EXP

Syntax

EXP(a)

Parameters

Formula

EXP(x) = e^x,   where e is approximately 2.71828

The output is always positive. Positive exponents grow the value above 1, a zero exponent returns 1, and negative exponents give a value between 0 and 1.

How it works

EXP models continuous exponential growth or decay. It accepts any real input and always returns a positive result, so it never produces zero or a negative number. Large positive exponents grow very fast, which is worth keeping in mind when the argument is derived from price.

EXP and LOG are inverses: EXP(LOG(x)) returns x for any positive x, and LOG(EXP(x)) returns x for any x. This pairing is the basis for working in log space, for example compounding returns.

Examples

Example 1, Basic exponential values (Indicator)

// e raised to a few exponents
variable1 = EXP(1)   // approximately 2.71828
variable2 = EXP(0)   // exactly 1
variable3 = EXP(-1)  // approximately 0.36788
RETURN variable1 AS "e^1", variable2 AS "e^0", variable3 AS "e^-1"

The three calls show the growth for a positive exponent, the fixed value at zero, and the decay for a negative exponent.

Example 2, Compound a log return (ProScreener)

// Turn a summed log return back into a price ratio
logRet = LOG(close / close[20])
ratio = EXP(logRet)
SCREENER[ratio > 1.05](ratio AS "20-bar ratio")

LOG measures the return in log space and EXP converts it back to a plain ratio, showing the round trip between the two functions.

Example 3, Exponentially decaying weight (ProOrder)

// Weight recency with an exponential decay factor
barsSince = BarIndex - BarIndex[5]
weight = EXP(-0.2 * barsSince)
IF NOT LongOnMarket AND close CROSSES OVER Average[20](close) AND weight > 0.3 THEN
  BUY 1 CONTRACT AT MARKET
ENDIF

The negative exponent produces a weight that decays smoothly toward zero as bars pass, a common way to emphasize recent events.

Common errors and gotchas

• Output is always positive. EXP never returns zero or a negative value, so testing its result against a negative threshold is always false.
• Grows very fast. A large positive argument can produce an enormous value. Keep the exponent bounded when it comes from raw price differences.
• Inverse of LOG, not the reciprocal. EXP undoes the natural logarithm. It is not 1 / LOG. To raise an arbitrary base to a power, use Pow.

Related instructions

• LOG, natural logarithm, the inverse of EXP.
• Pow, raises any base to a power, unlike the fixed base e of EXP.
• SQRT, square root.
• SQUARE, squares a value.
• ABS, absolute value.
• ExponentialAverage, exponential moving average built on similar decay ideas.
• ROC, rate of change, often analyzed in log space using EXP and LOG.