module 5 chapter 3

regression coefficients

based on correlations between security and mimicking portfolios

surprises for factors

cant anticipate them or effects - all 0

don't have way to measure risk premia in most cases

create factor mimicking portfolios to estimate the risk premia

Mimicking portfolio will be proxy for

expected and shock portfolio (adjust when shocks f occur)

alpha would be (α)

expected return - E(ri)

risk premium on mimicking portfolio proxies for

factor risk premium

Factor mimicking portfolios

factors are the excess returns to what are known for

book to market is proxy for

financial distress risk

Conservative Minus Agressive (CMA)

firms who invest more heavily tend to underperform firms who do not

Robust Minus Weak

high profitable firms tend to outperofrm low profitability firms

Small size stocks outperform

large size stocks

high book to market value stocks outperform

low book-to-market growth stocks

view SMB and HML factors as risk premiums similar to

market risk premium

Market factor (Mkt - Rf)

market risk premium (same as CAPM) - portfolio bears the risk

high book to markets

may potentially be near financial distress

Surprises in investor confidence

measured by changes in default premium of corporate bonds

Surprises in GNP

measured by industrial production index

use derivative prices

more active data

regression forms

moves risk free rate over and drops expectations

well-diversified portfolio

no firm-specific risk

high R2

not everything

avoid

p hacking or data mining

following guidelines ensure model has some

predictive power rather than qurik

factors loading or beta

represent each stocks sensitivity to the factor - Kenneth French Data Library

Size factor (SMB)

reutrn difference between a portfolio of small stocks and portfolio of large stocks - small - big - portfolio doesn't bear the risk

λk

risk premium factor

Violation of law of one price

same assets sells for different prices in two different markets

Zero investment portfolio

shorting overpriced security and buying the underpriced security

APT factor model

stock returns are result of exogenous shocks to set of factors

SMB risk premium demanded by investors for

taking on the additional risk of holding small firms relative to large firms

HML risk premium demanded by investors for

taking on the risk of owning high book to market stocks

Fama French factor to

tease out the abnormal return

build portfolios to estimate what

think factor's value is

understand ideas of regression

use past to predict future

APT assumptions

- All securities have finite expected values and variance - Some can form well diversified portfolios - There are no taxes, no transaction costs

Fama French 5-Factor Modle

- Fama French (2015) - adds profitability and investment factor

APT issue

- at most 1 less factor than we have assets in our data - S&P only 499 - need for regression

Carhart 4 Factor Model

- carhart (1997) - fama french 4-factor model - adds momentum

Extensions for factor model

- carhart 4 factor model - fama french 5-factor model

CAPM

- equilibrium model - single factor completely described expected return - unobservable market portfolio - individual assets or portfolio

Adds momentum factor (carhart)

- form portfolios of over and under performers - buy over performs - short under performs - generate alpha over 3 factor

Value

- high B/M - low M/B - distress

No universal answer

- how much data - frequency of data - what model to use

Empirical work

- include a lot of control variables - fixed effects - count towards limit

Mispricing can occur

- investors able to profit from these through trading on arbitrage in expectations - two stocks with equivalent risk - shorts lower return and buys higher return

Observations

- momentum factor for Carhart model is not included - value factor is statistically insignificant

APT

- no arbitrage model - multiple risk factor (don't specify) - fewer assumption (no market portfolio0 - well diversified portfolios - loosely to individual assets

Arbitrage in expectations

- not true arbitrage - market may move against us

Riskless arbitrage opportunity

- positive payoffs are realized with certainty with zero upfront

create factor mimicking portfolios

- postively correlated returns (even if not traded) - beta = 1 with own factor - 0 with all other

Book to Market factor (HML)

- return difference between a portfolio of high book-to-market stocks and a portfolio of low book to market stocks - high minus low

APT factors probelms

- slow - reported monthly or quarterly (not fast enough)

Chen Ross and Roll used these factors (1986)

- surprises in inflation - surprises in GNP - surprises in investor confidence - surprises shifts in yield curve

differences with mimick and fama french

▶ The mimicking portfolios subtract the risk free rate instead of the "opposite" portfolio ▶ We have to make the mimicking portfolios ourselves

APT: Factor Mimicking Portfolio

▶ Trying to isolate the effect of a single specific factor ▶ not like Fama French, we'll only use a long position bearing the risk ▶ It can be difficult to identify a portfolio that does not bear some of these systematic risks, so we can't make a true "long-short" portfolio

Arbitrage Pricing Theory

-Ross 1976 - relationship for expected returns that relies on no arbitrage requirements - price securities dont exist in well-functioning capital markets

epsilons should have average of

0

APT factors

1 impact on asset through unexpected movements 2 undiversifiable influences (typically macroeconomic) 3 Timely and accurate information is required 4 theoretically justifiable relationship on economic grounds