Specifying a Trend Signal

"Buy what is going up" is not a rule. It becomes one only when you answer three questions: over what window you measure the move, in what units you express it, and how large a position each level of the signal earns. Two managers who agree completely on trend-following can produce books with a correlation of 0.4 purely from these choices. This page is about making them deliberately.

Three ways to say "going up"

• Past return sign. Is the 12-month return positive? Long if yes, short if no. The academic default.
• Moving-average crossover. Is a fast moving average above a slow one? A 16-day exponential average versus a 64-day is a common pair.
• Breakout. Is today's price at a new 20-day high? The original Turtle rule.

These are less different than they look. A crossover of two exponential averages is algebraically a weighted average of past returns, with weights that rise then decay — so it is a smoothed version of the return-sign rule, and it changes state less often. Breakouts are the same idea with a step response, and they trade least of all. Pick on turnover and robustness, not on lore.

Standardise before you compare

A 70-point move in gold and a 70-tick move in Eurodollar futures are not comparable. Divide by the instrument's own volatility so every market speaks the same language:

$x_t = \frac{\mathrm{EMA}_{16}(P) - \mathrm{EMA}_{64}(P)}{\sigma_t}$

In words: take the gap between the fast and slow averages of price, and divide it by one day's typical price movement. The result $x_t$ is a risk-adjusted trend strength — how many daily standard deviations of trend you are looking at — and it is directly comparable between crude oil and the Bund. Scale it so its long-run average absolute value is 1, and a reading of 2 means "twice a normal-strength trend" in any market.

Worked example: gold to contracts

Gold trades at 2,400 with a 16-day EMA of 2,380 and a 64-day EMA of 2,310. Daily volatility is 1.1%.

1. Raw signal: $2380 - 2310 = 70$ points.
2. Daily price volatility: $2400 \times 0.011 = 26.4$ points.
3. Standardised signal: $70 / 26.4 = 2.65$.
4. Capped: most books clip at $\pm 2$, so the forecast is 2.0.
5. Annualised gold volatility: $1.1\% \times \sqrt{256} \approx 17.6\%$.
6. Position value: gold's slice of the book is $10m at a 10% volatility target, so the notional is $2.0 \times (10/17.6) \times 10 \approx 11.4$ million dollars.
7. Contracts: a gold future is 100 ounces, so $240,000 each, giving $11{,}400{,}000 / 240{,}000 \approx 47$ contracts.

Every step is mechanical. Change one input — the cap, the volatility estimate, the target — and the contract count moves proportionally.

The response function is the real design choice

Step 4 hid the most consequential decision: how position size varies with signal strength. Three shapes dominate.

The binary rule is maximally responsive at zero: a signal wobbling around 0 flips a full-size position back and forth and pays the spread every time. The linear rule fixes that but has no ceiling, so a market in a historic move can grow to several times its risk budget. Capped linear takes the informative middle and truncates the tails, which is a risk control disguised as a signal choice.

Speed costs money

Faster signals see turns earlier and trade far more. Suppose the gross edge is 5.0% at a 10% volatility target — a gross Sharpe of 0.50 — and compare two speeds on the same 60-market book:

Crossover	Round trips per market per year	Annual cost	Net return	Net Sharpe
8 / 32 (fast)	~14	1.2%	3.8%	0.38
32 / 128 (medium)	~4	0.4%	4.6%	0.46

The fast version is not worse at forecasting; it is worse after costs. This is why fast trend survives mainly in the cheapest markets and why cost estimates belong in the signal-selection step, not in a post-hoc adjustment.

In interviews

Walk the full chain out loud: raw signal, divide by the instrument's volatility, cap the forecast, scale by the volatility target, convert to contracts. Then say the thing most candidates miss — the response function matters more than the lookback, and the cap is a risk control. Close on the cost trade-off: faster signals forecast fine and lose to turnover, which is why blending speeds beats picking one.