Factor
-a variable or characteristic with which individual asset returns are correlated
What is CAPM
- a kind of single factor model
- in equlibrium
Equity Risk Premium
risk factor return
systematic or market risk
Why is CAPM an incomplete description of risk
- small cap outperforms large cap
- value outperforms growth
- momentum exists
Intercept in a multifactor model
-this is the expected return of the asset E(Ri), if all the factor premiums F are 0
correlations between all the factors in a multifactor model
the correlations between them all are 0
3 key assumptions of multi factor models
- factor model describes asset returns
- with many assets, investors can form well diversified portfolios that eliminate asset specific risk
- no arbitrage exists between well diversified portfolios.
Arbitrage pricing theory
given a set of expected returns and factor sensitivities, you can create linear equations to solve for the betas and risk free rates. If no arbitrage holds, that equation can be used to price any well diversified portfolios
Carhart model
- model for excess return on a portfolio above the risk free rate.
- alpha
- RMRF-return on a value weighted index minus one month t-bill rate
- HML-average return on 2 high BV/MV portfolios minus average return on 2 low BV/MV portfolios
- WML-past 12 month’s winners (top 30%) minus 12 months losers (bottom 12%)
Macroeconomic factor model
- the factors are surprises in economic variables.
- if the actual variable turns out to be the expected value, it was already reflected in the expected value.
fundamental factor model
-attributes of stocks or companies (BV/MV, market cap, E)
statistical model
-applied to historical returns to extract factors
-
two components of portfolio active risk
- Active factor risk: contribution to active risk resulting from the portfolio’s different-from-benchmark exposures to factors (factor sensitivity in the portfolio different from the benchmark)
- Active specific risk or security selection risk: measures the active non-factor or residual risk assumed by the manager (Security weightings in the portfolio different from the benchmark).
Difference between macroeconomic and fundamental factor models
- macroeconomic: we develop factor (surprise) series first and then estimate the factor sensitivities through regression.
- fundamental: first specify the factor sensitivities (attributes) then estimate the factor returns through regression.
Asset sensitivity to a factor (in fundamental factor model)
-expressed as a standardized beta
b = (value of attribute - average value of attribute)/(sd of attribute)
