Most of us desire investments that provide high returns at little risk. Unfortunately, in the real world, risks abound. Decades of study show that diversification is a powerful way to reduce the risk that any one badly performing asset or asset class would ruin your overall return. Diversification, which here means simply a diversity of investments, requires that different assets be correlated with each other only weakly. Thus, even if stock prices crashed, another asset class, such as gold, might soar. Researchers have developed several variations of diversification theory since its inception in 1952.

## Modern Portfolio Theory

Modern portfolio theory was invented by Harry Markowitz in 1952 with the idea that the investments in a portfolio should be selected based on their correlation to other assets. "Correlation" is a mathematical term that here describes how the price movement of one asset is related to the total value of the portfolio. Modern portfolio theory aims to extract the maximum return for any level of risk. Although this approach is highly theoretical, it requires that an investor start with a risk-free asset, such a three-month Treasury bills. The investor then adds diversified risky assets that yield an “efficient” portfolio -- one with minimum risk and maximum return. It is very complex to actually design efficient portfolios this way; the same goes for putting most diversification theories into practice.

## Post-Modern Portfolio Theory

Post-modern portfolio theory was created in 1991 to answer some criticisms about the Markowitz model. The new theory measures risk using internal rate of return, which is the minimum acceptable return an asset must provide to be included in the portfolio. The higher the internal rate of return, the more desirable the asset. The main advantage of post-modern portfolio theory is that it focuses on downside risk rather than total risk. The mathematics of the theory evaluates the internal rate of return of an asset relative to a target desired return, and it adjusts this number for downside risk. Post-modern portfolio theory requires the use of calculus.

## Risk Parity Theory

The idea behind risk parity theory is to allocate assets to your portfolio based on their riskiness rather than on their dollar value. Many people seek diversification by following rules such as 60 percent of a portfolio’s value in stocks, 15 percent in bonds, 10 percent in gold, and so forth. Risk parity theory instead has you use the volatility, or price variation, of each asset class as the measure of risk. You then construct a portfolio by purchasing an amount of each asset class that contributes the same volatility as every other asset class in the portfolio. In this way, the volatility of one asset class will not swamp that of other classes.

## Maximum Diversification Theory

Maximum diversification theory also uses volatility to measure risk. To construct a portfolio this way, you measure the volatility of each asset class, take the average weighted volatility -- the volatility multiplied by the amount invested in the asset class -- and divide it by the portfolio’s actual volatility. This diversification ratio should ideally exceed 1, meaning that the portfolio risk is less than the risks of its components. The ratio increases as you add different, low-correlated asset classes. So it emphasizes very diverse portfolios, containing assets classes such as real estate and commodities in addition to stocks, bonds and gold. You can even add in artworks, collectibles, or any other valuable asset that shows a low correlation to the other assets.

## Afterword

Each of these theories is complex and requires a good deal of study to master. However, the basic message is clear: Diversify your portfolio to reduce risk. Mutual funds and exchange-traded funds offer instant diversification for a particular asset class. A multifund approach can give you diversification across many asset classes.

#### Resources (3)

- Portfolio Selection: Efficient Diversification of Investments; Harry M. Markowitz
- Portfolio Design: A Modern Approach to Asset Allocation; Richard C. Marston
- Portfolio Construction, Management, and Protection; Robert A. Strong

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