What Is The Best Way To Measure Risk? Part 2

This is the second part of a guest article by Market Wizards author & hedge fund expert Jack Schwager about the best way to measure risk based on a question submitted by a reader on Bidnessetc.com - read Part 1 here.

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In the previous article, we looked at the relative appropriateness of using volatility as a measure of risk and found that volatility (as measured by the standard deviation) was a useful proxy for risk in some instances, but insufficient, or even totally misleading, in other circumstances. Certainly, volatility alone is an inadequate risk measure. In this week’ s article we will look at other risk measures.

Although volatility is the most common measure of risk, there is an inherent problem in using volatility to measure risk. Investors and traders are not concerned about the variability of returns, which is what the standard deviation measures; they are concerned about the variability of returns on the downside. I have yet to meet an investor who was concerned about large deviations of return on the upside. When investors and traders think of risk, they think in terms of losses, not return variability. So it seems sensible that a good risk measure should focus on losses. Loss-based risk measures can be broken down into two general categories: those based on average losses and those based on maximum losses.

The average loss is probably the simplest risk measure to calculate, but it is also one of the most meaningful. To calculate the average loss, sum all the losses and divide by the total number of intervals. For example, if using monthly data, sum all the months with negative returns and divide by the total number of all months (winning as well as losing). An average loss can be calculated using daily data in an analogous fashion by summing all the returns on loss days and dividing by the total number of days. The reason why an average loss calculation is so meaningful is that it penalizes every loss, and it does so in proportion to the magnitude of the loss. The more losses and the greater the size of the losses, the worse the average loss measure will appear.

The calculation using daily data is more meaningful because it will reflect risk that is invisible in monthly data. Even winning months will have losing days—and sometime large losing days—that will not show up or have any impact if using monthly data. For example, using monthly data, a strategy that has an intramonth loss of 15% and then recovers fully to finish up 1% will be indistinguishable from a strategy that finishes up 1% while never pulling back more than 1% from an existing monthly high. But the two return series are radically different. Some readers may disagree based on the argument, “What difference does it make if they both ended up in the same place?” The difference is that where the month ended is a matter of luck. If the month had ended in a different spot—and, in the future, the month-end could well occur near the month’s worst point—then the first strategy would have been revealed to be much riskier based on that month’s data, as indeed it is. In contrast, the second strategy’s low-risk performance is not dependent on the vagaries of the calendar.

To place the average loss in context (whether it is a monthly or daily figure), it is best to view it relative to return. The Gain to Pain ratio does exactly this. Using monthly data as an example, the Gain to Pain ratio can be defined as the sum of all monthly returns (positive and negative) divided by the absolute value of the sum of all monthly losses. This calculation is exactly equivalent to the average monthly return divided by the absolute value of the average monthly loss, where the average loss is calculated by dividing by the total number of months. not just losing months. (It is the same because to get the average, both the totals in the numerator and denominator are divided by the same number of months.) An analogous calculation would apply using daily data. The Gain to Pain ratio based on monthly data will always be much higher than the Gain to Pain ratio based on daily data because even positive return months will almost invariably have some losing days. Based on comparing monthly and daily Gain to Pain ratios for multiple managers, I have found that the monthly ratio tends to run roughly 6-7 times as high as the daily ratio, although it can vary higher or lower. I consider the Gain to Pain ratio to be a more meaningful statistic than the widely used Sharpe ratio because it normalizes return by the amount of losses required to achieve that return rather than by the variability of returns—an approach that comes much closer to reflecting what traders and investors perceive as risk.

It is useful to look at not only average (or, equivalently, total) losses but also maximum losses. The most common statistic of this type is the maximum retracement, commonly called the “maximum drawdown,” which is defined as the largest percentage decline from any equity (NAV) peak to a subsequent equity (NAV) low. Although the maximum retracement is useful in defining the worst-case situation based on the historical track record, it is highly inadequate as a stand-alone risk statistic because it is based on a single observation and essentially throws away all other data. So the maximum retracement should be used only as a supplemental measure to other more comprehensive risk measures, such as the average loss. Also, even as a supplemental measure, an average of the five largest retracements would probably be more meaningful than just the single largest retracement.

An even better approach, though, would be to calculate the average maximum retracement (AMR), which is based on a maximum retracement calculation for each month. It is best to define the maximum retracement for each month as equal to the greater of the following two numbers:

1. The largest cumulative loss that could have been experienced by any existing investor in that month (i.e., the percentage decline from the prior peak NAV to the current month-end NAV);
2. The largest cumulative loss that could have been experienced by any new investor starting in that month (the percentage decline from the current month-end NAV to the subsequent lowest NAV).

Although the standard definition of a retracement would use only the first of these two conditions, the reason for using both metrics to determine a maximum retracement for each month is that each of the two conditions would be biased to show small retracement levels during a segment of the track record. The first condition—the standard definition of a retracement— would invariably show small retracements for the early months in the track record because there would not have been an opportunity for any large retracements to develop. Similarly, the second condition would inevitably show small retracements during the latter months of the track record for analogous reasons. By using the maximum of both conditions, we assure a true worst-case number for each month. The AMR is the average of all these monthly maximum retracements.

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Graphs employing maximum retracement measures can provide an excellent visual representation of risk. One popular such depiction is the underwater chart, which shows the worst possible cumulative percentage loss any investor could have experienced as of the end of each month—i.e., the maximum retracement from a prior NAV peak as of the end of every month in the track record.

One shortcoming of the underwater curve is that it will understate risk for months in the early portion of the track record because there is an insufficient lookback period for a prior NAV peak. For these earlier months, there is no way of assessing a true worst-case loss representation because a prior track record of sufficient length simply does not exist. Also, the underwater curve is constructed from the perspective of the worst cumulative loss that could have been experienced by an existing investor. Arguably, the worst loss suffered by new investors may be an even more relevant measure. One solution to these inadequacies in the underwater curve calculation is to also consider the worst loss that could have been experienced by any investor starting in each month, assuming they exited at the subsequent lowest NAV point. We can then create a Two Direction Underwater Curve (2DUC) that for each month would show the maximum of the following two losses:

• The cumulative loss (in percent terms) of an existing investor starting at the prior NAV peak.
• The cumulative loss (in percent terms) of an investor starting that month-end and liquidating at the subsequent NAV low.

The average of all the points in the 2DUC chart would, in fact, be the graphic depiction of the previously described AMR statistic. (More detail and illustrations of 2DUC charts and the risk measures discussed in this article can be found in Chapter 8 of my book Market Sense and Nonsense.)

To simplify the explanation, I have described the AMR and its graph equivalent, the 2DUC, as based on month-end data. It should be noted, however, that these risk measures could be defined and depicted even more precisely using daily data.

As a last word, I would note that even though the alternative risk measures discussed in this article are superior to volatility, their relevance still depends on the past track record being relevant. If the strategy being assessed is subject to sporadic event risk (discussed in previous article), then any track record based risk measure will be misleading if it does not include such events.

By Jack Schwager

Jack Schwager is an industry expert in futures & hedge funds, perhaps best known for his best-selling series of interviews with the greatest hedge fund managers of the last three decades, which includes Market Wizards ,The New Market Wizardsand Stock Market Wizards. 

Schwager was also a partner at London-based hedge fund advisory firm Fortune Group and has 22 years experience as Director of Futures research for some of Wall Street’s leading firms, most recently Prudential Securities.

He is now the co-founder of FundSeeder, a platform designed to find undiscovered trading talent worldwide & connect unknown successful traders with investment capital.