What do we really mean by put-call ratio and how should it be expressed?

Question

I need to calculate the put-call ratio for an American option. But I'm a complete naïf: I don't know how. I think I'd use the put open interest and the call open interest. I can imagine two ways to calculate PCR:

1. Simply (as some references tell me) take OI_puts divided by OI_calls and there's my number, right there:

   PCR = OI_puts / OI_calls

2. Or (as other sources seem to suggest) take OI_puts divided by the sum of OI_puts and OI_calls:

   PCR = OI_puts / ( OI_puts + OI_calls )

Further, I don't even know if the ratio can most usefully be expressed as a decimal (i.e., 0.667) or as a fraction (i.e., 2/3) or as the ratio notation I learned in grammar school (i.e., 2:3).

What's the usual, expected, and/or "right" way to calculate PCR?

Answer 1

There is, unfortunately, no broad agreement on this point. In fact, put-call ratios may be constructed from volume as well as open interest, and they can even be constructed from certain subsets of the options chain (e.g., only certain strikes or tenors). I have usually used your option #2, because option #1 has a tendency to be extremely high or even undefined whenever call open interest is very low. This nonlinearity is an undesirable feature for any indicator going into a trading model. Most academic studies, such as Pan and Poteshman (2006), use this version as well.

Answer 2

CBOE defines Put Call ratio as PCR = OIputs / OIcalls and I have always seen it defined this way. You should express it in a decimal way, a fraction doesn't really make sense here if you have 9999 in OIcall and 9998 in OIput for instance.