With this post I want to share some very interesting research insight from the world of correlation. Correlation metrics get a lot of attention during severe bear markets. That’s because most markets go down together, hence correlation is rising among the various markets and asset classes. Conventional market wisdom says: high correlation among markets and assets classes is a sign of fear. But what about the opposite? So I wanted to understand if conventional wisdom is right and what short-term impact correlation has on the US stock market and how to use this in my trading.

### Background

- SPY is used as a proxy to trade the US stock market.
- Data is adjusted for cash dividends and splits
- Tests don’t consider trading cost / slippage
- History: January 1993 – February 2012

I calculated correlation among all SP500 members (survivorship bias free) using daily bars. The calculation is conducted after the last trading day of the week has finished, that’s most likely Friday. The actual trade is taken the next day @OPEN, that’s most likely Monday. The trade is then held until next week (Monday). No other stops or exists are used.

In the second column of each test you find a benchmark value. That is the strategy as described until here without any filter or market timing components. So we end up with almost 1000 trades, hence the benchmark strategy is 100% invested. The following columns show weekly returns (=weekly trades) under different correlation conditions.

### Test 1: Looking at absolute correlation levels

The test is dividing the correlation measure into quartiles. We see very little difference among the first two buckets where the market is in 90+% of the time. Though high (peak ) correlation has a positive impact on next week’s performance.

### Test 2: Higher or lower correlation

For this test we look into falling or rising correlation regardless of it’s absolute level. Friday’s level compared to previous day (t-1) or five days ago (t-5). There is a significant difference in performance and risk adjusted measures.

Weeks after falling correlation are way better than weeks after rising correlation!

### Test 3: Using relative strength or weakness

In the final test we look at the RSI2 level of the average market correlation. RSI2 has the advantage that it’s less binary compared to looking at absolute changes to previous days. I think the results are outstanding! Being invested in weeks after RSI2 is bellow 25 delivered higher returns than the benchmark strategy while only being invested 38% of the time. Furthermore volatility is reduced significantly. The benchmark strategy had a max. drawdown of about 55% while the RSI2<25 strategy had 21% only.

### A picture says more than thousands word

Now the pessimists among us might ask if this is time stable?

### Let me know what YOU think about this test or how YOU use correlation in your trading.

This post is based on research that I’ve turned into an important component of my Portfolio Trader trading systems. Get a 30days trial of Portfolio Trader for free (here).

Should you be interested in a weekly correlation outlook ,then read my weekly 360° view here.

# Frank

Hi Frank, very interesting analysis. Great application of RSI() and promising results. I would like to learn from you on this topic and see if I can contribute. So I am trying to replicate your analysis. How do you calculate the correlation of the S&P components? Do you sum the correlations of all potential pair-combinations and average or do you use average of the correlation between component and SPY?

Thanks again for sharing!

Michel

Hello QD,

I use correlation among all SP500 members (correlation matrix)

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Regards,

Frank

Hi Frank,

Sorry but I need more clarification from your side in order to understand what you do.

You wrote:

“I use correlation among all SP500 members (correlation matrix)”

How do you get a value? Do you mean you make a correlation matrix which consists of (500*499)/2 unique values, you add them up and divide by (500*499/2) and you get a value this way?

Thank you in advance.

Hello Capone,

that’s about right. Correlation among all holdings divided by number of calculations.

Frank

Hi Frank, long time! Great analysis as usual, thanks.

Ramon

Frank, some questions please. Are you using RSI2 of the correlation on daily bars or weekly bars? i.e. are the inputs for the RSI2 calculation covering 2 weekly bars, or two daily bars?

Also, I wonder if using implied correlations as opposed to realised correlations will make a difference? CBOE has some indices KCJ, ICJ, etc, that implied correlations from 2009 onwards . . .

Thanks!

Hello Ramon,

good to see you here! Hope you are alright.

I take the RSI2 value of the correlation at the most recent bar. All calculations are done using DAILY bars, though the trades are hold for a week.

Correlation is also calculated using daily bars.

Interesting to hear about implied correlation, need to check it out. Thanks for the hint.

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#Frank

Really interesting results. Thanks!

Hello Jared,

Thanks for your feedback!

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#Frank

Frank, nice work. Just one question: Are the results significantly different on other rotating days compared to Fridays?

Cheers

Andreas

Hello Andreas,

Actually the point is: these are not trades on Friday’s, I take the signal from Friday’s close and execute the trade on Monday. That’s important, because it will be difficult to calculate that correlation matrix right at the close.

I have not tested this on other days, as this is my way of working. I’ve made other tests taking the signal right after it occurred (on any weekday), the findings remain valid. Might have another post soon about daily trading and correlation.

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#Frank

Given that you analyze correlations of individual stocks vs. SPX index, it probably makes sense to attempt an analysis that goes long the stock and short SPY. I would imagine that these results would bear much higher significance

Also: Rising, not raising ;)

Hi Nik,

thanks for your comments … already corrected it!

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#Frank

Hi Frank,

May I ask what is the look back period you use for the correlation calculation?

Cheers

Hello Pablo,

simple 20 days.

Regards,

Frank

Well, I would say the following statement, although often heard, is plain wrong: “That’s because most markets go down together, hence correlation is rising among the various markets and asset classes.”

The first point is that correlation is the tendency for markets to move together around their trend, not the fact they go up or down together on a certain period of time. The paper here below nails down the facts pretty well.

papers.ssrn.com/sol3/papers.cfm?abstract_id=1808267

The second point being that correlation is NOT equivalent to conditional correlation. Correlation conditional on large variance returns is indeed higher, but this is a natural mathematical thing and would apply to plain random data as described in the following paper.

http://www.federalreserve.gov/pubs/ifdp/1997/597/ifdp597.pdf

Hope this brings my small brick to the wall.

Best

Hello Thierry,

Thanks for your comment – very much appreciated!

Already downloaded the papers…

Have a great week.

Frank

Hello Thierry,

spent some time reading the papers you pointed me to…

Have you found a better why to measure dependence of two time series?

Frank

Hi Frank,

I have been playing with a measure on my own, but I have not found a use for it yet. I call it degree of synchronization and it is based on the concept that “synchronized” securities will tend to have common turning points. I would be happy to give you more details if you are interested.

Cheers,

Pablo

Hi Pablo,

sure,s ent me an email on hassler.blog (at) gmail.com

Best,

Frank

Great post, Frank.

“correlation is the tendency for markets to move together around their trend, not the fact they go up or down together on a certain period of time”… I totally agree. I wonder if that actually might be what’s behind the good results that are happening here. One question might be “do markets that are falling apart tend to move together around their trend”? Point being, it’s possible you might not want a better measure of the dependence of two time series – you might just want the measure you have with regards to the deviations. Two cents, anyway. Good study, Frank – appreciate your work.

Tom C

Hello Tom,

Thanks for your feedback. The two papers (link in one of the first comments) provide excellent insight about the problem the correlation calculation has! During this/next week I want to look into that.

Have you got a better measure?

Frank

No, Frank, I don’t…that was exactly my point…your measure as is appears to be predictive in giving me a trading edge!!! Why would I want a better measure, regardless of the “problem” the correlation measure has?

Tom C

Do you have similar result in other index ? With 0.47% average, do u think it is tradable?

Hello Ellis,

i only tested this on SP100 and SP500, works on both.

This isn’t a system in it self. You should rather consider this as a filter when conditions are favourable.

Frank