Performance Evaluation

Question 1

Performance measurement

Answer 1

A component of performance evaluation; the relatively simple procedure of calculating an asset’s or portfolio’s rate of return

Question 2

Performance attribution

Answer 2

A comparison of an account’s performance with that of a designated benchmark and the identification and quantification of sources of differential returns

Question 3

Performance appraisal

Answer 3

The evaluation of portfolio performance; a quantitative assessment of a manager’s investment skill

Question 4

Rate of return with contribution made at the beginning/end of the period

Answer 4

Question 5

Time-Weighted Rate of Return (TWR)

Answer 5

Question 6

Money-Weighted Rate of Return (MWR) (same thing as IRR)

Answer 6

Question 7

TWR versus MWR

Answer 7

• 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

Question 8

Linked Internal Rate of Return LIRR

Answer 8

Chain link of MWRs calculated periodically

• Example: (1 + r₁) * (1 + r₂) * (1 + r₃) * (1 + r₄) where r_n is the MWR for the week

Question 9

Returns due to style and active management

Answer 9

• 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)

Question 10

Value-added return on a long–short portfolio where the active weights sum to zero (calculation)

Answer 10

• r_v = rp – rB  
• r_ν = value-added return
• r_p = portfolio return
• r_B = benchmark return
• w_νi = the active weight of security i in the portfolio
• w_pi = the weight of security i in the portfolio
• w_Bi = the weight of security i in the benchmark

Question 11

Ex Ante CAPM (SML) over a single period

Answer 11

• E(R_A) = the expected return on the account, given its beta
• r_f = the risk-free rate of return (known constant for the evaluation period)
• E(R_M) = the expected return on the market portfolio
• β_A = the account’s beta or sensitivity to returns on the market portfolio, equal to the ratio of covariance to variance as Cov(R_A, R_M)/Var(R_M)

Question 12

Ex Post Alpha (also Jensens alpha)

Answer 12

• R_At is the return on the account
• r_ft is the risk-free return
• R_Mt is the return on the market proxy (market index)

Question 13

Treynor Measure

Answer 13

Question 14

Sharpe Ratio

Answer 14

Question 15

M²

Answer 15

Question 16

Information Ratio (IR)

Answer 16

• σ_A−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

Question 17

Properties of a valid benchmark

Answer 17

• Unambiguous
• Investable
• Measurable
• Appropriate
• Reflective of current investment opinions
• Specified in advance
• Owned

Question 18

Incremental return contribution of the asset category investment strategy

Answer 18

Question 19

Incremental return contribution of the benchmarks strategy

Answer 19

• r_IS is the incremental return contribution of the Benchmarks strategy
• r_Bij is the return for the jth manager’s benchmark in asset category i
• r_Ci is the return on the ith asset category
• w_i is the policy weight assigned to the ith asset category
• w_ij 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

Question 20

Incremental return contribution of the active management strategy

Answer 20

• r_Aij represents the actual return on the jth manager’s portfolio within asset category i
• r_Bij is the return for the jth manager’s benchmark in asset category i
• r_Ci is the return on the ith asset category
• w_i is the policy weight assigned to the ith asset category
• w_ij 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

Question 21

Sector weighting/stock selection attribution

Answer 21

• w_pj = Portfolio weight of sector j
• w_Bj = benchmark weight of sector j
• r_pj = Portfolio return of sector j
• r_Bj = benchmark return of sector j
• S = number of sectors

Question 22

Hypothesis testing error types

Answer 22

• 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.)

Question 23

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

Answer 23

• 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

Question 24

Information coefficient (IC) - formula

/

IC is the ex ante risk-weighted correlation

Answer 24

• σ_i is the forecasted volatility of the active return on security i
• μ_i is the forecasted active return

Question 25

E(R_A) of the full fundamental law

Answer 25

Question 26

Information ratio (IR) of the full fundamental law

Answer 26

* Unconstrained → IR = (IC)√BR * Constrained → IR = (TC)(IC)√BR

Question 27

Transfer coefficient (TC) - definition

Answer 27

The TC is the cross-sectional correlation between the forecasted active security returns and the actual active weights, adjusted for risk

Question 28

Transfer coefficient (TC) - formula

Answer 28

* σ_i is the forecasted volatility of the active return on security i * μ_i is the forecasted active return

Question 29

Fixed-income management effect

Answer 29

* **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.

Question 30

Steps in creating a custom security-based benchmark

Answer 30

* 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

Question 31

Capital allocation line (CAL)

Answer 31

Question 32

Capital market line (CML)

Answer 32

Question 33

Security market line (SML)

Answer 33

Question 34

3 main features for independent variables used in a return-based style analysis

Answer 34

* Mutually exclusive * Exhaustive * Represent distinct sources of risk

Question 35

R-square in a return-based style analysis

Answer 35

* 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

Question 36

Advantages of holdings-based analysis versus return-based style analysis

Answer 36

* 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