The ideal investment is one that offers the greatest return, with the least amount of risk.
Thus, given the choice between two investments with identical returns, the one with the least fluctuation, or variability of returns, is generally deemed the superior investment. But as Jack Schwager points out in Managed Trading, Myths & Truths, "Too many investors take the mistake of focusing solely on return...It is also critical to incorporate some measure of risk as part of the evaluation process.
Adjusting for Risk
Opportunity involves risk. It is important, therefore, to understand the risks we take, in order to evaluate whether we are being justly rewarded. Measures of risk-adjusted return (such as the Sharpe and the MAR Ratios, do just that: They literally divide an investment's return by the risk required to achieve it.
They are all, in one form or another, ratios of gain-to- pain.
Between risk and return, return is by far the more tractable concept. Looking at an arithmetic average or a compounded rate of return will tell you just about everything you need to know about reward.
The evaluation of risk, on the other hand-trying to determine what risk is, and how to measure it-is a more daunting task, and one that is complicated by the fact that the human perception of risk, and our tolerance for it, varies greatly with circumstances such as age, health, and wealth (to name just a few), along with a host of psychological and emotional factors.
If you manage money for others, for instance, your tolerance for risk will be influenced strongly by your clients' risk preferences, and will be entirely different from that of an individual trader whose goal may be to shoot for the highest possible returns without blowing out.
Drawdown is measured as a percentage retracement from a previous equity peak (or account balance high). This downside risk statistic is sampled peak-to-valley, and typically uses marked-to-the-market daily or monthly data points.
Maximum Drawdown is the largest such negative excursion during the life of the simulation, and conveys the maximum pain an investor would have had to endure in order to achieve the resulting return. Maximum Total Equity Drawdown is the denominator of the MAR Ratio (which uses daily data points), and the Calmar Ratio (monthly data points).
Duration of the Longest Drawdown, like Maximum Drawdown, is a one-time event, and is measured from previous equity peak, to new equity peak. It is also an important performance statistic psychologically not only for individual traders, but for fund managers, who are prone to losing clients during extended underwater periods.
One reason why various measure of drawdown and its duration are such important statistics to many traders is that even good systems typically spend far more time in periods of drawdown than they do making new equity highs.
But while Maximum Drawdown and Period of Longest Drawdown represent unique, extreme downside risk events, they convey almost no information about overall volatility.
The overall variability of investment returns is best described by Standard Deviation. It is typically calculated based on monthly, or annual percentage changes (rather than dollar fluctuations of the equity curve series itself).
Standard Deviation measures both upside and downside volatility, and is literally the square root of variance, which describes the dispersion of data points around an average. Standard deviation is the denominator of the Sharpe Ratio, a classic measure of risk vs. reward.
Standard Deviation is an easy concept to convey without resorting to mathematical formulae, and the following example demonstrates why averages with large standard deviations can be misleading, and why two investments with similar returns can have dramatically different risk characteristics:
The U.S. Virgin Islands have an average annual temperature of approximately 80ºF. This is paradise, and it is habitable year-round.
Let's compare this with an actual location in Southern California, not too far inland from the Pacific Ocean. It has a year-round average temperature of 76ºF, which is a little cooler than paradise. So far, so good.
Research shows that the average daily high throughout the year is 90ºF, and the average daily low is 62ºF. Still habitable, but it's beginning to sound a little hot. Maybe not, though; the Virgin Islands has an average daily high/low of 86º / 74ºF (http://www.orcasailing.com/bvi-details.html)
Our pleasant California locale also has very mild winters. More research, though, shows that while the average daily low for the summer is 77°F, the average daily summer high is...105°F. So it's apparent that, even thought its average annual temperature is slightly lower than the Virgin Islands, the range, or variance of its temperature is significantly higher, and may even be cause for alarm, where habitability is concerned.
Further digging turns up the fact that 1996 was the hottest summer on record: There were 40 days over 120°F, and 103 days over 110°F. The summer of 1974 was no more hospitable, setting a record of 134 consecutive days with a maximum temperature of over 100°F. In 1913, the temperature reached 129°F or above, five days in a row (a world record at the time), and the hottest temperature ever recorded was 134°F on July 10 of that same year. (http://wrgis.wr.usgs.gov/docs/parks/deva/weather.html)
Our pleasant-sounding climate, with a year-round average temperature lower than the Virgin Islands, now sounds more like an inferno. And it is: It's Furnace Creek in Death Valley, CA, the hottest, driest place in North America.
So the vast difference in habitability between these two locales-which share similar year-round average temperatures-lies solely in the standard deviation of their respective temperatures.
There is no doubt that, by treating upside and downside volatility the same, Standard Deviation does a very good job of describing the overall variability of investment returns. However, there is a school of thought which maintains that Standard Deviation is an inappropriate risk measure under certain circumstances because it unfairly penalizes the high upside volatility often experienced by trend-following Commodity Trading Advisors.
Trend-following CTAs typically employ rigid stop-loss strategies that produce a return profile characterized by a small number of well-contained losses, and an even smaller number of large winning trades. So the argument that standard deviation unfairly penalizes their risk-adjusted returns may well have merit.
In response, some risk-adjusted metrics-such as the Sortino Ratio-look only at downside Standard Deviation (also called semi-deviation). While similar to the Sharpe Ratio in general form, the denominator of the Sortino Ratio calculates the standard deviation of the negative data points only, against the mean of the population (of all data points).
Determining Your Own Measures
The various risk-adjusted return statistics all look at the same picture from slightly different angles, and there simply isn't a single metric that will satisfy every investor, under all circumstances. But understanding the components of these various statistics will allow you to determine which combination is right for you, and Trading Blox offers a number of risk-adjusted metrics that help you to do just that.
As a parting thought, it is worth noting that the distribution of returns from the world's financial markets are non-normally distributed, which means simply that extreme events are likely to occur more frequently that randomly (normally) distributed returns would dictate. In addition, there is evidence that the volatility of financial markets increases steadily with time. (Bernstein, Peter L. - Capital Ideas; The Improbable Origins of Modern Wall Street, pps. 21-22. The Free Press, 1992.)
Therefore, it is imprudent to think that the maximum risk statistics derived from any amount of historical testing will not be exceeded in the future. They most likely will be. Good traders count on it, and plan for it.
Edit Time: 5/9/2017 10:23:12 AM
Topic ID#: 106