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Put-Call Ratio Definitions and Options for Constructing the Measure

Article Quant Q&A · Author: Pete Wilson
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Summary

The document compares two common ways to calculate a put-call ratio from options open interest: puts divided by calls, and puts divided by the combined put and call total. It also notes that the ratio can instead use trading volume or a selected subset of an options chain, such as particular strikes or maturities. The answers disagree on whether one formula is standard, reflecting a lack of broad agreement across sources.

One answer favors the combined-total denominator because the puts-over-calls form can become very large or undefined when call open interest is small. It says academic studies, including Pan and Poteshman (2006), use the combined-total form. Another answer attributes the puts-over-calls definition to CBOE and recommends expressing the measure as a decimal. The practical lesson is to define the data and formula explicitly before interpreting or comparing PCR values; the thread does not resolve which convention should be universal.

Key ideas

  • Put-call ratios may use open interest or trading volume as their underlying data.
  • A common formula divides put open interest by call open interest, while another divides it by total put and call open interest.
  • The puts-over-calls formula can become unstable when call open interest is very low.
  • Ratios can be calculated on selected strikes or maturities, so the options-chain scope should be specified.

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


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












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:

- Simply (as some references tell me) take OIputs divided by OIcalls and there's my number, right there: PCR = OIputs / OIcalls

- Or (as other sources seem to suggest) take OIputs divided by the sum of OIputs and OIcalls: PCR = OIputs / ( OIputs + OIcalls )

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 by Tal Fishman (score 4, accepted)

https://quant.stackexchange.com/a/2120

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 by Lliane (score 2)

https://quant.stackexchange.com/a/2117

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.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.