What Is Random Walk Index

The Random Walk Index is a technical indicator that compares a security’s price movements to random movements in an effort to determine if it’s in a statistically significant trend.

Breaking Down Random Walk Index

The Random Walk Index was created by Michael Poulos in order to determine if a security’s current price action is exhibiting “random walk” or is the result of a statistically significant trend, higher or lower. Random walk refers to market or security movement within the realm of statistical "noise" levels and not consistent with a confirmed or definable trend. The technical indicator was originally published in Technical Analysis of Stocks and Commodities (TASC) magazine in a 1990's article entitled, “Of Trends And Random Walks”. Market trend and random walk studies go back for decades, highlighted by R.A. Stevenson's publication of "Commodity Futures: Trends Or Random Walks?" in the March 1970 issue of The Journal Of Finance. 

Calculating the Random Walk Index

William Feller, a mathematician who specialized in probability theory, proved that the bounds of randomness, also known as displacement distances, could be calculated by taking the square foot of the number of binary events, which refer to two-sided outcomes with equal probability (like a coin toss). Logically speaking, any movement outside of these bounds suggests the movement is not inherently random in nature. The Random Walk Index applies these mathematical principles when measuring an uptrend and downtrend to determine if it’s random or statistically meaningful.

The calculation for high periods:

HILO.nATR.1(n)×n\dfrac{HI - LO.n}{ATR.1(n)} \times \sqrt{n}ATR.1(n)HILO.n×n

Random Walk Index (RWI) is computed for each time segment by calculating the maximum of the following values for low periods:

HI.nLOATR.1(n)×n\dfrac{HI.n - LO}{ATR.1(n)} \times \sqrt{n}ATR.1(n)HI.nLO×n

Trading the Random Walk Index

The Random Walk Index is typically used over two to seven periods for short-term trading and scalping and eight to 64 periods for long-term trading and timed investment but market players may wish to experiment with these settings to determine what works best for their overall strategies. Readings above 1.0 indicate that a security is trending higher or lower, while readings below 1.0 suggest that a security may be moving randomly.

Often times, traders and market timers will enter long positions when the long-term RWI is greater than 1.0 and the short-term RWI lows peak above 1.0. Short positions may be entered when the long-term RWI of the lows is greater than 1.0 and the short-term RWI of the high peaks above 1.0.