Using Standard Deviation Risk Measurement to Better Manage Your Investment Portfolio

There are several different ways to measure risk. If you read popular financial publications, you'll often see them refer to such measures of risk as standard deviation, alpha, beta, R-square, shape ratio and Treynor ratio. Fortunately for you, one of these is far more important than the others. Standard deviation is the real key to understanding the risk of your investment portfolio. If you're lucky, you remember learning about standard deviation in high school. If not, don't panic; I'm going to explain it in detail.

Standard deviation describes the probability of the distribution of a series of data. It's commonly referred to as the "bell curve," because when placed on a graph a normal series of data will tend to look a bit like a bell.

Standard deviation is a unit of measurement expressed as a percentage. For example, a portfolio may have a standard deviation of eight percent. The eight percent represents one "standard" unit of deviation from the average. If the average expected return of a portfolio is ten percent and it has a standard deviation of eight percent, then you could expect that the majority of the time the returns of that portfolio would fall into a range bound by the expected return plus one standard deviation and the expected return minus one standard deviation. Thus, if the expected return is ten percent and the standard deviation is eight percent, then our range of returns would be eighteen percent (ten percent plus eight percent) and two percent (ten percent minus eight percent). In other words, in most years an investment portfolio with an expected return of ten percent and a standard deviation of eight percent would deliver a return of between two percent and eighteen percent. The smaller the standard deviation, the more accurately you can predict what the return of your portfolio will be in any given year.

If your portfolio has a standard deviation of eight percent, then the range of possible returns is fairly high. Your portfolio could make as little as two percent or it could make as much as eighteen percent. What I need you to understand is that as time passes, the standard deviation of your portfolio will drop. The outcome isn't at all random. If you give your portfolio enough time, there will be exactly as many years when it performs above the expected rate of return as there are when it performs below. As time goes on, the average return of the portfolio will continue to get closer and closer to the expected return.

Most pension plans avoid considering standard deviation for periods of less than three years. The common feeling is that three years is about the shortest period of time over which investment performance can be accurately measured. Given the magnitude of the resources that pensions allocate toward reducing risk, it should come as no surprise that many plans achieve long-term standard deviations below three percent.

For our purposes, you only need to remember two things.

1 . There's a sixty-eight percent likelihood that, in any given year, the possible range of returns will be between the expected return minus one unit of standard deviation and the expected return plus one unit of standard deviation. In our example, this means returns will be between two percent and eighteen percent.

2 . There's an additional twenty-eight percent chance that, in any given year, the possible range of returns will be wider by another unit of standard deviation. Again using our example, if the range of one standard deviation is between two percent and eighteen percent as above, then there's a much smaller chance that the returns could lie outside that range by as much as eight percent (the value of a unit of deviation for this portfolio). Our lower range is now negative six percent (two percent minus eight percent) and our upper range is now twenty-four percent (eight­een percent plus six percent).

The two points above may look confusing, but stay with me- they aren't really that bad. Let me summarize what we've learned: In any given year, there's a sixty-eight percent chance that the return of your portfolio will fall within a range bound by one standard deviation. There's an additional twenty-eight percent chance that your return will be within a range bound by two standard deviations.

For our sample portfolio with an expected return of ten percent and a standard deviation of eight percent, in any single year there's a fourteen percent chance that the return would be between negative six percent and two percent and there's a thirty-four percent chance that the return would be between two percent and ten percent. The above-average side is the mirror image of the below-average side, so in any given year, there's also a thirty-four percent likelihood that the return would be between ten percent and eighteen percent and a fourteen percent chance that the return would fall into the highest expected range of eighteen percent to twenty-four percent.

I know there are a lot of numbers here, but please trust that this is important. Please take the time to review the example again. If you have to, read it a third time.

You may be disappointed to see a range of possible returns that's so wide. I know our goal is safe, consistent returns. Don't worry about it yet. For one thing, this was simply an example; your optimal portfolio may require less risk. This would mean a smaller standard deviation and a tighter range of possible returns. The other major reason not to pay much attention to a range of returns this wide, is that we're only talking about a period of one year. With every additional year in which we consider the standard deviation of your returns, your short-term risk, or volatility, diminishes. Most of the great pension funds have long-term standard deviations of less than three percent. Think about that for a moment. Consider what you've learned, then imagine what a risk level of three percent would mean to you. It could mean a lot of different things, but foremost it means safety, security and peace of mind. The great pension funds have figured out how to deliver these things, and now that you understand risk you're well on your way to achieving them for yourself. You can start by training yourself to consider risk over progressively longer and longer periods of time.

Taking the chance of being repetitive, I'd like to summarize what you'll be able to do with this knowledge:

You now understand that risk can be managed. It can be reduced and, in some cases, eliminated.

You should understand that risk is not a dirty word. Short-term risk is really just volatility; it'll disappear completely over time. Long-term risk is still nothing more than the chance that you'll fail to achieve your goal.

There's some type of risk attached to every type of investment. Just because you didn't know what it was -called, doesn't mean it wasn't there. Sometimes there's even risk attached to not making a certain type of investment.

You know that the risk of your individual investments isn't important, because they're not perfectly correlated. What is important is the risk level of your entire investment portfolio.

You now understand that the risk of your entire portfolio is best expressed in percentage terms. For you, risk isn't scary any more. It's simply the chance that you'll fail to reach your goal.