Half-span and full-span moving average (Hurst)

Who this entry is for — Chapter 3 explained what a moving average really is; here it becomes a forecasting tool: when the half-cycle average reverses, the trading cycle's move is exactly halfway done. The rest is measured with a ruler.

Source: J. M. Hurst, The Profit Magic of Stock Transaction Timing, Prentice-Hall, 1970 — Chapter 6, How to Construct and Use Half-Span Moving Averages and Other Uses… (pp. 97–109).

Prerequisites

Cyclic moving averages (span, cutoff, −½-span placement) and a trading-cycle duration measured with the envelope.

The lab to get your hands on the placement:

Same average, two placements: centred at −½ span it runs down the middle of the channel.

The geometry of the half span

In plain words — 20-week trading cycle → 10-week average. Its lag is 5 weeks = a quarter cycle. When the average turns, price has already covered half of the move that cycle will produce. Another half remains: there is your forecast.

The 10-week average zeroes 10-week fluctuations and drastically reduces shorter ones; the 20-week cycle comes through at nearly full strength. So the average only changes direction when the 20-week cycle makes it do so — and the 5-week lag is precisely the time the cycle needs to drive price halfway. At the average's top, the stock has been falling for 5 weeks and is half way down; at its bottom, half way up. "That it does work — time after time — is very powerful evidence indeed for the validity of the model."

Card — The basic procedure

1. Average trading-cycle duration from a quick envelope.
2. Average with span = half that duration (rounded; preferably odd).
3. Plotted −½ span on the stock's chart.
4. On reversal: how much has price already moved? As much again remains.

The precision version: two averages

In plain words — Add the full-cycle average: it is the channel's centre line. On the half-span's reversal, carry both through their lags to the price crossing: that level is the exact middle of the move. Target = crossing + the road already travelled, ±10%.

The full-span (20 weeks in the example) zeroes the trading cycle: what remains is the sum of the longer components — the channel's centre line, theoretical and clean (small "leaks" of short components smooth out graphically). On the half-span's reversal you extrapolate both averages through their lags to the crossing with price — easy for the full-span, it is so smooth. Then the ruler:

crossing − previous extreme = half the move;
target = crossing + the same distance;
tolerance = ±10% of the total move → the prediction zone;
rough timing: zone entry ≈ crossing date + ½ the half-span (broad tolerance: in the book, 5 weeks predicted against 9, 3–6 and 3–5 observed).

Figs. VI-1/VI-6 redone: the half-span turns, the extrapolations cross the price, the zone waits ahead.

Tap the reversal, the crossing and the zone

The full-span's other gift

Warning — The full-span sees channel turns before the envelopes, real or non-real-time. On Alloys: a cycle high of 48¾ under the previous 49¾ — everything suggested the channel was still down. But the 20-week average was rising: the long sum had turned, the channel had bottomed at 32⅛. Envelope analysis alone could only confirm it three weeks later, at the 52⅞ top.

And the graphics-computation duet works both ways: where the channel is not obvious, plotting the two averages "makes identification of channel bounds very much easier" — then the refined duration rebuilds better averages.

Summary card

Element	Rule
Half-span	Span = ½ trading cycle; reversal = half the move
Full-span	Span = trading cycle; it is the channel's centre line
Target	Extrapolation crossing + leg already done
Zone	±10% of the total move
Time	Crossing + ½ half-span (broad tolerance)
Bonus	The full-span anticipates channel turns