# Modern Portfolio Theory (MPT)

Modern Portfolio Theory (MPT) is a widely used practice for optimizing investment portfolios to achieve the greatest potential reward for the amount of risk an investor is willing to assume. Learn what MPT tells us and how investors can use it to develop optimally diversified portfolios.

## What Is MPT?

MPT, or modern portfolio theory, is a mathematical technique for developing the "optimal" mix of assets (or asset classes) in a portfolio for a given amount of risk. *Optimal* in this instance means the asset mix that will theoretically deliver the maximum return for the level of risk in the portfolio. Risk is defined by the standard deviation of historic returns in the selected assets (which relates to their volatility). In plain language, MPT is a tool for optimizing portfolio diversification.

At its core, MPT is a statistical analysis that uses the historical returns of any asset or asset class and the correlation of those returns with that of other assets in the portfolio to determine the proportion of each asset that will maximize the reward for any given amount of risk. Portfolios are said to be most “efficient” when they can return the most reward for a given amount of risk and MPT tells us that combining assets in certain proportions can lead to better risk-reward characteristics for the overall portfolio.

An accepted premise in investing is that the higher your potential reward with an asset or asset class, the higher the risk (as measured by its standard deviation in historical returns). What MPT discovered was that you can often achieve better overall results (i.e. more return for the same amount of risk or lower risk for the same expected return) by combining multiple assets in a portfolio–and MPT can tell you which assets and in what proportion.

### What Is the Efficient Frontier?

The results of an MPT analysis for a portfolio of specified assets can be shown on a graphical plot of the standard deviation (i.e. risk) versus the expected return of all combinations of those assets. In the simple case of just two assets, say stocks and cash, the plot would show all possible portfolios from 100% stocks and 0% cash to 0% stocks and 100% cash. When a line is drawn through the highest return portfolios for all levels of risk, it forms a curve that is called “the efficient frontier”.

## History of Markowitz Portfolio Theory

MPT was pioneered by Harry Markowitz in his 1952 paper called “Portfolio Selection”, which earned him a Nobel Prize in Economics. Also known as “Markowitz portfolio optimization” or simply “mean-variance analysis”, MPT is a portfolio management tool that is widely used by institutional investors such as mutual funds, pension funds, and hedge funds.

## Modern Portfolio Theory Key Assumptions

One can never know exactly how a risky financial asset will perform in the future, but classic financial theories such as the Efficient Market Hypothesis, Capital Asset Pricing Model, and Modern Portfolio Theory use statistical methodologies to predict the performance of a large number of stocks and they have worked well for institutional investors for decades.

Two of the key assumptions that MPT is based on include:

### 1. That Standard Deviation of Past Returns is a Valid Measure of Risk

While standard deviations in returns represent a widely used proxy for risk, they do not specifically address the downside risk in any asset. Furthermore, standard deviations are not a constant and will vary in different time periods.

### 2. That Correlations Between Different Assets and Asset Classes Will Remain Constant in the Future

Correlations are also not constant and will vary in different time periods. For situations where these assumptions are not valid, MPT may not be a useful tool. In addition, MPT can only optimize a portfolio against idiosyncratic risk, which is the risk of a specific asset. It cannot optimize against market risk, which impacts an entire portfolio.

## Modern Portfolio Theory vs. Behavioral Economics

Behavioral Economics tells us that absent a particular diversification discipline, investors will tend to herd in and out of stocks at the wrong times, thereby reducing their performance relative to the market. Two ways in which MPT can be used to keep investors on the right track are as follows.

### 1. Two-Fund Theory

The two-fund theory is an outgrowth of MPT that can be used practically by individual investors. It says that optimal portfolios at different risk levels can, in essence, be constructed with just two assets: a diverse mutual fund and a risk-free asset such as a money market fund, cash, or Treasury Bills. This implies that investors with modest portfolios need not attempt to find enough individual stocks to perform an effective MPT analysis and instead can merely hold a combination of a single mutual fund and cash to achieve a similar result.

### 2. Strategic Asset Allocation

Strategic asset allocation seeks to diversify a portfolio with a mix of different asset classes that take a long-term view of investing and then rebalance those allocations periodically. That means that as asset classes appreciate or depreciate relative to the target allocation, the rebalancing brings them back into line.

As an example, assume that an optimal long-term allocation was determined to be 60% in stocks, 30% in bonds, and 10% in cash and after six months stocks outperformed bonds such that the portfolio was now 65% stocks, 27% bonds, and 7% cash, a rebalancing would sell some of the stocks and buy more bonds and cash to restore the original mix.

## Benefits to Understanding MPT

While the mathematics of MPT can be a bit complex for individual investors, there are important lessons from MPT that can be used to improve overall performance. These include:

- Increasing asset diversification to achieve better risk-reward characteristics in an overall portfolio.
- Improving a portfolio’s overall performance by mixing in non-correlated or negatively-correlated assets (i.e. assets that will go up when others go down).
- Combining high-risk assets (i.e. stocks) with low-risk assets (i.e. bonds or cash) to provide better long-term risk-reward characteristics overall than either asset class by itself.
- Diversifying by asset
*class*as well as individual assets. A large number of stocks helps to diversify, but mixing stocks with bonds, government securities, cash, gold, or other types of assets can even be more important.

## Bottom Line

Investors often focus too much on what stocks to own and not on the risk-reward profile of their overall portfolio. An understanding of what has been learned from Modern Portfolio Theory can be very instructive in establishing more of a perspective on the portfolio as a whole and the diversification of asset classes within it.

This article was written by

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