Portfolio Management Flashcards
Grinold-Kroner Model
ERP =
(+) Dividend Yield
(+) Expected Inflation
(+) Real GDP Growth
(+) % change in P/E
(-) % change in S/O
——–
(-) Real risk-free
Optimal active risk
IR / SR_B * sd_B
Placeholder
Revise using multi-factor models
How must economic factors affect market values according to the PV model?
To impact value, factors must affect: 1) Default-free interest rates (discount rate component), 2) Timing and/or magnitude of expected cash flows (numerator), or 3) Risk premiums (discount rate component).
What is the Intertemporal Rate of Substitution (mt)?
Measures the marginal utility of consuming one unit in the future relative to consuming one unit today. In equilibrium, the price of a risk-free bond P0=E(mt), and the risk-free rate Rf=(1/E(mt))−1. It’s influenced by expectations of future income/wealth and risk aversion.
How does the business cycle affect short-term interest rates and the yield curve slope?
Expansion: Economy overheats, inflation rises. Central bank tightens policy (raises short-term rates). Yield curve often flattens or inverts as LT rates may rise less (or fall) due to lower future growth expectations/inflation control. Recession: Economy weakens, inflation falls. Central bank loosens policy (lowers short-term rates). Yield curve typically steepens (bull steepening).
How does the business cycle affect credit spreads?
Credit spreads typically narrow during expansions (lower default risk, higher recovery rates) and widen during recessions (higher default risk, lower recovery rates). Lower-rated bonds are more sensitive.
How does the business cycle affect earnings growth expectations and valuation multiples?
Earnings Growth: Expectations are pro-cyclical; rise during expansions, fall during recessions. Valuation Multiples (e.g., P/E): Tend to expand during early expansion (anticipating recovery) and contract during late expansion/recession (higher risk aversion, lower growth expectations). Shiller CAPE often counter-cyclical.
What is Value Added by active management?
The difference between the portfolio’s return (RP) and the benchmark’s return (RB). RA=RP−RB. Can be decomposed ex-post into asset allocation and security selection returns.
Define the Information Ratio (IR).
Measures active return per unit of active risk. IR=E(RA)/σA=(RP−RB)/σ(RP−RB). Ex-ante IR measures expected skill; ex-post measures realized skill-adjusted return.
What are the components of the Fundamental Law of Active Management?
Basic Law (Unconstrained): E(RA)=IC×BR×σA, or IR=IC×BR. Expanded Law (Constrained): E(RA)=TC×IC×BR×σA, or IR=TC×IC×BR. IC: Information Coefficient (skill, correlation of forecasts & outcomes). BR: Breadth (number of independent bets). TC: Transfer Coefficient (efficiency, constraint impact, 0 to 1). σA: Active Risk (aggressiveness).
How is the optimal level of active risk determined?
σA∗=SRBIR×σB, where SRB is Sharpe Ratio of benchmark. Optimal portfolio Sharpe Ratio SRP∗=SRB2+IR2.
Describe the ETF creation/redemption process and the role of Authorized Participants (APs).
Creation: AP delivers a basket of underlying securities (creation basket) to ETF issuer, receives ETF shares. Redemption: AP returns ETF shares to issuer, receives underlying securities (redemption basket). APs act as market makers, ensuring ETF price stays close to NAV via arbitrage. Process is typically “in-kind” (shares for shares), enhancing tax efficiency.
What causes ETF tracking error?
Fees/expenses, sampling/optimization instead of full replication, cash drag, index changes, fund accounting practices, tax rules, depository receipts timing differences.
What affects ETF bid-ask spreads?
Liquidity of the ETF itself, liquidity of the underlying securities, risk premium for AP hedging, AP’s arbitrage costs. Wider for illiquid underlying or during market stress.
Define Arbitrage Pricing Theory (APT) assumptions.
1) Asset returns described by a factor model. 2) Asset-specific risk can be diversified away. 3) No arbitrage opportunities exist among well-diversified portfolios. Unlike CAPM, does not assume investors are rational mean-variance optimizers or specify the factors.
Contrast Macroeconomic, Fundamental, and Statistical Factor Models.
Macro: Factors are observed macro variables (e.g., inflation, GDP growth); sensitivities estimated via time-series regression. Fundamental: Factors are company attributes (e.g., P/E, size, industry); sensitivities derived from attributes. Statistical: Factors derived statistically (PCA, factor analysis) from historical returns; factors may lack economic meaning.
Define Active Risk (Tracking Error) and its sources.
Standard deviation of active returns (σA=σ(RP−RB)). Sources: Active Factor Tilts (difference in portfolio vs benchmark sensitivities to factors) and Security Selection (difference in portfolio vs benchmark exposure to specific/residual risk).
Define Value at Risk (VaR).
Minimum loss expected over a specific time horizon at a given probability level (e.g., 5% daily VaR of $1m means 5% chance of losing at least $1m in one day).
Compare VaR estimation methods (Parametric, Historical, Monte Carlo).
Parametric: Assumes distribution (e.g., normal), uses mean/std dev to calculate VaR (VaR=μ+zσ). Simple but relies on assumptions. Historical: Uses past return distribution; ranks historical returns to find VaR cutoff. No distribution assumption but depends on lookback period. Monte Carlo: Simulates many possible future paths using models/distributions for risk factors; calculates VaR from simulated outcomes. Flexible but complex/model-dependent.
Define extensions of VaR (CVaR, IVaR, MVaR).
Conditional VaR (CVaR): Expected loss given that the VaR threshold has been exceeded (average tail loss). Incremental VaR (IVaR): Change in VaR from adding/removing a position. Marginal VaR (MVaR): Change in VaR for a small change in a position’s size (sensitivity).
Compare Sensitivity Risk Measures and Scenario Risk Measures to VaR.
Sensitivity (Beta, Duration, Greeks): Measures impact of small change in one risk factor. Simple but ignores correlations, non-linearities, and probability. Scenario: Measures impact of large move in multiple factors (historical or hypothetical event). Captures correlations/non-linearities but doesn’t give probabilities. VaR: Probabilistic measure of potential loss, considers portfolio effects but can be complex and model-dependent.
Describe the process and potential problems in backtesting investment strategies.
Process: Design strategy (hypothesis, rules, rebalancing), Simulate over historical data (often using rolling windows: in-sample parameter estimation, out-of-sample testing), Evaluate results (returns, risk, ratios, plots). Problems: Survivorship bias (excluding failed firms), Look-ahead bias (using future info), Data snooping (overfitting to historical data). Use point-in-time data and cross-validation to mitigate
