Time-Series Momentum Volatility Scaling and Decay Weights

Summary

The note raises two implementation questions about the time-series momentum method described by Moskowitz, Ooi, and Pedersen. First, it asks how to interpret the paper’s ex-ante volatility estimate when the strategy uses a twelve-month return signal: whether volatility should be estimated from daily returns over that same lookback, and what the summation notation extending to infinity means. Second, it asks how to choose the decay parameter delta when the stated center of mass for its weights is sixty days, proposing a particular ratio as a possible value.

These questions identify practical details needed to reproduce a volatility-scaled momentum strategy: the return horizon used for risk estimation, the meaning of the weighting sequence, and calibration of its decay. The document offers no answers, calculations, or empirical evidence, so it should not be treated as a resolved recipe. Readers would need to consult the original paper’s definitions and conventions before implementing either estimate.

Key ideas

• The note asks whether volatility for a twelve-month momentum signal uses daily returns from that same lookback.
• It questions how to interpret an infinite summation in the volatility estimate.
• It asks how a sixty-day center of mass determines the decay parameter delta.
• The document presents unresolved implementation questions rather than validated formulas or results.

Tags

# Questions on the calculation of time series momentum


# Questions on the calculation of time series momentum












I read Moskowitz, Ooi, Pedersen's Time series momentum (2012).

The ex-ante volatility estimate (equation (1) in the paper) is

- I am not sure about the period of the return reflected in the volatilty calculation above. Since the Time series momentum consists of a portfolio based on 12 months of return, does it mean to calculate geometrical mean and weighted volatility based on daily returns over the past 12 months? Then why is the infinity symbol above the sigma attached? It's written as if to add an infinite number of daily returns.

2.Let me ask you a question on delta. The paper says that the delta value is set so that the center of mass of the weight of the delta is 60 days. Does it means delta=60/61?

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