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Mathematical/probuilder · probacktest · proorder · proscreener

LOG

LOG in ProBuilder returns the natural logarithm of a value, the logarithm to base e. Input must be positive. Syntax, the inverse link to EXP, examples.

Syntax

probuilder
LOG(a)

Parameters

NameTypeDescription
anumberA strictly positive value or expression. Zero and negative inputs are undefined and raise an error.

Formula

code
LOG(x) = natural logarithm of x,   base e,   defined for x > 0

LOG(1) returns 0, LOG(e) returns 1, and values between 0 and 1 return negative results. As a approaches zero the output falls without bound.

How it works

LOG is the natural logarithm, base e, sometimes called the Neperian logarithm. It answers the question: to what power must e be raised to reach a. The input must be positive; feeding it zero or a negative value is undefined.

LOG and EXP are inverses, so LOG(EXP(x)) returns x and EXP(LOG(x)) returns x for positive x. The most common use in trading is the log return, LOG(close / close[1]), which is additive across bars and symmetric for equal up and down moves, making it well suited to volatility work.

Examples

Example 1, Natural log of a value (Indicator)

probuilder
// Natural logarithm of a fixed input
variable1 = 7.389
logValue = LOG(variable1)
RETURN logValue AS "LOG(7.389)"

LOG(7.389) returns approximately 2, since e squared is close to 7.389.

Example 2, Log return over one bar (ProScreener)

probuilder
// Screen instruments by their latest one-bar log return
r = LOG(close / close[1])
SCREENER[r > 0.01](r AS "Log return")

The ratio close / close[1] is always positive on valid data, so the LOG input stays inside its domain.

Example 3, Log-based volatility filter (ProOrder)

probuilder
// Standard deviation of log returns as a volatility gate
logRet = LOG(close / close[1])
vol = STD[20](logRet)
IF vol < 0.02 AND NOT LongOnMarket AND close CROSSES OVER Average[20](close) THEN
  BUY 1 CONTRACT AT MARKET
ENDIF

Log returns feed a standard deviation that measures volatility, and entries are only allowed while volatility stays contained.

Common errors and gotchas

  • Input must be strictly positive. LOG(0) and LOG of any negative value are undefined and raise an error. Guard the argument when it can reach zero or below.
  • Natural log, not base 10. LOG uses base e, not base 10. For a base-10 logarithm, divide by LOG(10).
  • Inverse of EXP, not the reciprocal. LOG undoes EXP. It is not 1 / EXP. To raise a base to a power, use Pow.
  • EXP, the natural exponential, the inverse of LOG.
  • Pow, raises a base to a power.
  • SQRT, square root, often used together in volatility formulas.
  • ABS, absolute value.
  • ROC, rate of change, an alternative return measure.
  • Variation, percentage change between bars.
  • HistoricVolatility, built-in volatility measure related to log returns.