Golden Rule of Forecasting - Be conservative

One of the leading experts on forecasting is J Scott Armstrong, from the Wharton School. He has produced numerous papers and books on forecasting but has encapsulated all of his decades of thinking with his paper, The Golden Rule of Forecasting. There is a right and a wrong way to do forecasting and Armstrong walks through the key issues, whether it is through an econometric model or a judgmental forecast. His golden insight is that when in doubt be conservative. More deeply, his comment is that the forecaster must seek out and use all knowledge relevant to the problem, including knowledge of methods validated for the situation.

He has a list of twenty-eight guidelines that stem from his golden rule. These guidelines include rules for problem formulation, judgmental methods, extrapolation methods, causal methods, combining forecasts from different methods, and avoidance of unstructured judgmental adjustments. Ignoring these guidelines will lead to greater forecast error especially if there a high degree of uncertainty and complexity. Fortunately, the simple guidelines should be easy to follow, but in reality, too many forecasters ignore these simple steps and create their own forecasting doom. 

The golden rule is consistent with the comments of another leading forecasting expert, Arnold Zellner, who argued for the KISS forecasting method, "Keep It Sophisticatedly Simple". A sophisticatedly simple model is one that "takes account of the techniques and knowledge in an field and is logically sound". Don't make forecasts in vacuum. Use all of the help you can get from previous work. Do your preparatory work for forming the problem and watch out for biases. Yes, it is simple, but Armstrong provides a good reminder. 

Trend-following, portfolio insurance, and market selling pressure

A recent FT article, "Rise in the new form of 'portfolio insurance' sparks fear - Popularity of trend-following funds - and their promises - carry echoes for some of 1987 crash" focused on the threat of trend-following to create selling pressure on equity markets. This speculative topic has been a recurring theme for decades and has been extensively researched. The empirical question is very straight forward. Do futures prices lead cash prices and are futures prices driven by systematic trend-followers? That is, is there a positive feedback loop whereby the selling of equity futures by some strategies will lead to more selling and a price crash? The research on the impact of speculators has generally shown that this is not an issue. 

There is no focused empirical evidenced that trend-followers create downward pressure that pushes equity cash prices lower. In the blue ribbon panel reviewing the 1987 crash found mixed evidence for CTA's or portfolio insurance causing the crash. Certainly portfolio insurance may have hastened the decline but systemic selling from trend-followers has not be a cause of crashes. Momentum studies showed there is crash risk with following these strategies but not evidence that momentum trading causes the crashes.

There have been a number of theoretical papers on "noisy" traders which could cause prices to be distorted. There are also theoretical papers which suggest that a positive feedback loop from trend-followers could cause bubbles and crashes. It is possible for bubbles and crashes to be caused by trend-followers if their market size is large enough. Reality may be different.

This is a question of the size of selling pressure. A look at the commitment of traders from the CFTC suggests that there is not a strong level of net short positions from levered accounts or institutions. Of course, that can change and create the selling pressure suggested in the article, but there are no warning signs in the current data.

Nevertheless, we can review the type of behavior for the major groups who are offering some type of downside protection and what is there impact on prices. Trend-following CTA's are not portfolio insurance. Being diversified long/short managers across a broad set of asset classes is not the same thing as being a mechanistic buyer and seller of equity futures based on the notional exposure of the insurance provided. Portfolio insurance is close to option replication. CTA's are not option replication strategies but price based opportunistic traders.

What CTA's and portfolio issuance have in common is path dependency based on price, but the exposure to equity futures from any given amount of notional funds will be significantly less than what will be seen with portfolio insurance. In fact, CTA's may have declining exposure in equity futures if falling prices are matched by higher volatility. Risk parity may generate selling pressure on equities, but from changes in volatility. Option selling will generally not be based on positive price feedback, and tail risk management may come in many forms not all of which are path dependent. 

We have agreement with the FT on the fact that downside protection schemes have grown in the last few years and they will have a greater impact because of their size. However, the behavior of different strategies will mean that their impact on prices will be varied and complex and may not come in the form of selling pressure waves like a portfolio insurance strategy.

What kind of model to choose?

"For people who like that kind of thing, that is the kind of thing they like" 
"History does not repeat itself. The historians repeat one another."
- Max Beerbohm

Approaches to modeling go through fads and fashions. What was learned yesterday by MBA's will be the model of choice tomorrow. Certain approaches are employed because that is the approach the modeler wants or likes. The same applies to strategies. A value investor will not likely to turn into a growth investor. He likes that sort of thing. A quant will not become a discretionary storyteller. He likes the precision of the model.

If you believe the world can be described by factors, those are the type of models you will use. If you believe in trend-following, then that is the approach that will be employed in your portfolio. Sometimes an approach will be used regardless of its efficacy with actual performance results. Damn the data, I like the elegance of my model. If one specification does not work, another will be tried in an effort to find the right factors without looking at alternative approaches. For example, if some modelers use a Fama-French three factor model, then others will repeat that approach. Everyone will start to use the Fama-French approach as a baseline. There is nothing wrong with this in concept, but it can be taken to extremes.

We are not arguing that that there is anything inherently wrong with being a specific model follower or being biased with a specific framework. We are not arguing for an atheoretical approach. However, focus on one approach can create a myopic view of the world at the expense of performance. The simple question should always be, does the model work? Whether trend-following versus factor modeling, systematic or discretionary, longer-term versus short-term, the question is not acceptance by peers of the approach employed but whether it generate the results expected.  

Drawdowns - worth a closer look as a risk measure

While there is a strong interest in short-term return performance and volatility of hedge funds, drawdown is still the risk where most investors have placed their focus. Maximum drawdown, as a risk measure, can be formalized as the conditional expected drawdown or the measure of the tail mean of a maximum drawdown distribution. The figure below shows what that distribution will look like. What makes this risk measure especially useful is that it can be employed in any optimization and has a linear attribution to factors. Maximum drawdown can have traded off against return or specific risk factors. It can be compared or related to the marginal contribution of risk measure which has gained popularity with many investors.

Perhaps more important, drawdowns are serially correlated with the return pattern of a manager. This means that if the returns of the manager show serial correlation, it will show-up in the drawdown data as more significant drawdowns. The drawdown of a portfolio will be related to the correlation across managers.  See "Drawdown: From practice to theory and back again" by Lisa Goldberg and Ola Mahmoud. 

Drawdowns are path dependent. How the returns of the manager evolve over time is relevant. It is notable that volatility and expected shortfall do not capture the impact of small cumulative loses like a drawdown measure. In this case, the path dependency within drawdowns provides useful information on risk.

Drawdown has been used as a descriptive measure of risk, but more formal analysis suggests that it would be a good measure to optimize against other factors. It may be more useful than expected shortfall or volatility to help minimize the worse case scenarios faced by investors.

Dollar variations - the two main levels of uncertainty

“There is no sphere of human thought in which it is easier to show superficial cleverness and the appearance of superior wisdom than in discussing questions of currency and exchange.” 

Winston Churchill, Speech to the House of Commons, Sept 29, 1949 

What makes currency forecasting so difficult are two levels of uncertainty. This uncertainty is playing out today with the dollar declining on the Fed raising interest rates.

First, there is the uncertainty associated with relative policies and behavior. Since the exchange rate is a relative price, the forecaster always has to get the macroeconomics of two countries right. The policies of the Fed have to be contrasted with the policies of the ECB. The growth of the US has to be compared with the growth of Canada for CAD. It is always a problem associated with the forecast of two. 

Second, there is the changing dynamics of any regression results. Parameter uncertainty is greater because the weights on what is important are constantly changes. This has been shown to be an empirical reality. Today, the important variable may be monetary policy. Tomorrow, the most important weight may be on growth. The shifting weights causes differences in rational beliefs that may prove false for forecasting. Monetary policy is important but its important may be less today than last month. Two analysts may both be right on the impact of monetary policy, but their level of emphasis may be wrong.

This is why heuristics and simple rules may be helpful. As a first pass, the price trend may be the most important indicator because it is the weighted value of all beliefs and opinion. It is the aggregation of all views on relative price and relative emphasis. If the weighted opinion is moving the dollar lower, it is sending us a signal on underlying economic variables.

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.

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. 

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.

Interest rates, risk aversion, and uncertainty - It's about precautionary savings

What drives real interest rates? The answer seems to be associated with a demand for precautionary savings. That is, the real rate of interest will be driven by changes in uncertainty and risk aversion. If uncertainty or risk increases, there will be an increase in the demand for safety. if there is a increase in the level risk aversion, there will also be an increase in the demand for safety savings. Past research has shown that the real rates are associated with changes in growth volatility, but another recent paper called "Precautionary Savings in Stocks and Bonds"  looks more closely at measures of volatility and changing risk aversion or attitudes to risk in the stock market which can be useful at linking change in real rates to market behavior.

The authors look at a novel measure of market uncertainty that will drive precautionary savings, the difference in valuation between low and high volatility stocks. Now, this is not a measure that will naturally jump in the minds of most investors. I would be interested in the author's "data-mining" techniques for stumbling on this measure, but this measure does exist and is informative.  Look at the valuation differences between high and low risk stocks. It does make some intuitive sense as a measure of cash flow growth and risk.

What is interesting is that when this measure of risk is included with more traditional measures of valuation and growth, the volatility measure is statistically significant and meaningful as a measure of demand for precautionary savings. 

The importance of thinking about risk and precautionary savings is that a meaningful portion of rate movements is not related to growth but to risk aversion and volatility. If we get a jump in risk aversion, rates will go down and if there is less risk aversion, then downward rate pressure will be gone and rates will rise. Yet, the rate rise will not immediately mean a decline in the stock market. The correlation link between stock and bonds may not exist going forward. 

Uncertainty and what drives interest rates

One of the leading questions for any investors or asset allocator is what drives interest rates. If you know the factors that will cause rates to rise or fall, you have a significant edge in the market. Any decomposition of rates will fall into three broad categories, the real rate of interest, expected inflation, and a risk premium. What has been a puzzle for many researchers is that while there is an expectation that there should be a positive relationship between growth and interest rates based on inter-temporal smoothing, there has not been found a strong empirical relationship like what has been with expected inflation.

An alternative channel for driving rate moves is that a precautionary saving story can explain a negative relationship between real rates and macro economic uncertainty. A carefully researched paper by Samuel Hartzmark called "Economic Uncertainty and Interest Rates" finds a strong negative empirical relationship between rates and growth uncertainty. This statistical relationship is found not only in the US but also around global bond markets and through long historical periods. The relationship all exists through a number of measures of macroeconomic growth as well as the VIX measure of uncertainty. 

What this research provides is a strong foundation for looking at uncertainty as a key driver of rates. If there is significant dispersion in expected economic growth, there will be a precautionary demand for short-term cash instruments. If uncertainty declines there will be less downward pressure on rates. The precautionary savings story suggests that rate changes may not tell us anything about growth but will suggest a link with demand for safety during periods of uncertainty. 

Global themes on one page

Investors may have thought at the end of the year that fiscal policy would dominate macro discussions over monetary policy. Here we are in March and the key issue for the month will be the Fed meeting. Fed officials have telegraphed a possible rate hike which has been the driver in rate markets. 

Surprisingly, the Fed talk has not significantly impacted equity prices. Equities continue to go up on business and consumer survey optimism and the expectation that fiscal policy will bend the economic growth curve. This optimism exists even with little headway on fiscal policy discussions. We see more talk about overvalued stock indices, but February moves show investors are little concerned and want to put money to use.  Our biggest concern is that risk-seeking behavior is not discounting a more hawkish Fed. 

More on Bubbles - trends last longer than expected

There is the old adage that "trends last longer than expected", so hang onto your positions. Since you don't know when trends will end, just stay with those trends as long as possible. Always hold those winners regardless of how long and how far they have run-up. I could place some qualifiers on this adage but it a good base view for anyone who wants to be a trend-follower.

If you look at the data on bubbles, the hold your trends strategy makes sense. Momentum and trend-following is susceptible to crash risks, but the downside may not be as bad as popular narratives suggest. The paper "Bubbles for Fama" by Greenwood, Schleifer, and You takes a deep look on many price booms to determine whether they are always followed by crashes.

There will be crashes after big run-ups in price but it in not a certainty. The numbers suggest a equal chance of having a crash or continuing to run-up in price after a 100% gain. The risks are high, but large gains do not necessitate a crash. The trend is still your friend. And, if there is some form of risk management the chance a trader could end with a gain may actually be high.

The paper also shows that there are indicators which may suggest when a crash is more likely. Factors like volatility, turnover, stock insurance and the price path may all help identify when a crash ay occur. I don't take boom, bubbles and crash lightly. There are real effects on the economy through the misallocation of resources and there will be losers when the market turns, but the risks should be placed in perspective.

All bubbles are not trouble

Without a doubt there has been significant concern about asset price bubbles. Even though there still is not a good working definition of a bubble. Many define bubbles as booms that go bust, but that only means that we will never know we are in a bubble until after the fact.  Clearly, there has been vivid descriptions of some famous cases including the technology bubble in the US; nevertheless, a closely look at history suggests there have been many booms that have not been busts. While the chance of a boom leading to a bust is higher than a unconditional forecast, the number and frequency of busts is not so high as to say confidently that all large price moves will turn into crashes. 

The work of Yale economist/historian William Goetzman in his paper, "Bubble Investing: Learning from History" analyzes the behavior of large asset price booms to determine whether all extraordinary increases lead to large crashes. His conclusion is that bubbles don't always bust. This is odd given the view that whenever there is a market with accelerating prices, say a doubling in price, there is talk of a bubble. There is often as much talk of the potential price reversal as discussion for the price increases, yet the numbers tell us something different.

What makes this important is that the fear of booms and the potential for a bubble may be misplaced. There is a higher probability for a bubble when there is a boom, but the conditional frequencies are such that the idea that all booms should be avoided because there will be a crash may be misplaced. What goes up quickly does not have to reverse quickly. Concern for accelerated price increases, yes. Fear from market doubling as a basis for a bust, no.

Sector and style behavior all positive

Style returns were all positive for February with the largest gain for the large cap US SPX index. International stocks lagged given the increase in the value of the dollar. Small and mid-cap indices did not gain as much in February after stronger movements over the last few months since the US election.

All market sectors were positive with the exception of energy which saw a slight decline as oil prices moved to the lower end of a range. The largest gains were in health care, finance, and utilities. The higher returns in health care and finance may be due to the expectation that regulations will change for betterment of company earnings. All trend indicators suggest that gains will continue except for the energy sector.

Bond ETF's showed more muted gains with the only loss in the short-term Treasury sector based on expectations of a Fed rate increase in March. Year to date gains have been strong for international bonds, long duration portfolios and high yield.

Sovereign ETF's also generally showed positive gains with the only exceptions focused on EU countries such as Italy and France. The only other negative return in February was with Canada, albeit the index is still positive for the year. Non-US stocks have not been hurt by the upheaval concerning trade wars at this time. 

Our trend and break-out indicators suggest that positive returns for style, sectors, countries and fixed income will continue. The high correlation across returns is unusual.

Credit Suisse survey - Changing the hedge fund mix

The latest Credit Suisse hedge fund survey for 2017 provides a detailed review of where there is the most investor demand for hedge fund strategies. Number one is global macro based on a desire to have greater portfolio diversification. This appetite is followed by fixed income arbitrage.  The swing in demand shows a movement away from long-short equity and a movement to credit and sector specific strategies.

Nevertheless, there has been a decline in net demand across many strategies with strong declines in discretionary global macro and managed futures. Hedge fund investors are being more selective with their demand as opposed to a general increase across a number of strategies.

A consistent theme across many of these hedge fund investor surveys is the disappointment with hedge fund performance. Well over 2/3rd of investors believe that hedge funds did not meet expectations. It is odd that investor demand is still strong for hedge funds even though they do not think hedge funds are doing their jobs. This is not a good statement on the quality of the industry.

I found the most interesting survey table the sources of risk for the coming year. Number one and two for the second year in a row are the same; crowded trades and market liquidity. These risks are very difficult to measure, yet these uncertainties seem to be the chief concern of investors.

The CS survey confirms many of the conclusions of other surveys. There are differences, but what seems to be unmistakable is that managers have disappointed investors and have not been able to provide them what they want. Investors are looking for diversification and returns that can meet expectations. It is the job of managers to control expectations by generating returns that are consistent with what has been marketed. It is also the job of managers to offer a different return stream that is independent of traditional asset class beta. The difference between what investors want and what managers provide has to be closed. 

Market prediction and using dispersion as a guide

I was having a discussion with friends for where the SPX will end over the next three and six months as well as what could be the ending value for the year. The predictions were all over the map with a mix of investors saying the market will be either higher or lower. I also had some that said it would be both, first higher then lower, and others suggesting the first leg will be lower only to then go higher again. 

These predictions should be grounded in reality, so looking at the distribution of returns given current volatility and the probabilities of a particular move are important to anchor predictions. The table below is a simple guide of what may be possible over different horizons. The question for someone making a prediction is whether they think the market will be more or less likely to move outside of the range depicted by volatility.

We can take current market volatility for an at-the-money option over the next three months and use it as a base case for finding probabilities for different sized moves. The annualized volatility can be converted into the volatility that will exist over a shorter horizon. Finally, simple benchmarks of up or down 5, 10, and 15% can serve as likely placeholders for some realism on possible gains or loses. Of course, it is simple, but it provides a grounding in current market reality.

In this simple case, if there is no trend, the likelihood that there can be an up or down 10% move over the next 3 months is slim, less than a 5% chance, but there is over a 15% chance of that occurring for year-end. So to say that the market will have a better than 50% change of being up 10% over the next 3-6 months is a very strong bet on a uptrend. Perhaps that is obvious, but there can now be a serious discussion of predictive risk once the distribution is overlaid onto the predictions.