Performance Evaluation Flashcards
Performance measurement
A component of performance evaluation; the relatively simple procedure of calculating an asset’s or portfolio’s rate of return
Performance attribution
A comparison of an account’s performance with that of a designated benchmark and the identification and quantification of sources of differential returns
Performance appraisal
The evaluation of portfolio performance; a quantitative assessment of a manager’s investment skill
Rate of return with contribution made at the beginning/end of the period
Time-Weighted Rate of Return (TWR)
Money-Weighted Rate of Return (MWR) (same thing as IRR)
TWR versus MWR
- TWR represents the growth of one unit of money invested into the account
- MWR represents the average growth of all the money invested into the account
- MWR is sensible to the timing of cash flow whereas TWR isn’t
Linked Internal Rate of Return LIRR
Chain link of MWRs calculated periodically
- Example: (1 + r1) * (1 + r2) * (1 + r3) * (1 + r4) where rn is the MWR for the week
Returns due to style and active management
- M = Return on market index
- S = Return from manager’s investment style (B – M)
- B = Return on selected benchmark
- A = Return from manager’s active decisions (P - B)
Value-added return on a long–short portfolio where the active weights sum to zero (calculation)
- rv = rp – rB
- rν = value-added return
- rp = portfolio return
- rB = benchmark return
- wνi = the active weight of security i in the portfolio
- wpi = the weight of security i in the portfolio
- wBi = the weight of security i in the benchmark
Ex Ante CAPM (SML) over a single period
- E(RA) = the expected return on the account, given its beta
- rf = the risk-free rate of return (known constant for the evaluation period)
- E(RM) = the expected return on the market portfolio
- βA = the account’s beta or sensitivity to returns on the market portfolio, equal to the ratio of covariance to variance as Cov(RA, RM)/Var(RM)
Ex Post Alpha (also Jensens alpha)
- RAt is the return on the account
- rft is the risk-free return
- RMt is the return on the market proxy (market index)
Treynor Measure
Sharpe Ratio
M2
Information Ratio (IR)
- σA−B is the standard deviation of the difference between the returns on the account and the returns on the benchmark
- IR = active return / active risk
Properties of a valid benchmark
- Unambiguous
- Investable
- Measurable
- Appropriate
- Reflective of current investment opinions
- Specified in advance
- Owned
Incremental return contribution of the asset category investment strategy
Incremental return contribution of the benchmarks strategy
- rIS is the incremental return contribution of the Benchmarks strategy
- rBij is the return for the jth manager’s benchmark in asset category i
- rCi is the return on the ith asset category
- wi is the policy weight assigned to the ith asset category
- wij is the policy weight assigned to the jth manager in asset category i
- A and M are the number of asset categories and managers, respectively
Incremental return contribution of the active management strategy
- rAij represents the actual return on the jth manager’s portfolio within asset category i
- rBij is the return for the jth manager’s benchmark in asset category i
- rCi is the return on the ith asset category
- wi is the policy weight assigned to the ith asset category
- wij is the policy weight assigned to the jth manager in asset category i
- A and M are the number of asset categories and managers, respectively
Sector weighting/stock selection attribution
- wpj = Portfolio weight of sector j
- wBj = benchmark weight of sector j
- rpj = Portfolio return of sector j
- rBj = benchmark return of sector j
- S = number of sectors
Hypothesis testing error types
- Type I error—keeping (or hiring) managers with zero value-added. (Rejecting the null hypothesis when it is correct.)
- Type II error—firing (or not hiring) managers with positive value-added. (Not rejecting the null hypothesis when it is incorrect.)
Target active risk, max sector deviation and max risk contribution for a single security for the 3 following approaches:
- Diversified multi-factor
- Sock picking
- Sector rotation
- Diversified multi-factor
- Target active risk → low
- Max Sector deviation → medium
- Max. risk contribution for a single security → low
- Stock picking
- Target active risk → high
- Max Sector deviation → low
- Max. risk contribution for a single security → medium to high
- Sector rotaiton
- Target active risk → high
- Max Sector deviation → high
- Max. risk contribution for a single security → low
Information coefficient (IC) - formula
/
IC is the ex ante risk-weighted correlation
- σi is the forecasted volatility of the active return on security i
- μi is the forecasted active return
E(RA) of the full fundamental law
Information ratio (IR) of the full fundamental law
- Unconstrained → IR = (IC)√BR
- Constrained → IR = (TC)(IC)√BR
Transfer coefficient (TC) - definition
The TC is the cross-sectional correlation between the forecasted active security returns and the actual active weights, adjusted for risk
Transfer coefficient (TC) - formula
- σi is the forecasted volatility of the active return on security i
- μi is the forecasted active return
Fixed-income management effect
- Interest rate management effect: Indicates how well the manager predicts interest rate changes. To calculate this return, each security in the portfolio is priced as if it were a default-free security. The interest rate management contribution is calculated by subtracting the return of the entire Treasury universe from the aggregate return of these repriced securities. The interest rate management effect can be further broken down into returns due to duration, convexity, and yield-curve shape change
- Sector/quality effect: Measures the manager’s ability to select the “right” issuing sector and quality group. The sector/quality return is estimated by repricing each security in the portfolio using the average yield premium in its respective category. A gross return can be then calculated based on this price. The return from the sector/quality effect is calculated by subtracting the external effect and the interest rate management effect from this gross return
- Security selection effect: Measures how the return of a specific security within its sector relates to the average performance of the sector. The security selection effect for each security is the total return of a security minus all the other components. The portfolio security selection effect is the market-value weighted average of all the individual security selection effects
- Trading activity: Captures the effect of sales and purchases of bonds over a given period and is the total portfolio return minus all the other components.
Steps in creating a custom security-based benchmark
- Identify prominent aspects of the manager’s investment process
- Select securities consistent with that investment process
- Devise a weighting scheme for the benchmark securities
- Including a cash position
- Review the preliminary benchmark and make modifications
- Rebalance the benchmark portfolio on a predetermined schedule
Capital allocation line (CAL)
Capital market line (CML)
Security market line (SML)
3 main features for independent variables used in a return-based style analysis
- Mutually exclusive
- Exhaustive
- Represent distinct sources of risk
R-square in a return-based style analysis
- The R-squared resulting from a regression against a benchmark represents passive management → R-squared is the variation that can be explained by the variation of the benchmark and is therefore passive
- (1 - R-squared) represents active management
Advantages of holdings-based analysis versus return-based style analysis
- The method characterizes each position rather than looking only at the portfolio as a whole
- The method facilitates the comparison of individual positions
- The method is likely to capture changes in style more quickly
