Interpreting Conflicting Factor Regression Results at Different Frequencies
Summary
The document compares monthly and daily regressions of a portfolio described as 70% India and 30% USA against SMB, HML, WML, and a market excess return. It reports different coefficient estimates and significance levels across frequencies: the monthly intercept is significant under the author's 1% cutoff, while the daily intercept is not. Several factor coefficients also change in significance, despite both regressions showing highly significant overall fits and market exposure.
The author says Newey–West standard errors were substituted into Excel's OLS output to account for autocorrelation and heteroskedasticity. The post raises a useful inference question but does not resolve it or provide enough information to decide which regression is more trustworthy. It omits details such as return construction, sample alignment, HAC lag choices, and how monthly observations relate to daily data; these choices can affect uncertainty estimates and comparability. The results therefore illustrate frequency-sensitive inference rather than establishing reliable alpha.
Key ideas
- The monthly regression reports a significant intercept at the author's stated 1% threshold, while the daily regression does not.
- Factor coefficient significance differs between the two return frequencies.
- The regressions use Newey–West standard errors to address autocorrelation and heteroskedasticity.
- The document asks which result to trust but provides no resolution or diagnostic evidence.
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Full text
# 71231
# Statistically Significant Four Factor Alpha for Monthly Returns Regression but non stat sig alpha for Daily Returns. Which one should I trust?
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SUMMARY OUTPUT
Regression Statistics
Multiple R 0.918998992
R Square 0.844559147
Adjusted R Square 83.8%
Standard Error 0.016734114
Observations 94
ANOVA
df SS MS F Significance F
Regression 4 0.13541299 0.033853248 120.8912625 4.08362E-35
Residual 89 0.02492272 0.000280031
Total 93 0.16033571
Coefficients Standard Error t Stat P-value
Intercept 0.49% 0.00156481 3.114167288 0.25%
SMB 0.078908101 0.048220136 1.636413884 10.53%
HML -0.083405428 0.039201937 -2.127584361 3.61%
WML -0.132884557 0.030054328 -4.4214783 0.00%
70% India 30% USA Minus RF 0.892777286 0.07200324 12.39912652 0.00%
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.704712899
R Square 0.49662027
Adjusted R Square 50%
Standard Error 0.005459587
Observations 1928
ANOVA
df SS MS F Significance F
Regression 4 0.056549346 0.014137336 474.2944151 1.1288E-284
Residual 1923 0.057319035 2.98071E-05
Total 1927 0.113868381
Coefficients Standard Error t Stat P-value
Intercept 0.02% 0.000102977 2.371487639 1.78%
SMB 0.124288777 0.02670111 4.654816873 0.00%
HML 0.052914661 0.018226336 2.903197921 0.37%
WML -0.003336562 0.019884054 -0.167800906 86.68%
70% India 30% USA Minus RF 0.634035625 0.037499927 16.90764944 0.00%
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I have used Newey West Estimator to correct for autocorrelation and heteroscadicity in both regressions. Both regressions were done using Excel. The first output is the monthly returns regression and second is daily returns regression. I am considering a p-value of less than 1% as statistically significant. The output is from "Regression" which is part of Excel Data Analysis Addon. Only modifications I done was input the HAC standard errors for Market Beta, SMB, HML,WML and Intercept (which also effects the t-stat and p-values of these coeffiecients) as the Excel Regression is OLS.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.