95% Profitable Trade

Have you ever seen an ad like that? Who wouldn’t want 95% of their trades to be profitable?

This is the “picking up quarters in front of a bulldozer” trade.

Usually, what they are touting is selling far out of the money options. You will be paid a quarter in premium and 95% of the time the stock you are selling the option against does not reach your strike. But 5% of the time it does and all the profits from the 19 successful trades is wiped out by that one bad trade.

Let’s look at an example. We’ll take Baidu, since there is a chance to make more than the transaction cost in that stock.

Baidu

Today is Tuesday, so there are three days to Friday’s close if we put the trade on near today’s close.

The one day one standard deviation move averaged over the last twenty trading days in BIDU is $7.24. To look at the three day one standard deviation price move we multiply this by the square root of three, since price is a random walk. That gives us $12.54 as our one standard deviation move over the next three days. This means that we expect BIDU to end up within $12.54 of its current price 68% of the time after three days. Since it is trading at $173 that means at Friday’s close, we expect BIDU to be between $160.46 and $185.54

If we want a bigger margin of safety, we can go out two standard deviations to plus or minus $25.08. That is, 95% of the time, after three days of trading, a stock with a normal distribution will be within two standard deviations. That gives us a range of $147.92 and $198.08.

Let’s see what we can earn in premium two standard deviations out. The $200 call is selling for $0.05 and the $145 put is selling for $0.25. So if we sold the pair we would be credited with $0.30.

We can do a different analysis and look at the actual tradinig of BIDU, and that way not make any assumptions about its distribution. If we do that, we find that from 31 July 2007 to yesterday, 16th March 2009 there were 410 trading days and 409 price changees.

Looking at those price changes, there were 18 that were bigger than two daily standard deviations and 14 that were smaller than -2 standard deviations (that is, big moves downward). That gives us a probability of 32 / 409 = 7.8% to have a bigger than two standard deviation move in one day. If BIDU’s price changes were normally distributed, that should be 5% so it looks like BIDU has more large moves than the normal distribution and we are closer to 92% safe in this trade than 95% safe.

To give you a fuller picture, of the 18 one day moves that were bigger than two standard deviations, one was a five standard deviation move, two were four standard deviation moves, five were three standard deviation moves, and ten were between two and three standard deviation moves. The downside is safer. Of the 14 big moves there, two were between three and four standard deviations and 12 were between two and three.

So it looks like it is safer to sell the puts. You also make more premium.