The following trades illustrate a put-ratio spread on the S&P 500 that, at the time of the trade, exhibits a high skew. Set up as a premium-neutral trade with three months until expiration, the resulting position has a slightly positive delta at initiation. The example is based on a current spot price of 1400 for the S&P 500.
- Buy 100 put contracts with strike 1400 and expiry in three months.
- Sell 280 put contracts with strike 1275 and expiry in three months.
As the black line in “Valuing the trade” (below) indicates, the profit and loss at expiration would be flat for prices above 1400 and would increase for falling spot prices until 1275 where the short puts expire worthless. Losses would be expected for prices around 1205 and lower.
For those investors who believe that the skew is not high enough, the reverse position in the form of short at-the-money options and long out-of-the-money options is an alternative. Because the out-of-the-money options would outnumber the at-the-money options, the position gains if we see a huge downturn in the market.
An analysis of a long put spread before maturity is important for understanding the trade. If the position is set up with a low positive delta and theta at initiation, the trade profits from a positive performance of the S&P 500 and time decay. The “Greeks,” however, change during the term of the trade. For example, closer to expiration, the delta can turn negative (positive) if the spot stays above (far below) 1275. The theta, although usually positive, can turn negative for high S&P 500 values close to expiration. That’s because at initiation the investor doesn’t want the S&P 500 to drop too quickly, which would result in trade losses. On the other hand, getting closer to maturity, the spot should move to where the trade becomes most profitable, which in this example would be 1275.
Note that this position is not a pure skew position. Like the changes in the Greeks, the spot movements lead to movements on the volatility surface. The trade does not necessarily profit directly from a change of it. That is, if the spot moves from 1400 to 1275, the at-the-money and out-of-the-money options change into in-the-money and at-the-money options. Without any adjustments, the skew analysis is no longer properly applicable.
Still, because of the long and short positioning in those options, a high skew at initiation is beneficial: The higher the skew, the lower the number of out-of-the-money put options necessary to reach a delta- or premium-neutral position at initiation.
Marco Erling is a portfolio manager and quantitative analyst for structured products with HSBC Global Asset Management. He studied mathematics at the University of Dortmund in Germany and earned an MBA from ESADE Business School in Barcelona. He is a CFA Charter holder and a Certified FRM holder. Email him at firstname.lastname@example.org.