Portfolio Risk: Advantages of Semivariance

Semivariance: Preferred Risk Measurement

Portfolio risk is given lip service, but rare is the investor who takes pains to actually measure the risks involved in the makeup of their portfolio. It is common to hear an investor indicate they have a well-diversified portfolio if it is made up of more than 15 to 20 stocks. The correlation between the investments might be a mystery, yet the claim is that risk is lowered by increasing the number of stocks held in the portfolio. This may be true, or it could be a false assumption.

An index investor may hold hundreds of stocks within index funds or index ETFs and still possess a high risk portfolio. Numbers to not make the problem of risk go away. To understand portfolio risk required digging a little deeper than many readers want to go. Nevertheless, follow along as this is a concept that ranks right up there with measuring the Internal Rate of Return (IRR) of the portfolio.

Variance and standard deviation are well-known measurements of portfolio volatility. These measurements are well-integrated into most financial software, particularly standard deviation. Less well-known is semivariance, the preferred method (my opinion) for measuring portfolio risk. If you find these definitions obtuse, Google the terms and examine other definitions. Different wording will likely make the ideas easier to understand.

I'm not exactly sure when I first became aware of using semivariance as a portfolio risk measurement. Harold Evensky writes about it in his excellent book, "Wealth Management: The Financial Advisor's Guide to Investing and Managing Client Assets." Harry Markowitz advocated using semivariance in 1952, but the computing power was not readily available. That hurdle is no longer a problem, even for the small investor. The portfolio tracking software, Captool, alludes to it, but does not come out and say this is what they are using. Much later, I ran into something called the Sortino Ratio where semivariance is part of the ratio calculation. After running into this risk measurement from many different sources, I finally became convinced I wanted to measure portfolio risk using semivariance rather than mean variance or standard deviation.

When I use the term semivariance, I really mean relative semivariance as I am using a benchmark as the reference or relative reference. For purposes of this discussion, assume the benchmark is Vanguard's Total Market Index Fund, VTSMX. Our semivariance calculations work with the IRR values for both the portfolio and VTSMX. Relative semivariance avoids many shortcomings that plague risk measurements such as standard deviation (SD) in that the semivariance calculation is asymmetric and focuses only on the downside of the probability distribution. SD "worries" about both the upside and downside probability distribution. Volatility to the upside or variation above that of the benchmark is desired by all investors so why fuss over it. We desire deviation to the upside of the benchmark reference as our goal is to outperform the benchmark. SD penalizes the manager who adds value or alpha to the upside, an inherent problem with this risk measurement method. Semivariance, on the other hand, avoids this problem. The relative semivariance calculation also has the advantage of being nonlinear in the sense it penalizes larger negative values more than smaller negative values due to the squaring of the tracking errors. Investors are much more concerned about large dips to the downside, as many experienced in 2008 and early 2009, than they are about smaller and more frequent market declines. Relative semivariance hones in on these large loss events, sometimes called "Black Swans."

Are there disadvantages to using the relative semivariance method for determining portfolio risk? Yes, but none that cannot be overcome with portfolio tracking software such as the TLH spreadsheet. Here are a few disadvantages.

1. The concept of relative semivariance is not well understood. At least it is more abstract than standard deviation.

2. Semivariance is not a calculation to be found in Excel. At least this is the case for the version I am using. Standard deviation is built into Excel.

3. Semivariance requires special programming and some mechanical manipulation to make it work properly. This is a hassle many investors choose to avoid.

4. The investing community is clamped into using standard deviation to measure portfolio risk making it difficult to pry them away from this entrenched method.

5. Selecting a benchmark is always a problem as each portfolio is different. Therefore no one benchmark works for all portfolios. This is why I came up with the ITA Index. It is not a single benchmark, but rather a customized benchmark designed to fit any portfolio made up common stock, index funds, index ETFs, and other standard investment vehicles. One major problem with the ITA Index is that it is still an infant. We should have a minimum of twenty years of data before we have much confidence in the ITA Index. Someone else will likely need to carry this torch into the future.

6. Relative semivariance does not work well for individual securities. Instead, its power comes when working with a portfolio where the individual parts are treated as a whole.

Investors serious about measuring portfolio risk are welcome to try the latest version of the TLH spreadsheet. I make it available free of charge to all investors as I only had a small part to play in its development.


Photograph: In memory of Louise