December 12, 2012

Trend Following

When I was a young account executive with Merrill Lynch in the mid-1970s, I became friendly with the top producer in our office. One day he shared with me one of the secrets of his success – he would only promote stocks when a certain percentage of Dow Jones Industrial stocks were above their 39-week moving averages. Few investors knew much about moving averages back then, and there were no PCs for calculating them. So I dug up all the old stock charts I could find with moving averages on them and verified that this moving average filter was useful. Not long after that, I was accepted into the PhD programs at both the University of Chicago and Wharton. I turned them both down based in part on the how well this moving average method had done. (I was also impressed with Bob Levy's research on relative strength momentum and the Nick Darvas book describing his remarkable success using momentum.) The efficient market hypothesis, which said the market could not be beat using publicly available information, was akin to religion in the academic world at that time. I had frightening visions of being burned at the stake in the University of Chicago quadrangle.

Things have certainly changed since then. During the past 20 years, academics have found strong evidence of profitability from trend following methods. Behavioral finance opened the door to serious trend following and momentum research by the academic community. A large body of research now shows that price trends exist in part due to long-standing behavioral biases by investors, such as anchoring and hoarding. Price trends are created when investors initially underreact and subsequently overreact to information because of strongly ingrained behavioral tendencies. 

There are now over a dozen well-researched academic papers documenting extraordinary risk-adjusted returns from trend following methods. Here are two excellent, recently released papers on the subject:



The first paper deals with moving averages applied to U.S. stocks. The second is a white paper from the folks at AQR. It features time series (absolute) momentum applied to 59 markets in 4 asset classes: equity indices, bonds, commodities, and currency pairs. The authors use a weighted combination of 1, 3, and 12 month look back periods on data back to 1903. Their paper provides convincing evidence that trend following absolute momentum is just as robust and pervasive as cross-sectional or relative strength price momentum.

The expanded version of my paper, Risk Premia Harvesting Through Dual Momentum, shows that trend following absolute momentum is actually more valuable than relative strength momentum. Both enhance returns, but absolute momentum is more effective in reducing expected volatility and drawdown. The best of all worlds is to use them both together.  

September 15, 2012

More Time Series Momentum...

Absolute momentum is a key factor in my latest momentum paper. Positive absolute momentum exists when an asset shows a positive excess return over the look back period. Others call this time series momentum. The more common momentum approach, which appears in most research papers, is relative (or cross sectional) momentum, where one asset is compared to its peers, and you select the strongest. Based on my research, relative strength momentum and time series momentum make for a great combination.

In September of last year, Moskowitz et al. wrote a detailed working paper on time series momentum. Since then, there have been several other working papers dealing with time series momentum. One of the more interesting ones appeared on SSRN earlier this month. It is called Improving Time Series Strategies: The Role of Trading Signals and Volatility Estimators, by Akindynos-Nikolaos Baltas and Robert Kosowski. In it, the authors look at the implications of trading signals and volatility estimators on the profitability of monthly time series momentum strategies. Last December, the authors issued a paper called Momentum Strategies in Futures Markets and Trend-Following Funds in which they looked at time series momentum patterns cross monthly, weekly, and daily frequencies for commodity contracts..

The authors went on to compare various ways of identifying time series momentum. These included whether an asset has been up or down over the look back period, a moving average trend identifier, and several methods based on the t statistic of the regression slope. The most complicated method looked at 30 minute time periods and daily data in order to add an R squared cut-off filter. Based on the Ziemba Sharpe ratio, this method looked attractive. However, it also had the highest volatility. Looking at the performance chart of all the methods, the simple up/down method seemed to be the most consistent.

I found one of the most interesting parts of their paper to be the exploration and comparison of different volatility estimators. These could be useful for risk parity style asset allocations, which I may address in another post.

August 14, 2012

How to Judge an Investment Opportunity


Whenever a new investment approach comes along, there are always risks associated with data snooping and selection bias. Even with the best thought out methods using plenty of past data, there is still some data mining involved in selecting portfolio assets, weighting methods, re-balancing intervals, etc. Just as one can never become a virgin again, so one can never unlearn all the ideas that may become embedded in an investment methodology.

So how can one minimize the risks associated with a new investment approach? The first way is to require that the method make sense. Is it in tune with the nature of the markets?

Portfolio insurance, an idea promoted by academics having little market experience, caught on briefly in the 1980's. The idea was for investors to allocate more capital to stocks as they rose on a short term basis, and pull money away from them quickly as they declined. Any experienced market practitioner knows this is a bad idea, since the stock market is short-term reactionary by nature. Sure enough, portfolio insurance incurred large whipsaw losses soon after it began. Investors gave up on it right away, with nothing to show for it but loses. 

Momentum, on the other hand, has always made sense. It is based on the phrase "cut your losses; let your profits run on," coined by the famed economist David Ricardo in the 1700s. Ricardo became wealthy following his own advice. Many others, such as Livermore, Gartley, Wycoff, Darvas, and Driehaus, have done likewise over the following years. Behavioral finance has given us solid reasons why momentum works. The case for momentum is so strong that two of the fathers of modern finance, Fama and French, call momentum "the premier market anomaly" that is "above suspicion."

The second criterion for accepting a new investment approach is robustness. One way to judge this is by a model's complexity. Simpler is better. Fewer moving parts means fewer unanticipated consequences and less danger of model over specification. Over fitting data by adding complexity to a model can also make it too rigid. It may then perfectly predict the past, but not the future.

Momentum, on the other hand, is pretty simple. Every approach, including momentum, must determine what assets to use and when to re-balance a portfolio. The single parameter unique to momentum is the look back period for determining an asset's relative strength. In 1937, using data from 1920 through 1935, Cowles and Jones found stocks that performed best over the past twelve months continued to perform best afterwards. In 1967, Bob Levy came to the same conclusion using a six-month look back window applied to stocks from 1960 through 1965. In 1993, using data from 1962 through 1989 and rigorous testing methods, Jegadeesh and Titman (J&T) reaffirmed the validity of momentum. They found the same six and twelve months look back periods to be best. Momentum is not only simple, but it has been remarkably consistent over the past seventy-five years.

The opposite problem of too much complexity is omitted variable risk. For a model to be robust, it needs to incorporate all relevant explanatory variables. As Einstein pointed out, a model should be as simple as possible, but no simpler. Perhaps the most dramatic example of omitted variable risk is the case of Long Term Capital Management (LTCM). Academics again sold the investment community on what at first appeared to be a good idea – exploiting anomalies identified through equilibrium-pricing models. The omitted variable in this case was potential risk from a combination of high leverage and low liquidity. By ignoring this, LTCM almost brought about a collapse of the world's financial system.

Momentum, however, appears safe from omitted variable risk. Momentum does not depend on esoteric markets, derivatives, leverage, or anything else out of the ordinary. As I show in my latest research paper, momentum has been highly effective when applied to the world's most liquid markets and most well-known asset classes.   

Another way of judging robustness is by seeing how well an approach holds up in multiple markets, over different time periods, and with different parameter values. Risk Parity (RP) is popular based on its attractive pro-forma performance record over the past ten years. RP puts an emphasis on fixed income assets, which have done well over this period. However, it is not logical for bonds to outperform equities indefinitely, since stocks are riskier than bonds and should command a positive risk premium. In line with this, RP portfolios are not as attractive when looking at pro-forma portfolios going back more than twenty years.

Momentum, on the other hand, is one of the most robust approaches in terms of its applicability and reliability. Following the 1993 seminal study by J&T, there have been nearly 400 published momentum papers, making it one of the most heavily researched finance topics over the past twenty years. Extensive academic research has shown that momentum works in virtually all markets and time periods, from Victorian ages up to the present.

The final way to judge investment worthiness is through real-time performance. This is often the primary criteria used to evaluate investments. On its own, however, it has drawbacks. First, the time to establish statistically meaningful results is longer than most people realize. Ken French has said that seventy years of past performance data may not be a sufficiently long performance record. Some analysts believe they are being diligent by requiring a one, three, or five year real time track record before they will consider an unfamiliar investment opportunity. However, as disclosure requirements point out, past performance may not be indicative of future results. This is especially true when dealing with shorter term track records and complicated investment models. Success over a handful of years may still be due to chance and a favorable set of market conditions. In fact, studies show that 3 to 5 years of past performance data is mean reverting. Assets that di especially well during that time frame are likely to disappoint going forward.

When someone questions how long momentum has been around, I point out the Cowles and Jones research findings from seventy-five years ago and the Levy results from forty-five years ago, along with the subsequent validations of their work. Their simple approaches are the underlying basis for momentum investing, even now. 

June 28, 2012

Time Series Momentum

Moskowitz, Ooi, and Pedersen recently posted a paper on SSRN called "Time Series Momentum." This same paper was published in last month's Journal of Financial Economics. Most momentum papers deal with cross-sectional momentum in which a security's out performance relative to its peers predicts future relative out performance. In time series momentum, a security's own past excess return predicts its future performance. This is functionally equivalent to "absolute momentum," that I described in my paper.

The authors examine time series momentum across equity indices, currencies, commodities, and bond futures. They find that a diversified portfolio using 12-month time series momentum with monthly rebalancing earns substantial abnormal returns and performs best during market extremes.

It is good to see validation of the absolute momentum concept. The best scenario, however, is a combination of both absolute and relative momentum as per my latest research paper. That way you can potentially benefit from relative strength momentum with respect to asset selection and the drawdown reduction that comes from absolute momentum.

May 14, 2012

Currencies, Emerging Markets, & Commodities


I am asked frequently why I do not include additional asset classes. This question probably stems from the popular, but erroneous, belief that more is always better. Some also believe that being more inclusive may reduce data snooping issues. However, there is method to my madness, and logical reasons why I exclude several commonly-used asset classes. 

First, as my latest research paper points out, high volatility is a success factor for momentum investing. Even though currencies, like most every other asset, benefit from momentum, their low volatility is one reason we exclude them from our portfolio. As cross rates, currencies also have little inherent risk premium. This contributes to their having low expected momentum returns. In Asness et al.(2009), "Value and Momentum Everywhere", currency returns and alphas were among the lowest of the assets they looked at.

An asset class that does have the requisite volatility is emerging market equity. Many investors feel that emerging markets merit being a separate asset class. However, there are unknown risks associated with these thin and illiquid markets. First, they have only about twenty years of price history. No one knows how emerging markets would have performed in October 1987, for example. It likely would not have been a pretty sight. Because they can suffer from sharp and rapid price declines, one often aggregates emerging markets into baskets that trade as a group. This stems from the belief that diversification among emerging markets will reduce their risk. However, baskets of emerging market stocks have contagion risk causing them to trade together as a whole. Aggregation and contagion can amplify and accentuate liquidity and other systemic risks. During the Russian debt crisis, markets as far away as Singapore suffered major outflows of capital and extreme price volatility.

Not only are correlations higher now among the emerging markets themselves, but they are also higher between emerging and developed markets. The following chart shows how correlations between emerging and EAFE markets have risen substantially over the past fifteen years. (The correlations between EAFE and US markets have also risen substantially, but that's another story.) The five-year rolling monthly correlations were below .30 in the 1990's. For the past three years, the correlations have remained steady at over .90. From a diversification point of view, emerging markets have lost some of their appeal.

correlation over time

Another volatile asset class that has attracted a large following in recent years is commodity futures. The logic here is that commodities act as an inflation hedge. Yet real estate, natural resource, other high tangible book value stocks, and even Treasury bills can serve that same purpose. The underlying problem with commodity futures is that they, like currencies, are not an asset class in the normal sense. Stocks and bonds exist as vehicles for raising capital. In return for this, investors can expect streams of payments from bonds or residual cash flow from equities. 

Commodity futures, on the other hand, are a zero sum game in which the profits and losses of contract buyers and sellers are equal, disregarding transaction costs. Futures contracts cease to exist on their expiration dates, and there is no wealth created in these transactions. Because gains and losses are symmetrical to the buyer and seller of a futures contract, one cannot say that the buyer, by taking on volatility, is entitled to a positive return, since the seller, by the same reasoning, would also be entitled to a fair return. One of them must lose for the other to gain.

In the past, buyers of commodity futures oftened enjoy a systematic positive return called the "roll yield" that flowed from hedgers to speculators. Hedgers were generally short sellers who felt a need to lay off risks of the unknown in their capital-intensive business. Speculators, who had no need to participate in commodity markets, were induced to take the other sides of these trades because of the roll premium they received.

However, all this has changed during the past 15 years. Using data through the 1990s that showed commodities to be a decent portfolio diversifier, academic papers, like the one by Gorton et al. in 2004, induced institutional investors to invest heavily in portfolios of passive commodity futures. Since then, endowments, pensions, hedge funds, risk parity programs, and the public have all scrambled to add over $300 billion of long commodity index futures to their portfolios.

Many pension programs now feel they should have 5-10% of their portfolio assets committed to commodities. This new group of speculators insists on going long regardless of price. They became increasingly large compared to the number of hedgers, so the overall roll yield dissipated and became negative. From 1969 to 1992, the roll return averaged 11% per year. Since 2001, it has averaged -6.6%. The odds are therefore stacked against investors who passively hold long commodity futures.

Several commodity indices, like the PowerShares DB Commodity Index or the Summerhaven United States Commodity Index, try to reduce the roll yield disadvantage by selectively seeking futures contracts, when possible, that still offer a positive roll premium.

However, all commodity index funds, regardless of their roll premium capture inclinations, face another formidable obstacle. These are the front-running costs from regularly rolling over their positions. They occur when others trade in front of the commodity futures rollover dates, then take profits afterwards. Zyiquan Mou of Columbia University estimates front-running costs at 3.6% annually from January 2000 through March 2010. JP Morgan Commodity Research reorted in 2009 that roll returns have put a drag of 3-4% per year on commodity index returns since 1991. These hidden costs can quickly take the wind out of the sails of commodities futures indices.

Rising correlations are another problem associated with commodities.  The average correlation coefficient between equities and commodities was -.27 from 1970 through 2003. It has risen into positive territory over the past five years. More importantly, during both the 1929 stock market crash and the 2008 financial crisis, the correlation between equities and commodities shot up to over 80%. Commodities diversification was lacking when it was needed the most. 
  
A 2011 research paper by Daskalaki & Skiadopoulos called "Should Investors Include Commodities in Their Portfolios After All? New Evidence," shows that the introduction of commodity instruments in a traditional stock/bond portfolio is no longer beneficial for a utility maximizing investor. This is based solely on past performance and not the additional reasons given above. From January 1975 through December 2011, the GSCI had an annual average return of 6.1% and standard deviation of 19.3%, versus a 7.7% return and 4.3% standard deviation for five year Treasury bonds. We see from several points of view now that passive commodity indices are no longer such an attractive addition to traditional stock/bond portfolios.

May 8, 2012

2012 NAAIM Wagner Awards

The 2012 NAAIM Wagner Awards for Advancements in Active Investment Management were announced yesterday by National Association of Active Investment Managers.  I'm in Atlanta now to accept the first place award and $10000 prize, and to present my  paper at their annual conference. I'm honored to be receiving this recognition for my research work.    
 
During the past 20 years there have been some 300 published research papers written about momentum. Most have dealt with momentum applied to individual stocks, bonds, commodities, or currencies. (All four publicly available, fully disclosed momentum funds apply momentum only to individual stocks or commodities.) Less than five percent of momentum research has looked at asset groups. Fewer still have applied momentum simultaneously to multiple asset or risk classes, even though this gives the best results.

My research paper last year (the second place winner of the 2011 NAAIM Wagner Award) used fixed income as a safe haven from riskier markets under appropriate market conditions. This was an ad hoc step in the right direction. What was really needed was a logical framework that systematically deals with regime change in order to better exploit momentum's profit-making potential. 

In my new paper, I believe I've accomplished this. You can download from NAAIM  my paper and all the other papers submitted for the Wagner awards, or you can download an updated version of my paper here. I welcome feedback and comments.
  

April 21, 2012

Momentum Crashes Revisited


Last December I did a blog post called "Is Momentum Really Dead?" in response to several research papers that purported to show that momentum had lost its edge. Those papers were written due to two unusual occurrences in which long/short stock momentum suffered large loses. The first time this happened was in July/Aug 1932. The second occurrence was in Mar/May 2009. The losses occurred on the short side during sharp market rebounds following periods of extreme, once-in-a-generation, market weakness. I showed that long only momentum and multi-asset momentum never experienced this crash.  

Momentum research continues to focus on long/short stock momentum. But long only momentum across asset or risk classes gives better results than long/short momentum using individual stocks. Furthermore, most investors do not care to invest from the short side.

There is a recent paper called Managing the Risk of Momentum by Barroso and Santa-Clara that  adjusts position size according to volatility. This eliminates the crash, substantially reduces drawdown, and gives a boost to the Sharpe ratio.Volatility based position sizing is similar to risk parity and is related to mean variance portfolio sizing.

There are, however, some potential drawbacks to volatility based position sizing in a multi-asset context. First, volatility based portfolios are often heavily concentrated in fixed income. This creates a new risk factor not accounted for in portfolio modeling. With interest rates at such low levels now, the risk of a bear market in bonds is greater than the probability of continued bull market appreciation. On the positive side, interest rates don't often mean revert. They instead tend to drift. There may still be some profits if long bond rates drop further.

The second reason to be cautious of volatility-based position sizing is that lower returns often accompany lower volatility. Although bonds have been a strong performer during the past 15 years, a portfolio heavy in fixed income securities has lower long-run expected returns than a portfolio that is oriented toward higher risk premia assets like equities. One can leverage a lower return fixed income  portfolio to boost returns, but some investors have constraints against the use of leverage. Leverage also increases a portfolio's interest rate, left tail, and correlation convergence risks. Increased leverage may be fine for hedge funds, but it has its drawbacks with respect to other accounts.





























March 12, 2012

Value and Momentum...Not Here

Asness' firm, AQR Research, created the first momentum mutual funds available to the general public (AMOMX, ASMOX, AIMOX). Asness also has a sense of humor, saying he has recurring nightmares about being hacked to death by a pack of rabid black swans. More money managers should have such nightmares.

In 2009, Asness and his colleagues released a working paper called "Value and Momentum Everywhere". The paper did a nice job showing that momentum works with different asset classes - foreign and U.S. stocks, country bonds and indices, commodities and currencies. Asness et al. also tried to show how value would have performed with these same assets. Identifying value with equities is pretty straight forward; book-to-market is commonly used. However, trying to find comparable value metrics for other assets is not so easily done. Nevertheless, Asness et al. reach the conclusion that value and momentum do well when mixed together 50/50, since the correlations between them are very weak. But they reach this conclusion using long/short portfolios of both momentum and value stocks. Very few actually invest this way. Long-only value and momentum portfolios are highly correlated because of the market factor. It is value and momentum premia that are uncorrelated.

Also, the Asness momentum results are not as good as the ones we get from momentum using asset classes and a combination of relative and absolute momentum.

Since determining non-equity value can be problematic, let's look at just equities to see what I mean. Below are the returns from January 1975 through December 2011 for the MSCI U.S. Value and MSCI EAFE Value indices, as well as a dual momentum strategy that is long either U.S. Treasury bills, the MSCI U.S. index, or the MSCI EAFE index based on 12 month momentum. Positions are rebalanced monthly. Transaction costs for momentum switches are negligible, with just 1.4 switches per year.


Dual Momentum
U.S. Value
EAFE Value
Annual Return
14.3
13.1
14.1
Annual Std Dev
12.4
15.1
17.7
Sharpe Ratio
0.66
0.47
0.45
Max Drawdown
-26.0
-54.6
-58.6
You can see that dual momentum approach outperforms the value indices. Let's now combine momentum with value as per Asness by weighting momentum 50% and each of the value indices 25%. Which results would you choose?


Dual Momentum
Momentum w/ Value 50/50
Annual Return
14.3
13.6
Annual Std Dev
12.4
12.3
Sharpe Ratio
.66
.61
Max Drawdown
-26.0
-37.8
The superiority of momentum over value is greater when you construct multi-asset dual momentum portfolios instead of using a portfolio that is limited to individual equities. Should there be value and momentum everywhere? I don't think so - not here anyway.

Results are hypothetical, are NOT an indicator of future results, and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Please see our Disclaimer page for more information.
 

February 8, 2012

Residual Momentum

"Residual Momentum" by David Blitz, Joop Huij and Martin Martens is available on SSRN. It was published last June in the Journal of Empirical Finance.

It's an interesting paper in that they determine momentum by the relative strength of the residuals after regressing stocks on market risk factors. They throw out beta and alpha and look only at the residuals, which represent each stock's idiosyncratic (non-market related) risk. In comparison to total return momentum, residual momentum earns the same return with about half the risk. I suspect  results would also have been good had the authors only removed market return as a risk factor, rather than also excluding size and value factors.

According to the authors, residual momentum is more consistent across different economic environments and has much lower drawdowns than total return momentum. The authors show that from 2000 through 2009, total return momentum had an average loss of 8.5% per year, while residual momentum gained an average of 4.5% per year.

I should point out that total return stock momentum has been stronger since then. Its average annual loss on the long side since 2000 is now around 0.5%. There are also better ways to use momentum than with individual stocks, as my momentum papers demonstrate.