Unless you own just one asset, you are not exposed to single asset risk. Rather, your portfolio has a risk profile that is different from the sum of the individual risks. In other words, when you hold multiple assets in your portfolio, you need to consider how those assets act when taken together, which is different when taken separately. The idea that portfolios have a particular risk and reward profiles was one of those things that make so much sense that everyone should have seen it, but no one did for a very long time. In 1952, an economist named Harry Markowitz figured it out and published the results in a famous paper titled simply “Portfolio Selection,” which appeared in the *Journal of Finance*.

As you would expect from a paper written by an economist, his ideas were proven mathematically, and most of the papers that furthered his work since it was published are math based as well. Investors who are not economists must rely on secondary sources to help us understand what is going on. Modern technology has made it such that we do not actually have to do any of that math. We can feed investment ideas into the computer, and it shows us the associated risks for various allocations and even gives us the pretty graphs that must have been a real pain for Markowitz to draw back in 1952.

The software cannot search all possible investments and produce the perfect portfolio for you. I expect that AI technology will allow us to do exactly that in the next 25 years, but we are not there yet. You still have to have your own vision of what your portfolio will look like and what basic asset classes you will include. I say that AI will improve this process because the machines will need the ability to forecast future performance of assets as well as a human can. Data-driven models of anything can produce some startling bazaar results, and those are the only models that even our best AIs are capable of today. For the near future, we need the human ability to reject forecasts of US stock prices based on the volume of goat milk sold in Pakistan last year and other such spurious nonsense.

The theory allows investors to choose a portfolio allocation that maximizes returns given a specified level of risk. We can graph those expected returns such that risk runs horizontally across the graph and the expected return runs up and down on the vertical axis. For each given level of risk for a group of assets, there is an optimal portfolio that maximizes returns. If we plot each level of risk and its expected return, we get a curved line that economists refer to as the **efficient frontier**. It would never make sense to allocate your portfolio any other way than the portfolio that falls on the efficient frontier because you would (by definition) be taking on more risk with no increase in reward.

Unless you hold the risk free asset (one-year government securities), the curve isn’t a straight line as one might suspect. The fact that the line curves is why MPT has value; it may be imperfect, but it allows us to see the important point that portfolios risks and returns don’t behave as the sum of their component assets returns. The **efficient frontier** is really a boundary where you cannot find a better combination of assets that yield higher returns for a given standard deviation.

Our goal is to create a portfolio that makes great returns with as little risk as possible. It may be helpful to think of the efficient frontier graph in terms of *quadrants*. The Southeast quadrant is the most dangerous and offers the least reward. We want to avoid any portfolio that is anywhere near that quadrant. The Northwest quadrant is where risk is minimized, and returns are maximized. That is the mythical land where we want a portfolio to dwell. When we are designing portfolios, we are always looking for assets that shift us toward the northwest quadrant.

There are many limitations to MPT, and economists have been tweaking it for years to try to improve it with varying levels of success. Some of the problems are theoretical. A major drawback is that it bases allocation decisions strictly on the returns and variances of past security price behaviors. The lookback period can be as far back as we have data. Since most of us will be building a portfolio with a cross-section of mutual funds, the data will only go back as far as the fund’s inception date.

Stock index funds and bond performance is available for a long period, but commodity baskets and high-performance tech funds will not reflect a period much longer than the past decade. Without data from bear market periods, it is too easy to derive portfolios that meet our specified criteria during bull markets, but that will perform differently when economic conditions change for the worst.

Another practical limitation of the theory is that it doesn’t help us choose which asset classes to include in our analysis is in the first place. We know that we want exposure to equities for returns and exposure to bonds for risk reduction. The efficient frontier can almost always be pushed into the northwest quadrant by adding subsequent asset classes. In his lectures on the topic, Professor Shiller uses oil and a third asset class with remarkable results. Ray Dalio recommends a broad basket of commodities. Both of these are difficult for the individual investors to access. Commodity baskets tend to perform poorly and can be seen as a hedge against inflation and perhaps as a safe haven of value when markets are collapsing. This has not always been the case, and it may not hold true in the future.

One solution is to invest in a broad portfolio of energy stocks, which contain oil companies and oil service companies that have balance sheets that are tied to the commodity price of oil. Real estate funds, which are often composed of REIT equities, are another excellent candidate. You will find that ETFs offer much more diversity than the universe of mutual funds and that individual investors that have IRAs that allow investing in ETFs have a diversification advantage. Regardless of what the extra assets are, an investment that is risky as a standalone exposure can actually improve the risk-return characteristic of the combined portfolio, and thus adds a diversification benefit. We can map this effect by graphing the efficient frontier, or we can use a point estimate such as the Sharpe’s ratio.

My criticism of the theory boils down to concern over the standard deviation of prices. Portfolio managers have to be concerned with short-term price shifts because fickle investors will pull out of a fund as soon as they see red. Fund managers, then, have no choice but to treat volatility as they do. Nevertheless, why should the individual investor care? If we graph the efficient frontier of a stock and bond portfolio, we see that the largest returns are to be had with an equity only version. We can also see that the standard deviation is somewhat higher, and this is the MPT definition of risk. The question that you must as yourself as an individual investor is this: How do I personally define risk, and how much can I take before I act irrationally and hurt myself?

It is worthy of note that Mr. Buffett has left instructions that upon his death, all of his funds bequeathed to his wife are to be put in a portfolio of mostly S&P 500 index funds. I think the reason that this does not fit into MPT is that *Mr. Buffett does not define risk in terms of standard deviations*. He defines it in terms of his first rule of investing: Never lose money. I suspect that when the market is down, and standard deviations are off the charts, Mr. Buffet sleeps like a baby. That is for the best since when the market crashes, Mr. Buffett has a lot of shopping to do and he needs his rest.

Last Modified: 07/02/2018

### References, Resources, and Tools

-You can test your own portfolio ideas and find the efficient frontier with the free Efficient Frontier tools on PortfolioVisualizer.com.