Thinking about skew - Alternative skew measures

I was having a discussion about the merits of managed futures relative to other hedge fund styles. Managed futures funds will often have positive skew versus other hedge fund styles. The measurement of skew is tricky and is not present with all managers but for trend-followers who allow profits to accrue, it is more likely. The argument for positive skew is embedded in the behavior of the managers. 

A trend-following CTA will structure their trades to create positive skew by holding onto winners and sell losers. More precisely, a manager who uses stop losses to reduce downside exposure and will follow trends for upside returns creates pay-offs which generate more upside potential. The profile shows many small loses with the opportunity for a few very strong gains.

The return pay-off will be like a synthetic option. If these synthetic options are created for both up and down markets, the result will be a profile like option straddles which are effectively employed to describe CTA performance. 

Still, skew is not intuitive when described through the standard moment formula. Skew is referred to as the third moment of the distribution which is defined as the cubed scaled deviations from the mean or more precisely [(x - mean)/stdev]^3. Notice that it is easy to calculate and Excel will provide a normalized measure of skew. The skew can be tested for significance, but there are some simple rules of thumb. A skew above 1 is positive or below -1 negative. The range between plus and minus .5 is considered normal and the ranges between .5 and 1 or -.5 and -1 is considered mildly skewed. 

If you say that a managers has positive skew of x, it does not tell the investor much about what excess returns they will actually be receiving other than the right tail of the distribution is pulled positive relative to a normal distribution. Volatility or fat tails may dominate any skew. A positively skewed distribution will actually be left leaning versus a normal distribution. The distribution is contorted away from symmetry around the mean. A positive (negative) skew will have a mean greater (less) than the median or mode.

There are different methods of looking at skew that may be more intuitive and provide a more useful means of thinking about skew. There are two Pearson measure of skew and the Bowley's (Galton) quartile skewness measure. The Pearson measure is the difference between the mean and mode divided by the standard deviation. The Pearson second measure of skew measures three times the difference between the mean and median divided by the standard deviation. If the mean is higher than the median there is positive skew. This has a nice intuitive feel because it says that the average return is higher than the middle value of a return series. The Bowley measure looks at the difference in quartiles (q3+q1-2q2)/(q3-q1) which again has a simple intuitive appeal. If the third quartile is much further away from the median than the first quartile, the distribution has positive skew.

The skew will change through time based on sampling. Enclosed is a simple example of 36 month rolling average skew for the CS managed futures index. Notice that skew changes and the skew measures generate slightly different results. The moment skew which cubes deviations will have big changes when there are outliers. The Bowley skew based on quartile will not be as affected by outliers. The Pearson second skew coefficient will be sensitive to the difference between mean and median. 

These differences are partially due to sampling and the mixture of samples. The skew will differ based on market conditions. The managed futures skew moved to strongly positive during the out-sized 2014 return period. Looking at the different measures of skew, the classic moment measure used in excel can generate big jumps when there is a large outlier. This is less likely to happen with the Pearson and Bowley measures.

Managed futures trend-following performance - It is not volatility but the stress that matters

"Crisis alpha" is used as a quick description of managed futures trend-following, but there has been very little work to explain what the term means. A generic definition is that a crisis is when equity markets have a significant decline, but that definition tell us nothing about what will be the conditions for a crisis or when a crisis will occur. 

It is a frustration for investors when this term is used. We only know by this definition that, ex post, if equities go down a lot, trend-followers are supposed to do well. That is not a basis for explaining when or why trend-following will do well. Wait until you lose 20% of your equity principal and then you will be happy with your managed futures exposure. While it is true, it is hardly an effective sales pitch. 

We want to examine the idea of crisis alpha a little more closely. This is a topic for ongoing research. A crisis should be defined by some set of economic factors that represent stress in the macroeconomy. The stress or crisis will impact the pricing of financial assets and lead to price divergences. These divergences offer opportunities for trend-followers who profit long and short from price trend dislocations. By following variables that represent stress, we should expect above average trend-following returns. 

Trends is stress tell us something about trends in prices. Periods of financial stress are associated with price dislocations and these are the times that are likely to be profitable as markets reprice across the broad set of asset classes. Stress represents "bad times" and this is when prices fall to provide a premia for holding risk assets. Increases in stress are associated with declines in demand for risky assets.

While there is a connection between equity returns and spikes in volatility, the link between volatility and managed futures is less clear. However, overall financial stress may be a better measure of when returns will be above normal. Financial stress includes volatility but is a broader concept that looks at a wider range of indicators. 

Financial stress will change the risk preference of investors and force adjustment of portfolio exposures. The simplest investment response would be an adjustment from risk-on to risk-off behavior which will manifest in equity, fixed income, rates, currencies, and commodities. The broad repricing of risk increases the set of trend opportunities and returns in a manner that would not occur if there is a localized price disruption to a single market. Significant repricing allows for significant trend trading returns.

The times of maximum opportunity for trend-followers may be during times of increased market stress. Some may call this alpha but more likely it is just related to the lower beta or dynamic adjustment of beta. Remember the market risk premia is compensation for risk during "bad times" There is no risk premia if an asset actually does well during bad times because it exploits price dislocations by adjusting risk exposures or selling short. The low beta means trend-following does not receive a risk premia during normal times but positive returns during times of abnormal stress. 

Look for periods of stress and investors will find better trend-following returns. No stress, like the post Great Financial Crisis period, and there will be limited return opportunities. Increased stress in the 2018's fourth quarter generated returns for many trend-followers in December. The reversal of stress showed a reversal in trends and loses in January. 

FX intervention - Analysis says central bank activity works

Many have held the view that central bank FX intervention is ineffective. It can be disruptive and have some temporary impact, but central banks cannot make currency markets do what they don't want to do. Research using public data, a limited sample and mainly focused on floating exchange rate regimes, shows, at best, mixed value for intervention. Nevertheless, intervention does create market frictions and an investor can take advantage of those central bank actions. 

The latest economic research based on extensive private central bank intervention data tells a different story and suggests that central bank intervention is effective at meeting bank goals. See "When Is Foreign Exchange Intervention Effective? Evidence form 33 Countries" American Economic Journal: Macroeconomics 2019 by M Fratzscher, O. Gloede, L Menkhoff, L Sarno, and T Stohr. 

When looking at the private information from central banks with a data set never before assembled, the evidence shows that central banks are very good at getting the policy goals they want. The authors find that central banks have a success rate of over 80 percent when using specific goal criteria. Intervention is effective at both smoothing exchange rates, and stabilizing exchange rates that are controlled by a band. The success of intervention in floating exchange rates, however, is lower and needs larger trading volume, public disclosure of the intervention, and supported by communication of goals. There is less success if central bank attempt to move rates against fundamentals or try to change the direction of exchange rates is response to an event.

For traders, there are some straightforward take-aways:
1. Read intervention based on the context of the currency regime, policy objectives, and communication.
2. Listen to what central banks tell you - They signal their actions. 
3. Don't fight with central banks especially in currencies that have bands.  
4. Central banks are good at controlling currency levels especially in EM and less liquid currencies in the short-run. 
5. Central banks are not as good at using intervention to stop fundamentals.
6. Central banks will smooth prices, create frictions, and can be exploited given the currency regime (flexible versus bands). 

Central banks have a stronger impact on currency rates than has generally been seen in research. Central bank actions against macro fundamentals will not be effective, but the path to central bank currency control failure can be long and bumpy. In the meantime, use intervention as a means to exploit trends and short-term mean reversion. 

Alternative risk premia overreaction in 2018 - Don't fall for recency bias

What happened to alternative risk premia returns in 2018? This was a major discussion topic at a UBS risk premia conference last week. It was a difficult year. In fact, it was a the worst performance year since 2008, and the decline for many strategies was a multiple standard deviation event.

Yet, there is a good opportunity for investors who focus on the longer-run. Since the performance for many risk premia seemed unrelated to macro factors, there is strong potential for mean reversion to longer-term strong positive performance. To extrapolate recent performance as representative of history would be to fall into a recency bias. 

The talk of alternative risk premia extremes started well before year-end. See "Alternative Risk Premia: Crisis or Opportunity?" by Michael Aked, CFA, Brandon Kunz, and Amie Ko, CFA of Research Affiliates.  Using their categorization for hedge funds, we find that their analysis and conclusions through November does not change when analyzing the full year. It is notable that January was a major reversal of the earlier negative extremes.

Research Affiliates breaks alternative risk premia into four major categories: equity market neutral, volatility, trend, and macro. Investor should consider ensuring diversification across these categories other classification schemes. 

• The equity neutral category focuses on long/short strategies that have low correlation with market beta. 
• The volatility category is sensitive to increases in volatility because of embedded optionality. 
• The trend category is viewed as a defensive strategy that will do well during market disruptions. 
• The macro category focuses on strategies across asset class such as carry, momentum, or value that will have low correlation with equity returns. 

Each of these categories underperformed in 2018, but for different reason. The equity neutral category showed increased correlation with market beta and was dragged lower by dislocations in the value style sector. The volatility category was hurt by spikes in volatility during February and the fourth quarter. Trend was harmed by volatility spikes and limited or choppy trends until December. Macro strategies that have an equity bias like carry were hurt during the year and shocks to both global and emerging markets negatively affected overall performance. 

Any shock to risk premia performance is a wake-up call and should not be dismissed as just an aberration. 2018 proved that alternative risk premia are not immune to market disruptions, but an over-reaction may also be viewed as an opportunity to reset or reengage with these styles and strategies. Clearly, January proved to be a significant offset to fourth quarter loses.