Random Walk Index and Uses

What Is the Random Walk Index?

The random walk index (RWI) 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. It can be used to generate trade signals based on the strength of the underlying price trend.

Understanding the 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 movements that are 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 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 RWI applies these mathematical principles when measuring an uptrend and downtrend to determine if it's random or statistically meaningful.

Because the indicator measures both uptrend and downtrend strength, the indicator has two lines and requires separate calculations for both.

The calculation for high periods, or RWI High, is:

RWI High = High − Low n ATR × n where: n = number of days in the period ATR = average true range \begin{aligned} &\text{RWI High} = \frac { \text{High} - \text{Low}_n}{ \text{ATR} \times \sqrt{n} } \\ &\textbf{where:} \\ &n = \text{number of days in the period} \\ &\text{ATR} = \text{average true range} \\ \end{aligned} RWI High=ATR×nHigh−Lownwhere:n=number of days in the periodATR=average true range

In other words, if you're calculating the RWI High of the last five days, take the high from today minus the low from the prior period and calculate RWI High. Then calculate using today's high minus the low two days ago. Do this for each day going back five trading sessions.

Your RWI High value is the highest value of the last five days or for however many periods (n) were chosen.

RWI Low is calculated as follows:

RWI Low = High n − Low ATR × n \begin{aligned} &\text{RWI Low} = \frac { \text{High}_n - \text{Low} }{ \text{ATR} \times \sqrt{n} } \\ \end{aligned} RWI Low=ATR×nHighn−Low

The method is similar to the approach above, except now we will use today's low and the high from the prior period to create the first calculation. Then use the high from two days ago. Do this for each of the n periods. The RWI Low value is the lowest number of the n calculations completed.

Each day (or period) the calculations are completed again.

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 investments. 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. If RWI Low is above one, it indicates a strong downtrend; if RWI High is above one, it indicates a strong uptrend.

Often times, traders and market timers will enter long positions when a long-term RWI High is greater than 1.0 and the short-term RWI Low is also above 1.0. This means the trader tracks two RWI calculation, a longer-term one, say 64-periods, and a short-term one, say seven-periods.

A trader buys when the long-term RWI High is above 1.0, which indicates a long-term strong uptrend, but the short-term RWI Low is also above 1.0, showing that in the short term the price has dropped, providing a favorable entry into the long-term uptrend.

Short positions may be entered when the long-term RWI Low is greater than 1.0 and the short-term RWI High peaks above one as well.

Some traders may look to use crossovers of the two lines to indicate potential trades. This will work well when strong trends develop, but it will result in lots of losing trades if the price doesn't trend well since crossovers could occur without a strong trend resulting. That said, some traders may wish to utilize this approach, potentially in conjunction with other forms of technical analysis.

Example of How to Use the Random Walk Index

The daily chart of Apple Inc. (AAPL) has a 30-period RWI indicator applied to it.

When the price is falling the red line, or RWI Low, is on top.

When the price is rising the green line, or RWI High, is on top.

When either one of these lines is above one, the black horizontal line, it indicates a strong trend.

Image by Sabrina Jiang © Investopedia 2021

On the left, there is a strong uptrend. The RWI High moves above 1.0, and the RWI Low is below 1.0.

Then a strong downtrend begins. The RWI Low moves above 1.0, and the RWI High is well below 1.0.

This is followed by another uptrend with similar conditions to the prior uptrend.

Then the stock enters a weak trending period. Neither the RWI Low or High maintains its position above 1.0 for long. For a brief period, the two lines even become tangled around the zero mark, signaling a very weak trend, or choppy trading, in both directions.

The Difference Between the Random Walk Index and the Average Directional Index (ADX)

These two indicators look quite similar and, in fact, are quite similar. The average directional index (ADX) is composed of directional movement lines (DI+ and DI-) which move in a very similar ways to the RWI Low and High. The ADX is a third line on the ADX indicator and shows the strength of the trend. Readings above 25 indicate a strong trend.

Limitations of the Random Walk Index

The RWI is a lagging indicator. It uses past data in its calculation and there is nothing inherently predictive about it. While the indicator can move above one to signal a strong trend, it can easily slip back below one very quickly. It can also go from a weak trend to a strong trend with little forewarning from the indicator.

Waiting for the indicator to move above one before taking a trade in that direction can sometimes result in a poor entry. The price has already been moving in that direction for some time and may be ready to reverse or enter a pullback.

The random walk index is best used in conjunction with price action analysis or other forms of technical analysis.