Wednesday, June 29, 2005

The Gamma-Trading experiment.

I have no big positions for July expiration. I'm just sitting here mostly in cash, waiting for the next buying opportunity. It sucks that I have few positions for the July expiration coming up, but I want to be patient and only sell puts when conditions are favorable for that type of trade. I feel like better buying (naked put selling) opportunities are ahead. I closed out my RIMM puts at $0.20 today ahead of the earnings announcement. This is a $0.63 profit per put. I would have liked to have heald out for the remaining $0.20, since I probably won't put that capital back to work anytime soon. Too many times I have waited to make an extra 10 or 20 cents and ended up losing money. I'd feel pretty stupid If I lost a buck tomorrow to make 20 cents. PALM also reports after the bell today (or is that tomorrow). Anyway, I'm not covering my PALM puts, as they are farther out of the money and still retain about half their premium (these are NOV puts anyway.)

I bought a SPY 119 straddle on Monday I think (maybe it was Friday). I rarely buy straddles. This is mainly an expiriment, so I only bought one straddle. The market seems complacent. Regular readers know I usually like to sell premium...particularily naked puts. I haven't seen any options I've really wanted to sell lately, so this seemed like a good time to experiment with a different type of position while I wait for the time to put on big positions to come around. According to McMillan on Options, volatility often reaches a seasonal low in June or July. Furthermore, the market seems especially complacent right now. Complacency often precedes big moves. The complacency can be measured with the VIX index. This is a measure of the implied volatility of the S&P 500. It has been fairly low for some time, and even though the market sold off fairly hard last week, the index hardly moved at all.

I originally bought the straddle for the reasons explained above, but I am also thinking of using the position for expirimenting with" gamma scalping". To explain what that means, I'll have to get into the Black-Scholes model. The Black-Scholes model is a differential equation that gives the price of an option as a function of the stock price (or the price of any underlying instrument), time to expiration, the strike price, future volatility, and the risk-free interest rate. If you take the partial derivitives of the equation with respect to each of the individual parameters you get what is called "the greeks". Each greek tells you how the option price will move in response to a unit movement of the respective input parameter.

Probably the most important greek is the derivitive with respect to the underlying stock price. This is called Delta. Delta is the amount the price of the option will change when the stock price changes. If a position has zero delta then it is said to be "delta-neutral". For example, an exactly at the money straddle would have a delta of 0 since the put's negative delta would exactly cancel out the call's positive delta. Gamma is the second derivitive of the option price with respect to the underlying price. This tells us how much delta will change as the underlying stock price changes. Gamma can be thought of as the profit potential to be gained from hedging the delta of an option position. Theta is the derivitive of the option's price with respect to time.

For example, when I sell naked puts I have a negative gamma and a Positive theta. This means that the passage of time tends to be profitible, but if I want to hedge my delta as the underlying moves (to protect myself from large losses), I will tend to lose money doing so. A Straddle has negative theta, and positive gamma. So here is how scalping the stradde's gamma works:

Assuming the straddle was exactly at the money when purchased, it would have a delta of zero. Then if the stock moves in one direction, one could compute the delta at that time, and then buy or sell a quantity of stock to bring the delta back to zero. An option will always have a delta between -1 and 1. A share of stock always has a delta of 1. As one buys and sells stock in this way to bring the delta back to zero in response to the movements of the underlying stock, then this will tend to result in buying high and selling low, producing small profits over time. It's important to remember that even as one may be profitably scalping gamma, those profits may not be enough to overcome the time-decay (negative theta) of the position. It's kind of like a race between the gamma trader and theta. If the stock isn't volatile enough to profitibly trade the gamma enough times before expiration, then the trader will lose the race.

Yesterday the SPY's moved up about a buck. This morning as a result of that move my put contract was down about 40 bucks, and my call contract was up about 40 bucks. According to Interactive Broker's trading software (TWS), The delta of my position was around 30, so I sold 30 SPY shares short to bring my delta to zero. Now, if the S&P moves down again, I will have to buy back some of those shares I sold short to bring the delta back to zero which would result in a profit. I plan on re-adjusting the hedge every time SPY moves about a buck. With such-infrequent adjustments, I doubt I will make enough money to overcome time-decay, but I am curious how much can be made. The danger of hedging the delta like this as the stock moves, is that I may give up substantial profits if the stock makes a big move against the hedge.

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