# Technical Studies Reference

### Market Facilitation Index Colored

This study calculates and displays a Market Facilitation Index (MFI) for the Price and Volume Data. The MFI was created by Dr. Bill Williams and it is an attempt to determine the efficiency of price movement by quantifying the price movement per unit of volume. We describe the calculation below.

Let $$H$$, $$L$$, and $$V$$ be random variables denoting the High Price, Low Price, and Volume, respectively, and let $$H_t$$, $$L_t$$, and $$V_t$$ be their respective values at Index $$t$$. Let $$v$$ be the Multiplier Input. We denote the Market Facilitation Index at Index $$t$$ as $$MFI_t(k)$$, and we compute it for $$t \geq 0$$ as follows.

$$\displaystyle{MFI_t(k) = v\cdot\frac{H_t - L_t}{V_t}}$$

This study also colors the MFI Subgraph according to the following rules.

• $$MFI_t(k) > MFI_{t - 1}(k)$$ and $$V_t > V_{t - 1} \Rightarrow$$ green
• $$MFI_t(k) < MFI_{t - 1}(k)$$ and $$V_t < V_{t - 1} \Rightarrow$$ brown
• $$MFI_t(k) > MFI_{t - 1}(k)$$ and $$V_t < V_{t - 1} \Rightarrow$$ blue
• $$MFI_t(k) < MFI_{t - 1}(k)$$ and $$V_t > V_{t - 1} \Rightarrow$$ red