Pairs trading and Beta coefficient

[leonarda]

Hi,
I am new to trading (8 months) and still learning fast. I am looking at building a Stock Pairs Trading strategy using my own custom software. One of the issues I can't find much of an answer for in the forums is Pairs selection and Beta analysis. Say take for example at the moment BTEM.L and TEM.L are well correlated and nearly 2 stddev from their mean, shown good mean revertion in the past, but their Betas are:
BTEM.L 0.90
TEM.L 1.58
That means if BTEM.L moves 1% with the Index then TEM.L will move 1.75%, obviously not market neutral. So a simple fix to that would be to Position size accordingly to make it neutral. Is that a correct/good thing to do?, or is there a limit to the difference in Betas that would deem a good pair? I can see over the very short term 1-3 days it's probably Ok, but say the trade lasts 7 days or so and volitility goes back and forth could such a difference in Betas start to become non-market neutral? say the market trends in one direction over that 7 days...

Thanks

 

[Martinghoul]

I would think it would be better to trade using the weights suggested by your mean reversion framework. This will probably result in some exposure to the outright mkt (as your weights are not necessarily in line with your betas), which you can hedge by going long or short the index.

I am not an expert in equities, I might add, but that's how I would approach it.

 

[leonarda]

I would think it would be better to trade using the weights suggested by your mean reversion framework. This will probably result in some exposure to the outright mkt (as your weights are not necessarily in line with your betas), which you can hedge by going long or short the index.

I am not an expert in equities, I might add, but that's how I would approach it.

Interesting idea. My mean reversion statistics are done simply by backtesting the performance of the pair over the past year. I get a value that represents how good it is at reverting. Are you saying I should perhaps analyse the pairs movement in backtesting during a mean reversion, to gauge the relative price movement? ie.calculate a price swing ratio for price movement during a backtested trade?

Thanks

 

[Rhody Trader]

I'm with Martinghoul on this one. Beta is a correlation to the market index while you're more interested in correlations against each other. Mathematically, if you're using the same lookback periods, the ratio of the betas should equate to the direct correlation, of course.

 

[leonarda]

I'm with Martinghoul on this one. Beta is a correlation to the market index while you're more interested in correlations against each other. Mathematically, if you're using the same lookback periods, the ratio of the betas should equate to the direct correlation, of course.

Hi,
I think in essence you're right. However, I'm not sure that last sentence is quite correct, Correlation measures the degree in which one Stock mirrors another but not a comparison of magnitude, i.e. one stock could always move exactly twice the percentage of another, and they would thus be 100% correlated, but the ratios of their Betas to the market would be 1/2.

In reading articles i've found it seems Beta is more of a degree of volatility of a Stock to the market index, but usually measured over a 5 year or so period with monthly prices based on Stock returns. So for pair trading on a 3 to 8 day period Beta is not too relevant. It in fact could explain why the pair became out of sync from their mean, because one is more volatile (or swings more intensely) than the other (Beta larger than other) and caused the mean diversion.

Also, a large Beta difference would mean a sharply trending Ratio chart, which is not ideal for pair trading.

I think on this basis i'm going to Position Size relative to Stock price only, but still be wary of relative Betas that are close together as more ideal trades than others...

Many thanks for your help.

 

[Rhody Trader]

I think in essence you're right. However, I'm not sure that last sentence is quite correct, Correlation measures the degree in which one Stock mirrors another but not a comparison of magnitude, i.e. one stock could always move exactly twice the percentage of another, and they would thus be 100% correlated, but the ratios of their Betas to the market would be 1/2.

Even as I wrote it I was wondering on the actual stats side, but I think we agree on the main point that the correlation between two stocks, given a same measurement period as beta, should reflect to a large degree the relationship in their betas - making beta really a parallel calculation which doesn't add any additional value. Besides, as you say, betas are generally measured over relatively long timeframes - ones you won't be trading in - and even the academics have come to realize the short-comings of measures that historically derived.

 

[leonarda]

Even as I wrote it I was wondering on the actual stats side, but I think we agree on the main point that the correlation between two stocks, given a same measurement period as beta, should reflect to a large degree the relationship in their betas - making beta really a parallel calculation which doesn't add any additional value. Besides, as you say, betas are generally measured over relatively long timeframes - ones you won't be trading in - and even the academics have come to realize the short-comings of measures that historically derived.

yep, well said.
Thanks for helping clear my mind on this one.

 

[Weighbridge]

Even as I wrote it I was wondering on the actual stats side, but I think we agree on the main point that the correlation between two stocks, given a same measurement period as beta, should reflect to a large degree the relationship in their betas ...

FWIW I'd be wary of that assumption. Two stocks with the same beta could be quite uncorrelated, if they experience their more market-correlated behaviour on different days.

I'd ignore beta until the very end, after you've decided on position sizes. Then you can use it as a best-guess measure of your overall market exposure and hedge accordingly. i.e. what Martinghoul said.

 

[luckyd1976]

But for me its KISS.

Find two pairs. (QQQQ/AAPL or SPY/AAPL)
If they test out and correlate well. Trade as Pair. (QQQQ/AAPL)
If they dont correlate well, trade Unilaterally using highest Beta as the instrument to trade. (AAPL/SPY only trading the AAPL)

Choose your side then choose your weapon.

 

[Rhody Trader]

FWIW I'd be wary of that assumption. Two stocks with the same beta could be quite uncorrelated, if they experience their more market-correlated behaviour on different days.

Be wary of ALL assumptions.

What you describe, though, are stocks in opposite trends which are not impacted by the market's contrary action, which of course would be fantastic pairs candidates.

 

[leonarda]

I'd ignore beta until the very end, after you've decided on position sizes. Then you can use it as a best-guess measure of your overall market exposure and hedge accordingly. i.e. what Martinghoul said.

Hi,
Can you explain this to me (simply as a newbie..) i'm not quite sure I understand what you're saying with regard position sizes?
Thanks

 

[leonarda]

I'd ignore beta until the very end, after you've decided on position sizes. Then you can use it as a best-guess measure of your overall market exposure and hedge accordingly. i.e. what Martinghoul said.

Having had some more thought, are you and Martinghoul saying based on the historic mean reversion testing and results, basically hedge with more weight based on the Stock more likely to be out of sync? (most likely the more volatile one, ie. the one with higher Beta?)

 

[Weighbridge]

Hi,
Can you explain this to me (simply as a newbie..) i'm not quite sure I understand what you're saying with regard position sizes?
Thanks

Sure.

Imagine two companies on the London Stock Exchange.

Company A is priced at £5 per share and has a beta of 0.7
Company B is priced at £8 per share and has a beta of 0.5

Your analysis tells you to go long A and short B. You decide to buy 8,000 shares of A and short 5,000 shares of B.

Your position sizes are +£40,000 in company A and -£40,000 company B.

Your exposure to market risk is esitmated by multiplying the size of each position by its beta. So:

Company A £40,000 x 0.7 = £28,000
Company B -£40,000 x 0.5 = -£20,000
Overall exposure = £8,000

So your two positions expose you to the same sort of market risk as being long £8,000 in the FTSE All Share. If the market tanks you'd most likely feel it - even if there weren't any stock-specific reasons for A and B to drop.

If you were uncomfortable with that exposure you could balance it out by shorting the index to the value of -£8k with a future or a spreadbet.

In practice I think most people would hedge this example using the FTSE100, as it's similar to the All Share but much cheaper & easier to trade.

Well that's how I work it out anyway - if I'm off then hopefully someone will set me straight.

 

[Weighbridge]

Having had some more thought, are you and Martinghoul saying based on the historic mean reversion testing and results, basically hedge with more weight based on the Stock more likely to be out of sync? (most likely the more volatile one, ie. the one with higher Beta?)

Personally, I would keep my analysis and hedging separate. My analysis would drive my choice and weighting of stocks. Then only as an afterthought, I'd measure my overall exposure to market risk and if I was uncomfortable with it I'd hedge per the example above.

I should disclose that I don't do much pairs trading though However, my normal trading often leaves me uncomfortably long and a hedge lets me leave the screen!

 

[leonarda]

Thanks for explaining... that was what I thought originally, although i'm not sure of the difference between covering against the FTSE, and simply altering the position sizes of A/B according to Beta ratio?

There seems to be a difference of opinion on the forum between doing this, and what Rowdy Trader said that Beta is not so relevant, especially on short time scales. So i'm at a bit of a quandary as ever.... I will have to have a think on this one...

Thanks again.

 

[Weighbridge]

Thanks for explaining... that was what I thought originally, although i'm not sure of the difference between covering against the FTSE, and simply altering the position sizes of A/B according to Beta ratio?

There seems to be a difference of opinion on the forum between doing this, and what Rowdy Trader said that Beta is not so relevant, especially on short time scales. So i'm at a bit of a quandary as ever.... I will have to have a think on this one...

Thanks again.

My pleasure.

IMHO (and I have strayed out of my field here...) I would want both legs of the pairs trade to be of the same value.

If company A and B's prices are tracking each other, and A's price goes up then it will create a gap that you can try to exploit. But who knows whether the gap will be narrowed by A going down or by B going up? To capture the benefit you'd need to be equally exposed to A and B.

And yeah, beta is historic so not super-reliable. But good enough for getting a sense of whether you're too long/short the market.

 

[leonarda]

My pleasure.

IMHO (and I have strayed out of my field here...) I would want both legs of the pairs trade to be of the same value.

If company A and B's prices are tracking each other, and A's price goes up then it will create a gap that you can try to exploit. But who knows whether the gap will be narrowed by A going down or by B going up? To capture the benefit you'd need to be equally exposed to A and B.

And yeah, beta is historic so not super-reliable. But good enough for getting a sense of whether you're too long/short the market.

Thanks, appreciate your HO. I think I feel inclined to go equally as well, and just use Beta as a risk factor relative to market. We're talking about short time frames so market movement should hopefully be small (!)