Equity Spread Trading Hedge Ratios

rodmike9 · Aug 10, 2009

Quote from sjfan:

Not True. For two stocks A and B

Hedging Ratio = Beta(A,B) = Cov(A,B)/Var(B)

Correlation = Cov(A,B)/Std(A)Std(B)

If Correlation = 1, then

Cov(A,B) = Std(A)Std(B)

Then, substitute this back into the hedging ratio calculation, you get

Beta(A,B) = Std(A)Std(B)/Var(B) = Std(A)/Std(B) Since Var(B) = Std(B)*Std(B).

So, under 100% correlation, the correlate hedging ratio is the volatility ratio.

The correct hedging ratio for 0% correction... is 0! If the pair isn't correlated, it's not a pair trade.

you need to read what I wrote again

sjfan · Aug 10, 2009

Okay. I just did. Did I misread you?

You said: "whereas volatility-weighted would be an adjustment to compensate for the lack of correlation."

I just showed that mathematically that volatility weighted is only the solution when correlation is 100%... so it's not the lack of correlation.

Quote from rodmike9:

you need to read what I wrote again

rodmike9 · Aug 10, 2009

Quote from sjfan:

Okay. I just did. Did I misread you?

You said: "whereas volatility-weighted would be an adjustment to compensate for the lack of correlation."

I just showed that mathematically that volatility weighted is only the solution when correlation is 100%... so it's not the lack of correlation.

how do you assume volatility is constant?

sjfan · Aug 10, 2009

wtf? I was showing that under the cannonical derivation of beta hedge ratio, the vol ratio is the beta assuming 100% correlation, which you argued is incorrect. what does any of this have to do with constant volatility?

And for the record, my simple derivation doesn't assume constant volatility. One can use forward volatility as well. In any case, the hedge ratio is only the vol ration under 100% correlation, not zero - which is what you stated.

I'm beginning to think you have no clue what any of this means and are just being argumentative for being arguentative's sake.

Quote from rodmike9:

how do you assume volatility is constant?

dtrader98 · Aug 10, 2009

Quote from sjfan:

If the pair isn't correlated, it's not a pair trade.

Nor does a correlated pair imply a pair-spread trade.

Not sure why anyone is even debating correlation at all. To answer OP/OQ, look up cointegration.

rodmike9 · Aug 10, 2009

Quote from sjfan:

wtf? I was showing that under the cannonical derivation of beta hedge ratio, the vol ratio is the beta assuming 100% correlation, which you argued is incorrect. what does any of this have to do with constant volatility?

And for the record, my simple derivation doesn't assume constant volatility. One can use forward volatility as well. In any case, the hedge ratio is only the vol ration under 100% correlation, not zero - which is what you stated.

I'm beginning to think you have no clue what any of this means and are just being argumentative for being arguentative's sake.

Cannonical derivation of beta hedge ratio? ARE YOU SERIOUS??????? How about a practical derivation? Please, enlighten me.

AND WHEN DID I ARGUE THE BETA ASSUMING 100% correlation is incorrect? I didn't even mention betas.

Forward VOLATILITY, YOU CAN'T BE SERIOUS??? Did your foward volatility model predict the 2008 4q move?

Your assumptions and implicities may be great for your sales trading job but this isn't a discussion board for RBC or JPM. And frankly, we are talking about spreading stocks where you might want to consider earnings or rebalancing when VOL WEIGHTING the spread.

I would be more than happy to discuss convexity or modified durations with you another day.

sjfan · Aug 10, 2009

Okay. First, I'm not a sales & t; So let's put all the resentment aside.

Second, you said in your earlier post that I was wrong and that vol ratio is when there is no correlation; That's so nonsensical that it's stupid. But please, show me how that actually works. A pair trade requires that the pair is correlated. So show me how it's possible to construct a hedge ratio (which is exactly what beta is, convexity adjusted or not) when there is no correlation. Please, enlighten me.

You are a child. Completely ignorant of how this all works. The only thing more pathetic than your attempt at discussing this topic is the fact that the rank amateurs here can't distinguish what you are saying and what I'm saying. Go forth, internet tough guy, you can claim that you've won this debate. Meanwhile, I got some portfolios to manage - in real life (you know, that place outside of your mother's basement)

Quote from rodmike9:

Cannonical derivation of beta hedge ratio? ARE YOU SERIOUS??????? How about a practical derivation? Please, enlighten me.

AND WHEN DID I ARGUE THE BETA ASSUMING 100% correlation is incorrect? I didn't even mention betas.

Forward VOLATILITY, YOU CAN'T BE SERIOUS??? Did your foward volatility model predict the 2008 4q move?

Your assumptions and implicities may be great for your sales trading job but this isn't a discussion board for RBC or JPM. And frankly, we are talking about spreading stocks where you might want to consider earnings or rebalancing when VOL WEIGHTING the spread.

I would be more than happy to discuss convexity or modified durations with you another day.

spreadem · Aug 10, 2009

Quote from FastandFurious:

right, but my question is, do most people trade it 1:2 or 1:1? What are the benefits of each

In this case if you trade it 1:1, you'll tie up $4600 and if you trade it 1:2, you'll tie up $6100 per position.

TheROTrader · Aug 10, 2009

Can someone tell me why you would ever want to go into a 1:1 or 1:2 ratio in these 2 in the first place? doesnt seem to make much sense to me.......thanks

rodmike9 · Aug 10, 2009

Quote from sjfan:

Okay. First, I'm not a sales & t; So let's put all the resentment aside.

Second, you said in your earlier post that I was wrong and that vol ratio is when there is no correlation; That's so nonsensical that it's stupid. But please, show me how that actually works. A pair trade requires that the pair is correlated. So show me how it's possible to construct a hedge ratio (which is exactly what beta is, convexity adjusted or not) when there is no correlation. Please, enlighten me.

You are a child. Completely ignorant of how this all works. The only thing more pathetic than your attempt at discussing this topic is the fact that the rank amateurs here can't distinguish what you are saying and what I'm saying. Go forth, internet tough guy, you can claim that you've won this debate. Meanwhile, I got some portfolios to manage - in real life (you know, that place outside of your mother's basement)

Where did I say vol ratio is when there is no correlation?

A pair trade requires that the pair is correlated? That is a very broad stroke sir, especially from someone who memorizes from a text book.

Did you just finish school?