There's an old business adage that says "You can only manage what you can measure." This applies equally well to the world of investing. Without a way to *measure* how risky our investments are, we have little chance of *managing* our risk in an effective way.

The traditional way to measure the riskiness of your investments is to look at the volatility in their price movements. This article will discuss how to do this, as well as its advantages and limitations.

## Risk as Volatility

**In finance, risk has a very precise definition: the risk of a portfolio is often assumed to be the standard deviation of its returns ( also called "volatility"). **Standard deviation is a mathematical calculation that looks at how widely a series of data "moves around" from its trend-line average.

To make this concrete, imagine that you want to relive your childhood and decide to stand at the beginning of your driveway and count the number of cars that go by during every fifteen minute period (this doubles as a great activity to entertain any eight year old for hours on end). If when you are finished, your data looks like 6, 5, 6, 8, 5, 4, 7, 6, 7, 6, 7, 5, 9 then you know without even running any calculations that your data has a pretty low standard deviation. You know that in the next fifteen minutes you can fairly accurately predict that there will be around 7 cars that go by, and that the number will probably vary from about 5 to about 9. If on the other hand your data looked like 0, 15, 13, 2, 8, 11, 1, 5, 9, 0, 7, 15 then you would know without even doing any math that you are dealing with a problem that has a much greater standard deviation. While your best estimate of how many cars will go by your house in the next fifteen minutes might still be around 7, the range of outcomes that you could reasonably expect to see would be much wider, say anywhere from 0 to 15.

Similarly, a portfolio that has a high volatility will "move around" much more than one with a low volatility. While over a long time period the two portfolios might produce the same returns *on average*, in any given year the return of the higher volatility portfolio will be much more unpredictable.

As a rule of thumb, the returns of a portfolio will usually fall into a range of their average return plus or minus their annual standard deviation about seventy percent of the time. So if a portfolio of stocks has an annual return of 10% and a standard deviation of 10%, you should expect your annual returns to fall in the 0-20% range about 70% of the time, with a 15% chance of making more than 20% and a 15% chance of losing money.

## The Significance of Volatility

While volatility is a bit of an academic concept, it is also a practically important measure of risk for two reasons.

First, portfolios that have large swings in value from day to day and month to month are generally much harder to "live with" than portfolios that fluctuate less. High volatility can cause anxiety and stress and make it difficult to stick to a strategy. One of the most common and tragic stories of an investment mistake (and one that you will hear repeated often on these pages) is of the investor who is unable to cope with the volatility of their portfolio and pulls out at the bottom of a bear market, only to miss the subsequent rebound.

Second, while volatility may seem innocent enough *after * the fact, when looking *forward, *highly volatile investments have a greater chance of losing money than less volatile ones, especially if you believe that movements in stock prices are more or less random. While the math here can get complicated, at a basic level this is just common sense. A highly volatile portfolio that swings wildly in value every week probably has a greater chance of losing a lot of its value if things go bad then does a portfolio that barely seems to move.

Going back to the "cars going by" example that we discussed earlier, it is pretty easy to see that there is a much greater chance of getting three periods in a row with no cars going by (a catastrophe in this example, as the 8 year old gets bored and returns to playing video games) with the second data set that is more volatile than with the first data set that is less so.

Similarly, with investments, there is a greater chance that a highly volatile portfolio will undergo a "losing streak" right before you need it than there is a with a lower volatility portfolio that remains more constant in value over time.

Given that all of our investment time horizons are finite to one degree or another, this is important to consider.

## The Limitations of Volatility Alone

While volatility can certainly be a useful starting point in considering the risks of a portfolio, it is unfortunately often also a stopping point. Volatility provides "easy answers" because it is easy to calculate a precise value using historical data.

But as we shall see later in the section on Managing Volatility Risks, one problem with this is that volatility tends not to be constant over time. So just assuming that your portfolio will continue to swing around about as much as it has in the past is not always a good idea, but unfortunately is what most of the financial services industry seems to do.

The second reason is that volatility is, after all, just a theory. Some processes have a very defined standard deviation that follows what is called a "normal distribution." For instance, imagine that you toss two dice 10,000 times and record the sum of each toss and then plot the frequency that each sum came up. This process has a very defined average outcome and standard deviation.

Applying standard deviation to investments assumes that investment returns are like tossing a dice every year. In fact, we know that is not the case; tossing a dice is totally random, whereas investment returns depend on all kinds of things that we cannot totally predict so we just assume they must be random.

The next section on black swan risks will look into some other cases measuring risk purely on the basis of volatility can fail as an accurate measure of the kind of risks that most people really worry about at night.

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