No. of Recommendations: 126
It's been a while since we were given a rundown on the RRS family of stock screens, and not exactly an uneventful time at that. I've been sitting for a while on the necessary data to do this, waiting until I could add it to the "new backtester" that keeps getting further and further behind. So I'm taking another tack on that and just run the RRS screens on their own.

These tests were run from 1986 through 2002 with holding 5 stocks for 21 days, with staggered start dates. The importance of start-day variation has been shown before, and I'm not going to go into it here (as my program doesn't measured it). I've included start dates up to 31 Dec 2002, so Jan 1986 and Jan 2003 are both about half-represented in the test. I could have gone earlier, back to the backtester's start date of 1969, but the 86-02 range is so familiar I decoded to stick with it. The input set of stocks is the T1 list (except where noted) from the most recent available month, as defined by the backtester calendar. Even where I have access to weekly Timeliness data, I kept with monthly stocks for consistency.

Basic Results

RRS CAGR GSD

21 23.49 50.64
42 32.14 52.16
63 30.82 52.67
126 38.62 53.74
189 42.30 55.03
252 33.55 55.30
Not shown here is a pretty smooth progression of CAGRs, peaking around the two highest shown, 126 and 189, and falling off at either end. I got downright poor results with a both 2-week and 2-year lookbacks, and the very best I found was a 160-day lookback, with a 45% CAGR.

There's little variation in the GSDs. I've found this same 50-55% GSD range in almost all of the backtests I've done with this data, and won't generally report GSDs for that reason.

Projected RRS

A variation of RRS I came up with a while is "Projected RRS", which projects a future price from the RRS regression line, and chooses the stocks that would rise the most if that price were reached. Based on Robbie's earlier work, I've been running a screen with a 42-day lookback and a 21-day (one month) projection period. This turned out to be not only a good variation, but one of the few workable ones. A few samples illustrate this:

RRS CAGR

21p21 28.15
42p21 35.69
63p21 27.44
189p21 24.04

42p5 30.37
42p10 32.02
42p21 35.69
42p42 35.45
42p126 33.64
42p252 33.10
42 32.14
Using the natural 21-day lookahead for 21-day holds, only the 21 and 42 day lookbacks showed an improvement over the plain RRS screens. With longer RRS lookbacks, the 21-day projection actually hurts performance by quite a bit.

The two factors in the ProjRRS screens are the RRS line and the current price. As the lookahead period gets longer, the current price becomes less important, with an infinite lookahead equivalent to regular RRS. As the second set of runs shows, the difference is small even at the best. Looking for this best ProjRRS, I found 35p25 with a 37% CAGR (vs 33% for RRS35).

Projected RRS doesn't seem to have much value, except that the few variations that work will typically pick different stocks than regular RRS. The stocks' current prices relative to the RRS line generally aren't as good a predictor of future performance as the RRS lines themselves.

Sigma Adjustments

Part of the orginal concept of the exponential screens, the idea of adding (or subtracting) the stock's volatility to the RRS slope is supposed to present "optimistic" or "pessimistic" versions of the screens. Typically, one or two (or more) times the sigma is added to or subtracted from the slope. This sigma is sometimes using the same lookback as the RRS, and sometimes using a 1-year (252-day) lookback. For brevity, I'll show only the 2-sigma adjustments; the 1-sigma numbers are in a similar vein, and I didn't really look into others.

RRS CAGR -2s +2s -2s252 +2s252

21 23.49 20.46 25.59 21.98 23.41
42 32.14 31.71 31.81 32.37 30.23
63 30.82 31.98 28.36 35.65 28.23
126 38.62 33.83 36.47 29.05 35.59
189 42.30 36.37 37.14 38.20 38.00
252 33.55 32.00 29.50 32.00 29.50
As was the case with Projected RRS, there may be some help from sigma adjustments in the lower RRS lookbacks, but it degrades performance when added to longer-lookback screens. It's not clear whether it's better to add or subtract sigmas, or whether it's better to use the RRS's lookback or a 252-day sigma: RRS21 and RRS63 offer opposing data.

It appears to me that simga is like the current price: RRS is better off without it, though it may offer a different selection for shorter lookbacks. One cited reason for negative sigma adjustment didn't appear: the GSDs remain in the 50-55% range.

Drop High

Dropping the highest recent (i.e. 5-day) performers from consideration before picking stocks is supposed to protect a screen from reversion to the mean that often goes with large fast moves. I tried dropping the top 5 and 10 best performers over the last week, and picking RRS screens from the remaining 95 or 90 stocks.

RRS CAGR DH5 DH10

21 23.49 22.33 22.65
42 32.14 31.44 31.68
63 30.82 30.52 29.86
126 38.62 38.45 38.77
189 42.30 41.40 42.27
252 33.55 33.35 34.03
The trend here, as much as there is one, is opposite the last two tweaks: the longer-lookback screens benefit from drop-high. This seems reasonable, as the 5-day performance accounts for a bigger chunk of the whole smaller lookbacks. Where there are gains, they're small: this looks like another case of a metric that pales in comparison to RRS.

Grabbing the Dogs

A variation of the "drop high" strategy is "grabbing the dogs". While the steps are the same, the meaning changes dramatically. Instead of excluding the best recent movers for fear of mean reversion, only the worst recent movers are considered with hopes to take advantage of the same phenomenon. I looked at selecting the 10 and 25 worst 5-day RRS, and selecting the top 5 from those.

RRS CAGR B10 B25

21 23.49 23.96 22.80
42 32.14 26.39 30.34
63 30.82 29.80 32.86
126 38.62 28.74 33.99
189 42.30 29.71 33.45
252 33.55 28.21 29.88
This wasn't generally helpful, but has the same advantage of ProjRRS that a different set of stocks are considered. Especially in the bottom-10 case, the first step dominates the screen with the final sort only choosing the better half.

A more drastic approach than this is going only with the dogs and no final sort. Going only with the bottom 5 5-day performers gives a respectable (though not really good) CAGR of 21%. Since this is a screen mean to capture short-term reversion, I looked at shorter holding periods of this dogs-only screen:

Hold CAGR

21 21.43
5 71.05
2 119.29
1 159.26
These would be amazing results, were it not for costs. Assuming a conservative 0.5 round-trip spread and commission cost, the best real CAGR would be the weekly hold at 31.6%. the 2-day CAGR of 17.8% barely beats the monthly 14.4%, and the daily hold would actually lose money at -26.1%. This assumes a full turnover every period, but this isn't too far from the reality of this short-term screen. If only it weren't for costs.

Timeliness 2

Including both Timeliness 1 and 2 stocks gives a broader base of stocks to choose from, at the expense of lower quality stocks. This tradeoff adds up to similar results to Timeliness 1 only, though not quite as good. My hope was that the greater selection would allow greater depth, so I tested both 5-stock and 10-stock screens:

RRS ranks T1 T1-2

21 1-5 23.49 25.02
1-10 18.54 21.48
42 1-5 32.14 31.14
1-10 27.21 31.56
63 1-5 30.82 27.47
1-10 29.20 28.39
126 1-5 38.62 34.43
1-10 31.65 28.02
189 1-5 42.30 30.26
1-10 36.31 32.42
252 1-5 33.55 33.21
1-10 31.96 31.66
The T1-2 versions of many screens do better with 10 stocks, but the T1-only screens still manage to win all but the short lookbacks. The better performance still belongs to the higher Timeliness.

RS vs. RRS

The origin of the RRS screen family lies in the venerable Relative Strength screens. These much simpler screens took only the prices at the endpoints of the lookback periods, i.e. "now and then", and ignored everything in-between. The expectation of the RRS screens is that by examining not only 2 data points, but every closing price available, more data would lead to a more valid measurement, and hence to better results.

Days RS RRS

21 19.99 23.49
63 29.33 30.82
126 35.42 38.62
252 29.49 33.55
Whew! There'd be problems if plain ol' RS won. Before the days of RRS, there were other attempts to make relative strength depend on more than just two endpoints, using different combinations of the "available" lookbacks. Even though it's overkill, I've compared these to RRS counterparts.

Days RS RRS

RSW 31.73 38.72
FOG 30.47 17.61
RS2020 26.41 30.28
Overlap 31.95 35.40
Even the composite RS screens were improved with one notable exception. RS-FOG rewards high 1-year growth, but heavily penalizes more recent growth. This gives some of the same effect as ProjRRS, where a relatively low current price is an asset. The idea of penalizing recent growth via RRS, which doesn't overly care about endoints, doesn't work out: the return is nearly cut in half.

These aren't the RS returns you're used to, which come from the monthly backtests. These RS screens, like the RRS screens they're compared to, use 21-day holds and the spread out start dates to ensure maximum use of the data. This generally leads to big differences.

Screen Daily Monthly Diff.

RS4 19.99 29.18 -9.19
RS13 29.33 38.50 -9.17
RS26 35.42 35.72 -0.30
RS52 29.49 36.26 -6.77

RSW 31.73 31.09 +0.64
RSFOG 30.47 37.20 -6.73
RS2020 26.41 49.16 -22.75
Overlap 31.95 40.82 -8.87
RS26 and RSW performed nearly the same in the daily and monthly tests, RS2020 completely fell down, and the rest test 5-10% lower given daily data. This general lower trend has two possible explanations (that I can think of off hand):
1. The monthly tests always use the freshest Timeliness ratings.
2. Lag (see below)
3. Chance.
I suspect the third reason explains most of this. I also think part of the failure of RS2020 under daily scrutiny comes from its late invention, and the constraints of finding a screen that "made it" in 2000 and 2001. This is ammunition to suspect other high-performing screens of recent invention.

I've found that with most RRS screens, the best performance comes from a portfolio of 5 stocks. With the plain RS screens, the sweet spot is 3 stocks: reducing from 5 to 3 stocks will add an average of 1.89% to RS returns, while RRS screens improve only 0.06% in an uneven mix.

Lag

A more passive approach to the mean reversion problem is simply to wait it out. This is lag, an important component of RS screens: as with reducing from 5 to three stocks, the introduction of a 2-day lag adds an average of 2% to an RS-based screen. As with the other reversion prevention strategies, RRS screens don'e gain much from lag:

RRS CAGR Lag 1 Lag 2 Lag 5

21 23.49 25.68 27.54 29.60
42 32.14 32.22 32.14 29.82
63 30.82 30.89 30.84 29.43
126 38.62 38.40 38.02 37.28
189 42.30 41.92 41.44 39.37
252 33.55 32.98 32.32 30.51
The longer the lookback, the less important the current price is, and the less lagging it helps. The shorter lookbacks, which are helped by lag, are also the ones helped by sigma adjustment, projection, and drop-high.

Switching

Index-based screen switching is one of the more contraversial ways we've been trying to beat the bear market. One switch I've particularly liked used RSFOG when last month's index was high, and RS4 when it was low. Not only did its reasoning sound good (tied to this whole mean reversion thing), but a 3-stock version of this based on the S&P 500 and a 1% cutoff gives a 66% CAGR, substantially beating out RSFOG's 35% and RS4's 42%. As the proof of out ideas is in the backtest, this was a proven success. Since I can get daily index data as easily as daily stock data, I can run this same switch daily. To better match the backtester's conditions, I'm using the plain RS screens, with a plain RS index measurement and a 2-day lag, though changing to RRS or no lag gives a similar outcome.

Screen CAGR

RS4 29.73
RSFOG 29.76

Switch 31.96
That's a long ways from the improvement the monthly backtest give, and in fact other conditions (such as 5 stocks) gives a switch CAGR between the two input screens' CAGRs; the only reason it didn't happen here was probably the almost identical gains of the two input screens.

Not to be cowed by a bad backtest run, I went with a RRS counterpart to this switch. For my high-index "defensive" screen, I went with RRS42p21, and for my "aggressive" low-index screen RRS126; these were chosen partly for their closely matched CAGRs. Since this is an RRS test, I'll switch on RRS21.

Screen CAGR

42p21 35.69
126 38.62

Switch 42.24
Again, not bad, and not particularly good; it's about the same CAGR as a non-switched RRS189. Other tests with different screens, and different index lookback lengths did well sometimes, and poorly others, but never too far from the average of the input screens.

The evidence doesn't give me any reason to believe in index switching.

Timeliness 5 and shorting

If RRS on Timeliness 1 stocks can find good investments, then (negative) RRS on Timeliness 5 stocks should find good shorts.

RRS CAGR

21 -0.39
42 0.95
63 -0.58
126 -10.72
189 -13.79
252 -12.49
These actually started out as pretty good (bad) CAGRs, in the -30% range, until I took out the under-$5 stocks. The problem is that straight RRS tends to find stocks that have aloready fallen so low as to be unshortable. I found better success with projected RRS:

RRS CAGR

d42p21 -7.87
d63p21 -13.43
d126p21 -23.26
d189p21 -23.47
Unlike the long screens, a longer-lookback projection seems to do better for shorting.

A promising RS-based short screen in the monthly backtests is the "Dead Cat Bounce", which is the counterpart of T1's equally colorfully named "Grabbing the Dogs". The idea is that the best-performing T5 stocks are still losers, ready to sink back down to where they were before. This performs about as well as the better ProjRRS variations, with a -21.62% CAGR.

What Have You Done For Me Lately?

The past few years have been tough on MI screens, and RRS is no exception. Many of the screens list here have lost money in 2000-2002. Here's a sampling:

RRS 2000 2001 2002

21 5.82 -31.02 -17.62
42 -16.38 -30.84 -16.68
63 -27.91 -29.51 -8.07
126 8.90 27.62 6.59
189 24.67 12.90 -9.53
252 42.86 -3.90 18.02

63-2s252 -1.56 -9.62 -8.94
189-2s 28.47 11.75 -9.80
42p21 -18.33 -3.92 -21.54
The survivor is RRS126, with a gain in all three of these hard years. If you've seen RS26's preformance in the backtester, this may be unexpected, as RS26 (a close cousin to RRS126) lost 32% in both 2000 and 2001. But this turns out to be an illusion: according to daily data, it gained 3% in 2000 and lost 3% in 2001. That's an example of the variance you get with just one data point per month.

Another example is in the last two screens listed, RRS189-2s and RRS42p21. I included the first in this list mostly to demonstrate that sigma adjustment made as little difference in the bear market as elsewhere (though it made a big difference to RRS63). But I also run both these screens in my own portfolio. The first, which did pretty well lately, was one of my own worst performers, and the second, with its bad 2002 loss, has been the year's brightest star for me. This made me suspicious enough to hand-check my data-daily test results, but the right stocks are indeed being picked and the right gains applied. It just comes down to luck: I was apparently luckier with my ProjRRS than RRS189-2s. So if you're running some of the screens mentioned in this post, and your results are very different, there's a good chance everything is as it should be.

Conclusion

RRS continues to work well. Various tweaks may make some screens work better, but the best strategy is generally to leave it alone. Daily data is more valuable than monthly.

- Jamie
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