# Combine Momentum with Low Volatility?

October 7, 2009 • **Posted in** Momentum Investing

A reader commented and requested: “I got a lot of ideas from Michael Carr’s recently published *Smarter Investing in Any Economy*, which focuses on momentum investing. One idea that the author demonstrated works well, and which I don’t recall having been discussed on your web site, is that one can greatly reduce drawdowns in momentum investing, with little impact to returns, by accounting for volatility when determining Relative Strength. For example, defining a low-volatility Relative Strength as the six month return divided by the standard deviation seems to give a much better risk-adjusted reward than Relative Strength alone. If you read the book some time, I’d be interesting in your views on this. The author seems very diligent in thorough, professional testing (good sample sizes, out-of-sample verification, etc).”

Here are a few observations (based only on excerpts from the book derived from search terms).

The following formal research is relevant to the author’s investigation of volatility-adjusted momentum, but it does not appear to address the volatility-momentum hypothesis directly. It offers an implication that adding a low-volatility screen to a momentum screen might help avoid stocks with the sharpest momentum reversals.

“Price Momentum and Idiosyncratic Volatility” – “We find that returns to momentum investing are higher among high idiosyncratic volatility (IVol) stocks, especially high IVol losers. Higher IVol stocks also experience quicker and larger reversals. The findings are consistent with momentum profits being attributable to underreaction to firm-specific information and with IVol limiting arbitrage of the momentum effect. We also find a positive time-series relation between momentum returns and aggregate IVol. Given the long-term rise in IVol, this result helps explain the persistence of momentum profits since Jegadeesh and Titman’s (1993) study.”

The description of *Smarter Investing in Any Economy* states:

“After running millions of relative strength calculations, Carr proves that relative strength investing works in any market climate. By strictly following his methodologies outlined in this book, you can more than double the returns of the S&P 500, with less risk… Computing advances, coupled with new ETFs that limit risk have made relative strength a viable strategy for long-term investors and day traders alike.”

“Millions” of calculations raises the flag of data snooping (mining) bias. Using the Amazon.com capability to search the book for references to “data mining” generates:

Page 26: “Many investment strategies are based upon data mining – sifting through the mountains of market data available to discover what worked in the past in the hopes that it will work in the future. RS [Relative Strength] is different than most data mining strategies, because economic theory and experience confirms that it works.”

Page 104: “To provide the best answer possible, we tested all possible combinations… In all, 1,320 combinations were tested. One problem that can occur when so many possibilities are tested is that the results from the top-performing strategy will be superior to all other test results because of a statistical fluke. Running hundreds of tests to identify trading rules is known as data mining. This term refers to the idea of sifting through large amounts of data…and identifying potentially useful, but accidental relationships within the data. The danger is that in a very large set of data, there is the possibility that extremely rare events will occur…and as such they are unlikely to be available to investors in the future.”

Page 105: “To guard against potential data mining, we will perform several tests to ensure the result is due to the underlying logic of the trading rules.”

Page 144: “Some investors think that optimization is similar to data mining. As discussed earlier, this is not true. An exercise in data mining would be to find the stocks that performed the best week to week and then go back and identify characteristics to explain why this occurred.”

Page 145: “We began our system design with solid underlying logic…and we then tested the logic under a variety of conditions. That is the opposite of data mining.”

These excerpts and other material available via the Amazon.com search function (e.g., a search on “normal distribution”) raise some cautions:

- The relationship between economic theory and empirical evidence is an uneasy one. The quality of empirical evidence is mixed. Momentum seems to be one of the more reliable asset price effects, but the assertion “economic theory and experience confirms that it works” is too strong. Browse “Blog Synthesis: Momentum Investing/Trading” for some different explanations of momentum and for examples of momentum variability/instability. It seems fair to say that luck is more pervasive than momentum.
- The degree to which studies of momentum for individual stocks translate to ETFs, which subsume the trading frictions of portfolio rebalancing (and add a management fee), is not obvious. ETFs have not been around long enough to support rigorous momentum testing.
- The author’s treatment of data mining appears to be incomplete. The effects of data mining bias are generally more systematic than rare event capture and spurious hypothesis acceptance. Running different kinds of tests helps, but parameter optimizations do generally impound data mining bias. For example, regarding the quote from Page 104, there are statistical methods to correct for the data mining bias impounded in outcomes from a specific number of tested combinations (in this case, 1,320). See the summaries of Chapters 6 and 8 in “
*Evidence-Based Technical Analysis: Applying the Scientific Method and Statistical Inference to Trading Signals*(Chapter-by-Chapter Review)”. - The author appears to rely on the normality of return distributions (e.g., in interpreting standard deviation), but there is much evidence that equity return distributions are not normal. See “
*The Black Swan: The Impact of the Highly Improbable*(Chapter-by-Chapter Review)”. The “wildness” of actual return distributions can disrupt trading strategies that make an assumption of normality.

Searches in the book via Amazon.com on “transaction costs” are not illuminating. Momentum strategies applied to individual stocks tend to involve substantial trading frictions from portfolio rebalancing. Assumptions about these frictions can be crucial in translating tests to realistic expectations.

Best guess is that combining low volatility with high momentum might offer an edge but that any edge will not be as large/reliable as indicated in the book.

Mal Williams reported the following test results for his momentum-based asset class rotation strategy (see “An Investor’s Asset Class Momentum Trading Strategy”):

“A few years ago, I tried the exact same strategy of dividing the momentum calculations by the standard deviation to arrive at a volatility-adjusted momentum calculation. In fact, I still have a column for the volatility adjusted momentum each month in my monthly report. Unfortunately, the results obtained from my COP [Class OutPerformance] Research model showed a significantly lower return without a commensurately lower portfolio volatility.”

Michael Carr, the author of *Smarter Investing in Any Economy*, declined an offer to append here any substantive response he might have to the above comments. He regards commenting on the book without reading it in its entirety as intellectually lazy, irresponsible and unprofessional.

The approach used above to develop a quick reaction to the book uses the Amazon.com search function to focus on practices and assumptions that may cause backtests to overstate real, out-of-sample performance of investing strategies.

Readers can decide for themselves whether the approach has merit in screening books for reading.

The reader posing the original question added:

“Since the author of the Class OutPerformance strategy got quite different results than Michael Carr, I suspect the differences are due to other factors then the just the momentum formula, such as how often was trading done, what was the buy signal, what was the sell signal, how many funds were held at once, and so forth. Here are some specifics from Carr’s book on how adjusting for volatility helped:

“The initial data set consisted of 33 Fidelity Select Sector Funds. The tests were run from 01/01/1990 through 12/31/2007. The relative strength in test 1 was the 26 week rate of change. The relative strength in test 2 was the 26 week rate of change divided by the 26 week standard deviation. Friday closing prices were used for ranking (Thursday if Friday was a holiday), with trades executed on the Monday open. Initially, the top three ranked funds were bought. They were held as long as they were in the top half (top 17 of 33) rank. If they dropped below 17th place, they were replaced by the current top ranked fund. The results were as follows:

Test 1: Annualized return = 20.10%, Max drawdown = -52.26%

Test 2: Annualized return = 18.93%, Max drawdown = -27.18%

“A number of other tests were done, showing that holding the top 3 funds, and selling if they dropped out of the top 50%, is not at all optimized. Turns out that holding the top single fund is best.

“Tests in which the fund set contained money market funds and bear funds did poorly (worse returns and higher risk than the S&P 500 Index). Much of the momentum benefit apparently depends on the having the right kinds of funds in the fund set. Anyway, I’d recommend reading the book because there is too much detail to easily summarize in a brief space. For example the author studies a wide variety of momentum formulas, both adjusted for risk and not, and shows that some of the classic ones are not very good.”

Note that the sample period is not very long for 26-week momentum measurement testing. It consists of only 18 years (about 36 completely independent 26-week intervals). There may have been external peculiarities (e.g., secular disinflation) that relate to the hypothesized anomaly (momentum).

Note also that when results are not robust to different parameter settings or other choices not excluded by the basic hypothesized anomaly, such as which funds to use, elevated concern about data snooping (mining) bias is warranted. In other words, when some combinations work and others do not, it is reasonable to worry whether the best combinations work mostly because of luck rather than persistent anomaly. As noted above, there are statistical techniques that help filter out the luck.

Subsequently, Michael Carr, the author of *Smarter Investing in Any Economy*, wrote **[items in bolded brackets added]**:

“Please stop commenting on my work and post this email only in its entirity

[sic]if you do so.“You wrote:

‘Note that the sample period is not very long for 26-week momentum measurement testing. It consists of only 18 years (about 36 completely independent 26-week intervals). There may have been external peculiarities (e.g., secular disinflation) that relate to the hypothesized anomaly (momentum).

‘Note also that when results are not robust to different parameter settings or other choices not excluded by the basic hypothesized anomaly, such as which funds to use, elevated concern about data snooping (mining) bias is warranted. In other words, when some combinations work and others do not, it is reasonable to worry whether the best combinations work mostly because of luck rather than persistent anomaly. As noted above, there are statistical techniques that help filter out the luck.’

“1) People don’t invest for independent 26-week cycles – they invest for the 18 years. And, the method I used follows standard academic protocols, as you’d know if youe

[sic]read the book.[The note relates to sample size relative to parameter measurement interval and the associated inherent reliability of inference, not investing assumptions. For some interesting discussions of how timeframes might affect inferences, see “Basic Equity Return Statistics” and “Why the Story on Predictability Keeps Changing”.]“2) I test for parameter sensitivity, as you’d know if you read the book.

[The note relates to the risk of data snooping bias when testing many parameter settings within rules, many rules or many combinations of rules. See the summary of Chapter 6 in “Evidence-Based Technical Analysis: Applying the Scientific Method and Statistical Inference to Trading Signals(Chapter-by-Chapter Review)” for elaboration.]“Your conclusions are half-baked and I will not offer substantial comments because you don’t just get to say dumb things and create work for those of us actually earning a living in the markets.

[The first amendment to the U.S. Constitution accommodates the saying of many dumb things. And, those encountering sayings they deem dumb have a choice to ignore them.]“Again, raed

[sic]the book or stop commenting.”

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