The world of investments is an odd one. Various studies have shown that a monkey throwing darts can outperform most active equity managers, yet mutual funds are still widely distributed and the work of highly respected mathematicians is cited to explain certain investment choices.
However, some theories persist long after, arguably, they have been proven false. One such case is the efficient market theory (EMT), which Wikipedia defined this way: “EMT asserts that financial markets are informationally efficient, or that prices on traded assets, e.g., stocks, bonds, or property, already reflect all known information. The efficient-market hypothesis states that it is impossible to consistently outperform the market by using any information that the market already knows, except through luck.”
Another is that returns follow a normal distribution curve. This assumption has been built into several models used to measure the inherent risk within certain trading strategies.
Mathematician Benoit Mandelbrot’s work on fractals is widely cited as the starting point of a larger body of research that has shown that markets are not efficient, or at least not all of the time, and that the distribution of returns often exhibit “fat tails.”
Fat tails refers to a non-normal distribution curve of returns (see “Which is normal?”). These fat tails, or outlier events, create huge market moves and tend to create huge losses for strategies that depend on reversion to the mean principles.
Mandelbrot’s 1960s study of cotton prices looking back on many decades of data showed that markets don’t follow a normal distribution curve.
More recently author Nassim Nicholas Taleb in his book “The Black Swan” and various lectures has criticized the assumption of normal distribution and the risk measures and strategies that depend on them. Black swans are outliers, fat tail events. He expands on Mandelbrot’s work on fractals and notes philosophically that not only do Black Swans exist, but that our world is to a great extent shaped by them.
PICK A MODEL
Why the discussion about mathematics? Well a great deal of emphasis on how to measure the validity of investment is based on these models and measures like value-at-risk (VAR) and standard deviations (STD) that assume they are correct. VAR attempt to measure the risk of total loss in a portfolio. STD measures the volatility of returns and is often used as a measure of risk.
In an interview from the 1990s Taleb noted, “VAR is charlatanism because it tries to estimate something that is not scientifically possible to estimate, namely the risks of rare events. It gives people misleading precision that could lead to the buildup of positions by hedgers. It lulls people to sleep.”
In the 1960s William Sharpe developed the Sharpe Ratio, which is a measure of the excess return (or Risk Premium) per unit of risk in an investment asset or a trading strategy. A high Sharpe Ratio is good and may suggest additional leverage may be appropriate to optimize returns.
While the Sharpe Ratio is widely used, many managers believe it is a poor measure of risk and strategies that tend to produce strong Sharpe Ratios simply hide risk rather than reduce it.
One problem with the Sharpe Ratio cited by numerous managers is that it doesn’t distinguish between positive STD and negative STD and tends to punish strategies for strong returns. A more basic problem however, is that it is based on a normal distribution curve of returns. It doesn’t take into account fat tail risks.
Cook Pine Capital in November published a “Study of Fat Tail Risk.” In it they point out how an examination of 81 years of price patterns in the S&P 500 show that these “fat tail” events occur much more frequently than would be predicted by a normal distribution curve.
It states, “Whereas normal distribution of the daily return of the S&P 500 would suggest a three sigma event (three STD or -3.5% daily return) should have occurred 27 times over the last 100 years, this has occurred 100 times since 1927 (see “Reality bites,” above).
The numbers, according to the study, get more shocking when looking at even larger moves. The likelihood of a four STD move (-4.7%) is one in 100 but has occurred 43 times since 1927. A five STD move (-5.8%) is supposed to be virtually impossible but has happened 40 times in the last 81 years and seven times since Sept. 29 (see “Not again”). Cook Pine produces custom hedge fund portfolios for high net worth investors.
Edward (Bill) Dreiss has operated managed futures programs for more than 30 years and has used Mandelbrot’s work in developing trading systems.
“The markets are what they are. The debate is over what model works best. Normal and fractal distributions are just models, the qualitative of which model works best in nature,” Dreiss says. But Dreiss believes that the type of strategies that produce the best results in STD-based risk models actually hide risk rather than reduce it.
He says that once the Sharpe Ratio became popular there was a rush to produce strategies, the returns from which could be validated by it. This has produced some problems of late.
“Sharpe Ratio became a litmus tests for investments. [Bernard] Madoff looked at the market and said this is what people want, 10% returns with no risk,” Dreiss adds.
CTA Richard Scully says, “People have become entirely too complacent with quantitative [methodologies], value-at-risk is another example of a system that relies on normal distribution curves. These have an inherent flaw. They are good tools but you can’t use them without an intelligent qualitative overlay.”
OPTIONS WRITERS
Option writing was one of the more successful investment strategies from 2003 to 2007. Many professionals decry option writing because it tends to produce strong steady returns followed by major drawdowns. Anecdotally people describe it as picking up nickels in front of a steamroller, which is okay if you do not get run over. But the problem comes when risk measures only see the nickel and never the steamroller. This can happen with option writers during prolonged periods of moderate and shrinking volatility. They can sail along, earning extremely strong returns with no drawdowns. This creates remarkable Sharpe Ratios but when volatility spikes, like what happened in 2008, they can have massive drawdowns, which would seem nearly impossible based on their Sharpe Ratio if that was all you looked at.
While options writing is a legitimate strategy, many investors shy away from it because of this return profile. And any informed portfolio manager understands that measures like Sharpe Ratio and STD are particularly poor at revealing the real risk profile of this strategy. Many of the hedge funds strategies that have drawn attention and money in recent years have a similar profile. More elegant risk measures may reveal the true risk of these strategies. While the Bernard Madoff scandal involved a Ponzi scheme, that he drew so many investors was testament to the demand for strategies that produced consistent conservative returns.
“They look wonderful until they go absolutely bust,” Scully says of option writers. “If you want to produce interesting returns from options writing or arbitrage you generally need to leverage significantly. One needs a qualitative overlay that understands that these are inherently tail risk strategies.”
A DIFFERENT SOURCE OF RETURNS
Managed futures are generally thought of as long volatility strategies. They look for trends and when trends come and are extreme, they do well, like in 2008.
Managed futures, despite strong growth, have grown less robustly than hedge funds in general in the last decade. It is not as respected as many other alternative strategies despite having a longer track record and despite producing solid non-correlated returns over three decades.
One reason for this lack of respect could be the source of its returns. “Managed futures in the efficient market hypothesis should not work,” says Prav Sambamurti of Ssaris advisors.
Why then did managed futures do so well in 2008? The answer is that there is a non-normal distribution curve of returns, which includes fat tails. While researchers at the finest academic institutions in the world can design great academic studies and start by throwing out outliers in their research, investors can’t. You can’t just say Black Monday was an outlier, so we will not take that loss.
However it is a standard practice in research and even when managed futures produce the type of returns it did in 2008, many allocators are weary. They are weary most likely because they are looking at STD and Sharpe Ratios. Because managed futures — more specifically trend following strategies — depend on large moves in a few of the markets they follow, they tend to show more risk as measure by STD.
“Managed futures tend to exploit behavioral inefficiencies in the market. If we want to exploit behavioral inefficiencies we cannot allow them to bias our thinking, so we program our strategies into an emotionless computer because we are all subject to behavioral bias,” Scully says, adding, “We certainly don’t believe that following a mindless quantitative system is a good way to run an investment firm or invest period. We think that even the best quant systems require intelligent qualitative overlays.”
Scully hits on the basic disconnect when he talks of behavioral inefficiencies. If you don’t think they exist, then you will not invest in a strategy to exploit them.
A BETTER WAY?
Ssaris Capital Advisors is one of the earliest commodity trading advisors and from the start founder Mark Rosenberg saw the value of diversification. He not only had a diversified futures strategy but built a diversified portfolio strategy that included his divergent managed futures strategy along with select hedge fund strategies that tend to be convergent.
Divergence means that the source of returns is coming from movement away from a specific level and is a way to classify trend following and momentum strategies. Convergence strategies, on the other hand, involve taking advantage of temporary market anomalies and include relative value, fixed income arbitrage, convertible bond arbitrage, merger arbitrage and long/short equity among other hedge fund strategies. They are strategies that attempt to identify fair value.
Markets move away from a perceived mean and convergent strategies profit on the reversion back to the mean.
Fund of funds managers who performed very poorly in 2008 could have taken a page out of Rosenberg’s book by including divergent strategies in their portfolios of mostly convergent hedge funds.
Divergent strategies tend to be long volatility, whereas convergent strategies tend to be short volatility. Managed futures tend to earn returns from market anomalies whereas the majority of equity based hedge fund strategies earn returns from reversion to the mean as with various arbitrage strategies.
“Long volatility programs are looking to exploit movement away from the mean. Short volatility strategies are betting on mean reversion and convergence to fair value,” Sambamurti says.
Ssaris splits managers in divergent and convergent camps. “I don’t think there is an optimal mix,” Sambamurti says. They approach it from a top down and bottom up strategy.
“Generally you are going to have less allocation to managed futures but you want a fair risk allocation,” Sambamurti says.
The key is fair. If an allocator simply looked at Sharpe Ratio — and many do — perhaps there would be no allocation to managed futures. But Ssaris doesn’t simply look at STD risk measures. That is a big distinction as many convergent strategies tend to produce low risk adjusted return figures when using risk measures purely based on things like STD and Sharpe Ratio.
There are many hidden risks in various investment strategies, the biggest risk of which is illiquidity. “The temptation is to smooth the return skew, that hides inherent risk,” Sambamurti says, adding as much as half of this risk does not show up in typical risk measures based on value at risk, STD and Sharpe Ratio.
“From a quantitative standpoint, if we are long [one of these strategies] we have to give them a haircut,” he adds.
Ssaris looks at semi-deviation. This measures downside risk and does not punish upside risk. It looks at just negative performance. They also look at efficiency measures. One example is the Calmar ratio. It measures return over drawdown. “Looking at what kind of compensation you are receiving for [your] risk,” Sambamurti says.He points out though that “all of these ratios can be skewed by illiquidity.”
Using futures has an advantage because of liquidity and transparency. “[Managed futures] tend to have bigger swings but they are real. Futures markets are a truth serum,” he says.
He adds that the use of typical risk measures can “lull you into a false sense of comfort. The problem is many of these managers can become correlated in their [use] of risk. Many fund of fund managers don’t look at what we do — they are looking for that attractive profit, they are not utilizing the tools we look at.”
Convergent strategies can appear low risk for a long time until an event occurs. “You need a structurally non-correlated strategy. By the time the event occurs it is too late,” Sambamurti says.
Despite all the recent evidence Sambamurti says, “Many of the academics out there at Harvard, Yale and MIT still subscribe to the efficient market model. But that is not the real world. There is major pushback against the efficient market hypothesis.”
He points out that a similar event happened with Long-Term Capital Management in 1998. “The fat tailed risk is out there, you don’t know when it is going to hit. The smartest minds couldn’t figure it out.
“The best defense is a non-correlated return stream. You need a fair allocation to both at all times,” Sambamurti says. And to come to the right mix you need to look at risk from many different angles because, “It won’t be the model that gives you the best return stream in your quantitative testing.”
WHAT HAVE WE LEARNED
Market performance in 2008 was not only poor but it challenged many assumptions. There have been many obituaries for the buy and hold method and rightly so — though it is probably a better strategy today, with the Dow Jones Industrial Average below 7,000 than it was 18 months ago when it was above 14,000—but other long-held assumptions need another look.
The EMT also is being challenged, as is the notion of a normal distribution curve of returns. The assumption of normal distributions is imbedded in risk measures that are often helpful but do not give the entire picture.
Various convergent hedge fund strategies have proven to produce strong returns but risk measures that assume a normal distribution do not reveal all the risk some of these strategies may be taking.
Managed futures on the other hand are risky but the risk is right there for you to see. STD models do a good job measuring their risk, probably because the measures were built to reveal that risk where, perhaps, other strategies were built for the risk models.
