Modern portfolio theory (MPT) is the scientific underpinning behind asset allocation. As I started writing about selecting the mix of asset classes, I realized I had to give a basic introduction to MPT, starting from the concepts of risk and return. Understanding MPT is not crucial to the practice of AA but knowing that a few Nobel laureates are on your side does make it easier to stick to the plan. And sticking to the plan is probably the most important part of AA based investing.

Most people have a good understanding of investment return: the gain or loss over the principle in a given period of time, usually expressed in percentage form. “Risk” seems a more amorphous concept. When pressed, most people will define it as something like “the likelihood to lose money” which is not a bad answer. In the theory of portfolio selection, risk, also known as volatility, is a measure of the spread in the returns. Volatility is defined as the standard deviation of returns in the language of statistics,.

There is only one thing about volatility you need to remember: it is not your friend! The simplest way to see this is through the following example:

Assuming there are two portfolios. Portfolio #1 returns 5% per year for two years. Portfolio #2 loses 10% in the first year, but gains 20% in the second. Which one is better?

The compound return after two years can be calculated easily. For portfolio #1, it is (1+5%) (1+5%) – 1 = 10.25%. For portfolio #2, it is (1-10%) (1+20%) -1 = 8%. Portfolio #1 wins handily.

Note that the average return (arithmetic mean) is 5% for both portfolios even though the compound returns are quite different. The difference being the volatility or the spread in return is much greater for portfolio #2. In this simple example, it can be shown that portfolio #1, with zero volatility, due to its identical returns in both years, produces the greatest compound return for all combination of two-year returns that average 5%. Thus the goal of portfolio selection can be summed up as: maximizing return given the same volatility, and minimizing volatility given the same return.

In a nut shell, MPT uses some math – well, maybe a lot of math – to figure out how to select securities, or asset classes (you know there's a connection to AA somewhere!), to optimize portfolio risk and return. Much of its development can be traced back to Harry Markowitz and William Sharpe, both Nobel laureates in Economics. Markowitz pioneered the concept of “efficient frontier”, a curve that describes a set of portfolios with optimal trade-off between volatility and return. The efficient frontier curve can be used to demonstrate that uncorrelated securities or asset classes can combine to reduce volatility – a central tennet of MPT. Here "uncorrelated" means that the price movements are out of sync, such as Microsoft vs. Exxon, or stocks vs. bonds. The other Nobel laureate, William Sharpe, got his name attached to the Sharpe ratio, a measure of risk adjusted returns that allow portfolios of different return and volatility to be compared (see example here). Thus a portfolio with a few years of out-sized returns may not be that good if the returns are achieved at the expense of out-sized volatility. Case in point, millions of tech investors in the late 90's had "diversified" portfolios consisting of the four horsemen of the new economy: Cisco, Dell, EMC and Intel. They did extremely well for a couple years, until eventually the concentration risk caught up with them. While that particular eventuality may have materialized in March 2000, there's no denying that their concentrated portfolios were predisposed to being wiped out by large movements.

Source: Money Chimp

So to recapitulate, volatility has a real deleterious impact on portfolio return, but can be reduced by having diversified, uncorrelated assets as demonstrated by MPT. We only need to turn to the real-life popularity of portfolio diversification to witness the success of MPT as an academic theory.

Ok, that was probably way more than you needed to know. But do remember to drop some choice tit bits like “MPT” or “risk adjusted return” at the next cocktail party or meeting with your financial advisor, and be prepared to be treated with a newfound respect.

Recommended Reading

The story of Modern Portfolio Theory, with insights into the thinking and personalities of its big names, including Markowitz, Tobin, Sharpe, Fama, and other stars. The author also reveals enough about his own background to make things interesting: he was a financial advisor and stock picker before becoming a convert to MPT. This is a non-technical and informative overview; well-told and enjoyable to read.