March 12, 2013

More Momentum Research Papers

As the advantages of momentum investing become more widely known, there is naturally more research being done to explore its potential. Some of that research, such as the Moskowitz, Ooi, and Pedersen paper "Time Series Momentum," has been excellent. We prefer to point out and discuss positive things like that, but since this is a blog about momentum, we feel an obligation to also talk about momentum research that may be a bit off base

At the end of last year, Keller and van Putten issued a paper called "Generalized Momentum and Flexible Asset Allocation." The authors applied absolute and relative momentum to the top 3 of 7 assets using data from 1998 through 2012. They developed their parameters on 8 years of data from 2005 through 2012, and validated their
 results on 7 years of additional data from 1998 through 2004.They call this an out-of-sample validation, yet they mention elsewhere in their paper that they determined the look back period and number of funds to invest in by looking at a longer span of data that includes the entire 1998 through 2012 period. To split a modest amount of data in half and call part of it an out-of-sample test is not correct. No one can tell how many times they may have repeated this procedure.

With respect to their results, eight years of data is a small sample size for determining  model parameters. Their results on 7 more years of data may look decent because momentum is so robust that most parameters over a certain range work out OK. However, back testing on eight years of data may not give what are the best parameter values.

Elsewhere, the authors' paper can also be confusing. Here is an example, "Sometimes our relative momentum is called relative strength (RS, see Faber 2010) or time series momentum (see Thomas 2012). We will also use the term return momentum to contrast better with volatility and correlation momentum."

Time series momentum is different from relative momentum (See my post Whatchmacallit). Furthermore, what they call volatility and correlation momentum has nothing to do with momentum. Momentum is about selecting assets based on persistence in performance, either against their peers (relative momentum) or against themselves over time (absolute momentum). The authors actually use volatility and correlation as ranking factors.

The authors end up ranking assets using arbitrary weights of 1.0, 0.5, and 0.5 for return momentum, volatility, and correlation, respectively. They do not explain how they came up with these weightings. I would be cautious about using the information in this paper without doing considerably more analysis and back testing.

"Time Series Momentum Versus Moving Average Trading Rules," by Marshall, Nguyen, and Visaltanachoti is an academic paper that attempts to determine if long-only momentum trading rules beat comparable moving average trading rules. They do this by comparing absolute momentum (which they call time series momentum) to comparable (according to them) moving averages of size based quintiles of US stocks using 10, 50, 100, and 200 trading day look-back periods. They have confidence in their comparisons because their correlations between momentum and moving average returns are generally in excess of 0.8. However, this may have something to do with their use of daily, rather than monthly, data. Since momentum is an intermediate term anomaly, most researchers study it using monthly returns.

We get correlations ranging from 0.45 to 0.47 when comparing 12-month absolute momentum monthly returns to a range of 4 to 32 month moving average monthly returns of the US stock market for the past 38 years. We use a range of moving average lengths because one cannot just use the same look-back period for momentum and moving averages and expect comparable results. The authors hint at this themselves when they say that moving averages enter and exit stocks sooner. Their paper also identifies the average holding periods for look-back intervals of 10, 50, 100 and 200 trading days as 8, 22, 31 and 47 days for moving average rules, and 10, 32, 46 and 83 days for momentum rules. Quicker entries and exits with moving averages means that their lengths should be longer if one expects their performance to match up with absolute momentum. Choosing the same look-back period does not make absolute momentum and moving averages comparable.

An old investment adage is that moving averages should be plotted half their length behind the current price on a stock chart. A half-span lag means that the look-back period for a moving average would be twice as long as the look-back period for momentum in order for the two to be roughly comparable.

Using twice the absolute momentum look-back period gives us a better equivalent moving average length. We can see that in Panel D from Table 2 of the paper:

 Table 2
Time-Series Momentum and Technical Analysis Performance and Comparison
         Q1 (Small)            Q2                Q3                Q4              Q5 (Large)
Panel D: Sharpe Ratios
10     0.47     0.38     0.41    0.31    0.42    0.28     0.37    0.25     0.16    0.04
50     0.37     0.26     0.30    0.21    0.28    0.22     0.25    0.19     0.12    0.08
100   0.27     0.19     0.22    0.15    0.21    0.18     0.19    0.16     0.12    0.11
200   0.20     0.13     0.17    0.12    0.17    0.15     0.19    0.14     0.13    0.10      

Stocks are in size-based quintiles from Q1 (small) to Q5 (large). Look-back periods from 10 to 200 days are in the first column. Reading across the rows, the Sharpe ratios are for moving average (MA) and absolute momentum (TSMOM) strategies using the same look-back period. We see, that except for Q5 (large), if we shift the MA strategies up one level so that their look-back periods are twice as long (or longer when going from 50 to 10) as the TSMOM look-back periods, we get an almost exact match of the Sharpe ratios. Based on using such shifted look-back periods that make MA and TSMOM strategies roughly equivalent, one can no longer say that portfolio-timing rules based on moving averages clearly outperform their absolute momentum counterparts.

March 9, 2013

Maximum Drawdown

There is a new research paper out by Wes Gray and Jack Vogel that is interesting not only to momentum investors but to all investors and researchers. The paper is "Using Maximum Drawdown to Capture Tail Risk." In it, Wes and Jack show that academic anomalies, identified by linear factor models (alpha), are often not great trading strategies.

Wes and Jack select eleven long/short anomalies from academic literature and show that a number of them, despite positive alphas and attractive Sharpe ratios, show very large drawdowns that would likely trigger margin calls and investor withdrawals at inopportune times. Six of the eleven strategies have drawdowns exceeding 50%, the three worst being 86.1%, 84.7%, and 83.5%. (Long/short stock momentum is the one with an 86% drawdown.).

Some researchers look at the Sortino ratio, which divides excess return by downside rather than total variability like the Sharpe ratio. Incorporating upside variability may be useful though, especially when evaluating investment opportunities with similar downside volatility.  Neither the Sharpe nor the Sortino ratio considers the full extent of downside exposure in the extreme left tail of a distribution..

Wes and Jack say it is important for researchers and investors to consider this tail risk. They suggest looking at the maximum peak-to-valley loss (drawdown) associated with a time series as a relatively easy way to do this. They have an explanatory video on their Turnkey Analyst blog, along with the Excel VBA macro code and a spreadsheet for calculating maximum drawdown.

Of course, maximum drawdown is not perfect as a risk measure. It is not amenable to traditional statistical analysis, such as confidence intervals. (But given the stochastic nature of financial markets, traditional statistical analysis may not be so accurate anyway.) Maximum drawdown is also time dependent – the longer a track record, the more likely that maximum drawdown will increase. Drawdown frequency, as well as magnitude, is also important. Furthermore, maximum drawdown shows only a single past event that may be a chance occurrence and not representative of what the future may bring.

Other ways of looking at tail risk attempt to deal with these concerns. Conditional value at risk (CVAR) shows what a drawdown will most likely look like given an extreme event. Extreme value theory (EVT) identifies large deviations from the medians of probability distributions. Both these approaches are computationally challenging and rarely found in finance literature. (I used to compute CVAR myself, but didn’t find it as intuitively appealing as maximum drawdown.)

Wes and Jack have done a service in showing how the usual ways of evaluating investment opportunities, such as alpha and Sharpe ratios, can be seriously lacking. Neither alpha, nor standard deviation, nor maximum drawdown, represent a complete measure of investment risk.

Maximum drawdown is good in that it gives some indication of extreme tail risk. However, I also look more broadly at strategy drawdown versus benchmarks drawdown under a variety of adverse conditions.

I examine interquartile ranges and extreme outliers using box plots of the data. You can see all four of these methods at work in my dual momentum paper. I hope other researchers catch on soon and start presenting more than just Sharpe ratio or alpha as their objective function. These often mean little on their own in terms of true risk exposure. Tail risk is important to investors, and it should also matter to researchers. 

March 6, 2013


In 1967, Bob Levy came up with the term relative strength in his paper "Relative Strength as a Criterion for Investment Selection." He soon afterwards wrote a book called The Relative Strength Concept of Stock Price Forecasting. Levy showed that stocks which outperformed the market over a pre-specified time period exhibited performance that tended to persist. Relative strength was a good name for this form of investing. When academics got a hold of the relative strength concept in the 1990s, they renamed it momentum. This was unfortunate, since momentum among practitioners also means investing in anything that shows price strength. I still run across this when uninformed investors want to dismiss momentum as something left over from the dotcom days.

In the early days, academics further defined momentum as "cross-sectional," since it was studied by sectioning the stock market into deciles or quintiles and comparing the top relative strength "winners" to the bottom relative strength "losers".

Recently, other researchers have discovered another form of momentum that looks at an asset's performance against its own past price action rather than against the past performance of its peers. This form of momentum was a key feature of my 2012 paper "Risk Premia Harvesting through Dual Momentum." I called it absolute momentum in contrast to relative momentum.

The researchers at AQR were also working on a paper published last year called "Time Series Momentum." To me, time series means something like ARMA or ARCH modeling, in which one studies a series of past prices. Moving averages are a time series. However, in absolute momentum one usually compares the current price to only a single past price in order to determine if the trend is up or down. I also prefer the term absolute momentum because practitioners are used to hearing about relative returns and absolute returns. Relative momentum and absolute momentum follow the same logic.

Some academics distinguish between only two types of momentum, what they call cross-sectional and time series momentum. In order to not confuse matters further, we will continue to use the terms relative and absolute momentum. You should be able to follow all the momentum players now without a program. Remember, a rose by any other name….