Regression to the mean, luck and picking hedge fund managers

There are few statistical facts more interesting than regression to the mean for two reasons. First, people encounter it almost every day of their lives. Second, almost nobody understand it. The coupling of these two reasons makes regression to the mean one of the most fundamental sources of error in human judgment.
-Anonymous from What the Luck? The surprising Role of Chance in our Everyday Lives by Gary Smith

Baseball players have hot bats. Basketball players get into the zone. Gamblers have their lucky streaks. There are players who choke and those that step-up at the right time. There are jinks, slumps, and superstitions in sports. Money managers win awards for their good year of performance and then have it "go to their head". The top managers of last year fall below the pack and expectations next year. All may be falling for the problems with regression to the mean. Too many follow the "law of small numbers" and make faulty statistical decisions.

This is the time for making new hedge fund allocations. Many investors in managed futures and hedge funds in general will be down in Florida for some big conferences to size up managers. Who gets a lot of meetings? The hot managers with the strongest performance from last year will be too busy and have a crowd surrounding them during the cocktail hour. Which managers will be disappointed? The losers with below average returns over the last year will be drinking alone.

Everyone wants to talk with the manager with the current high Sharpe ratio greater than the industry average. Everyone wants to talk with the "manager of year" award winner. What happens next is inevitable. The "hot manager" from last year is not so hot this year. Managers don't meet expectations after their awards and their new "rock star" status.

This problem applies for both hiring new manager and firing the old. So many times the manager you fired last year has a good year right after you kick them to the curb. Investors are frustrated. Managers don't understand it, and the process is repeated again next year. It is human nature and it is being frustrate by the regression to the mean.

Before you make your next hedge fund investment, ask a simple question, "Am I accounting for the regression to the mean?" If you are not, take a step back, review the numbers, and see if you are being hasty. There is a reason to hire and fire but don't do it because you are making an error in statistical reasoning. 

If it works for poker, it should work for investing...

More money is lost by players who know what the right thing to do is, but don't do it, than for any other reason. Having a strategy, a game plan and the discipline to stick to it are, along with a sufficient bankroll, the four most important thing that a player needs to be a winner. 
- Ken Warren poker writer on Texas Hold 'Em

Poker is a game. You play the odds. You play your opponents. You manage the risk, size your bets, and control your funds. The hard part is sticking to the plan in the face of losing and not letting the other players or your recent performance dictate your behavior. This is the discipline necessary for success.

The same applies to investing even though the markets will be tougher game. The nice part of any poker game is that the rules of the game are known. The players are limited and betting occurs with set bounds through turns. Investing is more difficult and thus requires even more discipline. There is more noise, more uncertainty, and more ambiguity even on what are rules being played. In this case, the only way to prevail is to change the dynamics to make it more structured through your own controlled behavior.

To adjust or not adjust volatility for momentum strategies

Risk management has taken the money management business by storm. If you run money, you have to say that you control volatility and manage the risk. It is the equivalent of saying, "I love my mother and apple pie." If risk goes up, you have to cut position exposure or at least that is what many will say is the path to good returns. Nevertheless, the empirical testing of this truism could be improved. A recent paper in the Journal of Alternative Investments called, "Volatility Weighting Applied to Momentum Strategies" looks at this important question in detail and concludes that it does help at improving the return to risk.

The authors provide a theoretical framework to explain when and why volatility weighting will work with momentum strategies. If there is an inverse relationship between momentum and volatility, then volatility weighting will generally be effective. That is, if there is a predictable link between strategy returns and volatility, weighing will be helpful. The authors provide both necessary and sufficient conditions for when volatility weighting makes sense and distinguishing between timing and stability effects for volatility weighting.  If that relationship does not exit, the impact of weighting will be ambiguous. Using volatility weighting without understanding the price dynamics within markets does not make sense.

Looking at momentum strategies through a broad set of 49 industry portfolios, the authors study the impact of volatility weighting for both market and portfolio level schemes across different time periods. The results conclude that volatility weighting makes good sense. The data show that volatility weighting will improve Sharpe ratios, reduce kurtosis, and reduce average drawdowns as well as just reduce overall volatility. These results apply to both strategy volatility and schemes looking at underlying or normalized market returns. Nevertheless, volatility controls can be unstable over time and may require more careful analysis especially with extrapolation this work to global macro. 

Maximizing the return to risk may not be the true objective for holding trend-following or momentum managed futures strategies. The unique feature of managed futures is its ability to generate positive skew or crisis alpha. You buy managed futures trend-following not to get the best return to risk but to have an investment strategy that will do well in "bad times". The results with respect to skew through looking at the difference between the mean less median returns are slightly ambiguous for this study.

A smoothing strategy that takes out the skew or crisis beta may make trend-following in managed futures more similar to other investments strategies. I am all for volatility control and cutting position sizes when the return to risk is no longer favorable, but too much smoothing may throw out the crisis alpha with the bath water. 

Speculation - It is not supposed to be glamorous

The history of the bull speculation in cotton of 1903 will never be fully written because, though the men who influenced it are very interesting, their operations are interwoven with bloodless statistics and tiresome technicalities.
-Edwin Lefevre Saturday Evening Post, August 29, 1903

from The Cotton Kings: Capitalism and Corruption in Turn-of-the-century New York and New Orleans

Speculation is not supposed to be glamorous. It never has been. You can go back 100 years and you get the same answer.  It is hard work. The investment edge relative to others comes from building better models, finding new information, sifting through data in new ways, searching for market imperfections or inefficiencies, and analyzing price relationships looking for anomalies. Most of the alpha generated by managers is fleeting. The smart money that flows into the market closes the opportunities and then looks for another trade. There are structural advantages that become known and are eliminated.

Even the systematic traders who don't tinker with models have to work hard. They have to show the discipline of being able to accept drawdowns while always looking to cut trading costs, and engage in research to find whether there really is something better out there. The hard work is setting a high bar for change and not revising models for the sake of showing you put in effort. For the discretionary manager, the hard work is constantly staying  abreast of new market developments even though much of what is studied will turnout to be useless. For the quant, it the work of building models that may have marginal significance but when employed over time can give a slight edge.

The risks are real and the horrible feelings of doubt when money is lost cannot be denied. The loneliness of following your investment process when other are following fads is a fact. This glamour cannot be written about or shown in a movie. 

Machiavelli could have been a trend-follower

Whoever wishes to foresee the future must consult the past; for human events ever resemble those of preceding times. This arises from the fact that they are produced by men who have been, and ever will be, animated by the same passions. The result is that the same problems always exist in every era. 

- Niccolo Machiavelli 

Perhaps he could have been a trend-follower or at least he would have understood the underpinning of many trend-followers who believe in repetitive behavior as a foundation for trend generation. Machiavelli was a student of behavior and modern political science who had a clear vision of analyzing behavior for what it is as opposed to what it should be. Appreciating this realism is important for any investment manager. It is not what markets should do, but what they actually do that matters. Many may say that a certain market should be lower, but that does not always matter. It is the weight of opinion with sentiment that matter for price direction especially in the short-run of a few days or weeks.

A recurring research work on valuation is the experiment of knowing whether perfect foresight on company earnings is enough to get prices right.  Surprisingly, this key knowledge can only explain a fraction of price behavior. This type of foresight research was the focus of Robert Shiller in the 80's and his conclusions still seem to be true today. Markets move more than what is expected from fundamentals. In spite of all of our knowledge about behavioral finance and theory, there still is a difference between model expectations and reality. In spite of all our work on multiple risk premiums, momentum is a foundational factor.

There are three kinds of intelligence: one kind understands things for itself, the other appreciates what others can understand, the third understands neither for itself nor through others. This first kind is excellent, the second good, and the third kind useless.  

- Niccolo Machiavelli

Downside risk - maybe you should be an insurer?

No investor wants to bear downside risk. Well, perhaps more precisely, no one wants to bear downside risk without extra return compensation. Strong asymmetric risk preferences create the reason for a volatility risk premium - the empirical fact that implied volatility is higher than realized volatility. What the volatility risk premium states is that if you buy an option you will pay more in terms of volatility than what the market will give you in actual volatility. In a very simple but elegant paper in the Journal of Alternative Investments called "Embracing Downside Risk", some practitioners look at the compensation toward downside risk through a decomposition of returns by strategy.

We know from parity conditions that the excess return for an asset can be broken up into two option strategies. For example, the returns for the S&P 500 index can be divided into a long call position and a covered call positions, or a short naked put and a long stock position with a protective put. The covered call or short naked put can be thought of as an insurer's component and will represent the return received for taking on downside risk. Alternatively, the long call or cash plus put position is the protected component which reduces downside risk. It is the return for a protected position. The combination of the insured and protected components will equal the underlying cash return. 

The authors find that in a set of cases across a number of assets classes over a long time horizon, the compensation for being an insurer is significantly higher than a protected position. The covered call or naked put excess return is not close to being the same as a protected position. The market prices downside risk greater than protected upside components. So maybe an investor should be willing to provide this insurance if you can avoid the really "bad times"? You are getting paid well to provide the insurance in the option markets.

We will say that market perception is that you should never take on this downside risk. If you go to your clearing firm and say you have a strategy that shorts naked puts or even follows a covered call strategy, risk manager will want to have a very serious talk to you about risk. Firms will also ask for more margin regardless of your reputation or the rates posted by exchanges. Good luck finding the firm to help you, yet the return data suggest that it may be a risk worth taking. Forgetting the numbers for a second, risk aversion is very strong even among risk experts. This tells me that there could be opportunity here by being an insurance writer. 

2017 - Living in a bimodal world

Most investors like to think of financial market risks as measured through a normal distribution. In reality, we know that it is not the case. However, how we incorporate and discuss fat-tails is not always clear. One thing that is clear is that fat-tails can be created when there is a mixed distribution or a combination of distributions that represent different regimes. A simple example will be the mixing of growth versus recession or good versus bad states of the world. This has been our theme for 2017 with a new year post. The potential for two different economic regimes will create fat tails in the return distribution of financial assets.

We have continued with our theme because with a new president many key policy issues will not just be up for discussion but will become potential reality. We already believe that growth in the US is expected to be stronger. The Obama administration gave the new president the best gift possible - a growing economy that seems to be improving. Nevertheless, the foundation for this growth is shaky.

The forward-looking issue is whether new policies can sustain or improve this growth and not detract through creating new risks and uncertainty. There is no doubt that there are economic pockets that need work, and there is the fear of the US economy losing steam after eight years and a global economy that still seems weak albeit expected to improve.

The tail risk problem is that the better growth on the surface still shows an economic foundation that could easily move to stagnation. Less than a year ago, the talk in most financial papers was still the Lawrence Summers meme on secular stagnation. His argument still holds even with his more nuanced views in editorials.

Our view is that the bimodal world requires two asset allocation actions. Continued diversification and exposure to strategies that can take advantage of fat tails through positive convexity. While many have suggested that lower intra-market correlations make for a stock pickers world, the potential macro extremes will still drive performance. This is why we have used the asset allocation checklist of BAG - Beta, Alpha, and Gamma.

Money management - Is the amount of talent important?

Money management is all about the talent, yet there is little economic analysis of human capital as an input in the creation of returns for the money management industry. That gap in research has changed with the new paper, "On the Role of Human Capital in Investment Management". This provocative paper studies over 10,000 RIA’s across a number of years and asserts that more human capital may not help return generation. Having more advisory personnel may help with attracting assets. More investment advisor employees creates the appearance of more talent, but having more bodies is more likely to generate behavior like a closet index with less active shares and lower tracking error. They call it – money management – and staff is needed for management and the gathering of assets.  Investors just have to be careful understanding why more staff is needed.

If we get the conclusions of this paper straight, the extra employees provide window dressing in order to create the appearance of more or better management. Firms assume that investors like more staff and will choose those managers that have advisor depth.

Reading the paper in detail and reviewing the data leaves me with a lot of questions. There is no issue that the authors were careful with looking at data, but the complexity of the data and the econometric problems with the samples suggest any bold conclusions should be tempered. Nevertheless, their conclusions make intuitive sense and opens up some interesting questions for due diligence. 

The paper also provides some interesting insights on the amount of talent applied to different asset classes. For example, private equity seems to require more talent than managing large cap equities.

If we apply this to managed futures or other hedge fund strategies, is there an optimal talent size? Many CTA's are small operations, are they properly staffed? The conclusion that I draw is that a good investment processes and philosophy are more important than the amount of staff associated with the firm. More talent is likely to generate decisions by committee and lead to closet index behavior. Don't count the investment staff. Study the process. Don't be fooled by the number of bodies. 

FX for 2016 - the betas say carry is back

The development of FX style betas has changed the way investors think about their foreign exchange trading exposure and risks. The approach is simple - trading risks in FX can be decomposed into four style factors, trend, carry, fundamentals, and volatility. The argument states that an investor can easily manage or decompose FX returns using these beta styles or strategies. It is an effective way to show how returns can be generated in currency markets.

We can use the style currency betas developed by Citibank to measure how returns could have been generated in currency markets last year. Their style or model breakdown is much more extensive than most of the currency academic literature. The models provide a good set of style betas. The breakdown includes trend for G10 and EM, carry for G10 and EM, fundamentals, two forms of PPP, relative equity performance, and a trend differentials in interest rates.

The 2016 returns show positive gains in carry as the main style driver in returns. Carry, the classic standard for FX trading profits, is back after its demise during the GFC and the period of no interest rate differentials. Returns also seem to follow purchasing power parity although more extensive fundamental models proved to be a poor representation of currency behavior. In spite of the market uncertain this year, the wider dispersion in monetary policy and rates have lead to more opportunities in currency markets.

VVIX vs VIX - Is something wrong here?

The VIX index is an effective measure of volatility expectations. The CBOE VVIX index measures the volatility of volatility for the VIX. If the volatility of volatility is increasing, there should be the expectation that volatility itself should also be increasing. We are seeing that the ratio of the VVIX to VIX is at high levels. Granted the VVIX index is off from recent highs, but the VIX index has continued to move lower even with the heightened policy uncertainty we have discussed in the past with our post on the one chart to look at for the new year.

Obviously when there is an elevated volatility ratio, it can return to normal through either a decline in the VVIX index or an increase in the VIX. Our view is that the change in US administration will continue to generate policy uncertainty as measured by the policy uncertainty index and thus the VIX should increase even if the volatility of volatility stays at current levels.

Measuring risks - Working against the downside

"I would've created CAPM around semi-variance, but no one would have understood the math and I wouldn't have won Nobel Prize..." H.Markowitz

Markowitz is probably right about his view on semi-variance, but there have been advancements that can help us employ semi-variance in our analysis. Still there is a need for more education on these dispersion measures. One recent paper in the latest Journal of Alternative Investments by Chambers and Lu called "Semi-volatility of Returns as a Measure of Downside Risk" effectively addresses some issues with these downside risk measures. Chambers and Lu develop the concept of semi-volatility as an alternative to semi-variance for looking at downside risk. The semi-volatility is less sensitive to some of the ambiguity that occurs with the number of sample observations in computing the semi-variance. Their measure has intuitive appeal relative to total variance and is easy to understand relative to skew and kurtosis which are both sensitive to outliers.

The idea is simple. Use as the sample the number of occurrences below the downside threshold and not the total sample. Of course, there is an adjustment factor, but this measure accounts for the actual downside events as opposed to the full sample which will reduce the impact of downside risk as the sample increases.

We have looked at the case of one manager who has two programs - a higher volatility version that is trend-following and another program which is diversified across a number of models. The diversified program has lower a volatility that makes it seem like it is less risky and it also has lower semi-volatility. Nonetheless, this semi-volatility is higher than what would be measured through the semi-variance. It is consistent with the skewness measures for each program. More importantly, it shows that the semi-volatility is higher for the "less risky" program on a relative basis. We think this new metric provides useful information on a manager's downside.

"I have set my life upon a cast,

And I will stand the hazard of the die."

-William Shakespeare, Richard III

Bond-stock correlation should be driver of managed futures decision

Why should I hold managed futures? This was a much harder question to answer when bonds had such a negative correlation with stocks. Bond provided safety, yield, and return. Allocations to bonds provided diversification and return during the post Great Financial Crisis period. It protected portfolios when volatility spiked, it generated return during the falling inflation, and it did this through the simple allocation scheme of just holding two assets. 

Managed futures is supposed to be a great diversifier and provide crisis alpha during strong negative economic events, but if bonds have a negative correlation much lower than managed futures and they do especially well during a crisis as a "flight to safety" asset, CTA's are less valuable for a portfolio. However, times are changing as evidenced by the recent correlation data.

If the stock bond correlation is rising and moving closer to 0, then managed futures will have similar diversification attributes. If bonds are underperforming because of low or negative yields and rising interest rates, managed futures programs are more likely to outperform on a total return basis. This makes holding managed futures more valuable.

The stock-bond correlation is increasing for a number of reasons, but the rise is primarily because of increasing inflation expectations. With inflation rising closer to 2% and the economy as measured by unemployment below 5%, inflation expectations has increased across most maturities. The negative correlation was associated with a "flight to quality" effect based on uncertainty, but with no current crisis, inflation expectations are the dominant driver. The low current volatility in equities as measured by the VIX index reduces any risk-off safety flows. 

If you believe that inflation should be rising, a consistent allocation approach would be to increase managed futures exposure.

In a tough investment world - investors will need help finding returns

It will be a tough investment world going forward for the simple reason the odds are against you. If you are a blackjack card counter in Vegas, you always know the odds, or the count. You know that on any draw, you can get lucky, but in some environments, the chance of success is just lower. Regardless of how smart you are, if the odds are not with you, your chances of getting good returns are lower. Your job as an investor is to know the odds and deal with the consequences.

Well, bad odds are the current situation with returns for bonds and stocks going forward. It does not matter whether you are a good stock picker or know the bond market better than your peers. The long-term average returns are lower than what you have received over the last few years; consequently, it will be hard to make money if we just follow the averages. This is not a prediction for 2017 or a view that the longer a rally persists the more likelihood there will be a reversal. This view only states that if you look at long-term returns over the last three decades, the numbers were very good versus longer-term averages.  This is the bleak view of McKinsey & Co. 

Granted their analysis is simplistic on the surface, but a decomposition of equity and bond returns over the last three decades tells us the environment going forward will not be able to generate the gains seen in the past. The main driver of both equity and bond returns has been lower inflation. The lower inflation allowed yields to decline substantially to our current low levels. Current yields cannot generate cash flow going forward and there are no drivers to push bond prices higher except bad growth. For equities, margins and lower inflation were able to provide strong tailwinds for equities. The inflation environment will not be favorable, valuations are not cheap, and margins may not be able to make up the difference for equities. 

The bottom line is that assumptions for pension fund returns are just too high even if based on smoothed historical averages. Higher bond allocations will lead to lower yields and higher stock allocations may increase risk. The choice between the two major asset classes will not lead to a set of viable options. 

The unrealized hope is that hedge funds will offer a third way to higher returns. Of course, this is based on a belief that skill will be able to move cash between higher returning opportunities. That skill may can come through finding alpha with individual securities or adjusting dynamically beta exposures. The third way will have to be based on greater manager skill since tailwinds will not be present.

WEF global risk report - what to be afraid of in 2017

The World Economic Forum (WEF) Global Risk Report serves as a useful guide on the broader set of risks that may impact the world over the next year. This report is important because it moves outside the narrow focus of finance and looks at a broader set of risks. Nowhere are economic issues in the top five for impact or likelihood in 2017. This is a big change from the 2007-2010 period. This is the first time economic issues are neither in the likelihood or impact top five. The dominant category is environmental which suggests that commodities markets are most likely to have the immediate impact if there is a shock. Extreme weather and natural disasters have the highest impact and likelihood combination from WEF analysis

What the WEF report highlights is that diversification is still the best strategy for any investor. This strategy is especially useful if one cannot isolate a potential economic shock.  Be prepared for the unexpected and for economic spillover from events that may not seem to be immediately linked to financial markets.