Portfolio Management Flashcards
Defined Contribution Plan
A retirement plan in which the firm contributes a sum each period to the employee’s retirement account
Defined benefit pension plan
firm promises to make periodic payments to employees after retirement
3 steps in portfolio management process
- Planning – risk tolerance, tax exposure, etc.
- Execution – analysis of risk and return characterisitcs of each asset class
- feedback step – rebalance portfolio
Investor Policy Statement Objectives and Constraints
R - Risk R - Return T - Time Horizon T - Taxes L - Liquidity L - Legal & Regulatory U - Unique
Standardized Sensitivities
b = (PEi - PEbar) / SigmaPE
Active Return
= Return on portfolio - Return on benchmark
Active return can be split into factor return and sensitivity selection factor
Information Ratio
(Return Portfolio - Return Benchmark) / Sigma(Rp-Rb)
Active risk squared
=active factor risk + active specific risk
Active specific risk
= SUM(WeightPi - WeightPb)^2 * Sigmaerror^2
Risk premium for ST and LT bond
ST risk premium = R + Pi
LT risk premium = R + Pi + Theta
R = interest rate Pi = Inflation Theta = uncertainty about inflation
Taylor Rule
= R + Pi + 0.5 (Pi-Pi) + 0.5 (Y-Y)
Pi* = central banks target inflation Y = Log of current level of output Y* = Log of central banks target output
Break Even Inflation Rate (BEI)
=Yield on non indexed bond - Yield on inflation indexed bond
= Pi * theta
Required return on a credit risky bond
= R + Pi + Theta + Gamma
Gamma = credit spread, where gamma increases during economic downturns
Discount rate of equity
= R + Pi + Theta + Gamma + k
k = additional risk premium relative to risky debt for an investment in equities,
Where, equity risk premium =
Gamma + k = credit spread + additional risk premium relative to risky debt for an investment in equities
Discount rate for real estate
= R + Pi + Theta + Gamma + k + Phi
Phi = risk premium or illiquidity
Credit Spread = Yield - BEI - R
When the credit spread narrows, lower rated bonds outperform higher rated bonds
Term Spread
= Yield of LT gov’t bonds - Yield on ST gov’t bonds
Information Ratio
=Information Coefficient * SqRt(Breadth)
= IC * SqRt(BR)
Active Return
= return on portfolio - return on benchmark
= SUM(delta(wi) * Rb) + SUM(wpRa)
= {Weight(stocks)Return(stocks) + Delta(weight[bonds]) Return(bonds)} + {Weight(stocks)Return(stocks) + Weight(bonds) * Return(bonds)}
Sharpe Ratio
absolute expected reward-to-risk measure. Compares the portfolio return in excess of a risk-free rate.
Information Ratio
relative reward-to-risk measure. The portfolio return relative to a benchmark portfolio
Information Ratio
= {Rp - Rb} / Sigma(Rp-Rb)
= Ra / Sigma (a)
= Active Return / Active Risk
= SRp^2 = SRb^2 + IR^2
SR of Actively managed Prtflio^2 =
SR of benchmark^2 + Information Ratio ^2
Sigma(Ra) = (IR/SRb) * Sigma(Rb)
…
Sigma(Rp)^2 = Sigma (Rb)^2 + Sigma(Ra)^2
…
Mean Variance optimal weights
Delta(w) = (Mew/Sigma(i)^2) * ( Sigma(a) / [IC*SqRt(BR)]
Information Coefficient
anticipated cross sectional correlation between N forecasted active return , Mew(i), and the N realized active returns, Ra.
Information Coefficient
anticipated cross sectional correlation between N forecasted active return , Mew(i), and the N realized active returns, Ra.
Breadth
= #independent decisions made each year
= #securities * #rebalancing periods
Basic Fundamental Law
E(Ra) = IC * SqRt(BR) * Sigma(a)
For an unconstrained portfolio, IC
IC* = E(Ra*) / Sigma(a) = IC * SqRt(BR)
Full Fundamental Law
E(Ra*) = TC * IC * SqRt(BR) Then, Sigma(a) = TC * (IR*/SRb) * Sigma(b) Then, SRp^2 = SRb^2 + TC^2*IR*^2
Ex Post Performance Measure
= E(Ra given ICrealized) = TC * ICrealizedSqRt(BR)Sigma(a)
TC^2 percent of the variation in performance is attributed to the sucess of the forecasting process, while (1-TC^2) percent is due to constraint induced noise.
TC measures the extent to which constraints reduce the expected value added of the investors’ forecasting ability
To address the uncertainty of the portfolio manager’s skill, …
Sigma(a) = Sigma(IC) * SqRt (N) * Sigma(RiskModel)
Active Risk = Risk in IC * SqRt(N) * Risk in Risk Model
A practical measure of breadth
BR = N / [1 + (N-1)*r]
where,
r=correlation between decisions
For Market Timing, the IC =
ICmt = 2 *(% correct) - 1
Annualized Active Risk
= Sigma(c) * SqRt(BR)
Annualized Active Return
E(Ra) = IC * SqRt(BR) * Sigma(a)
Sigma(c) = [ Sigma(x)^2 - 2Sigma(x)Sigma(y)*r(xy) + Sigma(y)^2]^(1/2)
…
