MIP Ch 12: Evaluating Portfolio Performance Flashcards
Describe how to calculate the time-weighted return (TWR) of an investment portfolio
Assuming n external cash flows occur between time 0 and time t at times t1, t2, . . . , tn,
there will be n 1 subperiod calculations:
rti
pMVti CFti q MVti1
MVti1
for i 1 to n
rti
pMVti q MVti1
MVti1
for i n 1
The TWR is the product of the subperiod growth factors
rTWR p1 rt1qp1 rt2q p1 rtn1q 1
Describe the money-weighted return of an investment portfolio
The growth rate R that solves the following equation:
MVt MV0p1 Rq
t
CFt1p1 Rq
tt1 CFtn p1 Rq
ttn
An IRR calculation can be solved for iteratively with a computer program
Describe a situation for a portfolio when the money-weighted return (MWR) is different
from the time-weighted return (TWR)
MWR and TWR can have material differences if funds are contributed/withdrawn
from an account prior to a period of strong or weak performance
MWR is sensitive to the size and timing of the cash flows, while TWR is not
Example: There will be a positive effect on MWR if funds are invested right before a
strong earnings period
When should an investment portfolio use MWR or TWR for measuring performance?
TWR is more appropriate when evaluating managers who have little or no control
over external investments
MWR is more appropriate if the investment manager has control over external
investments
Example: Private equity fund managers can determine when they receive and
return capital to investors
Compare and contrast the number of times one needs to value the portfolio for
calculating TWR and MWR
TWR requires a valuation of the account each date there is an external cashflow,
which is a drawback
In contrast, the MWR only requires a valuation at the beginning and end of period
This is computationally simpler
Describe how to calculate the linked internal rate of return (LIRR) of a portfolio
LIRR estimates the TWR by calculating the MWR over time intervals (i.e. weekly),
and then chain-linking these returns together
Valid approximation if there are no large external cash flows and volatile swings in
subperiod performance
Example: Suppose over a month, an account’s MWR is calculated each week
MWR’s are 2.1% in week 1, 0.16% in week 2, -1.4% in week 3, and 1.8% in week
4. The LIRR is:
RLIRR p1 0.021q p1 0.0016q p1 0.014q p1 0.018q 1
0.0265, or 2.65%X
Is it acceptable to annualize a return for an investment period that is shorter than one
year?
Returns should not be annualized for periods shorter than a year
Otherwise, we would be extrapolating the account’s returns over a sample period
to the full year
Describe some data quality issues in performance measurement
Accounts invested in illiquid assets may have inaccurate valuations
For many thinly traded fixed-income securities, estimated prices may be derived
on dealer quoted prices for securities with similar attributes (i.e. sector, credit
rating)
This is called matrix pricing
Breakdown of portfolio return into market return, style return, and active return
The portfolio return, P, can be broken down into the following components:
P M pB Mq pP Bq M S A
B = the return of the benchmark
M = the return of the market index
S B M = return that reflects the manager’s investment style
A P B = returns from active management decisions
List properties of a valid benchmark
- Unambiguous (identity and weights of securities are clearly defined)
- Investable (it’s possible to hold the benchmark as a portfolio)
- Measurable (benchmark return can be calculated on a frequent basis)
- Appropriate (consistent with the manager’s style)
- Reflective of current investment opinions
- Specified in advance (before the start of an evaluation period)
- Owned (the investment manager should accept the performance of the
benchmark)
List seven types of benchmarks
- Absolute
- Manager Universes
- Broad Market Indexes
- Style Indexes
- Factor-Model-Based
- Returns-Based
- Custom Security-Based
Describe the issues of an absolute benchmark
An absolute benchmark specifies a minimum return target for the portfolio (i.e.
must return at least 7%)
The main issue with this type of benchmark is it is not investable
Describe the manager universe benchmark
The manager universe benchmark compares the manager’s returns to a universe
of portfolios with similar characteristics
The investment objective may be for the managers’ fund to exceed the median
account return from the manager universe
Describe the problems with a manager universe benchmark
- The median account return from the universe cannot be specified in advance
- It is not investable
- Ambiguous, since the identity of the median manager typically remains unknown
- Unable to verify the benchmark’s appropriateness by examining whether the
investment style it represents adequately corresponds to the account being
evaluated - Survivors bias in the manager universe because poor performing accounts may
be removed
Describe pros and cons from using broad market indices
Pros: Easy to understand, widely available
Cons: Manager’s style may not be reflected in the market index
Describe factor-model based benchmarks
Simplest form is a one-factor model
RP aP PRI P
RP = the return on the account
RI = the return on the market index
P = sensitivity to returns on the market index
P = nonsystematic component of the return (the residual)
Multi-factor models that consider additional factors such as a company’s size,
industry, and growth characteristics
RP aP b1F1 b2F2 bKFK P
Describe the pros and cons from using factor-model based benchmarks
Pros: Help managers and fund sponsors better understand a manager’s
investment style, since they capture the systematic sources of return that affect an
account’s performance
Cons: Not always intuitive and may not be investable
Ambiguous, because one can build multiple benchmarks with the same factor
exposures, but generate different returns
Describe how to construct a Returns-based benchmark
This benchmark is constructed as a weighted average of the investment style
indices that most closely track the account’s returns
The weights can be constructed from a regression using historical data
Describe the pros and cons from using a Returns-based benchmark
Pros: Satisfies most benchmark validity requirements
Cons:
Some of the style indexes may have positions that the manager finds unacceptable
Requires many months of historical observations to establish a statistically reliable
estimate of the weights to each style index
Describe the pros and cons from using custom security benchmarks
A custom security benchmark weights a manager’s universe of investable
securities in a particular fashion
Pros: Can be more suitable than a published index
Cons: Expensive to construct and maintain, and can lack transparency
List the steps for constructing a custom-security benchmark
- Identify important aspects of manager’s investment process
- Select securities consistent with that investment process
- Devise a weighting scheme for the benchmark securities
- Review the preliminary benchmark
- Rebalance the benchmark on a set schedule
List some tests of having good benchmark quality
Low systematic biases
Low tracking error
Similar risk characteristics with the fund
Higher coverage
Low turnover
Positive active positions
What are the three inputs of macro attribution?
- Policy Allocations
The fund sponsor determines target asset allocation weights and weightings to
individual managers within the asset categories - Benchmarks
Broad market indexes (i.e. S&P 500) are normally used as benchmarks for asset
categories
More narrowly focused indexes (i.e. U.S. Large-Cap Growth) are used to represent
the manager styles - Fund Returns, Valuations, and External Cash Flows
Returns must be calculated at the manager level for each asset category
List six decision-making levels in macro attribution
- Net Contributions
- Risk-Free Asset
- Asset Categories
- Benchmarks
- Investment Managers
- Allocation Effects
The incremental return contribution of the Asset Category investment strategy
rAC
¸A
i1
wi prCi rf q
A = number of asset categories
wi = policy allocation to asset category i
rCi = benchmark return of the ith asset category
rf = risk-free rate
The incremental return contribution of Benchmarks investment strategy
rIS
¸A
i1
M¸
j1
wi wij prBij rCi q
i is the asset category and j is the manager
wij is the weight assigned to manager j in asset category i
rBij is benchmark return for manager j in asset category i
rCi is benchmark return on the ith asset category
wi is the policy weight assigned to the ith category
A and M are the number of asset categories and managers
The incremental return contribution of the Investment Managers strategy
rIM
¸A
i1
M¸
j1
wi wij prAij rBij q
rAij is the actual return on manager j’s portfolio with asset category i
Key Assumption: The fund sponsor is invested in each manager according to
the managers’ policy allocations
What is the formula for a manager’s value-added return?
The manager’s value-added return, rV , is given by:
rV
¸S
j1
wPj rPj
¸S
j1
wBj rBj
wPj and wBj : Portfolio and benchmark weights of sector j
rPj and rBj : Portfolio and benchmark returns for sector j
S = number of sectors
Decomposition of the value-added return in micro-attribution
- Pure Sector Allocation Return
Pure Sector Allocation
¸S
j1
pwPj wBj qprBj rBq - Within-Sector Selection Return
Within-Sector Selection
¸S
j1
wBj prPj rBj q - Allocation/Selection Interaction Return
Allocation/Selection Interaction
¸S
j1
pwPj wBj qprPj rBj q
Provide two risk-adjusted performance metrics that use systematic risk (through the
fund’s )
Ex-post alpha, or Jensen’s Alpha
It is the A from the following regression of account returns against market returns
RAt rft A ApRMt rft q t
Treynor Measure
TA
RA r f
A
Provide two risk-adjusted performance metrics that use total risk (through the standard
deviation of the fund’s returns)
Sharpe Ratio
SA
RA r f
^A
M2
M2A
r f
$’’%
RA r f
^A
,//-
^M
Measures what the account would have returned if it had taken on the same total
risk as the market
A skillful manager will generate a M2 that is greater than the market index return
Describe a situation where the type of risk-adjusted performance metric that is used
will change the evaluation of a fund manager
Suppose there is a large amount of nonsystematic risk in an account
It is possible for the Sharpe ratio and M2 to identify a manager as not skillful, but
have Jensen’s alpha and the Treynor ratio come to the opposite conclusion
Describe the information ratio
IRA
RA RB
^AB
Active Return
Active Risk
^AB = standard deviation of the difference between the returns on the account
and the returns on the benchmark
Written as a long position in the account that is funded by a short position in the
benchmark
Measures the reward earned from the risk of deviating from the benchmark
portfolio
Provide criticisms of risk-adjusted performance appraisal methods
Jensen’s alpha and Treynor measure rely on CAPM, which is an incomplete
model of security returns
May not be appropriate to use proxies like the S&P 500 for the market portfolio
Benchmark returns are not attainable because of transaction costs
The parameters estimated from historical data may be unstable
What are three assumptions of quality control charts?
- The manager has no investment skill (the null hypothesis)
This implies that the fund’s value-added return should not be statistically different
from zero - The value added-returns in different periods are independent and normally
distributed with a mean of zero - The manager’s investment process does not change from period to period
This implies the variability of the value-added returns stays constant
Describe properties of a manager continuation policy (MCP)
A manager continuation policy (MCP) helps fund sponsors evaluate investment
managers, and has the following purposes:
1. Retain superior managers and remove inferior managers
2. Utilize relevant nonperformance information in the evaluation process
3. Minimize manager turnover (firing a manager is expensive!)
4. Develop a consistent procedure
Describe the two steps in the manager continuation policy (MCP)
- Manager Monitoring
Fund sponsor meets with manager regularly to cover operational matters (e.g.
personnel changes) and investment strategies (retrospective and prospective) - Manager Review
Occurs if there is something alarming during manager monitoring
Will decide whether or not to rehire the investment manager
Describe the type of errors the fund sponsor can make during performance appraisal
Type I: Keeping managers that have zero value-added
Type II: Firing managers with positive value-added
