Editor's note: This article was updated with revised charts on September 20, 2010.
Felix Salmon kicked up a storm of consternation when he reprinted the Bank of England’s chart comparing Momentum vs Value strategy returns showing that the momentum speculators $1 stake would have grown to over $50k while the value investor’s $1 stake would have shrunk to 11 cents.
I have replicated the momentum strategy using Shiller’s data and achieved the same results, but my conclusion is the opposite!
First of all, as Salmon himself requested, I have compared the returns to the buy & hold strategy. I have also converted the returns into current dollars to account for inflation. Buy & Hold underperformed dramatically during the entire period, but look what happens when we trace the relative performance in Chart 2. All of the out-performance occurred prior to 1950. Since then, the momentum strategy has mostly under-performed buy & hold, and would have done so by a very significant margin if not for some significant catching up between 2000-2002 and between 2007-2009.
Even the performance during these recent two periods is subject to some debate. The Shiller data base includes only monthly closing prices. To follow the momentum model as it is stipulated, you have to know the closing price at the end of the month before you can decide whether to go long or short the market for the next period, but the model assumes that you made this purchase or sale at the close of the previous month.
That is impossible to execute in real life. It is possible for a very diligent investor to have bought the [[SPY]] ETF in the after-market with very little slippage, or for an institution to have bought the futures, but it would have been very important to do so. If we use Tradestation’s back-testing tools, we are required to close any existing positions and open any new positions at market on the next day’s open. With this constraint, the momentum strategy leads to a small net loss of 0.4% during the past 13 years, compared to a 38% gain from the buy and hold strategy.
These comparisons do not include dividends, but it is impossible for dividends to improve the case for the momentum strategy because the buy & hold strategy receives all dividends, while the momentum strategy probably does not and probably has to pay out some of the dividends when it is short.
As for the value strategy, it is a straw dog. No value investor would ever short the market just because it is a point or two over-valued. At any rate, a dividend discount model requires a long-term forecast, and it is highly problematic to back-test with accuracy what any given analyst would have used as a long-term forecast in each and every month of the test. What we can do is use the historical P/E ratio and come up with a slightly more realistic formulation of what an actual value investor might really do, which is to own more of the market when it is extremely cheap, and own less when it is extremely expensive. I cannot emphasize enough that we must use of the word “extremely.” Valuation is a crude way to set a price target in any environment. A well thought out assessment leaves you with a range of plausible prices. The idea that valuation can ever give you a precise target is drivel, so a reasonable value investor would only divest when the range of plausible price targets leaves little room for upside.
There are many reasonable valuation strategies that one might try to construct, but to compare with a buy & hold strategy, we need to have a benchmark weighting of 100%. If we do this, then the only way to assess whether or not the valuation strategy works is to suggest a weighting of more than 100% when stocks are extremely under-valued and less than 100% when they are extremely over-valued. I have arbitrarily selected 150% and 50% for these targets. Whenever the over-valued signal tripped, I reduced exposure and did not return to the benchmark weighting until the value fell back to the level defined as “fair.” Whenever the under-valued signal was tripped, I increased the weighting and did not return to benchmark weighting until the value rose back to that defined as “fair.”
You could set whatever weightings you like, but the point is that if value works, then this construction will out-perform buy & hold by some amount. If you prefer to set the benchmark at 75%, raising the weighting to 100% when extremely undervalued and lowering to 50% when extremely over-valued, then just be sure that you compare this to a fixed 75% weighted return. It would not be fair or meaningful to compare this to a 100% buy & hold strategy.
We still have to define fair value. Between 1880 and 2010, the average P/E, based on Shiller’s definition of earnings, has been 15x. Note that this definition is distinctly different from Wall Street definitions as it includes expenses that normal people would usually conclude are expenses, and also because it is historical and not a forecast. But in 1880, no one could have known that 15 was going to be the magic number. In 1890, for example, the average P/E for the previous 10 years was 11x. It is easy for us to say now that stocks were a bargain back then, but there was no way to be certain of this in real time.
As an experiment, I defined fair values as a running average of several different time horizons. Over-valued and under-valued were defined variously as 1 to 2 standard deviations above or below the fair value line. The time windows I tested were rolling 10-year, 30-year, and all available data. In the later, for example, in 1884, only 4 years of data were available, while in 1904, the amount of data available graduated to 20 years.
The only value strategy that outperformed buy & hold significantly was the one that used all available data and just 1 standard deviation as the mark of over- or under-valued. Strategies based on shorter time horizons were badly damaged by a propensity to re-enter the market and use leverage too early and for too long following declines from over-valued levels.
Although this value-based strategy out-performs the buy & hold strategy by nearly 3-fold over the entire period, there are periods of massive, stunning under-performance that would probably have been intolerable to most investors. Two episodes of supposed undervaluation were the most notable. From 7/1915 to 7/1921, the model called for leverage the entire period, but stocks nonetheless declined, and the value strategy underperformed by 45%. From 7/1980 to 11/1985 the model called for leverage, but stocks declined, and the value strategy underperformed by 46%.
Even with the inclusion of these two disastrous periods, however, the use of leverage helped the portfolio over the full range of the time period that was tested and contributed about 30% of the total outperformance.
Currently, the market trades at 17.3x Shiller’s definition of EPS, while the historical average is only 15. The model remains 50% invested and 50% in bonds. The market would need to drop 12% to return the model to a fully invested stance.
This is not a definitive study and isn’t meant to answer every question that could be raised in relation to the value vs momentum issue, but hopefully, I’ve unraveled some of the mysteries.
Note: For periods in which the value strategy was less than 100% invested, I used the 10-year Treasury bond yield to compute returns of the uninvested portion. I did not have data on changes in principal for such bond investments, but the periods effected were typically so short that they are unlikely to have had a significant impact. If anything, this probably distorts against the strategy rather than in favor of it. Anyway, for this distortion, I apologize.
Disclosure: No positions