Skip to content
All library documents

Testing Stock Return Forecasts with Newey–West Standard Errors

Article Quant Q&A · Author: Ocean
Read the original

Summary

The document frames a statistical problem: testing whether the average returns of stock decile portfolios differ from model-predicted returns. The data are monthly portfolio returns spanning a long historical period, and the target is an annual return estimate. The author considers treating monthly observations as independent and identically distributed, but recognizes that this assumption may be too strong for time series.

As an alternative, the question proposes using Newey–West heteroskedasticity and autocorrelation consistent standard errors. It suggests estimating the sample mean as the intercept in a regression containing only a constant, then comparing that estimate with the model prediction. The document asks how to choose the lag count and conduct the test in R, and whether a different test would better assess forecast validity. It provides no answer, implementation, empirical evidence, or guidance on annualizing returns, so it is a statement of the inference problem rather than a complete procedure.

Key ideas

  • The stated goal is to test whether observed portfolio returns differ from model predictions.
  • Treating monthly returns as independent may be unsuitable for time-series inference.
  • Newey–West standard errors are proposed to account for heteroskedasticity and autocorrelation.
  • A constant-only regression can express the sample mean as an intercept.
  • The document leaves lag selection and the testing procedure unresolved.

Tags

EquitiesStatisticsFactor investing
Full text
# Inference on Stock Returns (Newey & West t-statistics)


# Inference on Stock Returns (Newey & West t-statistics)












For my project, I want to determine if the yearly returns of some decile portfolios (calculated with the monthly returns over the last 50 years) are not significantly different from my predicted returns (based on my mathematical model). Initially, I had two ideas:

(1) My first thought was to assume all monthly returns are IID. Then I could easily argue with the CLT that the portfolio return will be approximately t-distributed and could calculate a confidence interval as well as a hypothesis test. However, this assumption is too strong for my purpose, especially while dealing with time series.

(2) My second thought was to use the Newey and West (1987) t-statistics which is well-used in papers with the emphasis on determining the predictive power of some factors on stock returns. Since the Newy-West procedure is used in regressions to obtain HAC standard errors, there would be the option to regress the monthly stock returns on a vector only consisting of ones (1,...,1) to obtain the intercept, which will equal to the sample mean. However, most papers refer to some lags (normally between 4 and 6), which I don't understand with my basic statistical knowledge. Also, I don't know how I can compute whether the sample mean is significantly different from my prediction based on the HAC standard errors in R.

I would greatly appreciate it if somebody could help me with the commands I should use in R. Or maybe, there would be even a better test to determine if my prediction is valid instead of simply computing if the sample mean is not significantly different from my prediction.

Any help would be desperately needed :D

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.