Single Factor Model Flashcards
Markowitz selection model requires what inputs
n estimates expected security returns, n estimates variances, n(n-1)/2 estimates of co-variances
how to reduce number of estimates needed in Markowitz selection
use the single factor model
common factor m in single factor model
generates correlation across securities because all securities will respond to the same macroeconomic news, while the firm-specific surprises are assumed to be uncorrelated across firms
single factor model equation for stock returns
ri = E(ri) + Bim + ei
common factor proxy
A variable used as a proxy for a common factor in asset returns
key requirements of common factor proxy
Must be observable to estimate volatility and sensitivity of individual securities
outcome of common factor proxy
Leads to the Single Index Model (SIM), which uses the market index to represent the common factor
benefits of single index model
when using SIM to construct efficient frontier need less variables than the Markowitz procedure
drawback of single index model
uncertainty is classified into simple dichotomy: macro versus firm specific risk, this rules out industry events
what happens when diversification increases in SFM
(as n increases) then total portfolio variance approaches systematic variance
whats the optimal risky portfolio in the single index model a combination of
active portfolio A and passive portfolio M
the full markwitz is better in principal to full-covariance but….
the full covariance matrix invokes estimation risk of thousands of terms, cumulative errors may result in portfolio that is actually inferior, the single-index model is practical and decentralises macro and security analysis
tracking portfolio
a portfolio designed to match thr systematic component of Ps return, this means the tracking portfolio must have the same beta on the index portfolio as P and as little systematic risk as possible
alpha transport
process of separating the search for alpha from the choice of market exposure
