The Hull Moving Average

There are many, many kinds of moving averages out there. All of them suffer from one kind of weakness or another, much like any sort of parameter does. The Weighted Moving Average and the Exponential Moving Average both try to address lag in the Simple Moving Average by placing emphasis in the calculation in the more recent minutes. I recommend going to Investopedia for calculations of the basic set of technical indicators. For the readers sake with regards to moving averages, an SMA is simply plotted as the average of the past ‘n’ periods. (usually the closing prices of said periods) General interpretations involve a faster (smaller ‘n’) MA crossing over a slower MA to indicate a trend. I prefer price action relative to the usual set of MA’s, myself, rather than MA’s relative to each other.

But, I digress. Enter the Hull Moving Average, or HMA, which attempts to address both lag as well as to smooth out what might otherwise be a choppy line moving in a choppy market. It’s an obscure moving average created by Alan Hull and many chart packages won’t have it available. Here is the equation based on period n (and, “of the price ‘p'”, obviously):

HMA(p,n) = WMA[(2*WMA(p,n/2) – WMA(p,n)), n^1/2]

A bit of a mouthful I know. Let me walk you through it. An HMA of the price ‘p’ based on ‘n’ periods is essentially a WMA of the difference between 2-times the value of a WMA of length ‘n/2’ and a WMA of length ‘n’, based on the square root of ‘n’ periods. Follow? Working from the bottom up, to find HMA(p,n), find WMA(p,n/2), double it, and take away the value of WMA(p,n) to get…. let’s say ‘h’. (as opposed to ‘p’, as in price) Now the HMA (p,n) = WMA (h, n^1/2). Oh and of course every parameter must end up being an integer so rounding occurs in the event of uneven, non-square numbers…. which is exactly why I prefer to use even square numbers as parameters.

Why those particular relations (n/2, n^1/2) exist in the equation is actually beyond me, (probably the result of lots of trial and error) but it doesn’t matter, because as a rule the HMA does what it sets out to do: produce a smoother, less-laggy line. But, as a side effect sometimes the line is prone to overshooting. This is because the two relations can sometimes overcompensate, as any two elements that attempt to eliminate lag are bound to overtake the issue at hand; kind of like rear-ending the guy in front of you if you’re following too close in your car.

Okay, interpretation: I would say that the slope of the HMA is best used as your filter and you wait for a pullback from the direction of the HMA and then a resumption of the movement. For example, the HMA has changed from pointing down to up, and the market is doing that ahead of it. This means that you shall only take long positions in the next short while. So, wait for a pullback from the upwards movement, and get in as the momentum resumes upwards, using the bottom of the pullback or the recent low as a stop. It’s noteworthy that the pullback might occur “within” a candle.

Another way to look at the HMA is, especially in a fast market, the price action relative to it. For example, breaking highs of candles above the HMA, that sort of thing.

Here’s the HMA(16 in blue, 36 in white) in action on Potash (NYSE: POT – which, incidentally is a buy anywhere below 100 I say) today. Also, Apple (NASDAQ: AAPL) and Exxon Mobil (NYSE: XOM) The HMA is useful on dailies as well, but unfortunately, given the incredibly large swings day-to-day in the equity markets these last many months using any indicator on a daily chart with that recent data won’t provide a good sample at all. The good news: daily activity in ’09 has been, while fast, a lot more reasonable than the craziness that was September through November.