efficient Frontier

The Efficient Frontier concept answers the question of how to find the best level of diversification. According to Markowitz, the Efficient Frontier is the set of all portfolios that will give the highest expected return for each given level of risk. Put another way, an efficient portfolio is one where no added diversification can lower the portfolio’s risk for a given return expectation (alternately, no more expected return can be gained without increasing the risk of the portfolio).

For every level of return, there is one portfolio that offers the lowest possible risk, and for every level of risk, there is a portfolio that offers the highest return. These combinations can be plotted on a graph, and the resulting line is the efficient frontier. Figure 2 shows the efficient frontier for just two stocks – a high risk/high return technology stock (Google) and a low risk/low return consumer products stock (Coca Cola).

Any portfolio that lies on the upper part of the curve is efficient: it gives the greatest expected return for a given level of risk. A rational investor will only ever hold a portfolio that lies somewhere on the efficient frontier. The largest level of risk that the investor will take on determines the position of the portfolio on the line.

If we treat single-period returns for various securities as random variables, we can assign them expected values, standard deviations, and correlations. Based on these, we can calculate the expected return and volatility of any portfolio constructed with those securities. We may treat volatility and expected return as proxy’s for risk and reward. Out of the entire universe of possible portfolios, certain ones will optimally balance risk and reward. These include what Markowitz called an efficient frontier of portfolios. An investor should select a portfolio that lies on the efficient frontier.

Investing is a tradeoff between risk and expected return. In general, assets with higher expected returns are riskier. For a given amount of risk, MPT describes how to select a portfolio with the highest possible expected return. Or, for a given expected return, MPT explains how to select a portfolio with the lowest possible risk. MPT is therefore a tool to illustrate the best possible diversification strategy.

Assumptions

Specific criticisms of MPT are suggested by WiseGEEK (What is Modern Portfolio Theory?) “modern portfolio theory has drawn severe criticism from many quarters. The principle objection is with the concept of Beta; while it is possible to measure the historical Beta for an investment, it is not possible to know what its Beta will be going forward. Without that knowledge, it is in fact impossible to build a theoretically perfect portfolio. This objection has been strengthened by many studies showing that portfolios constructed according to the theory don’t have lower risks than other types of portfolios.”

Pete Swisher and Gregory W. Kasten argue that “The primary reason MPT produces inefficient portfolios (even though the point is supposedly the building of efficient portfolios) is simple: standard deviation is not risk. Risk is something else, and we need a better mathematical framework to describe it.”

MPT makes assumptions about investors and markets. Some are explicit whilst others are implicit. None of these assumptions are entirely true, and each of them compromises MPT to some degree. Some of the principle assumptions include:

Assumptions about Investors

• All investors are rational, risk-averse and aim to maximize economic utility; and
• Investors have an accurate conception of possible returns.

Assumptions about Markets

• Investment returns are normally distributed and random variables;
• Correlations between assets are fixed and constant forever;
• Markets are efficient & all investors have access to the same information at the same time; and
• There are no taxes or transaction costs

Concluding Comments

MPT is 59-year-old theory with underlying assumptions which are questionable. We know that investors are far from rational. We know that markets are not efficient and that investment returns are not normally distributed. Yet MPT remains the cornerstone of most investment philosophy. Why is that? Is it because we are intuitively drawn to the elegance of the model? Is it because any alternatives are too complex to grasp? Or are we simply too lazy to think past MPT? I for one don’t know the answer – I would love to hear yours.