Modern Portfolio Theory is widely used in the world of finance. In this article, we take a closer look at what Modern Portfolio Theory is, review an example calculation, and explain the assumptions behind the theory.
What is Modern Portfolio Theory?
Modern Portfolio Theory (MPT) is widely used in finance and commercial real estate to create investment portfolios that maximize return at a given level of risk or minimize risk at a given level of return.
Harry Markowitz is known as the father of Modern Portfolio Theory (MPT). In 1952, while completing his doctoral dissertation in economics at the University of Chicago, Harry Markowitz published part of his research on “portfolio selection” in the Journal of Finance. This publication marked the beginning of an entirely new field of research on financial economics and investment. In 1990, Harry Markowitz won the Nobel Prize in Economics for his work on Modern Portfolio Theory. His work laid the foundation for how we think about investment decisions today.
With MPT, investors consider not only the risk and return characteristics of individual assets, but also the relationships between asset returns. Key to MPT is the idea of the benefits of diversification. In other words, investors should consider the optimal combination of different assets to achieve the highest return for a desired level of risk.
Fundamentals of Modern Portfolio Theory
According to MPT, investors should not consider individual investments in isolation, but as part of a portfolio of assets. This portfolio of assets should be constructed to maximize return for a particular level of risk. Investors can also reduce the overall portfolio risk by diversifying their holdings through separate, unrelated assets. Therefore, investors should consider the impact on the mean-variance characteristics of their portfolio when evaluating new investments. Using MPT, the two most important characteristics of an asset are the asset's expected return (mean) and the standard deviation of returns (variance).
Assumptions of Modern Portfolio Theory
Modern Portfolio Theory assumes that investors are risk averse. This does not mean that they do not take risk, but that they prefer low risk over high risk. For example, if two investments have returns of 10% each and the standard deviations of those returns are 4% and 2%, a risk-averse investor would prefer the asset with a return variance of 2%.
Risk-averse investors also demand a premium for taking on more risk. Therefore, assets with greater return variability should reward investors with higher expected returns. Risk-averse investors prefer the asset with the highest expected return for a particular level of risk. For example, if there are two assets with expected returns of 7% and 9% and the standard deviation of returns is 4%, a risk-averse investor would choose the asset with the expected return of 9%.
Diversification allows an investor to achieve the required rate of return on his portfolio while reducing the overall portfolio risk. Diversification cannot reduce systematic risk (risk associated with the entire financial market), but it can reduce what is called idiosyncratic risk. The idiosyncratic risk of an asset is a measure of the variability of returns attributable to a particular stock. It is different from systematic risk, which is associated with all investments in a market where the outcome is uncertain. Diversification cannot reduce an investor's exposure to systematic risk.
Ultimately, it is the correlation of assets' return distributions that provides the benefits of diversification. If two assets have a correlation of 1.0, they have roughly the same return distribution: if one asset grows 2%, the other should also grow 2%. On the other hand, two assets with a correlation of -1.0 have opposite return distributions: if one asset grows 2%, the other should also shrink 2%.
Modern Portfolio Theory and the Efficient Frontier
If we graph the standard deviation and expected return (risk vs. return) of all possible portfolios, we get a diagram like this:
Because a rational, risk-averse investor should always choose the portfolio with the highest expected return for a given level of risk, a scatter plot of all portfolios will exhibit a line called the efficient frontier. Investments along the efficient frontier provide investors with the highest expected return for a given level of risk. All portfolios that are not along the efficient frontier are suboptimal. The efficient frontier contains many different portfolios that incorporate many investments in different ways, thus demonstrating the power of diversification.
Modern Portfolio Theory Calculation Example
To see how this works, start with two assets, each with a 50% weighting in your portfolio. Property A has an expected return of 12% per year, with a standard deviation of returns of 10%. Property B has an expected return of 9% per year, with a standard deviation of returns of 8%. The risk-return trade-off required by a risk-averse investor dictates that the riskier the return, the higher the expected return. The correlation between the returns is 0.4.
To calculate the expected return on a portfolio, take the weighted average of the returns on the two assets.
Expected Portfolio Return = (0.5)(.12) + (0.5)(.09) = .105 or 10.5% per year
The formula for portfolio diversification is:
X1 = asset 1 weight
σ1 = standard deviation of asset 1
X2 = asset 2 weight
σ2 = standard deviation of asset 2
r12 = correlation coefficient between asset 1 and asset 2
So, in this example, the portfolio variance calculation would be:
Portfolio variance = (0.52)(0.12) + (0.52)(0.092) + (2)(0.5)(0.5)(0.4)(0.1)(0.09) = .0057
Taking the square root of the portfolio variance gives us a portfolio standard deviation of 0.075, or 7.5% per year.
Therefore, this example illustrates the benefits of portfolio diversification according to Modern Portfolio Theory. The asset portfolio has lower risk (standard deviation) than either of the two assets alone. Also, in this example, the portfolio earns a higher return at a lower risk level than asset B.
Postmodern Portfolio Theory
Software developers Brian Lom and Kathleen Ferguson introduced the concept of Postmodern Portfolio Theory (PMPT) in the Journal of Performance Management in 1993. PMPT is essentially an extension of Markowitz's Modern Portfolio Theory, since it places the risk-return tradeoff at its core. The definition of risk is the main difference between the two theories. In Modern Portfolio Theory, risk is defined as the standard deviation of returns, with positive and negative returns weighted equally. On the other hand, PMPT recognizes that investors are much more concerned about the downside risk of their investments. In other words, investors are more concerned about losing money than they are about making more money than expected. Therefore, PMPT focuses entirely on the negative component of the return distribution in its risk calculations.
Conclusion
Modern Portfolio Theory remains the foundation of investment management and portfolio selection today. Investors seek to maximize return at a given level of risk, and diversify across industries and asset classes to achieve the most efficient portfolio balance of risk and return. While new theories and models have refined behavioral trends with new technology, they have not strayed far from Markowitz's original theory.