In their September 2005 paper entitled “Acceleration Strategies”, Eric Gettleman and Joseph Marks examine the change in six-month stock price momentum (a second derivative of price with respect to time, which the authors call “acceleration”) for individual companies as a potential indicator of future performance. Does increasing (decreasing) stock price momentum indicate commensurate relative outperformance (underperformance)? Based on monthly data spanning 1926-2003, *they conclude that:*

- Stocks with extremely high price acceleration outperform stocks with extremely low price acceleration by 6.15% when controlled only for momentum and 4.5% when controlled for other possible effects.
- Trading on both stock price momentum and acceleration extends the outperformance of simple momentum strategies by about 3% over a six-month holding period, with a higher Sharpe ratio.
- These results are consistent with the behavioral view that investors react only gradually to firm-specific information.

In summary, *focusing on stocks with both high six-month momentum and rapidly increasing six-month momentum offers significant excess returns.*

A more precise analogy with physics suggests that “impulse” is more appropriate than “acceleration” as a name for this effect.

A reader asked: “Please help me understand the calculation of ‘acceleration.'”

Response:

In general (from physics), velocity is the change in position (first derivative of position), and acceleration is the change of velocity (second derivative of position). Similarly (again from physics), momentum is mass times velocity, and impulse is the derivative of momentum.

The author of the reviewed paper uses the term acceleration to mean the change in stock price momentum. The return of a stock or fund over some past interval of time (say six months) is a measure of its momentum. The change in this measure of momentum over some interval of time (say a month) is a measure of stock price acceleration.

For example, assume you measure momentum for a set of stocks or funds monthly as 6-month past return. This month, you find that a specific stock has advanced 30% over the prior 6 months, so its momentum is 30%. Next month, you roll your data by a month and find that the same stock has a revised momentum of 35%. Its momentum is accelerating. Conversely if you find the momentum of a stock decreasing from month to month, its momentum is decelerating.

The study finds that stocks with high and accelerating momentum outperform those with high momentum only.