Portfolio Management

MPT

efficient frontier is a line from the risk-free asset w/ a tangent to the optimal risky asset portfolio

Information Coefficient (IC)

measures manager skill (Accuracy)

Ex ante: expected correlation between active returns and forecast active returns

Ex post: measures actual correlation between active returns and forecast active returns

Transfer Coefficient (TC)

correlation between actual active weights and optimal active weights

TC = 1 for unconstrained portfolios, TC < 1 w/ constraints

Breadth (BR)

number of independent bets (forecasts of active returns)

ETF

shares in an index-tracking portfolio that trade on secondary markets (also on primary when APs create/ redeem shares)

lower costs and better tax efficiency than mutual funds; price alignment with NAV

issue manager portfolio + handles creation/redemption

Authorized Participants

large broker dealers; only entieis that can create / redeem ETF shares

Tracking Difference

= ETF return - index return

Tracking Error

volatility (std. dev) of tracking differences

Sources: Fees/Expenses, Sampling Optimization, Depository Receipts, Index Changes, Tax/Regulatory differences, Fund Accounting, Manager Operations

Roundtrip Trading Cost

= round-trip commission + spread

Total ETF Cost

= round-trip trading cost + management feeds

Counterparty Risk

Issuer defaults; relevant for ETNs; measured via CDS spreads

Settlement Risk

arises from OTC derivatives used by some ETFs; mitigate w/ frequent settlement & collateral requirement

*ADRs are exchange-traded so no settlement risk

Securities Lending Risk

ETFs lend securities to short sellers

Benefits → fee income offsets expenses

Risks→ borrower default, risk borne by ETF investors

Smart Beta Investing

Rules based, not discretionary; based on size, value, momentum

more popular for fixed income than equity due to low liquidity

Arbitrage Pricing Theory (APT)

developed as an alternative to the CAPM; unlike CAPM does not identify the specific risk factors and requires weaker set of assumptions

Assumptions:

• unsystematic risk can be diversified away from the portfolio

• returns are generated using a factor model

• no arbitrage opportunities exist

**in arbitrage strategy, take a short position in the asset w/ the lowest expected return per unit of factor sensitivity (Ra / Bp,a)

Macroeconomic Factor Model

Uses fewer factors; interest rates, inflation, business cycle, credit spreads etc.

Time-series of suprises, regression based factor sensitivity

Fundamental Factor Model

Uses more factors; B/M, market cap, P/E, leverage

explains cross-sectional differences in returns from attributes of individual stocks

Principal Components Model

Statistical factors; factors are portfolios of securities that best reproduce historic return variances

Factor Analysis Models

Statistical factors; factors are portfolios of securities that best reproduce historic return covariances

Active Return

difference between portfolio return and its benchmark

Active Risk

(Tracking error / risk) is the std. dev of the active return

Information Ratio

active return per unit of active risk; measures manager’s consistency in generating active return

Tracking portfolio

same factor risk, different specific risk compared to benchmark

Factor Portfolio

factor sensitivity of 1 to a specific factor and 0 to all other factors

Value at Risk (VaR)

measures the downside risk of a portfolio and has three components: loss size, probability, time frame

Parametric Method

uses variances and covariances; often assumes normal distribution; uses left-tail

Estimates are only as good as inputs; length of lookback period impacts parameter estimates

Historical Simulation

uses some prior lookback period to get a distribution of possible values; assumes stationarity

Monte Carlo Simulation

draws from assumed distribution; repeated thousands of times to get a distribution of possible portfolio values

Conditional VaR

expected loss, given that the loss is equal to or greater than VaR; aka expected tail loss or expected shortfall in the left tail

Incremental VaR (IVaR)

change in VaR from a change in the portfolio allocation to a security

Marginal VaR (MVar)

slope of the tangent at a point in the VaR vs. the security weight curve; based on calculus

Inaccurate to interpret it as the change in VaR for a 1% increase in the security’s weight

Relative VaR (ex ante tracking error)

measure the VaR of the difference between the return on a portfolio and the return on its benchmark

can be calculated as the VaR of a combination of the subject portfolio and a short position in the benchmark portfolio

Vega

measure of sensitivity of option values to changes in the expected volatility of the price of the underlying asset

Sensitivity Risk measures

inform a portfolio manager about a portfolio’s exposure to various risk factors to facilitate risk management

Scenario Analysis

evaluates portfolio performance under hypothetical or historical events; captures impact of simultaneous changes in multiple risk factors

Reverse Stress Testing

final step after sensitivity analysis; highlights risks from extreme events or correlation shifts

Stress Testing (Single Factor)

often used by leverage firms measures how much a single factor must move to threaten volatility

Active Share

the difference between the weight of a security in the portfolio and its weight in the benchmark; risk measure more specific to asset management

Maximum Drawdown

the largest decrease in value over prior periods of a specific length

Surplus at Risk

VaR for plan assets - liabilities; a negative surplus must be made up by the firm if higher than expected asset returns do not reduce it significantly over time

Glide Path

multi-year plan for adjusting pension fund contributions to reverse a significant overfunded or underfunded status

Risk Budgeting

determine total acceptable risk; allocate risk across strategies, activities, or asset classes

Positon Limits

restrict size of exposures to ensure diversification; applies to individual securities, asset classes, countries / currencies, long vs. short postions

Scenario Limits

limit maximum expected loss under spcific scenarios; focus on stress-testing outcomes

Stop-Loss Limits

require reducing exposre when losses exceed a threshold

Economic Capital

capital needed to overcome severe losses in the business

Backtesting

process by which historical data is used to emulate the investment process

goal is to assess the risk & return of an investment strategy

Survivorship Bias

when using data that only includes entities that have persisted until today

Look Ahead Bias

when using data that would have been unavailable at the time of the investment decision

Data Snooping

when a model is chosed based on backtesting results (eg. large t-stat or small private)

Cross Validation

when a model is first fitted using training data, and then its performance is assessed (often over several rounds) using separate testing data

Skewed Multivariate T-distribution

helps to take fat tails and skewness into account; but also increases probability of estimation error