Performance Measurement (10.31.24) Flashcards
Ex post vs ex ante
ex post - looking back in time
ex ante - looking forward in time
Performance attribution
The process of disaggregating a portfolio’s return to determine the drivers of its performance
Return attribution
A set of techniques used to identify the sources of the excess return of a portfolio against its benchmark
Macro vs. Micro attribution
macro - measures the effect of the sponsor’s choice to deviate from the strategic asset allocation
micro - measures the impact of pm’s allocation and selection decisions on total fund performance
Returns-based attribution
Uses only the total portfolio returns over a period to identify the components of the investment process that have generated returns (Brinson-Hood-Beebower)
when is returns based attribution appropriate
when the underlying portfolio holding information is not available with sufficient frequency at the required level of detail
hedge funds, for example, because it can be difficult to obtain the underlying holdings
easiest to implement, but least accurate
Holdings-based attribution
“Buy and hold” approach which calculates the return of portfolio and benchmark components based upon the price and foreign exchange rate changes applied to daily snapshots of portfolio holdings
when is holdings-based attribution most appropriate
for investment strategies with little turnover (passive strategies)
Transactions-based attribution
Captures the impact of intra-day trades and exogenous events such as significant class action settlement
most accurate, but most difficult to obtain
Geometric attribution
(1+R) / (1+B) - 1
OR
(R-B) / (1+B)
relationship between geometric excess return and arithmetic excess return
geometric = arithmetic divided by wealth ratio of the benchmark (1 + return on benchmark during the period)
Security selection answers which question
Was the return achieved by selecting securities that performed well relative to the benchmark or by avoiding benchmark securities that performed relatively poorly?
Asset allocations answers which question
Was the return achieved by choosing to overweight an asset category (e.g., economic sector or currency) that outperformed the total benchmark or to underweight an asset category that underperformed the total benchmark?
Interaction effect
The impact of overweighting and underweighting individual securities within securities that are themselves overweighted or underweighted
I = (w-w(b)) * (r-r(b))
BHB Model
Built on the assumption that the total portfolio and benchmark returns are calculated by summing the weights and returns of the sectors within the portfolio
Selection and allocation do not completely explain the arithmetic difference, interaction explains the third attribution effect
BF Model
All overweight positions in sectors with positive returns will generate positive allocation effects irrespective of the overall benchmark return, whereas all overweight positions in negative markets will generate negative allocation effects
Carhart four factor model
1) Market
2) Size
3) Value
4) Momentum
3 Approaches to fixed income attribution
1) Exposure decomposition (duration based)
2) Yield curve decomposition
(duration based)
3) Yield curve decomposition (full repricing based)
Exposure Decomposition
- (Duration Based)
- Top-down attribution approach that seeks to explain the active management of a portfolio relative to its benchmark
- Includes portfolio duration bets, yield curve positioning, sector bets (all relative to benchmark)
Yield Curve Decomposition
- (Duration based)
- Can be top-down approach or bottom up from security level, estimating the return of securities, sector buckets, or YTM buckets
%Total return = % Income return + % Price return
% Price return = -Duration * Change in YTM
Duration
measures the sensitivity of bond price to a change in the bond’s YTM
Yield Curve Decomposition
- (Full Repricing)
- Bottom up approach that is more precise and allows for broader range of instrument types and yield changes
- Reprices bonds from zero-coupon curve (spot rates)
Common measure of risk when portfolios are managed against benchmarks
Tracking risk
7 Types of Benchmarks
1) Absolute return benchmark
2) Broad market index
3) Style index
4) Factor-model-based benchmark
5) Returns-based (Sharpe) benchmark
6) Manager universes (peer groups)
7) Custom security-based (strategy) benchmark
Absolute return benchmark
a minimum target return that an investment manager is expected to beat
Broad market index
Measures of broad asset class performance; well known, readily available, and easily understood
Investment style index
a natural grouping of investment disciplines that has some predictive power in explaining the future dispersion of returns across portfolios
Factor-model-based benchmarks
Benchmarks constructed by examining a portfolio’s sensitivity to a set of factors, such as the return for a broad market index, company earnings growth, industry, or financial leverage
Returns based benchmarks (Sharpe style analysis)
Benchmarks constructed by examining a portfolio’s sensitivity to a set of factors, such as the returns for various style indexes
Manager universe
a broad group of managers with similar investment disciplines; also called manager peer group
Custom security-based benchmark
Custom built to accurately reflect the investment discipline of a particular investment manager
Criteria that a benchmark must satisfy to be valid in use
1) Unambiguous - clearly identifiable
2) Investable
3) Measurable
4) Appropriate
5) Reflective of current investment opinions
6) Specified in advance
7) Accountable
Sharpe ratio
The ratio of mean excess return to standard deviation (excess return)
(Return - risk free rate) / standard deviation
Treynor Ratio
Measures the excess return per unit of systematic risk
(return - risk free rate) / beta
When is treynor ratio useful
when the portfolios being compared as using the same benchmark index
Information ratio
Assesses performance relative to the benchmark, scaled by risk
(return portfolio - return benchmark) / (portfolio StD - benchmark StD)
Appraisal ratio (Treynor-Black Ratio)
Annualized alpha divided by the annualized residual risk, which are both computed from a factor regression
alpha/standard error of regression
Sortino Ratio
modification of sharpe ratio that penalizes only those returns that are lower than a user-specified return
(return - user-specified return) / risk