In working with a client today, a question came up about the validity of probabilities of success in certain risk-defined trades. The question was “How do you know that the probability of success in a vertical spread is equal to the max loss divided by the strike width?”. Wow, pretty technical question, and harder to answer than it would first seem.
In the market, there are millions of players out there chugging along with their models and calculations, doing their best to snatch up every free penny that floats by. Because of this, the instruments that have reasonable volume have prices that are based on the aggregate expectations of all the traders involved. This means the price of any sufficiently traded instrument is a “fair” one - it’s the agreed-upon value off all players at any given time.
Now, price can be seen as the current value of some set of future cash flows, or as the value of all future outcomes, weighted by their probabilities of occurrence. Don’t have a math degree? It’s ok, because the market pros do the work for you… you just have to look at one number, the price. We know the price represents all expectations for future price and performance by all players in the market, all at one time.
Because we know that each product is fairly priced (again, assuming it’s a liquid product), we can then place confidence in the prices of more complicated trades based on those individual prices (like spreads, condors, strangles, etc). Well, since we calculate the probability of success of a vertical spread based on spread width (an absolute, no issue trusting this!) and price (the agreed-upon value by all players in the market, we trust this too!) then we can safely trust the probabilities of success given by our calculations that are based on price.
Good news - the market works, and we love it! Now get out there and get trading!