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

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

3. 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

4. Generalized Method of Moments

5. 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)

6. 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)

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

8. 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)

9. 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?)

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

11. 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

12. Time Series Features

13. 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

14. Test of cross sectional pricing models

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

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

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

18. 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)

19. 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

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

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

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

23. 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)

24. Portfolio Sorts

25. 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

26. 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

27. 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

28. 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???

29. 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

30. Heterogeneous agents

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

32. 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)