HOW SELLING SHORT-DATED OPTIONS IMPACTS RISK ON POSITIVE GAMMA POSITIONS
WHY PAY RETAIL?
One popular options trading strategy is the calendar spread where short-dated and, generally, lower absolute delta options are sold to finance options with longer-dated maturities and higher absolute deltas. The intention is to reduce the purchase price of the long-dated option, but the structure also impacts the risk/return profile of the position and the passage of time makes that relationship more dynamic than a traditional long or short option by itself.
To illustrate the point, I built out the Optimized Positive Convexity model to account for variable maturity positions.
http://tancockstradingblog.blogspot.com/2015/08/follow-up-on-qihu-short-trade.html
I structured a bearish position around the SPY which I fully expect to breakdown in the coming days and weeks.
The position is composed of the following legs and the risk profile at inception is reflected in the chart below.
Long: 200 shares of SPY at $205.49
Long: 12 June $206 puts at $3.67 - 20 day options
Long: 12 June $202 puts at $2.14 - 20 day options
Short: 6 June 3rd $204 puts at $1.34 - 10 day options
Short: 6 May 27th $203 puts at $0.54 - 5 day options
By selling the June 3rd and May 27th options, we generate roughly $1,100 in premium to offset the nearly $7,000 spent on the long puts. The maximum loss at inception is roughly $3,700 and the breakeven price is $201.40
MODELING & MANAGING THE RISK
One of the cornerstones of my modeling is the expected value calculation which is built around a stochastic price simulation. For traditional positions with only one expiration date, the simulation of the underlying is conducted to that date and I reflect it in a histogram.
http://tancockstradingblog.blogspot.com/2015/08/projecting-equity-prices-using.html
For positions with multiple expiration dates, however, prices have to be simulated through time... to do this, I built out 500 price path simulations using the same inputs of expected return and volatility used in simulations to a single date. Here's a sample of what 20 price paths looks like for the SPY position that has an expected 20-day return of -1% and an expected volatility of 12.2%
Using this method, we can value each leg of the position to its respective expiration date to get its expected value and get a visual representation of how the overall risk profile changes.
After the first week, the May 27th options expire and the risk profile on the position changes to look like this:
The maximum loss (net of any gain/loss on the May 27th option) is now just over $4,000 and the breakeven price has risen to $202.3. Additionally, the position's upside has expanded (as seen by the higher values on the y-axis).
One week later, the June 3rd options expire and the risk profile changes again to look like this:
The maximum loss (net of any gains/losses on the already expired options) is now roughly $5,250 and the breakeven has risen to $202.60. Again, the position's upside has expanded with the expiration of the short options as reflected by the y-axis values.
By the final expiration, the maximum loss is roughly equal to the premium paid for the long options as all time value has decayed.
Going back to our simulated price paths, we can value each leg of the position and determine the overall expected value.
Short 6 May 27th $203 put options at $0.54 - expected value ($18)
Short 6 June 3rd $204 put options at $1.34 - expected value ($174)
Long 12 June $202 put options at $2.14 - expected value ($144)
Long 12 June $204 put options at $3.67 - expected value $456
Long 200 shares SPY at $205.49 - expected value ($229)
Total expected value: ($109) - The total trade exposure was roughly $47,000 so this is a bit of a let down. However, the strategy is still very useful when expected moves are not imminent.
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