Portfolio Concepts Flashcards
Variance and stand dev of 2 asset portfolio
o^2 = w1^2o1^2 + w2^2o2^2 + 2w1w2p1,2o1o2
o = sqrt(o^2)
Expected return for 2 asset portfolio
E(Rp) = w1E(R1) + w2E(R2)
Calculate covariance
Cov(1,2) = p1,2o1o2
What is the minimum variance frontier
Expected return variance combinations of the set of portfolios that have minimum variance for every given expected return
Portfolios on the efficient frontier have the highest _________ at each given level of risk
Expected return
Why are min var and efficient frontiers unstable? What is effect
Exp returns, variances, covariances change over time
May lead to large portfolio weighting areas
What is portfolio diversification
Strategy of reducing risk by combining different types of assets into a portfolio
Diversification benefits increase with _____ and ______
Decreases correlations
Increased number of assets
Calc variance of equally weighted portfolio
O^2 = o^2 *((1 - p)/n + p)
Variance of an equally weighted portfolio approaches average covariance as n gets large; this means…
- Reducing risk via diversification can be achieved w/relatively few stocks
- Higher average correlation => fewer stocks needed to reduce risk
What is the capital allocation line
Line from risk free rate to tangency to efficient frontier
Where does best risky portfolio lie
Point of tangency between CAL and efficient frontier
When combined with risky asset, optimal reward to risk ratio
Sharpe ratio
o (std dev)
expected risk premium per unit risk
CAL equation
E(Rc) = Rf+(E(Rt) - Rf)*oc
———
o (std dev)
Combo of risk free asset and efficient asset
Things to remember about CAL
If risk free available, combine to risky portfolio to increase returns Intercept = rf Slope = Sharpe ratio Use to assess risk at target return Diff asset expectations = diff CALs
Market portfolio is tangency portfolio CML equation:
E(Rc) = Rf+(E(Rm) - Rf)*oc
———
om (std dev)
Combo of risk free asset and efficient asset
Differences between CAL and CML
Only one CML; unlimited CALs
Market portfolio uses market value weights
Tangency portfolio differs across investors
CML special case for CAL
CAPM (Systematic market line)
E(Ri) = Rf + Bi(E(Rm) - Rf)
Key differences between SML and CML
Systematic risk vs. standard deviation
(Non diversifiable vs. total risk)
Use to benchmark returns vs. asset allocation
CAPM vs. efficient frontier
Slope is Market risk premium vs. sharpe ratio
How to calc beta
Beta = Oi * p(i,M)
—-
Om
Market model (regression model used to estimate betas for common stocks
Ri = Ai + Bi*Rm + Ei
What three predictions does market model make?
- E(Ri) = Ai + Bi*E(Rm)
- Oi^2 = Bi^2*Om^2 + Oe^2
- Cov(i,j) = BiBjOm^2
Adjusted beta (to correct for beta instability)
Forecast B(i,t) = A0 + A1*B(i,t-1)
Blume assigns A0 = 1/3 and A1 = 2/3
Difference between how macroeconomic, fundamental, and statistical factor models explain asset returns
Unexpected changes
Vs. returns from multiple firm-specific factors
Vs. determine which “factors” best explain on a cross section of securities
Unique features of Macroeconomic factor model
Sensitivities are regression slope estimates
Macro factors surprises in variables
Fewer factors that represent systematic risk
Intercept = stocks expected return
Unique features of fundamental factor model
Sensitivities are calculated from attribute data
Fundamental factors are rates of return estimated using multiple regression
Detailed - large number of factors
Intercept has no economic interpretation
What is Arbitrage pricing theory
Equilibrium asset pricing model with less restrictive assumptions
Intercept = risk free rate
Factors are actual risk premiums
Active return
Active return = portfolio return - benchmark return
Active risk
Active risk ^2 = active factor risk + active specific risk
Information ratio
IR = Rp - Rb
———
S
S= active risk
What is a factor portfolio
Constructed w/sensitivity of one
