January 5, 2010
Great in theory, but will it work today?
The analysis by D’Antonio assumes that you can sell a call option with a strike price that is 20% above the price of the S&P500 and use the proceeds to buy a put option with a strike price that is 10% below the price of the S&P500 on a consistent basis. As of this writing (Dec 21, 2009), SPY is trading at $111.48 per share. The strike price of the call would be $133.8 if it were exactly 20% above this price. The Dec 2010 call option with a $135 strike is trading at about $1.55. The strike price for a put option that is 10% below the current price of SPY would be $100.33. The Dec 2010 put option with a strike of $100 is selling at about $6.70.
We could not put the strategy into effect – the puts are far too expensive. To do a costless collar with put options with a strike at $100, we would need to sell calls with a strike at $117 because these are selling at about $6.90, the closest price to the $6.70 per share we would need to pay for the put options. Selling the $117 call option to purchase the protective put gives us a lot less potential upside return than if calls could be sold with a strike of $135. The $117 calls give us a potential gain of only 5% before the call options go into the money.
The $135 call option has an implied volatility of 18% while the $100 put option has implied volatility of 26% (see here). The put options, adjusted for the difference in strike prices, are disproportionately expensive relative to the call options. In light of recent market declines, this is not surprising.
The asymmetry in implied volatility between the puts and calls illustrates the pattern of risk aversion in the market.
We can keep all the return on the S&P500 up to a 5% gain, plus the dividend yield (2.1%) for a total potential gain of 7.1% if the market rises. If the market goes down, we can lose no more than 10% from a drop in price, but we still get the 2.1% yield so we will lose no more than 7.9%. The median payout for this collar is estimated to be on the order of 7% – very close to the maximum possible payout from the collared position – but the average payout is approximately 1.6%. These Monte Carlo projections are all highly approximate, of course, but the asymmetry between the call and put prices is very concrete: the calls are currently cheap relative to puts for the S&P500.
The degree to which call options and put options are inconsistently priced might be due to two factors. One of these is the volatility ‘smirk,’ which is the increase in implied volatility as the strike price goes further below the current price. In general, this effect applies to strike prices above the current price (the volatility smile), but the effect tends to be asymmetric, with considerably larger increases in volatility for strike prices well below the current price.
The second factor would be a breakdown in the relationship between put prices and call prices (in technical terms this would be a violation of put-call parity). This is easily explored.
A costless collar on the SPY with a +20% and -10% band can be almost exactly replicated if we buy a call option on SPY with a strike of $100 and sell a call option on SPY with a strike of $135, with both having the Dec 2010 expiration date. The current price of the Dec 2010 $135 call option is $1.50 and the current price of the Dec 2010 $100 call option is $16.50. If you buy the $100 call and sell the $135 call (call it the Two-Call Strategy), the net position is just like buying SPY and then executing the covered call:
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