Beta Weighted Greek Aggregations

[SteveGoTex]

I usually carry some positions that comprise long and short options at different strikes and maturities for a given underlying.

I trade on IB, so for these positions, I make extensive use of the IB Risk Navigator, which provides a real time tabular and graphic summary of the Greek aggregations for that underlying.

Recently I saw a presentation by someone from TOS. In this he advocated aggregating Greeks across multiple underlyings, "beta weighted" to SPY, for example. His claim was that he could better manage a large collection of positions on multiple underlyings. The TOS platform apparently provides direct support for aggregating Greeks, beta weighted against any underlying.

Does this approach make sense? II am not seeing a real advantage to this, which is why I am asking.

TIA
Steve G

 

[atticus]

It's dangerous. You're either too reliant on correlation, optimizing, or you won't believe what you see and you'll be forced to trade the number conservatively. I worked with it in 1999 and couldn't find a lot of utility.

 

[dd4nyc]

I second riskarb: correlations are very unstable, making betas unreliable. Nice idea - but really just does not work in practice (unless you're trading something like SPY and IVV or IWM and IWN that have 99% correlation)

 

[black diamond]

Quote from atticus:

It's dangerous. You're either too reliant on correlation, optimizing, or you won't believe what you see and you'll be forced to trade the number conservatively. I worked with it in 1999 and couldn't find a lot of utility.

Hey Atticus,

Do you think it is useless if you just use beta=1?

I saw an interesting published strategy a while ago that is simultaneously long and short a bunch of straddles on individual stocks and just letting delta drift over time. Very high returns but crazy high volatility, I was wondering if delta hedging with es futures would improve it enough to be tradeable.

I'm skeptical of betas too but it seems like hedging with the individual stocks would be expensive and unmanageble. I was wondering if assuming beta=1 spread over many positions would be worth trying.

 

[SteveGoTex]

On further thought, I think this idea would be useful if you are aggregating perfectly correlated underlyings.

For example, if you had a small RUT position and needed to make a small modification to your P&L curve using IWM. Then you could aggregate over those two underlyings, weighting it to one or the other.

Beyond that, over poorly correlated items, I agree that it can be dangerous.

Thanks for the responses.

Steve G

 

[nitro]

Quote from SteveGoTex:

On further thought, I think this idea would be useful if you are aggregating perfectly correlated underlyings.

For example, if you had a small RUT position and needed to make a small modification to your P&L curve using IWM. Then you could aggregate over those two underlyings, weighting it to one or the other.

Beyond that, over poorly correlated items, I agree that it can be dangerous.

Thanks for the responses.

Steve G

That is correct thinking, imo, but I would leave out the word perfect. Basically you are trading correlation when you do this. The more correlated the underlyings, the more correct the method of normalizing book greeks. That would make sense, no? If you were quantitatively oriented, you could adjust the equations for correlation as a parameter. Using Heston (or something similar) is probably the best way to get these greeks then.

It is somewhat related to skew (correlation leads to skew). I don't know if TOS supports vanna

http://en.wikipedia.org/wiki/Greeks_(finance)

But that is worth looking into as well.

"Cross greeks" is probably what you want to search on: e.g., cross gamma.

 

[nitro]

The biggest problem with all of this is that the solutions may be high-dimensional (the bigger your basket the worse it gets), in which case partial differential equation style approaches may be impossible.

I have come more and more to the conclusion that you have to have two models running concurrently when trading options: The Quasi-Monte Carlo/Monte Carlo methods, and whatever other model you are running.

 

[atticus]

Quote from nitro:

The biggest problem with all of this is that the solutions may be high-dimensional, in wich case partial differential equation style approaches may be impossible.

Absolutely not possible.

 

[nitro]

Quote from atticus:

Absolutely not possible.

There are special cases where it is possible from what I understand, but they are too specialized to matter.

Someone on nuclear phynance asked a very interesting question that I think is related:

"I have a basic question regarding the corr skew.

Since the market quotes are in terms of terminal corr and you can have high local corr and low terminal corr. how does one go about calibrating?"

http://www.nuclearphynance.com/Show Post.aspx?PostIDKey=117282

I think the answer is that you have to model correlation as a stochastic mean reverting parameter in a local model, but I really don't know enough to answer.