Constructing an exponent-weighted average of put-call ratios

A two-knob construction

Editorial note: TradersWeek reads the workflow as a two-knob recipe. Once a lookback and an exponent are chosen, the same reusable weight vector turns a raw put-call series into an inspectable regime filter rather than a black-box smoother.

A weighted moving average is specified by first choosing a lookback length and an exponent before any weights are computed.

Specify lookback and alpha

The worked construction uses a lookback of 8 observations and an exponent of 0.6. Alpha is that exponent, applied to each position index when the weight vector is formed.

The series being smoothed is a put-call ratio formed as put volume divided by call volume at the same observation.

Build the weight vector once

Each position index from 1 through the lookback receives a weight equal to that index raised to the chosen exponent, then divided by the sum of those powered indices.

The weight denominator is computed once because it does not change across the lookback. The resulting normalized coefficients are the weight vector assigned to the ordered observations in that window.

Form the smoothed put-call value

The smoothed value is the sum of the last lookback put-call observations, each multiplied by its corresponding fixed weight. That weighted sum is the smoothed put-call reading for the window.

The same construction is illustrated by applying the smoother to the put-call ratio of a yen futures contract.