Home | Exchange-Traded Funds | Thrift Savings Plan

facebook | rss

Right now, subscribe to our financial advisory newsletters absolutely free! No obligation.

What is risk?

Our asset allocation investment strategy consists of choosing the mix of investments with the highest expected return given a fixed maximum risk. This leads to a natural question — what exactly is risk? When it comes to investments, many people have an intuitive understanding of what risk is. For instance, if an investment strategy performs well during a market crash, then, intuitively, it has a relatively low risk.

However, to calculate the optimal asset mix, we need to have a precise mathematical definition of risk. Several such definitions exist, including the standard deviation of logarithmic return, used in modern portfolio theory, and the target semi-deviation of logarithmic return, used in post-modern portfolio theory. We use our own definition of risk that was developed by our founder, who is a Ph.D. statistician. We think that this definition is better than the other definitions on theoretical grounds.

An intuitive approach

Though risk is often discussed in the financial media, few people know its precise mathematical definition. Some people equate risk with the standard deviation of logarithmic return, though that is just one possible definition of risk.

Intuitively, many of us understand what risk is. When the price of an investment is moving relatively smoothly, the risk of the investment is low; when the price is jumping up and down, all over the place, the risk is high.

One intuitive approach to assessing risk is to consider what happens to an investment strategy during stock market crashes. As we learned in the 1990's, it's easy to make money in stocks when the stock market as a whole is booming. One could just pick a random collection of stocks and still make money. In the words of Burton Malkiel, a well-known economics professor at Princeton, “a blindfolded monkey throwing darts at a newspaper’s financial pages” could do well in those times.[1]

But picking random stocks is very risky. The issue is that when the market as a whole is booming, this risk is masked by the overall upward trend.

The risk of an investment strategy becomes more apparent when the market is in a decline. That’s why considering what happens to a strategy in a market decline is a good intuitive measure of its risk. For example, if an investment strategy has lost 5% while at the same time the stock market, as measured by some general index, has lost 40%, then clearly the strategy is much less risky than stocks.

While this is a great intuitive meaure of risk, its limitation is that, for the purposes of this measure, each market crash is just one data point. For accurate decision-making, more rigorous measures of risk are needed.

Maximum drawdown

Maximum drawdown (MDD), a popular measure of realized risk, is the maximum percent drop in equity, either over the lifetime of a strategy, or over some specific period of time, such as a year. A popular way of explaining the relevance of MDD is that if someone started following a strategy at the “worst” possible time and then stopped following it at the “worst” possible time as well, they would have lost the percentage of their equity given by MDD.

Another, and more useful, way of looking at MDD is that it measures the amount of psychological “pain” that a strategy has inflicted on the investors who followed it. Since investors tend to abandon a strategy if it inflicts too much pain on them, a high MDD means that few investors were able to follow the strategy. Remember that investors (including you!) are human beings with real emotions. A strategy with a high return might look good “on paper,” but you might not be capable of actually following it because it produces too much pain. What’s worse — investors might stop following this strategy right after a big loss.

MDD is a great intuitive way of measuring the amount of risk that a strategy undertook over a long period of time. However, one issue with MDD is that it cannot tell us the amount of risk that a strategy, or an investment, has at a particular moment. Since our asset allocation investment methodology requires a risk measure, we do not use MDD in making investment decisions. However, since MDD is a good intuitive risk measure, we do report it when discussing the performance of our strategies.

More rigorous definitions

In addition to the intuitive definitions of risk discussed above, more rigorous mathematical definitions exist as well. For example, a popular mathematical definition of risk is the standard deviation of logarithmic return.[2] This definition, also called “volatility,” is used in a financial model called modern portfolio theory. One criticism of this risk measure is that it penalizes both positive and negative deviations from the average return equally. That is, an unusually high return increases this risk measure by the same amount as an unusually low return. However, from an intuitive point of view, there is nothing risky about a return that is “too high.” Thus, this risk measure does not precisely correspond to what most people understand by risk.

There is another financial model, called the post-modern portfolio theory. It is called this because it builds on the modern portfolio theory. In post-modern portfolio theory, risk is mathematically defined as the target semi-deviation of logarithmic return.[3] That is, returns that are “too high” do not influence the risk measure. Risk, in this model, is only influenced by returns that are “too low” relative to some target. This risk measure is certainly an improvement on the simpler standard deviation that is used so often. However, it does have its own issues.

Our mathematical definition

In the asset allocation method that we use to allocate money among different investments, we use our own mathematical definition of risk. This proprietary definition was developed by our founder, a Ph.D. statistician. In our opinion, the definition is better than others that we have seen on theoretical grounds. From a practical point of view, we see, based on historical performance, that it has worked well.

Notes