Estimating Market and Momentum Sensitivity with Multiple Regression

Summary

The document asks how to measure a stock portfolio’s exposure to market returns and momentum, given daily stock and index prices. The author calculates market beta as the covariance of an asset’s returns with market returns divided by market-return variance, and defines a 200-day momentum score as the price difference between today and 200 days earlier.

The response distinguishes the two sensitivities as regression exposures: market sensitivity is the coefficient on market returns, while momentum sensitivity is the coefficient on momentum returns. It recommends estimating both in a multiple regression of portfolio returns against market and momentum returns. This gives the basic interpretation and estimation approach, but does not specify how to construct the momentum factor return series, whether to use individual stocks or a portfolio, or how to handle overlapping observations and other model choices.

Key ideas

• Market beta measures return sensitivity to market returns.
• Momentum sensitivity is exposure to momentum returns.
• Estimate both coefficients in a multiple regression of portfolio returns on market and momentum returns.
• A price-difference momentum score is distinct from a momentum return series used as a regression factor.
• The response leaves factor construction and regression details unspecified.

Tags

# What is market sensitivity and momentum sensitivity?


# What is market sensitivity and momentum sensitivity?












I have daily data of about 29 stock prices and 1 index prices of past 7 years

I calculated beta as the ratio of covariance(Rm,Ri) / variance(Rm)

I also calculated 200 days rolling momentum score as the difference between the price(t) of today and price(t-200) so the first 199 days have no data in it.

momentum_score(t) = price(t) - price(t-200)

I want to know whether the calculation is right or wrong so far. And next I have been asked to calculate market sensitivity (bi1) and momentum sensitivity (bi2)

How can I calculate those?

Is market sensitivity the beta of momentum and stock prices?

## Answer by Chris (score 2)

https://quant.stackexchange.com/a/50123

Market sensitivity is beta of your portfolio returns to market return, momentum sensitivity is beta against your momentum returns. You'd likely want to run a multiple regression of your portfolio returns against market returns and momentum returns to get those betas/sensitivities.

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