Momentum and trend

Time Series, lesson 7

Series that keep going, and how to tell the difference.

You know autocorrelation, the variance ratio and mean reversion. A Sharpe ratio here is yearly return divided by yearly volatility.

Part 1. Follow or fade

Twenty simulated markets, ten years each. One rule follows: hold the direction of the past return over some look-back. The other fades: hold the opposite. Slide the look-back.

Follow or fadeLive

Same markets, same days, opposite verdicts. Over a day or two, a rise tended to slip back, so fading won. Over months, a rise tended to continue, so following won. Whether a series trends or reverts depends on the horizon you ask about.

Momentum and reversal

Momentum, or trend, is when past returns over some horizon predict future returns of the same sign. Reversal is when they predict the opposite sign. Trading in the direction of momentum is trend following.

Your turn

A market's daily returns have a negative lag-1 autocorrelation, yet its 12-month return predicts next month's with a positive sign. Is that a contradiction?

The day-to-day bounce and the slow drift are different parts of the series. The markets in the lab were built exactly that way: a drift that lasts months, plus a small bounce from one day to the next.

Show the answer

D. The day-to-day bounce and the slow drift are different parts of the series. The markets in the lab were built exactly that way: a drift that lasts months, plus a small bounce from one day to the next.

Part 2. The bounce is often the spread

Keep going with Pro

You've done the first part. Pro opens the rest of this lesson, and every other one.

Still to come

The bounce is often the spread
A worked problem
The same thing, for real

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Next lessonAutoregressive modelsPredicting the next value from the last few. Start lesson 8

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07 · Momentum and trend