Nothing ventured, nothing gained. You can't have your cake and eat it, too. Life is a series of trade-offs.

We're all familiar with these mottos, which remind us that to get something, we have to give something up. Investing requires sacrifices, too. We have to give up safety and take on risk to achieve better returns. Modern Portfolio Theory (MPT) tries to make the most of the trade-off, illustrating how to generate as much return as possible for the least amount of risk.

This article will examine the relationship between an investment's risk and its return, how diversification allows you to achieve the maximum amount of return for the least amount of risk, and the role MPT can play in your portfolio.

Risk and return

With any reward - such as a great-performing stock or fund - there's always some element of risk. And the greater the potential reward, the greater the potential risk.

It's hard to imagine a time when the risk/reward relationship was considered revolutionary. But, prior to Harry Markowitz's 1952 dissertation, Portfolio Selection, investment theory didn't discuss the risks of investing. Instead, it was flush with ideas for maximising return.
Markowitz believed, and mathematically proved, that there is a direct relationship between an investment's risk and its reward. He saw risk as an equal partner with expected gain. As such, he argued that investors need to manage the tension between risk and return in the investment process.

Markowitz also argued that investors should be measuring, monitoring, and controlling risk at the portfolio level, not at the individual-security level. As a result, individual securities should be chosen based not only on their own merit, but also on how they affect the portfolio as a whole.

Diversification and an "efficient" portfolio

According to MPT, you can limit the volatility of your portfolio by spreading out your risk among different types of investments. In fact, by putting together a basket of risky or volatile stocks, the overall risk of the portfolio would actually be less than any one of the individual stocks in it.

Diversification depends more on how the securities perform relative to one another than on the number of securities you own, though. Markowitz compares a portfolio of 60 railway securities with another portfolio of the same size that includes railroads, utilities, mining, and manufacturing companies. He concludes that the latter is better diversified. "The reason is that it is generally more likely for firms within the same industry to do poorly at the same time than for firms in dissimilar industries," he says.

The "right" kind of diversification requires that you own securities that don't behave alike. In other words, their price movements have low correlation with each other. Correlation measures the degree at which two securities move in similar patterns. Its value ranges from -1.0, indicating two securities moving perfectly opposite each other, to 1.0, indicating two securities moving in tandem. So to spread out your risk, you would want the securities in your portfolio to have correlations closer to -1.0 than to 1.0.

According to Markowitz, the goal is to craft an "efficient" portfolio. An efficient portfolio is either a portfolio that offers the highest expected return for a given level of risk, or one with the lowest level of risk for a given expected return. The line that connects all these efficient portfolios is the efficient frontier. The efficient frontier represents that set of portfolios that has the maximum rate of return for every given level of risk.

No point on the efficient frontier is any better than any other point. Investors must examine their own risk/return preferences to determine where they should invest on the efficient frontier. But, theoretically at least, the efficient frontier allows you to reduce your risk at no cost in return. Or you can increase return at any particular level of risk.

Applying MPT to your investment reality

While the idea of an efficient portfolio and the efficient frontier graph make great theory, how can they be applied to your own investment situation? After all, few individual investors can create efficient frontier graphs for themselves, nor determine what their efficient portfolio would be. And even if investors had the time and technology to do so, market prices change, and the riskiness of asset classes isn't static.

What's important here isn't the details of the efficient frontier graph, nor finding the most efficient portfolio for you. Rather, the takeaways from MPT are:

  1. Risk and return are directly linked. If you want a chance at greater returns, take on more risk;
  2. Diversification across securities that do not behave alike reduces your portfolio's overall risk.

Whether you realised it or not, you probably used these two principles to build your portfolio. For example, your asset allocation is the direct result of your time horizon, risk tolerance, and financial goal. To reach that goal in the appropriate amount of time, you must take on a certain level of risk.

Further, you're likely controlling risk in your portfolio by mixing investments that have a low correlation with one another. For example, the equity and bond markets don't usually move in the same direction. By having a portfolio that includes both equities and bonds, you're one step closer to a more diversified and less risky portfolio.

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