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dlmusic
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Joined: October 21st, 2021, 4:29 pm

Purpose of Delta-Gamma-Vega-Neutral Portfolio?

October 23rd, 2021, 10:55 am

Delta-gamma-vega-neutral portfolios appear to be a complicated way of earning the risk-free rate compared to going long risk-free bonds e.g. government bonds (in theory). My understanding of such constructions in practice is that aside from theta, the other greeks are near zero. As such, it is possible, though not necessarily recommended, to maintain theta > 0. If theta < 0, negate portfolio weights to achieve theta > 0.

What can delta-gamma-vega-neutral portfolios help with?

Thank you for reading.
 
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DavidJN
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Re: Purpose of Delta-Gamma-Vega-Neutral Portfolio?

October 23rd, 2021, 4:39 pm

A particular hang-up the regulators have is explaining P&L and even relating it to capital. One use of delta-gamma-vega-neutral portfolios is to show how the movement of complex option pricing functions can only be imperfectly approximated using the function’s derivatives (e.g. the Taylor series), and that the slippage in the explanatory power grows the farther one moves away from the current state.  Of course this is well known about the Taylor series, but enough regulators do not seem to get it. All this is to suggest that such demonstrations can be used to carefully temper the naïve regulatory expectation of explaining everything.
 
More generally, one can conduct numerical simulations using this framework to gain a keener appreciation of hedge slippage, a concept that is fuzzy among too many people. One can see how and when hedges slip, and, as you note, how profit opportunities disappear as risk factors are hedged. When I traded, I always conducted simulated hedging experiments before offering more exotic products, just to derive some comfort before betting the shop on them. Any decent finance school should offer simulated trading exercises as a normal part of coursework.
 
 
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dlmusic
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Re: Purpose of Delta-Gamma-Vega-Neutral Portfolio?

October 25th, 2021, 9:11 am

Sounds like you're saying that it's employed as teaching material for regulators and traders. Hmm... come to think of it, I first encountered the delta-gamma-vega-neutral portfolio in a tutorial question in the widely used Hull's textbook.

At times, I can't help but wonder if such portfolios are able to, under certain market conditions, return more than the risk-free rate.
 
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DavidJN
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Re: Purpose of Delta-Gamma-Vega-Neutral Portfolio?

October 25th, 2021, 4:26 pm

Such portfolios can return more (or less) than the risk free rate if they contain residual unhedged risk, or if you have found a true arbitrage opportunity, or if the assumptions of the model prove to not be true.
 
You should try the simulation exercise sometime. While the average hedged option position yields a risk free return, that is definitely not the case for any one realization of the simulation. You can see how the P&L changes as the assumptions of the model are relaxed one by one and as the size of the hedging interval changes. I think anyone who trades options without using this kind of training is going into the game with less than a full deck. But that is just an opinion from a former option trader.
 
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dlmusic
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Re: Purpose of Delta-Gamma-Vega-Neutral Portfolio?

October 26th, 2021, 6:50 am

What software is handy for a simulation exercise of this nature? I've used Quantopian (now defunct) & QuantConnect for backtests on historical data. My guess is that a simulation is different from a backtest; prices are simulated as opposed to being marshaled from history.
 
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DavidJN
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Re: Purpose of Delta-Gamma-Vega-Neutral Portfolio?

October 28th, 2021, 12:37 pm

Similarities to backtesting are evident but simulation is the usual route, meaning you start with a good random number generator, I use public domain C/C++ algorithms for that. If you are teaching this stuff, Excel may be useful because of its visualization advantages.