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Managing Risk in an Option Portfolio...

DELTA DOESN'T CUT IT

Just a quick post about managing risk in an equity derivative portfolio.

A great deal of attention is given to option Greeks when discussing risk management and rightly so.  Greeks are useful tools to delineate the risk of a singe option.  We know delta is the first derivative of the option pricing function and describes the linear change in the price of an option given a change in the underlying security... this is a good thing to know.

But what happens when we structure trades using multiple options?

A few months back, I wrote a piece on using vol skew to structure a bearish position on the SPY:

http://tancockstradingblog.blogspot.com/2017/12/using-vol-skew-to-short-raging-bull_5.html

Here, I showed how shorting mispriced options can be an effective way to structure a trade to capture market drawdowns.  The example used was to short 23 contracts of a 30 day put that was far out of the money and buy two individual puts closer to the money (the SPY was trading at $265 at the time):
  • Short 23 January $230 puts at $0.29 to generate $667 in proceeds - total delta points: 78.2
  • Long 1 January $265 put at $4.17 - delta points: -50.08
  • Long 1 January $260 put at $2.42 - delta points: -32.46
Having replicated the trade, let's look at the risk metrics:

 
The delta on the $230 put contracts was +3.4 as this was a short position.  The delta on the long puts was -49 and -32 respectively.  The risk for the overall position works out as follows:


Here, we can see the position has an overall delta of -19.6 but that figure is somewhat misleading.  If the market were to experience a large drawdown right after this position was put on (say -1%), the value of all three options would increase.  However, the loss on the short contracts would mostly cancel out the benefits of the gains in the near the money contracts due to the 23:2 ratio and the immediate change in value of the overall position would be relatively small.

How do we know this?  Recall, this trade works until the point the short contracts have explicit value.  Here's the payoff structure at expiration:


If the market were to experience an immediate drawdown, the leverage of the short puts would kick in.  Going back to the position level risk of the trade, we see the overall leverage is just -1.6 indicating a flat risk exposure.  Here's a reminder on how option leverage works:

http://tancockstradingblog.blogspot.com/2016/03/understanding-option-leverage.html

To illustrate the point, let's simulate the impact of an immediate -1% market drawdown on the position.  Assuming the SPY goes from $265 to $262, an option calculator would now value each leg of the position at:
  • $230 put from $0.29 to $0.41
  • $265 put from $4.17 to $5.82
  • $260 put from $2.42 to $3.52
This would produce a position PnL of :-$1

It's also important to note that the implied volatility assumptions were not changed for this scenario analysis which is a completely unrealistic assumption in the real world... but it illustrates the point nonetheless.

Therefore, while delta is a good measure for the risk of an individual option, leverage is actually a better indicator of position level risk when structuring trades with multiple legs.

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