Download A Diagnostic Criterion for Approximate Factor Structure

EHL Finance&Real Estate Research Seminar
- Lausanne - February 16th 2017
Discussion on:
“A Diagnostic Criterion for Approximate Factor
Structure”
By:
E. Ossola
P. Gagliardini
USI Lugano and SFI
O. Scaillet
University of Geneva and SFI
E. Jurczenko
EHL
[email protected]
European Commission
Motivation of the Article
 Researchers rely heavily on multi-factor models with
observed factors to analyse high-dimensional financial data
sets (see FFM, affine model,….)
 However, since the “true” latent factor structure is usually
unknown, researchers are often working with potentially
misspecified multifactor models
 The aim of this article is to develop a new diagnostic
criterion that determines the true approximate factor
structure in both large cross-sectional and time series
datasets.
Main Contributions of the Article (1)
 Develop a new model specification criterion for approximate
factor models
 That can deal with large panel data sets either when the
cross section dimension is significantly larger than the
time series dimension (ultra-high dimensional regime) or
when the two dimensions are comparable (high-dimensional
regime)
 That is simply based on the sign of the difference between
the largest k-th eigenvalue of the covariance matrix of the
residuals and a penalty term (negative difference e.g well
specified model, positive difference e.g omitted
factors)
 That can also handled unbalanced panel datasets (missing
observations)
Main Contributions of the Article (2)
 Analyse several recent financial and macroeconomic
multifactor model specifications on US equity market
(unconditional and conditional versions)
 Find no omitted factors for the unconditional four
(3FF+QMJ, 3FF+BAB, 4-HXZ) and five (5-FF) financial
multifactor model specifications
 Find no omitted factors for all the conditional financial
specifications albeit for the CAPM one (3FF, 4FF, 3FF+QMJ,
3FF+BAB, 4-HXZ and 5FF).
 Reveal no (2) omitted factors for the unconditional
macroeconomic model specifications with (without) a market
factor (EZ vs CCAPM, YO vs NDC/DC)
Comments, Remarks and Questions
 How to interpret/use your empirical results for financial
multifactor model specifications?
 3FF+QMJ, 3FF+BAB, 5FF and HXZ are all well-specified (noomitted factors)
 However the relation that exist between BAB, QMJ or the
profitability/investment factors is not straighforward
 For instance, contrary to the time series spanning test results of
Novy-Marx (2016) and Fama and French (2016), Blitz and Vidojevic
(2016) show that the Low-beta anomaly is not resolved crosssectionally by adding profitability or investment factors to the original
three-factor model (Fama-MacBeth Regression setting)
 Difficult to believe that all these models are capturing the same
latent common factor structure
Comments, Remarks and Questions
 How your empirical results compare with the ones obtained by
the traditional model selection criteria of Bai an Ng (2002) and
Onatski (2009)?
 Please provide a comparison of the number of omitted factors under
the different approaches for all the linear factor models considered
 Are your diagnostic results robust out-of-sample?
 To my understanding all your empirical results are in-sample
 As an acid test, please extend your empirical analysis in an OOS
setting
 Why estimating the parameters of your unbalanced panel model
on an individual asset basis?
 One can think about imposing some constraints on all the individual
factor loadings (e.g; positive sign restriction if common risk factor is
priced in the market)
Relevant Literature
 Bai J. and S. Ng, (2002), “Determining the Number of factors in
Approximate Factor Models”, Econometrica 70, 191-221.
 Bai J. and P. Wang, (2016), “Econometric Analysis of Large
Factor Models”, Annual Review of Economics 8, 53-80.
 Blitz D. and M. Vidojevic, (2016), “The Profitability of Low
Volatility”, Working Paper, 22 pages.
 Fama E. and K. French, (2016), “Dissecting Anomalies with a
Five-factor Model”, Review of Financial Studies 29, 69-103.
 Novy-Marx R., (2016), “Understanding Defensive Equity”,
Working Paper, 39 pages.
 Onatski A, (2009), “Testing Hypotheses about the Number of ,
Factors in Large factor Models”, Econometrica, 1447-1479.
EHL Finance&Real Estate Research Seminar
- Lausanne - February 16th 2017
Discussion on:
“A Diagnostic Criterion for Approximate Factor
Structure”
Thanks for your attention...
Discussion by:
Emmanuel Jurczenko
EHL
[email protected]