Erroneous Errors

July 12, 2018

This is my first post in a series of regular posts with thoughts on relevant investment topics. In our ongoing research on our own dilemmas, we recognize that these same issues are likely at the heart of events that we all face.  With sometimes equal measure of frustration and excitement, we hope to contribute to the marketplace of information and discussion.  With the goal of interaction and feedback, please reach out with responses or topics of interest.

 

When I was a kid in school and made a mistake on a math test, perhaps having missed a step in the process, the incredibly evident reality was that the final answer was wrong. Regardless of how confident I was in the procedure, an answer in which the two sides just did not equal made me acutely and immediately aware of an “error” somewhere in the process. I liked this about mathematics -- it was straightforward and it was honest, if you did something wrong, you knew it by the clear inaccuracy in the end result.

Later in schooling, when I plunged more deeply into statistics, I came to learn that there was a new type of “error” that was, quite literally, NOT an actual error. The “error term”, or simply, “error”, was merely the deviation of a single measurement (or one observed value) away from the true value (the average, or more formally, the expected value) of the population of the quantity being measured. For example, if the mean length of a sunflower petal was 1in, and in hopes of concluding that “she loved me”, I randomly plucked a petal measuring 1.25in, then that petal had an “error” of 0.25in. And if my next pluck of “she loved me not” measured only 0.80in, I had observed a wholly acceptable petal with an “error” of -0.20in. But those were both still sunflower petals, so the model was still right!

Suddenly, errors were no longer errors, they were just potential movements that, over long expanse of time and many observations, converged around a favored level (Central Limit Theorem). More importantly -- and what really turned my world upside down -- was that these new types of errors didn’t give me much insight into whether the thing I had done was actually wrong. I hadn’t necessarily found an error if a particular observation was a perfectly “standard” deviation. Better yet, the more extreme errors became mere multiples of “standard”. That’s not a complete and utter failure, a teacher could say, it’s just a 3 standard deviation error -- totally expected 1% of the time. What had the world come to? Could a model not just be wrong?

In my current life, as a quant who builds systematic trading models, this conundrum rears its uncomfortable head fairly often, and with even greater consequences. When an observed outcome of a model measures at a relatively outsized level, such as our performance this past month, we naturally ask, “what’s gone wrong… is it broken?” Well, maybe -- or maybe it’s just a deviation of some number of units, totally expected, and quite literally “standard”.
 

To resolve this difficult question, there are two roads to pursue, one quantitative, one qualitative. The quant method is relatively straightforward, and of course, logically consistent with the original premise; does the event fall within the expected distribution? And unfortunately, the only thing that will further this fit is the continued passage of time and accretion of more observations. Thus, with that response “set in motion” and left to its own rigorous standards, the secondary method is the qualitative view, which is to simply ask, does what happened still mesh with my hypothesis, and do I still believe my reasoning to be sound? In life, when the healthy eater who runs twice a week gets a damaging prognosis, and the overeating couch potato lives to a ripe old age, we don’t change our hypothesis that a healthy and active lifestyle leads to longevity.

The outlier does not break the hypothesis. Similarly, in the equity markets, one believes that more attractive fundamentals will outperform their industry peers with less attractive fundamentals. All else being equal, one would go long the superior “value” and short the inferior “value”. Fama-French won the Nobel Prize for substantiating that the value factor is so widely used, but that does not change the fact that it is economically rational and objectively sane. Healthy eating is overused, but it still leads to longer life.

Accordingly, when an anticipated mean reversion keeps “expanding”, models based on rational hypotheses, and extensive empirical confirmation, further increase their weighting to the proven probabilistic edge. However, the obvious negative outcome of “betting with the odds” is the divergence continuing, and consequently, further losses. And so goes the feedback loop with the same question being asked again; was this NEXT move in the same direction within tail expectation of the estimated distribution? And, once again, is the hypothesis still sound? If yes, continue, if no, stop. But can this feedback loop continue ad infinitum? No, it cannot, for any single path of any otherwise acceptable probabilistic process may be the path that takes an investor past the point of no return (pun intended). I shall talk more about the path dependency (i.e. ergodicity) in a future post…
 

Wayne Himelsein

Chief Investment Officer

Logica Capital Advisers, LLC

Copy Of -Hedge Fund Alert - Manager Builds a Better Metric

October 18, 2017

The manager of a statistical-arbitrage fund has developed a measure of risk-adjusted returns that more accurately reflects the risks of investing in hedge funds than the widely used Sharpe ratio.

Logica Capital, a Los Angeles firm with $15 million under management, has shared its “skill metric” with several dozen institutional investors in the past week, telling them it offers a truer picture of a fund’s risk-adjusted performance than commonly used measures including the Sharpe and Sortino ratios. A well-known deficiency of the Sharpe ratio is that it doesn’t adequately capture the risks of portfolios whose return distributions are negatively skewed — an indicator of downside volatility. That includes most hedge funds.

 

“Assuming that an asymmetric distribution is symmetric when it is [negatively] skewed will cause any model to dramatically understate risk,” Logica chief investment officer Wayne Himelsein and research chief David Taylor wrote in a white paper titled “The Illusion of Skill” outlining the methodology for their skill metric. “We posit that if investors actually observed the true risk levels, relative to the respective reward of a potential investment, they would alter their allocation behavior.”


Analyzing historical return data from HFR, Himelsein and Taylor calculated that all but one major hedge fund strategy are negatively skewed, with multi-strategy funds, credit-arbitrage vehicles and volatility strategies displaying the highest degrees of “skewness.” The only positively skewed strategy is global macro.


Logica’s skill metric is designed to account for the higher volatility inherent in most hedge fund portfolios, whose return streams tend to be marked by occasional steep drawdowns. Applying the measure to 17 years of return data, Himelsein and Taylor found it produced substantially lower reward-risk ratios than Sharpe — at least 60% lower for funds in the HFRI Relative Value Index, HFRI Multi-Strategy Index, HFRI Credit Arbitrage Index, HFRI Fixed Income-Corporate Index and HFRI Credit Index. The HFRI Fixed Income-Asset Backed Index has a relatively strong Sharpe ratio of 2.21, but its skill metric is just half that measure.


“Overall, Sharpe ratios contract dramatically when adjusting for negative skewness, highlighting that allocators should broadly revise their expectations,” Himelsein and Taylor wrote.

 

  Among the investors who have been shown Logica’s ratio is Jonathan Dane, who oversees investments at $800 million multi-family office Coury Investment. He said he plans to begin incorporating the skill metric into his analysis of hedge funds and other investments. “We know the returns aren’t normally distributed and we know tail events happen more than they should,” Dane said. “When I look at funds, I spend a ton of time with Sharpe ratios, volatility and standard deviations, rolling returns, max drawdowns
and return distribution. What Wayne [Himelsein] has done is create an elegant way of taking these tail-risk events, allowing you to make an apples-to-apples comparison across strategies.”

The idea of the skill metric grew out of Himelsein and Taylor’s experience designing and running their Logica Fund. Their goal was to create a portfolio whose returns were normally distributed — that is, not skewed either positively or negatively. They appear to have succeeded. The fund’s skill metric is identical to its Sharpe ratio, which is what you would expect in the case of a normal distribution.


Since its inception in January 2015, Logica Fund has generated a gross annualized return of 8%.

For full publication, please visit www.hfalert.com

The Illusion of Skill

October 02, 2017

There is a wide range of investment statistics/metrics that evaluate Hedge Funds (“HFs”) to uncover manager skill and accurately assess the risk/return trade-off that a Hedge Fund (“HF”) should provide.

The overwhelming majority of HFs produce negatively skewed (non-symmetric) return distributions; but most conventional metrics, including the ubiquitous Sharpe Ratio ("SR"), assume normal (symmetric) distributions, and thus distort an investor’s effort to uncover true alpha generating skill.

Given the predominance of negatively skewed returns, risk is understated and SR is overstated. Since upside and downside volatility are asymmetric in a skewed distribution – the heavier but infrequent downside volatility is blurred by the smaller but more frequent upside volatility in the summarized "average". This leads investors to mistakenly accept risk-adjusted performance where the hidden risk has merely been transferred to a later date when the larger draw-downs will inevitably occur  - an analog to selling insurance. This is one of the biggest problems, amongst many.


Logica's research exposes the many problems with evaluating skewed HF return distributions as well as proposes a brand new risk-adjusted return tool, the Skill Metric; unlike SR that only accounts for mean and variance the Skill Metric infuses mean, variance and skew. Ideally, all metrics should dilute down to the key elements of risk vs. reward, not variance vs. reward. In this way, the Skill Metric truly illuminates skill.

 

Better yet, the Skill Metric provides its results in the same proportions as SR, wherein a zero skew return profile will precisely equal the output of SR. Similarly, the skewed return profiles will produce an equivalent range to a “skew-adjusted” SR, enabling side-by-side comparison.

 

Whether investors utilize our tool to assess the true SR, or to further rank otherwise similar SR’s, the end result is that investors can now find what they should be seeking — a maximized tail-risk-adjusted return.


To illustrate the HF categories that fare the best/worst when adjusted for their skew, the paper publishes a ranking of popular HF categories after adjusting for skew.  Since there is a negative correlation between skew and SR (the greater the negative skew, the higher the SR), alongside a positive correlation between skew and draw-downs (the greater the negative skew, the greater the expected draw-down), the paper also calculates how much higher HF draw-downs would be versus when assessed with common investment statistics/metrics that wrongfully assume that the underlying returns are normally distributed.

Copy Of -The Illusion of Skill

October 02, 2017

There is a wide range of investment statistics/metrics that evaluate Hedge Funds (“HFs”) to uncover manager skill and accurately assess the risk/return trade-off that a Hedge Fund (“HF”) should provide.

The overwhelming majority of HFs produce negatively skewed (non-symmetric) return distributions; but most conventional metrics, including the ubiquitous Sharpe Ratio ("SR"), assume normal (symmetric) distributions, and thus distort an investor’s effort to uncover true alpha generating skill.

Given the predominance of negatively skewed returns, risk is understated and SR is overstated. Since upside and downside volatility are asymmetric in a skewed distribution – the heavier but infrequent downside volatility is blurred by the smaller but more frequent upside volatility in the summarized "average". This leads investors to mistakenly accept risk-adjusted performance where the hidden risk has merely been transferred to a later date when the larger draw-downs will inevitably occur  - an analog to selling insurance. This is one of the biggest problems, amongst many.


Logica's research exposes the many problems with evaluating skewed HF return distributions as well as proposes a brand new risk-adjusted return tool, the Skill Metric; unlike SR that only accounts for mean and variance the Skill Metric infuses mean, variance and skew. Ideally, all metrics should dilute down to the key elements of risk vs. reward, not variance vs. reward. In this way, the Skill Metric truly illuminates skill.

 

Better yet, the Skill Metric provides its results in the same proportions as SR, wherein a zero skew return profile will precisely equal the output of SR. Similarly, the skewed return profiles will produce an equivalent range to a “skew-adjusted” SR, enabling side-by-side comparison.

 

Whether investors utilize our tool to assess the true SR, or to further rank otherwise similar SR’s, the end result is that investors can now find what they should be seeking — a maximized tail-risk-adjusted return.


To illustrate the HF categories that fare the best/worst when adjusted for their skew, the paper publishes a ranking of popular HF categories after adjusting for skew.  Since there is a negative correlation between skew and SR (the greater the negative skew, the higher the SR), alongside a positive correlation between skew and draw-downs (the greater the negative skew, the greater the expected draw-down), the paper also calculates how much higher HF draw-downs would be versus when assessed with common investment statistics/metrics that wrongfully assume that the underlying returns are normally distributed.

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Because of the stay-at-home order and related effects of COVID-19, Logica was unable to meet the original filing deadline for its ADV, and relied on the SEC CV-19 order to file by the extended deadline.

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