Thursday, March 16, 2017

Robust control and managed futures

How do we know whether a model is right if we are running a systematic managed futures program? This is not an easy question because a significant amount of data is necessary to distinguish the difference between models. Plus, there is just the uncertainty of structural changes, regime changes, and parameter variability which ensures that the best model yesterday will not be the best today or tomorrow. 

There are tools that can help with the process. One important direction that has not been effectively explored is robust control methods. Robust control assumes an "approximating model" which is then perturbed to find parameters that are penalized if there is failure. In this case, if we have a simple moving average model with stops, the robust control method will find the parameters that will reduce the risk of loss when there is uncertainty. This idea is not foreign to most modelers. While many managers have not explicitly used these techniques, it is intuitively used when there is an exploration of parameter choices or when multiple models used within a program.

You can think of robust control as another method for dealing with market unknowns. Your model is supposed to make predictions. The quality of the predictions is based on performance. A higher return model system is more predictive than a low return model. However, given the level of uncertainty in the market, it is hard to say what set or parameters or model will do best in the future. Hence, there is value through testing variations on a single model in order to find environments for when a model will do poorly. Using a min-max utility strategy, the parameter choice may not be to find the best performing model based on optimization of parameters, but to find the best model assuming that you want to minimize some max loss. Since there is uncertainty, don't find the fitted best model but one that will not generate a strong loss in any environment. 

The same approach can be applied when employing more than one model. By mixing weights with more than one model, the controller can minimize the worst case regardless of the future environment.  The objective is not to find the combination of models that maximizes returns but to find the combination that will not generate loses in unknown environments. The form of the robust control can be fit to the utility function of the controller-manager based on a set of criteria. The idea is to move beyond simple optimization and account for the fact that the future is uncertain, so you have to assume worse case scenarios. Researchers often implicitly do this but there can be explicit tools to solve the problem.

Tuesday, March 14, 2017

Absolute strength momentum and trend-following

Relative strength momentum has become very popular as an investment strategy. It is a relatively simple strategy and has been the driver of most of the equity momentum work, buy recent winners and sell recent losers as a long/short portfolio. This is not really a trend-following strategy because the focus is on relative performance and not on the time series movement in stocks. 

There has been research work on time series momentum which is more akin to classic trend-following. This has also been shown to be profitable albeit it has not been subject to the same amount of testing as relative strength momentum. Now there has been work on another variation of momentum - absolute strength, which provides another take on the theme which accounts for trend behavior.

The absolute strength momentum looks at portfolios of winners and losers based on breakpoints of past absolute strength performance. It is not based on relative performance or recent momentum but on relative performance versus the distribution of all past performance. See "Absolute Strength: Exploring Momentum in Stock Returns" by Huseyin Gulen and Ralitsa Petkova. The thesis of the work shows that large absolute price movements in one direction in the recent past continue in the same direction in the future.
Stock returns higher (lower) than the 90th (10th) percentile of the historical return distribution of all stocks over past ranking periods earn positive (negative) returns. Buy winners and sell losers based on past absolute strength. This approach combines recent information on cumulative returns with historical distribution of cumulative returns. What is notably is that the breakpoints for the 90th and 10th percentile are relatively stable over long time periods. This measure will be similar to relative strength moment when the current distribution of cumulative returns is similar to the historical distribution of returns.

While this is a different take on momentum, it can provide some support for the most general trend following rule of buying winners and selling losers. The measure is conditional on the historical distribution of performance and will not take positions of winner that are not in the extreme, but it shows that absolute strength supports the concepts of performance (trend) following. 

Sunday, March 12, 2017

The stock-bond correlation curve - risks from the Fed?

There has been a strong positive relationship between the correlation between stock and bonds and the level of yields. As rates have declined the stock-bond rate correlation has moved from negative to positive. This is a phenomenon which has been found around the world in all major markets. Many analysts have measured this through equity and bond returns (prices) which will show a strong negative correlation. The secular decline in inflation has pushed down bond yields during a time of long-term equity gains. Similarly, the decline in real yields through a fall in bond risk premiums has also been associated with an increase in stocks. 

The big question for any asset allocator is what will happen in the future if the level of bond yields increase. The stock-bond correlation will drive portfolio performance in the next year. If the estimate of this correlation is wrong, there will be a significant increase in portfolio risks. There are a number of reasons for the stock/bond relationship to change. The most likely reasons are changes in relative economic growth and inflation. There has been found in the past a positive relationship between the stock/bond return correlation, real rates as a proxy for economic growth, and inflation. 

What is the real risk are exceptions to the normal stock/bond correlation relationship such as the Taper Tantrum, or a mix of inflation and growth that are inconsistent with normal expectations or at odds with past relationships. A simple matrix between economic growth and inflation may be a good starting point for discussion. Assuming a simple relationship that economic growth will be good for stocks and bad for bonds returns and the fact that higher inflation is bad for bonds and not as bad for stocks returns since equities are a real asset, we can see why the stock/yield correlation will be positive.

Risky situations are when there may be higher inflation but less growth, or lower inflation and strong growth. In those cases the correlation effect is ambiguous. Additionally, shifts in risk appetite will affect the stock/bond correlation in ways inconsistent with growth and inflation. The Fed can impact the correlation if they push rates higher and stocks are pushed lower because the discount rate increases but there is no change in cash flows. This may be our most significant current concern.  

Disaster risk - priced in risk reversals

There has been a lot of discussion about crisis alpha with some hedge fund strategies like managed futures and the need for investors to build portfolios which will provide some crisis risk offset. There has been less talk about what is the definition of a crisis or how to measure the chance of a crisis. 

Most researchers who have investigated crisis alpha have looked at equity market declines as the measure of a crisis. A decline of a certain level or  drawdowns is compared with the performance of other strategies. There is nothing wrong with this approach other than the simple fact that any asset uncorrelated with equities could serve as a crisis offset or crisis alpha. The argument just becomes one of diversification and degree of offset. Any non-equity-like strategy will provide some risk offset. 

What is really needed is a closer analysis of what causes or drives crises or disasters and a measure of when the chance of a crisis being high. In this more general case, we can classify crisis alpha or risk offset as any asset that will do well during periods when a crisis is more likely. Research by Emil Siriwadane of the Harvard Business School looks at the portability of rare disasters through measuring it in risk reversals. In simple terms, the chance of disaster should be priced in puts but not in the prices of calls, so a risk reversal or the difference in price between puts and calls should capture this risk. His work provides an interesting look at probabilities of disaster and finds that it corresponds with large market moves and times of economic stress. More importantly, the greater likelihood of a disasters match with larger market moves. 

This crisis measure is actually associated with real economic risks, so a hedge fund strategy that is supposed to do well during economic as well as financial stress will provide a better crisis alpha. Managed futures may be a good crisis alpha producer because it goes long or short in a wide variety of asset classes which may better protect an investor. While this pricing of disaster risk was not meant to analyze the value of investment strategies, we think this provides more insight in how to construct portfolios and protect against broad risks.