Modern Portfolio Theory (MPT) is the mathematical framework that powers the investment concept of diversification, which posits that investors can minimize the volatility of their portfolio and maximize their expected return by investing in a diversified portfolio of risky financial assets.

Nobel Prize winner Dr. Harry Markowitz introduced Modern Portfolio Theory in his 1952 research publication “**Portfolio Selection**,” where he offered mathematical proof that a diversified financial portfolio will be less volatile than the sum of its individual parts. His work was later improved upon by his doctoral student William Sharpe, who created the **Capital Asset Pricing Model**.

### What is Investment Risk

Modern Portfolio Theory makes several important assumptions about the definition of a rational investor. Some of these assumptions appear to be unfounded, according to recent research, but others still hold true. One of the more common-sense assumptions is that investors are risk-averse, which means they prefer certainty over uncertainty when investing.

Suppose you have to choose between two investments that are expected to appreciate (increase in value) 10% each year. The only difference is that one investment is twice as volatile as the other, meaning that its value increases and decreases more frequently.

Modern Portfolio Theory suggests that investors will always choose the less volatile investment, assuming both provide an equivalent expected return.

### How to Reduce Investment Risk

Although some investments are riskier (more volatile) than others, Modern Portfolio Theory recognizes that risky assets can be combined into a diversified portfolio. When constructed properly, the portfolio as a whole carries less risk than the sum of its individual components.

For example, consider a small island economy that supports two businesses. One business, Sunshine Toys, produces beach toys while the other, Umbrellas Inc., produces umbrellas. Let’s assume that the island averages six months of sunshine and six months of rain each year, but that the wet and dry seasons are impossible to predict in advance.

The profits of each business will depend on the weather. During the dry months, beach toys will sell extremely well, but very few visitors will be interested in umbrellas. During the wet season, the opposite is true. Let’s assume that both businesses offer a 20% return on investment in high season, but that each business is forced to close during the bad times.

An investor who bought stock in Umbrellas Inc. would earn a 20% return during the rainy season, but earn 0% during the sunny season when Umbrellas Inc. temporarily closes. On average, he would earn a 10% return. An investment in Sunshine Toys would produce similar results in opposite months. Therefore, an investment in either company is risky, because the weather outcome is unknown and there could be several sunny or rainy seasons in a row.

Instead of investing in either company alone, an investor could diversify his portfolio and split his money evenly between both firms. In sunny seasons, his investment in Sunshine Toys would produce a 20% return while his investment in Umbrellas Inc. would produce nothing. In the rainy seasons, the exact opposite would be true. Thus, in any season, his diversified portfolio would produce a 10% rate of return.

Diversifying between both companies produces the same expected return, but eliminates all return volatility. The investor realizes a 10% return, regardless of the weather conditions on the island.

### Modern Portfolio Theory in the Real World

In the example above, the expected return of both companies is inversely related. When one company does well, the other does poorly. By owning both companies, the investor guarantees a profit at all times. In Modern Portfolio Theory, this phenomenon is captured by a mathematical notation called the correlation coefficient, which ranges from (-1) to (+1).

As was the case in our example, a perfectly negative coefficient (-1) means that two investments move in opposite directions at all times. At the opposite end of the spectrum, a perfectly positive coefficient (+1) means that two investments move in tandem. A correlation coefficient of zero means that two investments move independently of each other.

A negative correlation is highly desirable because it provides the greatest diversification benefit. In the real world, the only way to achieve a perfectly negative correlation coefficient is through derivative products. These are complex financial products that most investors will never use.

Even a slightly negative correlation coefficient is highly desirable and difficult to find. Historically within U.S. financial markets, there have been times of economic turmoil when stocks plummet in value. During this time, many investors mistakenly sell their stock holdings at a loss to purchase government-issued bonds. When this happens, stocks depreciate in value while government bonds appreciate in value, resulting in a negative correlation.

A correlation coefficient of zero means that there is no correlation. Both investments move independently of each other. In most economic conditions, stocks and bonds have a correlation coefficient that fluctuates just above zero. Similarly, commodities (physical goods) are often priced independently of both stocks and bonds.

A positive correlation coefficient means that both investments move in the same direction. A perfectly positive correlation results in no diversification benefits, but anything less than perfect correlation still provides a diversification benefit. Indeed, in his research, Markowitz showed that overall portfolio volatility can be reduced even when assets are highly, but not perfectly correlated.

This idea is the key takeaway of Modern Portfolio Theory. Investors can reduce the expected volatility of their investment portfolio by combining a variety of risky asset classes. Even if those asset classes are highly correlated, like domestic and international stocks, there is still an expected diversification benefit and the overall volatility of the portfolio will be reduced.