Chapter 6 - efficient diversification Flashcards
insurance principle
risk reduction by spreading exposure access to many independent risk sources
Market risk (Systemic risk)
risk that remains even after diversification
firm-specific risk, nonsystematic risk, diversifiable risk
Risk that can be eliminated by diversification
covariance
- Probability-weighted average of the products
- Measures the average tendency of the asset returns to vary in tandem
Cov(rS, rB) =
= ⍴SB x σS x σB
correlation coefficient =
= ⍴SB = Cov(rS, rB) / σS x σB
3 rules of two-risky-assets portfolios
- Rule 1/2: the expected RoR/RoR on a portfolio is the weighted average of the expected returns/returns on the component securities, with the portfolio proportions as weights
- Rule 3: the variance of the RoR on a two-risky-assets portfolio is:
σ^2p = (wB x σB)^2 + (wS x σS)^2 + 2(wB x σB)(wS x σS)⍴BS
Investment opportunity set
Set of available portfolio risk-return combinations
mean-variance criterion
- Investors desire portfolios that lie to the “northwest” in the investment opportunity set
- There are benefits to diversification whenever asset returns are less than perfectly positively correlated
optimal risky portfolio
- The best combination of risky assets to be mixed with safe assets when forming the complete portfolio
- Highest feasible Sharpe ratio
- Steepest CAL
efficient frontier
Graph representing portfolios that maximizes expected return at each level of portfolio volatility
separation property
- implies portfolio choice can be separated into two independent tasks:
(1) determination of the optimal risky portfolio, which is a purely technical problem
(2) the personal choice of the best mix of the risky portfolio and the risk-free asset
index model
Model that relates stock returns to returns on both a broad market index and firm-specific factors
Index model regression equation:
Ri(t) = ɑi + βi x (Rm(t) - Rf) + ei
Alpha(ɑi)
expected RoR in excess of what would be predicted by an equilibrium model such as the CAPM
Beta(βi)
The sensitivity of a security’s return to the return on the market index
beta greater than 1
cyclical/aggressive stocks
beta less than 1
Defensive stocks
Slope of the CAL =
= excess return / variance
e(i)
residual, firm-specific surprise in the security return
Security characteristic line(SCL)
Plot of a security’s predicted excess return given the excess return of the market
variance of the excess return of a stock:
variance(Ri) = variance(βiRm) + variance(ei)
Algebraic representation of the single-index model regression line:
E(Rdisney|Rm) = ɑDisney + βdisney x Rm
R^2 of the single-index model regression line:
R^2 = systemic(explained) variance / total variance
R^2 = (correlation coefficient)^2
mean reversion
high betas securities tend to exhibit a lower beta in the future and vice versa
Adjusted beta =
= ⅔ x (beta estimate) + ⅓ x 1
information ratio
Ratio of alpha to the standard deviation of the residual
active portfolio
The portfolio formed by optimally combining analyzed stocks
Global minimum-variance portfolio
the risky portfolio with the lowest possible variance and a Sharpe ratio lower than that at the point of tangency
time diversificaiton
A two-year investor puts her funds at risk for two years instead of one placing only half as much in the stock market each year as a one-year investor
risk pooling
Pooling together many independent sources of risk
