Don’t Get Fooled By Options Probabilities

Lately I have been seeing more and more newsletter authors beginning to offer options advice.  Often I find them advocating a trade by suggesting it is likely to succeed because it has a certain probability of success.  If a trade is touted as having a 91.3% chance of success it might seem attractive, but are these numbers truly accurate and what do they truly mean?

A more accurate description of the same trade would be “this trade is priced as if it has a 91.3% chance of success.”  This distinction may seem to be subtle and overly academic but for traders it’s an important one.  The purpose of this article is to explain where these numbers come from, what they mean, and, more importantly, what they don’t mean.

Let’s start by considering a bookie who is taking bets on the big Frisbee contest between the Springfield Sharks and the Centerville Condors.  You want to put a wager on your Sharks and the bookie is offering 6-5 odds; that is, you place $5 you’ll win $6 if the Sharks prevail.  That means the bet is priced as if the sharks would win 5 of every 11 times. But it doesn’t mean those are the odds of winning.

Bookies don’t like risk, they prefer if they have about the same number of bets on the Sharks as they do on the Condors.  So we could imagine that the two teams might be equally likely to win, but so many Condors fans have placed bets.  When that happens the bookie shifts the odds to slightly discourage the Condors bettors and encourage Sharks bettors.

Like bookies, options market makers are risk averse.  Market makers enjoy low trading costs and different margin requirements but in return they are required to completely hedge their book so they must take an equal number of bets on both sides.  Also like bookies, they will offer pricing to encourage certain trades and discourage others.  Put simply, just like the one open store after a storm a market maker is going to raise prices on whatever is most in demand.  This distorts price away from what it would be under fair conditions.  Our next step is to see how this affects probabilities.

Most option analysis platforms can tell us the probability of success of a trade.  These probabilities of are determined by an options pricing model.  These models use mathematical models can approximate what an option is worth based on the following information:

1. The type of options: put or call
2. The strike price of the option
3. The current price of the underlying instrument
4. The time remaining until expiration of the option
5. The volatility of the underlying instrument
6. Expected dividends
7. The rate which could be earned on an alternative investment with no risk (usually U. S. treasuries)

At any point in time we know what option type and strike we’re considering, we know the price that the underlying is trading at and all of the other inputs except for volatility.  In simple terms, volatility is a representation of the probability that price will reach various different price levels and, therefore, a means for us to calculate the probability that any trade might be profitable.  However, we do know the current price of the option.  So if we plug in all of the numbers we know we can figure out which volatility, combined with all the known inputs will give a price equal to what the option is trading for now.  This is what is known as implied volatility because we can’t know what the future volatility is going to be, but we know what current option prices suggest it will be.

This implied volatility is the link between option prices and the probability of a trade being successful.  We’ve already discussed how options market makers, like bookies, will move prices around to their advantage.  That means they will also move around the probability of success.

Let’s look at an example of how we can get fooled by these values.  Imagine that the creatively named, fictitious XYZ corp. is currently trading for $100/share.  Furthermore, let’s assume that a fair estimate of volatility is 30% and based on the other inputs that would suggest that the $110 calls expiring in 20 days are worth $0.30.  Based on all of these inputs, these calls have a 91.8% chance of expiring worthless and, therefore, the trader keeping the full $0.30.  But let’s say that the market makers will only let you sell the options for $0.20.  That pricing would imply a volatility of 27% and, therefore, a probability of success of 93.8%.

Market makers are always trying to give us bad prices so they can make a better deal for themselves.  In our example they hurt us in two ways:

1. They give us too little money by giving us only $0.20 when we should get $0.30; and
2. They make us think that it’s OK to only collect so little because we’ll only fail 6.2% of the time when, in reality, the trade will fail 8.2% of the time.

Trading platforms keep getting more and more advanced and, today’s platforms can give us volumes of very detailed calculations.  When looking at so many very precise numbers it is easy to get fooled into believing that these numbers, like the probability of success, are accurate representations of the true probability.  However, any model is, at best, just an approximation of reality even when given good data.  In the case of probabilities, we know that these calculations are based on prices which can be manipulated and therefore are unlikely to give us reliable information.  The lesson here is that it is better to treat numbers from an options model as rough approximations rather than accurate representations of probabilities as we’re conditioned to expect when we get precise numbers from a computer.