# Herrick Payoff Index

This study calculates and displays a Herrick Payoff Index for the Price Data. The Herrick Payoff Index helps to show the amount of money flowing into or out of a futures contract. This study uses Open Interest in its calculations. Therefore, the symbol of the chart must contain Open Interest. Only Historical Daily data charts provide Open Interest, not Intraday charts.

The best analysis will be achieved by using Open Interest data that includes the total Open Interest for all the contracts for the underlying market. Some data services will provide open interest data this way or use certain symbols to provide total Open Interest for all contracts for the underlying market.

Let $$H$$, $$L$$, $$OI$$, and $$V$$ be random variables denoting the High Price, Low Price, Open Interest, and Volume respectively, and let $$H_t$$, $$L_t$$, $$OI_t$$, and $$V_t$$ be their respective values at Index $$t$$. We define the High-Low Average Price $$\overline{P}_t^{(HL)}$$ and Modified Open Interest $$OI_t^*$$ as follows.

$$\displaystyle{\overline{P}_t^{(HL)} = \frac{H_t + L_t}{2}}$$

$$\displaystyle{OI_t^* = \left\{ \begin{matrix} OI_t & OI_t > 0 \\ OI_{t - 1} & OI_t \leq 0 \end{matrix}\right .}$$

Let the Value of a .01 Move, Divisor, and Smoothing multiplier Inputs be denoted as $$v_1$$, $$v_2$$, and $$v_3$$, respectively. We define an intermediate function in the calculation of the Herrick Payoff Index. This intermediate function is denoted as $$HPI^*_t(v_1,v_2)$$. The formula for this function depends on the setting of the Maximum or Minimum Open Interest: 1= maximum, 2= minimum Input.

If Maximum or Minimum Open Interest: 1= maximum, 2= minimum is set equal to $$1$$, then we compute $$HPI^*_t(v_1,v_2)$$ for $$t > 0$$ and $$\max\left\{OI^*_t,OI_{t - 1}\right\} > 0$$ as follows.

$$\displaystyle{HPI^*_t(v_1,v_2) = \frac{v_1V_t\left(\overline{P}_t^{(HL)} - \overline{P}_{t - 1}^{(HL)}\right)}{v_2}\cdot\frac{1 \pm 2 \left|OI^*_t - OI_{t - 1}\right|}{\max\left\{OI^*_t,OI_{t - 1}\right\}}}$$

Regarding the $$\pm$$ sign in the above function, $$+$$ is used when $$\overline{P}_t^{(HL)} > \overline{P}_{t - 1}^{(HL)}$$, and $$-$$ is used when $$\overline{P}_t^{(HL)} \leq \overline{P}_{t - 1}^{(HL)}$$.

We denote the Herrick Payoff Index at Index $$t$$ for the given Inputs as $$HPI_t(v_1,v_2,v_3)$$, and we compute it as follows.

For $$t \leq 1$$:

$$\displaystyle{HPI_t(v_1,v_2,v_3) = \left\{ \begin{matrix} HPI^*_t(v_1,v_2) & \max\left\{OI^*_t,OI_{t - 1}\right\} > 0 \\ HPI_{t - 1}(v_1,v_2,v_3) & \max\left\{OI^*_t,OI_{t - 1}\right\} \leq 0 \end{matrix}\right .}$$

For $$t > 0$$:

$$\displaystyle{HPI_t(v_1,v_2,v_3) = \left\{ \begin{matrix} HPI_{t - 1}(v_1,v_2,v_3) + v_3\left(HPI^*_t(v_1,v_2) - HPI_{t - 1}(v_1,v_2,v_3)\right) & \max\left\{OI^*_t,OI_{t - 1}\right\} > 0 \\ HPI_{t - 1}(v_1,v_2,v_3) & \max\left\{OI^*_t,OI_{t - 1}\right\} \leq 0 \end{matrix}\right .}$$

If Maximum or Minimum Open Interest: 1= maximum, 2= minimum is set equal to $$2$$, then we compute $$HPI^*_t(v_1,v_2)$$ and $$HPI_t(v_1,v_2,v_3)$$ in the same way, except that $$\max\left\{OI^*_t,OI_{t - 1}\right\}$$ is replaced with $$\min\left\{OI^*_t,OI_{t - 1}\right\}$$.

#### Inputs

• Value of a .01 Move: This is the price value of a .01 price move.
• Smoothing multiplier: A larger value of this multiplier makes the Herrick Payoff Index less smooth, and using a smaller value makes the Herrick Payoff Index more smooth.
• Maximum or Minimum Open Interest: 1= maximum, 2= minimum: In the calculation of the Herrick Payoff Index, it is necessary to determine the maximum or minimum of the open interest at the current calculation index and the prior index. Set this Input to 1 to use the maximum or to 2 to use the minimum between the current open interest and the prior open interest. Formulas: max(CurrentOpenInterest, PriorOpenInterest), min(CurrentOpenInterest, PriorOpenInterest).
• Divisor: This divisor is used to scale up or down the Herrick Payoff Index.

The spreadsheet below contains the formulas for this study in Spreadsheet format. Save this Spreadsheet to the Data Files Folder.

Open it through File >> Open Spreadsheet.