Monthly Archives: January 2012

Delta Neutral Call Option Writing

Advanced Call Writing Strategies

Delta Neutral Call Writing

Much has been written about the popular covered call writing strategy, where an investor will purchase 100 shares of a stock or an ETF and sell one call option for some income and partial downside protection. The term covered call means that for every option you sell that option contract is covered by 100 shares of the underlying investment.

Advanced option traders will be familiar with the term delta neutral. For those readers who are not familiar, the term means that your position is delta neutral, it has no market directional bias, in other words the position is neutral to market movement.  So, if we buy 100 shares of XYZ stock, that position alone will have a delta of 100, now if we sell an at the money call with a delta of 50, because we are short the call it will have a negative delta, so the net position delta will be 50, 100 deltas for the 100 shares of XYZ stock and -50 deltas for the short XYZ call. This is how your typical covered call position works. If you were to sell an out of the money call with a delta of 25 your net position delta would be 75, in other words the total position would behave like 75 shares of the underlying instead of 100.

Now, if we want to create a market neutral position, we’ll sell enough calls so that the net position is delta neutral. So, if we buy 100 shares of XYZ again we could sell two 50 delta at the money calls, three 33 delta out of the money calls, or four 25 delta out of the money calls and so on. If the net position delta is at or near zero, your position will not have directional risk as long as it remains delta neutral. Then you can earn the theta or the decay from the short options. You don’t have to sell the options at just one strike price, either. For example you could sell one at the money 5o delta call and two out of the money 25 delta calls.

Once a position is established, the delta will change by the rate of the gamma, and adjustments will have to be made to remain delta neutral. You can adjust the shares of stock you own, sell more calls, or buy some calls back to make the delta neutral adjustment.

As with any strategy there are risks, the underlying can drop rapidly before you can adjust and you can experience a loss. Since you have uncovered short calls, if the underlying explodes upward rapidly you can also experience a substantial loss. Stocks that have high volatility or may be potential takeover targets should be avoided. Mega cap stocks can be good candidates or broad based index ETFs can be good candidates for a delta neutral strategy. Indexes can rise and fall rapidly, but they have never dropped all the way to zero like individual equities can or explode upwards the stocks getting taken over can.

Looking at some current prices as of this writing, the SPY is at $131.82 and the Feb 135 calls are 21 days from expiration. The Feb 135 calls sell for $0.61 and have a delta of 24. You could sell 4 of those calls against a 100 share position of SPY and take in $2.44 in premium, the theta is -0.03 so you’d be getting $12 per day in decay. You could make delta neutral adjustments as time goes by on a regular basis, but you wouldn’t have to worry about loss unless the SPY rises to above 135 by expiration. This is not a recommendation for the above SPY trade, I like using some real numbers for illustrative purposes, this is a strategy for sophisticated investors who understand the risks and are familiar with options and making delta neutral adjustments.

Option Greeks ~ Vega and Theta

Vega and Theta

The Vega or Lambda is the change in option price due to a 1% increase or decrease in implied volatility. Vega is the most commonly used symbol however, it is not a Greek letter, so some practitioners prefer to use Lambda, and they can be interchangeable. Short term options will have a lower Vega and will not be as sensitive to changes in implied volatility. Longer term options will have higher vegas and the price will be much more sensitive to changes in implied volatility. The Theta is the rate of decay of an option’s price over time. Long option positions, whether they are calls or puts will have negative theta which means that time will work against the holder of an option through the process of price decay. Short options will have a positive theta which means that the option writer or seller can earn slow profits over time through the price decay process. Shorter term options will have a higher theta than long term options and the price can decline rapidly through decay in the final weeks or days to expiration. Longer term options will have a lower theta and a lower rate of price decay. The rate of price decay accelerates rapidly as the option approaches expiration. Covered call writers who sell call options for income usually do better by selling short term options and benefiting from the rapid price decay. In the money options will also have a lower theta and less time value than at the money options. Out of the money options that have no intrinsic value will have a relatively high theta.

One element that can make option trading tricky is understanding how many different moving parts there are and how they can affect the price of the option. For example say you a very bullish on a stock and decide to buy a call option for upside participation and to control your downside risk. The stock may move, but the stock price movement can be offset by a decline in implied volatility, so the vega can work against you. If you’re looking at a bullish strategy you need to know how the implied volatility priced into the option will impact the price. If you buy when the IV is at a very high level, even if the price of the underlying moves, if the implied volatility declines it will impact your profit. If you have a position that is long vega you want the IV to increase, if you are short vega you want the IV to decrease.

Covered call writers want to be short theta, they want the option decay to work on their side. When you sell an option, whether it is covered or not, you will be short theta and also short vega, so you want the IV to decrease, and the underlying to not move too much so you can earn the theta or the decay of the option price with time.

 

Option Greeks ~ Delta and Gamma

To determine the theoretical price of an option, an option pricing model is used. Buyers and sellers on the marketplace determine the actual price constantly throughout the trading day. The most commonly used pricing model is the Black Scholes Model. From the Black Scholes Model we can derive some calculations used to determine how an option price will react to market variables, known as the Greeks because letters from the Greek alphabet are used to designate them. The Delta is the rate of change of option price with a corresponding one point move in the underlying instrument. A one hundred share position in the underlying instrument will always have a delta of 100. I like to express the delta in terms of the number of shares of the underlying that you hold. If you are long 100 shares of XYZ then you are a positive 100 delta position. If you are short 100 shares of XYZ then you have a negative -100 delta position. When you combine complex option and stock positions you’ll have to keep track of the deltas which are additive. At the money options will have a delta of about 50. So, if you own 100 XYZ and decide to sell an at the money call with a delta of 50, your net position delta will now be 50, 100-50 = 50. Which means that as long as the delta of the short call remains at 50 your combined position will behave like 50 shares of the underlying, not 100 shares, so the risk of ownership in the underlying is reduced by a 50 share equivalent. As call options move in the money, the delta will increase, as they move out of the money, the delta will decrease. The delta is also roughly equivalent to the probability of the option being in or out of the money at expiration. An at the money option will have a delta of about 50, which means that it will move half of what the underlying moves, but also has a 50/50 chance of being in the money at expiration. A long call with have a positive delta and a long put will have a negative delta. Conversely the short call will have negative delta and the short put will be a positive delta position. If you hold a 100 share position and are concerned about risk you could sell an at the money call and use the proceeds to buy an at the money put. If the short call has a -50 delta and the long put also has a -50 delta you now have a delta neutral position, 100-50-50=0. As long as the position stays delta neutral you do not have market risk. The deltas, however are not fixed but are variable so they change when the price of the underlying stock changes and adjustments have to be made if the investor wishes to maintain a delta neutral position. The rate at which the delta changes is known as the Gamma, the gamma is the rate of change of the delta with a corresponding one point underlying move.

Option income investors who use short straddles, short strangles, iron condors, iron butterflies, etc. will have delta neutral positions with short gamma, meaning that they don’t want the underlying to move, if the underlying moves the delta will change and the position will take on a directional bias.  So they have to adjust to maintain a delta neutral position.

To determine the theoretical price of an option, an option pricing model is used. Buyers and sellers on the marketplace determine the actual price constantly throughout the trading day. The most commonly used pricing model is the Black Scholes Model. From the Black Scholes Model we can derive some calculations used to determine how an option price will react to market variables, known as the Greeks because letters from the Greek alphabet are used to designate them. The Delta is the rate of change of option price with a corresponding one point move in the underlying instrument. A one hundred share position in the underlying instrument will always have a delta of 100. I like to express the delta in terms of the number of shares of the underlying that you hold. If you are long 100 shares of XYZ then you are a positive 100 delta position. If you are short 100 shares of XYZ then you have a negative -100 delta position. When you combine complex option and stock positions you’ll have to keep track of the deltas which are additive. At the money options will have a delta of about 50. So, if you own 100 XYZ and decide to sell an at the money call with a delta of 50, your net position delta will now be 50, 100-50 = 50. Which means that as long as the delta of the short call remains at 50 your combined position will behave like 50 shares of the underlying, not 100 shares, so the risk of ownership in the underlying is reduced by a 50 share equivalent. As call options move in the money, the delta will increase, as they move out of the money, the delta will decrease. The delta is also roughly equivalent to the probability of the option being in or out of the money at expiration. An at the money option will have a delta of about 50, which means that it will move half of what the underlying moves, but also has a 50/50 chance of being in the money at expiration. A long call with have a positive delta and a long put will have a negative delta. Conversely the short call will have negative delta and the short put will be a positive delta position. If you hold a 100 share position and are concerned about risk you could sell an at the money call and use the proceeds to buy an at the money put. If the short call has a -50 delta and the long put also has a -50 delta you now have a delta neutral position, 100-50-50=0. As long as the position stays delta neutral you do not have market risk. The deltas, however are not fixed but are variable so they change when the price of the underlying stock changes and adjustments have to be made if the investor wishes to maintain a delta neutral position. The rate at which the delta changes is known as the Gamma, the gamma is the rate of change of the delta with a corresponding one point underlying move.

Option income investors who use short straddles, short strangles, iron condors, iron butterflies, etc. will have delta neutral positions with short gamma, meaning that they don’t want the underlying to move, if the underlying moves the delta will change and the position will take on a directional bias.  So they have to adjust to maintain a delta neutral position.