Momentum

Momentum is how strongly the price has been moving somewhere lately. If a stock has risen over recent months, it has positive momentum. If it has fallen, negative.

The idea behind it is simple: markets often do not react to new information all at once but gradually, so a trend can carry on for a while. It is not a law, only a tendency observed in the past.

How it is measured

Most simply as the return over a chosen number of trading days h, using the log return:

$$m(h) = \ln \frac{P_t}{P_{t-h}}$$

P is the price today (t) and h trading days ago. Common horizons are 21 days (a month), 63 days (a quarter) and 252 days (a year).

The raw return has a flaw, though: 8% over a quarter means something different in a calm market and in a nervous one. So it is divided by volatility scaled to the horizon:

$$z(h) = \frac{\ln(P_t / P_{t-h})}{\sigma \sqrt{h}}$$

σ is daily volatility (the standard deviation of daily returns) and √h scales it to the whole horizon. The result says by how many ordinary swings the price has moved.

Turning it into a score

z has no upper bound, which makes comparisons awkward, so it is often squeezed by tanh into −1 to +1 and multiplied by a hundred. In the example above: 100 × tanh(0.97) ≈ 75 in the calm market and 100 × tanh(0.48) ≈ 45 in the nervous one.

That is how the Trend Score in our investment models works: it is the average of such scores for 21, 63 and 252 days.

What to watch for

Momentum reverses, and sharply. The biggest losses of momentum strategies come in sudden market turns, when the long-run trend still points one way and the price is already going the other.

It looks backwards. It says what has happened, not what will. A past tendency to continue does not make continuation certain.

Costs. Momentum strategies tend to trade often, and fees and taxes eat into the result.