Best pairs

[volatileN]

Hi,

I have been working on a stat arb program for systematisation of pairs trading and come to a number of interesting conclusions that I had not previously considered.

To this end I have run scans on every pair one could generate from the Russell 1000 index.

Appreciating that there is a lot on the topic on these boards I will keep this brief but it does appear that when trading a portfolio of pairs hedging one's beta increases the Sharpe ratio over the long run.

It also seems that strict sector neutrality increases the Sharpe while industry neutrality reduces it. I guess the latter is attributable to the vast reduction in activity and therefore samples in the distribution.

Attached is my favorite individual spread plotted over an OLS line, anyone else have one?

Cheers,

VN?

 

[TheBramble]

VN - What exactly does hedging one's beta mean?

The Sharpe index is a measure of Risk:reward (I think). So are you saying trading pairs within the same sector is a better bet than not?

 

[volatileN]

VN - What exactly does hedging one's beta mean?

The Sharpe index is a measure of Risk:reward (I think). So are you saying trading pairs within the same sector is a better bet than not?

Yep,

Sharpe ratio = (return - Risk free rate) / Standard deviation of returns.

The reason that it is interesting that sector neutrality offers a higher Sharpe ratio (higher risk adjusted returns) is that it offers fewer trading opportunities per day. This could go either way, 1) it could mean that the lower sample gives rise to a greater volatility of returns as it is a numbers game. 2) The quality of the pairs in the same sector overrides this. The latter seems to be the case.

While this is intuitive there have been many arguments for pure statistical arbitrage with no fundamental analytical attachment. It seems that common sense prevails!

VN

 

[TheBramble]

...and hedging your beta...?

 

[volatileN]

...and hedging your beta...?

Beta is a tricky concept as it is itself dynamic. It presents the same problem as options market makers have when they try to flatten out their vega. That is: How do you hedge a random variable?

The approach I have been taking in my research it to measure my beta at the portfolio level. At the individual spread level I may find myself long of a stock with a beta of 0.7 and short one with a beta of 1.5. This gives me a long exposure to the market of 0.8.

That is to say, all else being equal, if the market rises by 1% I can expect to lose 0.8% as this is my residual beta.

If we aggregate the total long and short residual beta at the portfolio level one typically has a net long or short beta position. As this basically amounts to an exposure to a move in the broader market it can be hedged by trading index futures / options.

My tests have shown that simple long positions in the options offer the best risk adjusted returns. In selecting which strike / expiry to use I have considered time decay (theta) and delta.

As one is long of the option it is not desirable to purchase ones with less than 30 days to expiry because the theta increases at a greater rate. This being the case (i.e you are not going to have a delta of 1 for an ATM contract for some time) it makes sense to match up your beta with your delta. Rehedging this daily (as your beta position changes) eliminates entirely your exposure broader market moves.

By doing this, being dollar neutral (buying and selling equal dollar amounts of each pair) and maintaining the discipline of systemised stops you are truly market neutral.

I will have more info on this in the coming weeks as my research progresses. Currently I am finishing off the program to implement it and designing a VaR (value at risk) model to aggregate my exposure.

Sorry to ramble, just love this game!

VN

 

[volatileN]

SORRY,

Line 5 above, should read 'short exposure' not long obviously!

Beta is a tricky concept as it is itself dynamic. It presents the same problem as options market makers have when they try to flatten out their vega. That is: How do you hedge a random variable?

The approach I have been taking in my research it to measure my beta at the portfolio level. At the individual spread level I may find myself long of a stock with a beta of 0.7 and short one with a beta of 1.5. This gives me a long exposure to the market of 0.8.

That is to say, all else being equal, if the market rises by 1% I can expect to lose 0.8% as this is my residual beta.

If we aggregate the total long and short residual beta at the portfolio level one typically has a net long or short beta position. As this basically amounts to an exposure to a move in the broader market it can be hedged by trading index futures / options.

My tests have shown that simple long positions in the options offer the best risk adjusted returns. In selecting which strike / expiry to use I have considered time decay (theta) and delta.

As one is long of the option it is not desirable to purchase ones with less than 30 days to expiry because the theta increases at a greater rate. This being the case (i.e you are not going to have a delta of 1 for an ATM contract for some time) it makes sense to match up your beta with your delta. Rehedging this daily (as your beta position changes) eliminates entirely your exposure broader market moves.

By doing this, being dollar neutral (buying and selling equal dollar amounts of each pair) and maintaining the discipline of systemised stops you are truly market neutral.

I will have more info on this in the coming weeks as my research progresses. Currently I am finishing off the program to implement it and designing a VaR (value at risk) model to aggregate my exposure.

Sorry to ramble, just love this game!

VN

 

[Rognvald]

VN
It will be v interesting to see the results of your research

 

[volatileN]

VN
It will be v interesting to see the results of your research

Thank you.

If I have not mentioned it here again in a few weeks please PM me a reminder. By then I should have my scanning algorithms, VaR etc in place.

 

[Trader333]

I agree, I am finding this of great interest.


Paul

 

[volatileN]

Being a bit disorganised I failed to keep to one board on this topic. More on the same at:

http://www.trade2win.co.uk/boards/showthread.php?s=&threadid=9216

Cheers,

VN