Modeling Momentum Strategies with Regression and Diagnostics
Summary
The document considers whether a momentum strategy can be expressed as a regression using signals such as the ratio of short and long moving averages, or with a nonlinear model. The answer suggests defining a return horizon and a precise target return based on entry, exit, and whether performance is measured absolutely or relative to a benchmark. A linear relationship between return change and momentum could be explored with regression, followed by diagnostic checks.
It also recommends simulations using historical data from assets with similar prior returns and anticipated momentum behavior, and including relative performance measures to examine weak prior performance. Parameter estimation is framed as an optimization problem whose validity depends on the estimation method and assumptions about variance and return randomness. The response does not specify a concrete strategy, dataset, model comparison, or empirical results, and it explicitly leaves the validity of momentum trading unassessed. Regression is presented as a way to investigate a hypothesis, not proof that momentum predicts returns.
Key ideas
- Define the holding period and return calculation before fitting a momentum model.
- Regression can test whether momentum indicators relate linearly to a chosen return target.
- Simulation and regression diagnostics can help examine model behavior.
- Model validity depends on estimation choices and assumptions about return distributions.
- The proposed approach does not establish that momentum is profitable.
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Full text
# Can a momentum strategy be cast as a multilinear regression model?
# Can a momentum strategy be cast as a multilinear regression model?
Disclaimer: the question is similar to
Can momentum strategies be quantitative in nature?
and (to an extent)
What is the expected return I should use for the momentum strategy in MV optimization framework?
However (on the surface of it), I did not quite find a desirable answer.
Can a momentum strategy be expressed as something to the effect of $$r = \beta_0 + \beta_1 \frac{\mathrm{ten\_day\_moving\_average}}{\mathrm{hundred\_day\_moving\_average}} + \epsilon$$ or any other combination of predictors ($x_{2}$, $x_{3}$, ...); or maybe as some nonlinear model?
## Answer by user20928 (score 1)
https://quant.stackexchange.com/a/26304
Yes, they can be quantitative in nature. A way to think about this is to set a period of time to analyze the return and then to set it up as a differential equation model and estimate the unknown parameters. If you think the rate of increase in the return is linear, i.e. the momentum is linear then try running a linear regression model and run diagnostics.
For a first attempt try running some simulation models where you use historical data from another asset with similar prior to purchase return behavior and expected momentum behavior. Use your data to calculate your return (r), which is based on when you purchase and sell the asset and how you are calculating your return and whether you return is absolute or relative (you can simulate different scenarios and different calculations for r).
I also suggest adding in some relative performance measures to explore the notion of 'poor prior performance of a given asset' when building your simulation model.
The multivariate optimization occurs when you solve for the unknown parameters of the quantitative model. The validity of the optimization strategy depends on what method you use to solve and what assumptions you make for the model, such as whether variance is fixed and finite and furthermore whether the return is stochastic.
To be clear, I have no comment on the validity of the theory of momentum or its use for trading strategies.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.