# Calculation of price momentum using weekly price observations

In an empirical analysis I'm trying to predict stock returns using different firm characteristics. I would like to use price momentum as an explanatory variable, but I'm not quite sure how to calculate the price momentum with weekly prices for each stock. My questions are:

• is there a standard for calulating price momentum when using weekly prices?

• what is the typical time frame, for instance is it sensible to calculate price momentum over the last 4 and 8 weeks?

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I will try to answer both of your questions together. First, regarding

a standard for calculating price momentum

I would say no, there is no universal standard. In addition to what is simply called the momentum indicator (which @chjortlund described in his answer), there are dozens of additional momentum indicators, and each puts an emphasis on something else (at the end of this answer I've pasted a list of momentum indicators that one platform offers). Of course, each different indicator also has one or more parameters, most importantly the number of periods.

There is no magic number of periods, because it really depends on many factors, such as the sector and market (e.g. retail or technology), season, and broad market sentiment. Momentum indicators work great in trending markets, but generally do not perform well when the market is going nowhere.

For example, Katz and McCormick [2000] report that

Even though the momentum model performed more poorly on the entire portfolio, it performed better on a larger number of individual markets than did the crossover model. The momentum model, if traded on markets with appropriate seasonal behavior, can produce good results. [The Encyclopedia of Trading Strategies. p 171]

Finally, no indicator (in and of itself) is a complete trading strategy. So the indicator you choose and its parameters will also depend on how you intend to use them. What might work well for retail stocks in the holidays might not work as well for energy stocks in summer. What seems to hit home runs when there's a bull market might be very disappointing during a recession. So again, I am sorry I could not provide the magic number: it is all about adaptability. Good luck!

ADX - Average Directional Movement Index
ADXR - Average Directional Movement Index Rating
APO - Absolute Price Oscillator
AROON - Aroon
AROONOSC - Aroon Oscillator
BEARP - Bear Power
BOP - Balance Of Power
BULLP - Bull Power
CCI - Commodity Channel Index
CMO - Chande Momentum Oscillator
DMI - Average Directional Movement Index
DX - Directional Movement Index
FORCEI - Force Index
KAIRI - Kairi
KDJ -  Random Index
LAGACS1 - Laguerre-ACS1
MACD - Moving Average Convergence/Divergence
MACDEXT - MACD with controllable MA type
MACDFIX - Moving Average Convergence/Divergence Fix 12/26
MFI - Money Flow Index
MINUS_DI - Minus Directional Indicator
MINUS_DM - Minus Directional Movement
MOM - Momentum
MURRCH - Murrey Channels
OSMA - Moving Average of Oscillator
PERSBBANDS - Percent Bollinger Bands
PLUS_DI - Plus Directional Indicator
PLUS_DM - Plus Directional Movement
PPO - Percentage Price Oscillator
RMI - Relative Momentum Index
ROC - Rate of change : ((price/prevPrice)-1)*100
ROCP - Rate of change Percentage: (price-prevPrice)/prevPrice
ROCR - Rate of change ratio: (price/prevPrice)
ROCR100 - Rate of change ratio 100 scale: (price/prevPrice)*100
RSI - Relative Strength Index
RVI - Relative Vigor Index
SMI - Stochastic Momentum Index
STOCH - Stochastic
STOCHF - Stochastic Fast
STOCHRSI - Stochastic Relative Strength Index
TD_I - Tom DeMark Indicator
TRIX - 1-day Rate-Of-Change (ROC) of a Triple Smooth EMA
ULTOSC - Ultimate Oscillator
WILLR - Williams' %R

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To my knowledge do you just use the closing prices for the period you want to calculate the momentum for.

M = CP - CPn


Where:

M = Momentum
CP = Closing price in 'current' period.
CPn = Closing price n periods (weeks in this case) earlier.


The optimal time frame really depends on, your, or your algos, preferred time frame.

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Thanks for your comments. The one week example you give is actually my dependent variable, i.e. weekly returns. I would like to base the choise of time frame on something else than just pure arbitrary choice, e.g. if research has shown that 8 week momentum performs well with relation to prediction of stock returns. – Sunv Aug 28 '14 at 18:41
I do not think such research is available, and if it where the strategy would be populated fast. In the 80's the hedge funds had the "magic period numbers" for the MACD(200, 50, 10). What I would suggest, is that you run a strategy optimization. Write a script to feed your strategy with the interval of the parameters you are interested in e.g. momentum for every 1-16 weeks. – chjortlund Aug 28 '14 at 19:01