The Golden Cross and Other Lookbacks
Whenever we test something like the Golden Cross (50/200-day moving average crossovers), we are invariably asked “yeah, but what about 10/50-day crossovers, 50/100-day crossovers, etc.”
In this post I’m going to put those other moving average combinations to the test and try to answer which has been the best predictor of stock market performance.
The Test
In the four tables below I’ve tested 133 combinations of short and long-term moving averages trading the S&P 500 from 1932 to the present. CLICK TO ZOOM
In each test, I’ve assumed the investor went long the S&P 500 at today’s close when the short-term moving average crossed over the long-term today. I’m using simple moving averages (rather than exponential, etc.) but as we’ve shown, there isn’t a huge difference in performance with such long-term strategies.
Geek note: see end of post for assumptions about return on cash and trade frictions.
Results are broken out by four metrics: annualized return, Sharpe Ratio, average drawdown on any given day, and our own Consistency Metric.
The Results
In terms of both return and Sharpe Ratio, 1/150-day moving average crossovers have been the best performing (annual return = 10.5%, Sharpe = 0.58).
In terms of average drawdown, 65/175-day crossovers have been the best (-6.1%), and in terms of the Consistency Metric, 65/250-day crossovers have been the best (77.0%).
But all of that really misses the point.
In all four tables you’ll see a cluster of MA pairs (in green) that have performed best. All of those clusters cover more or less the same area (short-term MAs from 1 to 80-days and long-term MAs from 150 to 250-days), and any difference within those clusters is probably more random chance than anything else.
So I think the real point is that (over a long enough horizon) any debate over which MA combination is the best is silly. Any combination within those green clusters is probably as good as any other; 50/200-day crossovers are no better or worse than 10/150-day, 65/175-day, etc.
50/200-day crossovers (i.e. the Golden Cross) are nice round numbers right about in the middle of each cluster, and I think they make a good proxy for all other long-term MA crossover strategies.
Note: you can track the Golden Cross daily on the free State of the Market report.
[Click for a summary of our posts related to the Golden Cross]
Happy Trading,
ms
Test assumptions: (a) I’ve calculated the moving averages using the S&P 500 cash index (which traders generally use), but calculated returns based on daily dividend-adjusted data (dividends interpolated from quarterly data), (b) results frictionless (i.e. do not account for transaction costs/slippage) but could be closely reproduced in today’s market using mutual funds less part of an annual expense ratio, and (c) I’ve assumed a return on cash of half the nearest 13-week Treasury.
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Filed under: Trading Strategies, Trend-Following | 22 Comments
Michael:
Great job. Thank you.
When I first looked at the charts, I thought they were minutes not days. In processing this “flirt” I noticed most intraday MA “systems” should find some success around the 290 minute timeframe. If markets are self-similar, then moving average systems should be successful in period where the greatest number of participants are making decisions. For example, from 2 PM CST, commercials, Market Makers and Speculators are all viewing the close and potentially making decisions. A Moving Average system might help “find food” intraday during this period just like decisions are made around the 50 and 200 day MA.
What I am trying to say is that it’s just the context of how decisions are made: end of the day, the week, option expiration, month, year. The 50 MA and 200 MA make sense as participants need some time to make decisions on the quarterly and yearly basis.
This might not be “true” just reasonable expectation that social animals like reference points when making decisions…
Regards,
Tom
I might have missed the explanation in some other your postings, but how do you define “consistency” ?
Thanks
eb
RE to eb: that’s a pretty long, geeked out explanation. I’d suggest taking a look at the link in the post for more:
http://marketsci.wordpress.com/2010/05/25/measuring-the-%e2%80%9cconsistency%e2%80%9d-of-a-strategy/
michael
What is the sell signal? Short MA crosses below long MA?
RE to Ruschem: yes, shorter MA crosses below longer MA. michael
Hi Michael,
I’ve enjoyed this series, very timely.
I may have suggested this to you before, I can’t remember, but there’s a great academic paper by Mebane Faber where he looks at a similar idea, but somewhat different implementation.
The paper, “A Quantitative Approach to Tactical Asset Allocation”, can be downloaded here: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=962461
Faber’s approach just uses the crossing of the price line and the 10-month SMA, trading once a month, and he obtains outstanding results with it. The best part is that he then applies the same system to bonds, commodities and real estate, and obtains good results with all of these asset classes. As he says:
“Utilizing a monthly system since 1973, an investor would have been able to increase risk-adjusted returns by diversifying portfolio assets and employing a market-timing solution.
In addition, the investor would have also been able to sidestep many of the protracted
bear markets in various asset classes. Avoiding these massive losses would have resulted in equity-like returns with bond-like volatility and drawdown.”
The paper is double-spaced and full of charts, so it’s an easy read. But that doesn’t detract from it’s importance, in my view. I’d be interested in your take on it, and how that system compares to the Golden Cross and similar systems.
Your analysis is missing the point that trading patterns change over time. What worked 20 years ago does not work today. This is an over-simplification of automated trading algorithms. You need an algo which varies the optimal short and long average window sizes periodically.
RE to MT: it’s funny when someone says that given how much time I’ve spent talking about changing markets on this blog (readers know it’s a central theme here that I’ve talked about ad infinitum). But since you asked…
I disagree in this specific instance. The problem in this specific case is that you’re dealing with a strategy that trades so infrequently (ex. for 50/200-day xovers, 1.1/year). Trying to slice data into more and more recent chunks of time is going to be more and more subject to curve fit. The reason I provided the Consistency Metric is because the best you can do with a strategy that trades so infrequently is look for consistent performance over as long a period as possible.
Thanks for the smart comment (just please drop the snarkiness next time).
michael
Sorry, didn’t mean to be snarky. This is a dilemma I’ve came across quite a bit in my research. You’re right, trading that infrequently you cannot really optimize. Regimes nonetheless always change. I like your consistency metric, it addresses the problem somewhat.
I usually just read your posts and feel I do not have much to add. And again I feel this way but wanted to let you know how much I love your blog anyway. Your blog sits above the fold on my igoogle home page.
This post is so beautiful it made me want to cry.
Just so we are all clear, I didn’t.
Nothing like overoptimizing the hell out of something and making a pretty color coded table out of it to prove a point. It’s, uh um, It’s just beautiful man…
Notice the dark green line around the top of the Annualized Return graph. In other words, you don’t really need two MA crossover – the best results are concentrated around MA 1, which is price/slowMA crossover. It doesn’t get simpler than that, does it?
I have seen that in my extensive tests too (double crossover or MACD don’t add much). IMO MAs are the way to go, but I never was a day trader.
Thanks for the nice blog. Cheers!
Good point there, AI. It supports Faber’s method that I posted about above.
RE to AI: in terms of return/sharpe, yes.
I think a blended approach is the best of all worlds. For example, on the State of the Market report, I take an average of 1/150, 1/175, 1/200, 50/150, 50/175, 50/200 results to produce one % trend. Of course, this approach only makes sense when you don’t incur high per-transaction costs (ex. leveraged mutual funds, our weapon of choice).
michael
I’d second that and your reply to other comments suggesting that you should adapt the MA lengths based on trading regimes… Basically it is simply applying the principle diversification to systems/parameters, expecting some to perform better when others do not and vice-versa, therefore smoothing the equity curves (and possibly allowing you to increase leverage without dramatic drawdown figures).
If you check many big Trend Following CTAs/funds, this is what they seem to be doing.
Conquest Group have created a “Trend Following index/benchmark” – i talked about it here: http://www.automated-trading-system.com/betafication-alpha-commoditization-trend-following/ – and they apply the same principle by blending 20 different parameter values from short-term to long-term to the same system (Donchian Channel breakout) in order to smooth out the return and be sure to catch trends on “all” timeframes (since you cannot predict where they will arise)
MarketSci,
So, in the State of the Market report example, you basically follow the 21/150 (ave of the 6 crosses you listed)?
RE to drebg: no, I take the average result of those 6 and express it as a %. For example, if 2 of the 6 are long, the Golden Cross line reads 33% long. michael
I’m assuming the annualized returns in your charts assume that you also sold during the negative crossover (ie. the death cross), but wanted to confirm. Also wondering if you have ever done any testing with the moving averages where you bought the SH (the inverse of SPY) when you get the death cross? Once you got the golden cross you would sell SH and rebuy SPY? Seems like this would have worked great during the last 10-15 years with the 2 huge bear markets we have had.
jg
RE to jg: yes, assumes the investor moved to cash when the short MA crossed under the long MA. As to your second question, see this post:
http://marketsci.wordpress.com/2010/07/08/the-death-cross/
Shorting the death cross has not been a good idea over the long-term.
michael
I’ve uncovered a technique for eliminating the whipsaws that sometimes occur with the 50/200 strategy. I’m not an excel whiz by any means, but I know enough to get by and can brute force things when needed. I backtested my theory to 1961 and it beat buy/hold by 600%, had a max drawdown of < 8%, .7 trades/yr and 0 negative trades. The results seem to good to be true so I'm looking for someone with a more advanced spreadsheet to test the theory and confirm my results.
jg
As well as varying the periods, how about a few simple filters….
The UK-based FX commentator Ashraf Laidi in this video http://www.youtube.com/watch?v=wzWyscDS4YQ (Aug 4th), comments on his use of the Death Cross vs how others do it, using some recent Euro comment as an example: 50 falls below 100, AND both are above the 200 AND price is above the 200, hence more downside.
And vice versa I assume. Obviously this would reduce the number of trades. How easy to add these filters to your test? And can you test some main FX market too?
Cheers
Dave