A Very Short Summary of Empirical Finance Blake LeBaron Fin305: Fall 2017

Econometrics toolkit for finance GMM (Generalized Method of Moments) Regression Time series Cross section Factors Portfolio sorts Heterogeneous agents Data snooping???/ Science

Readings Cochrane: Chapter 10, GMM (skim) Cochrane: Chapter 12 Cochrane: Chapter 20 (totally optional/on your own) Campbell: Chapter 3 Bali/Engle/Murray: Chapters 1-4

Generalized Method of Moments

Generalized Method of Moments Very common econometric tool Probably should learn in first year PhD econometrics class Most all econometric estimators are basically GMM anyway Started in Finance (Lars Hansen, and earlier statisticians)

Basic moment conditions Strategy is to find b that makes g() as close to zero as possible Two key things to worry about This might be a vector objective (weights??) Identification (b might be a vector too)

What does this look like? Consumption model This could be many (j) conditions, two parameters Think identification

Estimator stage 1 Stage 1 estimator W can be any symmetric matrix Often identity. That is just the sum of squares This estimate is consistent (generally not efficient)

Estimator stage 2 Replace W with S S = sample estimate of covariance matrix for g() This does three things More efficient estimate Asymptotic distribution for b Test of model fit (J statistic, object function value – how close to zero?)

Instruments Adding time t info variables as we did before Now we might have lots of moment conditions Z could be really big!

GMM summary Powerful Well defined for finance/macro consistency is pretty robust relatively distribution free Well defined for finance/macro Could do other stuff (OLS/2 stage least squares are special cases) Extensions: Simulated method of moments (model simulations) Problems/difficulties Stationary Choosing assets Choosing instruments

Time Series Features

Time series predictability (one slide) Very little short term Low autocorrelations Mid range, Some persistence Time series momentum Long range, mean reversion (prediction) P/D, P/E ratios P/CAY Price volatility/mean reversion/long range regressions Little predictability in changes in many fundamentals Dividends Consumption

Test of cross sectional pricing models

Time-series approach Basic APT/Multi-factor structure Our basic null model

Special (but common) case What if the factors are returns? Rewrite factor structure in excess returns

Jensen’s Alpha This gives a basic test restriction Constant in factor time series regression should be zero

Performance test This is a common test for mutual fund performance Or strategy performance See Fama/French(2010) Implementation Test often run with portfolios, not individual stocks Test across multiple stock/portfolios (chi squared or F-test) Many other issues (see Cochrane)

Cross-sectional approach Estimate beta’s in time-series regression Then estimate cross section using generated betas from stage 1 Note: lambda is now the coefficient getting estimated Two pass approach Restrictions: Zero beta : a=0 Also, general model fit

Testing issues Testing “goodness of fit” Size of residuals (see Cochrane again) “Generated regressor” problem

Fama-MacBeth Very old method (1973) Still heavily used Combines time and cross-sectional dimensions

Fama-Macbeth First estimate beta’s Rolling 5 year periods Run cross sectional regression at each time period

What is Fama-Macbeth? Not your usual method (see Cochrane) Not pooled cross-section/time series Not pooled over time Related to panel regression Time variation in estimators can be interesting/important Connections to Kalman Filter (3 pass least squares)

Portfolio Sorts

Monster tool of modern finance Sort stocks into portfolios based on certain key features Form quintile or decile portfolios and look at returns Abnormal differences in sort? Generate extreme long/short (10-1) portfolios Call these returns factors Return to previous factor model testing

Sorts don’t have to give “factors” Think about an “alphabetic sort” Firms earlier in the alphabet have higher returns We now have a kind of anomaly/puzzle Now build the a-z portfolio Test a factor model for this Are stocks correlated at all this this factor (beta)? Is there a higher return for loading on this factor, APT? These two are not a direct result of the original anomaly

Pure anomaly (no beta correlations) Load up on low alphabetic stocks If they are independent, can diversify risk away Pure high return (zero risk) portfolio This does not seem to be the case for most common sorts

The classic 4 factors (Fama-French(93)/Momentum(Carhart, 1997) Market (beta) Excess return on market MKT Size: Sort: Market value SMB (small minus big) Value: Sort: Book/Market HML (high minus low) Related to value investing Momentum: Sort: last 3-12 month’s performance MOM Up-Down???

Few thoughts on factors All available on Ken French’s website Rational stories for all factors (see any Fama/French paper) Momentum is weird Not quite a time series prediction (this does exist) Not easy to explain with rational stories Many other factors Idiosyncratic volatility is an interesting one Turnover is another Three other issues Data snooping?? Anomaly detection/elimination (Lo/nnn/small firm Jan) When alpha becomes beta

Heterogeneous agents

Household Finance Look at individuals actual behavior Powerful/interesting Difficult to get data Big future area for understanding

Summary Very quick snapshot Still many puzzles Three monster issues Stationarity Snooping Models?? Two recent books of interest on this Bali/Engle/Murray(2016) Campbell(2017)