1. Static Equilibrium Asset Pricing
Chapter 3

2. Capital Asset Pricing Model (CAPM)
Section 3.1

3. CAPM Original portfolio-based asset pricing model
Most all modern asset pricing builds from this
Sharpe/Lintner (and sort of Treynor) 1960’s
Assumptions
All investors price takers
Common information/beliefs
Portfolios evaluated on means and variances
Pick some mean/variance efficient portfolio
Equilibrium
Market portfolio = tangent portfolio
Market portfolio is mean/var efficient
At market price (return) equilibrium, no way to better mean/var asset portfolio

4. CAPM with risk free

5. Portfolio change experiment (should look familiar from micro)

6. Guts of CAPM This isn’t very testable
Assume market portfolio is MV efficient

7. CAPM regression

8. Black CAPM (borrowing constraints)
Section 3.1.2

9. Risk free rates Assume lending, but no borrowing
This can get much more complex in terms of rates
We are just glancing at this quickly
People vary in their risk preferences (risky portfolios now differ)
Assume all portfolios on frontier
All portfolios are weighted sums of two fixed mutual funds (separation)
This implies that the market portfolio is also a weighted sum of these and lies on the frontier itself
Can yield a CAPM, but risk free replaced with “zero beta” portfolio

10. Black CAPM

11. CAPM Applications in real portfolios
Section 3.1.3

12. Harvard endowment portfolios through time

13. Sharpe ratios (market = line)

14. Security market line

15. A simple picture of return/beta from Malkiel and Fama/French

16. Black/Litterman CAPM (casual description)
Standard portfolio selection generates “crazy” portfolio weights
Noise in expected returns creates big swings in weights
Black/Litterman
Set a kind of prior for returns that follow a standard CAPM
W considers how strong beliefs are in current sample estimates versus CAPM prior
Fed into standard portfolio optimization
Black/Litterman sort of casual (see book)
This is a form of empirical Bayes estimation

17. Multifactor models/Arbitrage Pricing
Section 3.2.1

18. Thoughts on arbitrage Key concept in finance
Portfolios that generate same payoffs should have same price
Very powerful
Does not rely on preferences
Can sometimes be limited in scope
Examples
Arbitrage Pricing Theory (APT)
Black/Scholes
Much of fixed income pricing

19. Arbitrage pricing Important model And modeling style (arbitrage)
Few assumptions about preferences
Related to other models such as Black/Scholes
Also, related to CAPM, and modern multi-factor (Fama/French) factor models

20. Excess return and zero cost strategies
We often state stuff in terms of excess returns
They have many convenient features
One is that investors can add any excess return to a portfolio with no concern for budgets
They are “zero cost” investments
Increase risky asset, borrow risk free

21. APT factor structure

22. Basic arbitrage Buy portfolio
Then short (allowed) units of the market portfolio
This will give you a completely risk free payout
Absence of arbitrage implies these free lunches do not exist
Therefore,
What about for individual securities?

23. Individual securities
This does not say that each alpha is zero
This depends on thinking about N big, and lots of securities
If there are groups where alpha is big then
Buy them
Neutralize market risk
Take arbitrage profits
Alpha for individuals must stay close to zero

24. Technical aside Does this imply: No, this is only a limiting result
Some of these expected returns might be nonzero, but they generally need to be “pretty small”
This can get technical fast
See Campbell (pp 56-57) for proof that APT implies that:
Proof is not super difficult, but will skip

25. What else can screw up for APT?
Factor structure not correct
Other factors
Idiosyncratic errors not independent
This is a problem
You need to be able to build the diversified factor portfolios that let you ignore idiosyncratic risk
This is related to the “other factors” issue

26. Multifactor models
Section 3.2.2

27. Multiple factor structure

28. Implications Linear pricing (expected returns) structure (like CAPM)
MV efficient set is spanned by K factor portfolios
Why?
Think about portfolio with some idiosyncratic risk
One could replicate this exactly in terms of expected returns and systematic risk (factor risk) by purchasing factor portfolios
This would have same expected return and smaller variance
So no portfolio exists that we can’t do better using pure factor returns
Practical aside:
Some factor portfolios can be directly purchased as exchange traded funds (ETF’s)

29. Empirical history of APT
Principle components
Macro factors
Portfolio factors
This has been the most successful

30. Conditional CAPM and factors
Section 3.2.3

31. Conditional CAPM and multifactors
A conditional CAPM can be mapped into a multifactor model
Allow beta to move around through time
This is now a two factor model
Factor 2 is the market return “scaled” by info variable z(t)
This is a kind of synthetic strategy which increases/decreases market holdings depending on z(t)

32. Empirical evidence (light)
Section Test methodology

33. CAPM: Three basic tests
Time series
Cross sectional
Fama/MacBeth

34. Time series approach Could run for one security, and test alpha=0
Joint tests for alpha(i)=0
Assume errors iid
Asymptotic Chi-squared test on weighted squared alpha (3.45)
Adjusts for beta uncertainty in model
Finite sample F-test (3.46)
Distance of market Sharpe ratio from tangency Sharpe ratio

35. Cross-sectional approach
Estimate beta’s from time series regressions
Then run cross-section regression (no intercept)
This is again a chi-squared test
Estimation needs GLS (a’s not independent/cross sectional dependence)
Asymptotic test statistic (3.51)

36. Fama-MacBeth(1973) Cross-section with time series changes Useful test
Used outside of finance too (rolling cross sectional)
Method:
Run time series regression to get Beta’s
Then cross-sectional regression at each time t
FM get standard errors
Problem: Does not adjust for beta estimation
Interesting: Can be done with changing beta’s

37. Rolling Fama/MacBeth Set window (1,T) Set window (2,T+1)
Estimate beta in window
Estimate CAPM in T+1
Set window (2,T+1)
Estimate CAPM T+2

38. Returns and characteristics
Cross sectional F/M useful for adding other things to CAPM testing
In true CAPM world other stuff should not matter
Many flavors of this
X can be any firm level characteristic (profits, growth, size)
Drop beta
More factors
Trading strategy interpretation (see 3.55)

39. Choosing test assets
Occasionally individual stocks are grouped into portfolios for testing
All asset pricing theory should hold for portfolios
For example “high beta” and “low beta” portfolios replace R(it)
Designed to get more power/precision in tests
Can be controversial (see references on p66)

40. Empirical features
Section 3.3.2

41. Individual asset return time series features
Nearly uncorrelated
Prices near random walk
Non normal distributions at frequencies less than quarterly
Persistent volatility
Increasing when prices fall
Most of academic research is on cross-sectional features
This is where AP models operate

42. CAPM Early tests in 1970’s Works but Beta small Barely significant
Working less well after 1960

43. Size Size = market capitalization (shares*price)
Smaller firms have higher returns
Often in the month of January
The “January effect”
See next figure
Note: portfolio sort technology

44. Size portfolios

45. Value Extremely old strategy (Graham, Dodd, Cottle(1934), Buffet)
Key ratio (something)/(market cap)
Something = book value, dividends, earnings
High ratio
Cheap stocks
Buy!!

46. Value sorts

47. Momentum Persistence in returns
Autocorrelations are a little more subtle than zero
Negative at highest (intraday/daily) frequencies
Positive at mid range (monthly-yearly)
Strategy: Buy recent winners
Negative (reversals) at long horizons (5 years)
Strategy: Buy losers

48. Modern research midrange
Formation period
Previous 6-12 months
Sort (maybe 5-10 portfolios) based on returns in this period
Wait 1 month
Strategy test in next month after this
Long winner portfolio, short loser
Several different flavors of this
All strategies together (next figure)
MOM
SMB (small minus big, size)
HML (book/market, value)
Much of this data is available at Ken French’s website

50. More features Post-event drift Turnover/volatility Insider trading
Idiosyncratic risk negative with future returns
This is weird for many reasons
Insider trading
Growth
Earnings and accounting
Profitability
A predictor zoo?

51. Some response to this Data mining Anomaly elimination
Some of these results not real
Mined from data
See Harvey(2017, JF)
Anomaly elimination
McLean/Pontiff(2016,JF)
Many features change/disappear after they become well known

52. Small stocks (Jan versus other months)

53. Roll critique Roll critique Liquidity Conditional CAPM
Don’t observe the true market portfolio
Creative expansion on what market portfolio is
CAPM is untestable
Liquidity
Conditional CAPM

54. The Four Factor Model Modern work horse empirical model
Fama/French, Carhart
Four portfolio based factors
Market – risk free
Small – large stocks
High book/market – low book market
MOM: recent winners-losers
Estimate betas on these factors
Estimate expected returns
These factor loading should “explain” all excess returns
Seem to work well
Some tests on “factor sorted” portfolios might be problematic

55. Mutual funds and performance
All this is useful for evaluated mutual fund returns
Should deliver alpha
Testing the mutual fund industry
Regress fund returns on market, or favorite factor model
Time series tests (3.44)
Test alpha = 0
If alpha = 0, you are paying for portfolios you could construct yourself
“Don’t pay for beta risk”
Cite: Fama/French

56. Economic content
Four factor model needs more economic content (atheoretic)
Possible areas
Consumption/macro
Production/macro
Intertemporal details

57. Behavioral finance Investors irrational Often heterogeneous
Models tricky
A few things to read
Nice recent survey, Barberis(2019) (Yale website)
Campbell chapters 10 and 12
Classic questions
How do irrational types survive?
Why doesn’t rational money overwhelm them?