# Kaufman's Adaptive Moving Average (KAMA) – Formula and how does it work?

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It was created in 1988 by American quantitative finance theorist Perry J. Kaufman and is known as Kaufman's Adaptive Moving Average (KAMA). Even though the method was developed as early as 1972, it was not until the popular book titled "Trading Systems and Methods" that it was made widely available to the public. Unlike other conventional moving averages systems, the Kaufman's Adaptive Moving Average, considers market volatility apart from price fluctuations.

KAMAi=KAMAi-1+SC☓(price-KAMAi-1)

## What are the advantages of Kaufman's Adaptive Moving Average?

There is a co-relation between market volatility and the Kaufman Adaptive Moving Average (KAMA). As the market remains less volatile the KAMA stays close to the current market price but with an increase in volatility, it trails behind. The objective of the KAMA is to sort out small and insignificant price surges that are also known as “market noise”.

## How is Kaufman Adaptive Moving Average Calculated?

Kaufman Adaptive Moving Average is calculated in three stages:

• Efficiency Ratio (ER)

• Smoothing Constant

• KAMA

For the purpose of computing Kaufman's Adaptive Moving Average, the following standard parameters are employed −

• 10 − The number of periods for which the Efficiency Ratio is calculated.

• 2 − the number of periods in which the quickest exponential moving average is calculated

• 30 − Number of periods in the exponential moving average with the slowest decay.

To determine the value of the KAMA, you must first compute the values of the Efficiency Ratio and the Smoothing Constant. Then you may calculate the value of the KAMA.

## The first step is to calculate the efficiency ratio (ER)

Using the efficiency ratio, you may determine how effective pricing adjustments occur. It moves between 1 and 0 on a scale. ER equals zero (zero) when the price stays constant over a period of ten periods. In contrast, if a price increases or moves down for 10 consecutive periods, the ER is reduced to one.

ER = change/Volatality

Change = Absolute Value [Close − Close(Past 10 periods)]

Volatality Sum = 10 periods(Close − Prior Close)

Determined by dividing the absolute difference between the current price and its starting value by a total of the absolute differences between each pair of closes throughout the course of a time, it is a helpful indicator to track of market volatility. The following is the formula for determining the rate of return

• ER is an abbreviation for change/volatility.

• Change equals the absolute value of anything. [Close − Close (for the last ten sessions)]

• The sum of volatility periods is equal to ten periods (Close − Prior Close).

## Smoothing Constant is the (Second Step) (SC)

The smoothing constant is computed for each term in the time interval between two points. It makes use of the value acquired for the efficiency ratio, as well as two smoothing constants, in the following ways −

SC = [ER ☓ (Fastest SC − Slowest SC) + Slowest SC]2

SC = [ER ☓ (2 ÷(2+1)−2÷(30+1)]2

Fastest SC ☓ (Fastest SC − Slowest SC) + Slowest SC is the product of the two fastest SCs.

SC= [ER ☓ (2/ (2+1) − 2/(30+1)) +2/ (30+1)] + [ER ☓ (2/ (2+1) − 2/(30+1)] + [ER ☓ (2/ (2+1)− 2/(30+1)] + [ER ☓ (2/ (2+1) − 2/(30+1)] + [ER ☓ (2/ (2+1) − 2/(30+1)]

The smoothing constant for the suggested 30-period exponential moving average (EMA) is (2/30+1) in the equation above. In addition, the SC for the slowest 30-period EMA is the slowest smoothing constant, while the quickest smoothing constant is the SC for the shortest 2-period EMA is the fastest.

## KAMA is the third step.

The final and third step in Kaufman’s Adaptive Moving Average indicator is to collect the values from the above two steps of smoothing constant (SC) & Efficiency Function. Once could now calculate using the below formula.

KAMAi=KAMAi-1+SC☓(price-KAMAi-1)

Prices are calculated as follows: Price-KAMAi−1 = KAMAi-1 + SC ☓ (Price-KAMAi-1)

Where −

## KAMAi is the current period's value, expressed as a percentage.

KAMAi-1 is the value of the period before the period for which the calculation is being performed.

The source price for the time under consideration is represented by the term "price."

## What is Adaptive Moving Average and How to implement it?

Kaufman's Adaptive Moving Average indication provides traders with a clear image of the market's behavior, which they may use to make trading choices on the basis of that picture. The final values of the indicator are calculated based on historical data. On the basis of the assumption that future trends will continue to develop in the same direction as previous trends, traders make their decisions about where to place their money.

On a chart, traders may use the Kaufman's Adaptive Moving Average indicator to study the behavior of a market and make predictions about future price movement. Existing trends, indicators of a potential imminent trend shift, and market reversal points may all be identified using the KAMA indicator, which can then be utilized to enter or exit trades.