Using Option Prices to Justify a Directional Bet Is Fraught with Peril

I wonder what the authors of this article think now. Back in March, Bloomberg ran an article titled VIX Premium Shows Bear Market Lasting 2 Years on Trader ‘Panic’. The basis for the claim was the high cost of insuring a portfolio that mimicked the S&P 500.

The authors noted that the price of buying a 2-year put option on the S&P 500 Index cost a whopping $15,160. Using ODDS Online, I looked back at S&P 500 option prices the day before the article ran. Since the article ran on Monday March 2, I looked at the price on Friday February 27. The S&P 500 was 735.09 at the close that day. I then looked for near-the-money options approximately two years in length that were priced at 151.60 ($15,160). The only options listed in 2011 were the December options. The strike price that was closest-to-the-money was the 700 strike. Lo and behold, the December 2011 with a strike price of 700 was priced at 151.60 — an exact match.

We can calculate the breakeven at expiration by subtracting the option price from the strike price. That gives us a price of 548.40 — which would indeed represent a disastrous price decline of an additional 25% from the level the index at when the article was written.

But there’s a key part missing from the article, and that is the price of the call! As noted in prior posts about the Citigroup arbitrage situation, there are risk-free trades that someone can do in options if the option prices diverge too far from certain levels. The net effect of all of this is that, generally speaking, if you have non-dividend paying asset where an arbitrage is available, the time value of a short-term put and call at the same strike price and same expiration month has to be the same. You can extend that to a longer term and to a dividend paying stock by doing a little bit of math. Not too difficult. And unless interest rates and dividends are vastly different, and the time horizon quite long, the impact is going not going to be too large.

What this means is, if the put gets expensive, the call also has to be expensive. Otherwise, a risk-free option trade whose profit opportunity exceeds that available via a T-bill or CD is created. For instance, if you have a stock that is at 50, and the 50 put is 5 and the 50 call is 3, you can sell the put at 5, buy the call at 3, and then short the stock at 50 to lock in a sure-thing profit of 2. With S&P 500 Index options, you can do a similar thing: sell an expensive put, buy a cheap call, and then go short the S&P 500 futures. Another risk-free trade, is called ”buy the box“, which is used on index options that are European-style, meaning the options can’t be exercised early.

With that in mind, we can safely assume that in most cases, if any put gets expensive, the comparable call has to get expensive. That’s exactly what happened to the S&P 500 Index options in March. Although Bloomberg correctly points out that the puts got outrageously expensive, what’s not discussed is that the 700 call was $17,650. The breakeven at expiration on that option was 876.50 - almost 20% above the index price (the discrepancy between the 25% up and 20% down can be explained by the long-term impact of dividends and interest rates).

Bottom line, while the price of the put was forecasting a huge decline, the price of the call was forecasting a new bull market, and that’s what actually has happened!

Perhaps a better way of looking at this is by looking at some of the out-of-the-money options to see what the prices were at similar distances from the index price. I looked for a December 2011 put and call that were close to the same price. The 1000 call had an ask of 69.40. The 500 put had an ask of 72.60. Both close in price, and both around 250 points out-of-the-money. [Again, we’re rounding here.] In fact, when you calculate the exact breakevens, the stock market has a little bit further to travel for the call to finish above its breakeven (+45.5%) than the market has to travel for the put to finish below its breakeven (-41.9%). With the out-of-the-money options, traders thought there was a greater chance for a 40% gain than a 40% loss.

The point of all of this is that the conclusion reached by Bloomberg — that the high prices of the options implied that the bear market would continue for two more years — is itself fallacious. Option prices don’t imply direction. Option prices imply magnitude over time.