9A.4 The put–call ratio · M09A Options desk

Motivation

The put–call ratio (PCR) is quoted daily as a sentiment gauge. It is a ratio of two flows or two stocks of positions, and it moves for reasons unrelated to sentiment.

Definitions

For one expiry (or summed across expiries) with call and put OI $c_K,p_K$ and volumes $v^c_K,v^p_K$ at strike $K$ :

\mathrm{PCR}_{OI}=\frac{\sum_K p_K}{\sum_K c_K},\qquad \mathrm{PCR}_{vol}=\frac{\sum_K v^p_K}{\sum_K v^c_K}. \tag{9A.3}

The folk reading for index options is contrarian: a high PCR (many puts) is called "oversold" and bullish, a low PCR "overbought". Thresholds such as 0.7 and 1.3 are conventions without a published derivation.

9A.4.1Strikes, hedging and the ratio#

Proposition 9A.2PCR is not a property of the market alone

(a) $\mathrm{PCR}_{OI}$ depends on the set of strikes included: adding strikes below the forward raises it whenever their put-to-call OI ratio exceeds the current PCR. (b) If a fraction of the put OI belongs to protective puts held against long stock or futures, and a fraction of the call OI to covered calls, the ratio changes with hedging policy at an unchanged directional view.

Proof

(a) For positive numbers, $\frac{P+p}{C+c}>\frac PC$ iff $\frac pc>\frac PC$ (cross-multiply). (b) Write $P=P_h+P_v$ and $C=C_h+C_v$ with $h$ the hedging and $v$ the view-driven parts. Holding $P_v,C_v$ fixed, the ratio is strictly increasing in $P_h$ and decreasing in $C_h$ .∎

Index puts are bought for portfolio insurance by institutions and sold by others to earn the variance premium (M09 · 9.4); calls are written against holdings. So the "normal" level of index PCR is not 1 and drifts with the population of hedgers.

9A.4.2Evidence on the PCR#

Evidence Pan and Poteshman (2006) show, on proprietary CBOE data for 1990–2001, that stocks with low put–call ratios built from opening buy volume by non-market-makers outperform stocks with high ratios by more than 40 bp the next day and more than 1% over the next week, and they attribute the predictability to non-public information of option traders. The public, aggregate PCR mixes opening and closing trades and both sides, which is exactly the information their split removes. Their result is therefore not evidence for the broker PCR.

Indian data point For the 31 Nifty weekly and monthly expiries from 7 Apr to 3 Nov 2026, the day-before $\mathrm{PCR}_{OI}$ of the expiring series ranged from 0.49 to 1.67, and its correlation with the next day's index change was 0.007 (NSE F&O bhavcopies; computation in this module's scratch analysis). Thirty-one points cannot establish a small effect either way; they do show that PCR is not a strong one-day signal.

Practitioner notes

Read PCR as a description of how positions are distributed, alongside the strikes that carry them. A rise in $\mathrm{PCR}_{OI}$ from put writing near the money and from put buying far below the money are opposite risk transfers with the same effect on the ratio.

See it live: the put–call ratio by OI is on each F&O stock's page at https://oicharts.com/stocks/SYMBOL, next to the OI by strike that it summarises. Read the two together, per the note above.