Using A Constant False Alarm Rate In Trading
by John Ehlers
Modern information theory has existed for the last half century or so. This theory has been responsible
for man significant scientific advances, including recovery of photograph taken in deep space, pinpoint
accuracy of missile guidance and speech synthesis. With such a track record, why couldn't technical
traders apply some principles of information theory to trading methodology? Let's examine a trading
decision method using some of information theory's fundamental concepts.
First of all, trading involves value judgments. One example of value judgment involves a quarter lying in
the street. If you were penniless, you would promptly scoop up that quarter. On the other hand, if you had
just made a killing on 25 contracts of the Standard & Poor's, you would probably just step over the
quarter and go on your way. That quarter would have little value to you. To describe the value function in
a more continuous form, imagine the value of William Tell's arrow as a function of elevation in the
mythical incident in which he had to shoot an arrow through an apple on his son's head. There is a
negative value if the arrow flies too high; there is a large positive value if it flies a few inches above his
son ' s head into the apple; and there is a large negative value if the arrow flies too low. There is no doubt
the value function will influence decisions. You can bet Tell's aim was biased upward. It is difficult to
separate the value function and pure information theory, but let's try.
Assume there is a signal containing information, say a radar echo pulse, that is present some of the time.
The radar also receives noise that contains no information. The problem is to make a decision at each
increment of range whether or not the echo pulse is present, and we can vote yes or no at each increment.
Four outcomes are possible: