CFA level 3 volume VI trading and rebalancing, performance evaluation, and GIPS finquiz smart summary, study session 17, reading 33

2018 Study Session # 17, Reading # 33

“EVALUATING PORTFOLIO PERFORMANCE”
PE = Performance Evaluation
MCP = Manager Continuation Policies
CML = Capital Market Line

HF = Hedge Funds
YC = Yield Curve

1. INTRODUCTION

Performance Evaluation

Performance Measurement

Calculating accounts’
performance based on
investment related∆.

Performance Attribution

Analyzing sources of return&
importance of those sources.

Performance Appraisal

Assessing whether the return
was generated due to skills or
luck.
Assessing size & consistency

of accounts’ relative to
performance.

2. THE IMPORTANCE OFPERFORMANCE EVALUATION

2.1 The Fund Sponsor's Perspective

Fund sponsors ⇒ owners of large pools of investable assets.
PE is important because:
It provides an exhaustive quality control check of the fund & its
constituent parts.
It is a part of feedback of the investment management process.
It acts as a feedback & control mechanism.

2.2 The Investment Manager's Perspective

PE involves reporting investment returns along with the
return of some benchmark.
Measures the effectiveness of all aspects of the investment
processes.

3. THE THREE COMPONENTS OFPERFORMANCE EVALUATION

Account ⇒ one or more portfolios of securities managed by
one or more investment management organizations.

Copyright © FinQuiz.com. All rights reserved.


2018 Study Session # 17, Reading # 33

4. PERFORMANCE MEASUREMENT

4.1 Performance Measurement without Intra-period External Cash Flows
Rate of return on an account ⇒ % ∆ in the account’s MV over some
defined period of time after considering all external CF (contributions
& withdrawals).
If contribution is received at the start of the period:
‫ܸܯ‬௧ − ሺ‫ܸܯ‬଴ + ‫ܨܥ‬ሻ
‫ݎ‬௧ =
‫ܸܯ‬଴ + ‫ܨܥ‬
If contribution is received at the end of the evaluation period:
ሺ‫ܸܯ‬௧ − ‫ܨܥ‬ሻ − ‫ܸܯ‬଴
‫ݎ‬௧ =
‫ܸܯ‬଴
In case of withdrawals, CF signs will change

4.2 Total Rate of Return
Measures the ∆ in the investor’s wealth due to both investment
income & capital gains.
Use of total return measure due to:
Allocation to equities.
Computing costs.
Institutional investors.

4.3 The Time-Weighted Rate of Return

Measures the compounded rate of growth over a stated evaluation
period of one unit of money initially invested in the account.
TWR is preferred when manager has no control over the deposits

& withdrawals made by clients.
Account needs to be valued whenever an external CF occurs.
‫ݎ‬௧௪௥ = ൫1 + ‫ݎ‬௧,ଵ ൯൫1 + ‫ݎ‬௧,ଶ ൯ × … × ൫1 + ‫ݎ‬௧,௡ ൯ − 1

Advantage/Disadvantage of TWR

Advantage

Disadvantages

Not affected by external CF.

Valuation required each time when an external
CF occurs.
Administratively more cumbersome, expensive
& potentially more error prone.

4.4 The Money-Weighted Rate of Return

Measures the compound growth rate in the value of all funds invested
in the account over the entire evaluation period.
Preferred method when manager has discretion over cash flows.
MWR is an IRR of an investment.

Copyright © FinQuiz.com. All rights reserved.


2018 Study Session # 17, Reading # 33
Advantage/Disadvantage of MWR

Advantage

Disadvantages

A/C is valued at beginning & end of the evaluation
period.

Sensitive to size & timing of external CF.
Inappropriate when investor has no control
over external CF.

4.5 TWR versus MWR

When funds are contributed to an account prior to a period of strong
performance MWR > TWR.
MWR & TWR provide significantly different results if:
Large external CF occurs.
Account’s performance is highly volatile.

4.6 The Linked Internal Rate of Return

In LIRR, the TWR is approximated by calculating MWR over reasonably
frequent time intervals & then chain links over the entire evaluation
period.
Appropriate to use under normal conditions.

4.7 Annualized Return

Compounded avg annual return earned by account.
ଵൗ

‫ݎ‬௧௪௥ = ൫1 + ‫ݎ‬௧,ଵ ൯ × ൫1 + ‫ݎ‬௧,ଶ ൯ × … × ൫1 + ‫ݎ‬௧,௡ ൯ ௡ − 1
It is not advisable to calculate annualized returns when measurement
period < full year.

4.8 Data Quality Issues

Illiquid & infrequently priced assets with heavy external CF activity
generally not reliable in nature.
For thinly traded securities, usually matrix pricing approach is used.
A/C should be valued on the trade date rather than settlement date.

5. BENCHMARKS

5.1 Concept of a Benchmark

Components of portfolio return include:
Market (M).
Style (S) = manager’s benchmark-market index.
Active management (A) = manager’s portfoliobenchmark.
Portfolio return:
P=M+S+A

Copyright © FinQuiz.com. All rights reserved.


2018 Study Session # 17, Reading # 33

5.2 Properties of a Valid Benchmark

A valid benchmark should have the following properties.
Unambiguous ⇒ clearly defined identities & weights.
Investable ⇒ passive investment alternative.
Measureable ⇒ return can be readily calculate.
Appropriate ⇒ consistent with manager’s style.
Reflective of current investment opinions.
Specified in advance ⇒ known to all interested parties at the
start of evaluation period.
Owned ⇒ manager should be aware & accept accountability.

5.3 Types of Benchmarks

Absolute

Advantage

Disadvantage
Do not meet benchmark validity
criteria (not investable)

Simple & straight forward

Manager’s Universes

Definition

Advantage

Median manager or fund from a broad
universe of mangers or funds as a

benchmark.

Measureable

Disadvantage

Suffers from survivorship bias.
Except being measureable, it fails all the
benchmark validity criteria.
Reliance on compilers.

Broad Market Indexes

Advantages
Broad market indexes as
benchmark e.g. S&P 500.

Disadvantages

Well recognized & easy to understand.
Widely available & unambiguous.
Measureable & investable.
Can be specified in advance.

Style drift

Style Indexes

Definition

Advantages

Using specific portion of asset
category as benchmark

Well known & easy to
understand.
Widely available.

Disadvantages
Larger than prudent weighting
in certain securities.
May be inconsistent with
manager’s investment process.

Copyright © FinQuiz.com. All rights reserved.


2018 Study Session # 17, Reading # 33

Factor Model Based

Definition

Advantage

One or more systematic sources
of return to the returns on an
account.
Normal portfolio ⇒ portfolio

which has exposures to sources
of systematic risk factors that is
typical for a manager.

Disadvantage

Facilitate manager & fund
sponsors to better understand
manager’s investment style.

Difficult to obtain & expensive
to use.
Different benchmarks with the
same factor exposures can
generate different returns.
May not be investable.

Return Based Benchmarks

Definition

Advantages

Disadvantages

These benchmarks are constructed
using the series of a manager &
investment style index’s return.

Intuitive & easy to use.

Unambiguous, measureable
investable & specified in
advance.
Useful when only the
information regarding account
return is available.

May be inconsistent with
manager’s investment process.
Sufficient no. of observations
required.
Not appropriate for managers
who rotate among style
exposures.

Custom Security-Based

Definition

Advantage

Reflect manager’s research
universe weighted in a particular
manner.

Disadvantage

Satisfy all of the benchmark
validity criteria.
Effective allocation of risk across

all the investment managers.
Effective monitoring & control
of investment processes.

Expensive to construct &
maintain.
Lack transparency.

5.6 Tests of Benchmark Quality

Systematic Biases

Benchmark should have minimal systematic
biases relative to the account (Avg. historical β
of A/C should be close to 1).
Correlation b/w A&S should be zero.
Difference b/w (P-M) & S should be highly
correlated.

Tracking Error

Volatility of account’s return relative to a good
benchmark should be < than volatility of the
account’s return relative to a market index.

Copyright © FinQuiz.com. All rights reserved.


2018 Study Session # 17, Reading # 33

5.6Tests of Benchmark Quality

Risk Characteristics

Coverage

A/C’s exposure to systematic risk should be
similar to those of benchmark.
Systematic bias if A/C’s risk characteristics are
always greater or always less than benchmark.

Benchmark coverage:
‫ݐݏ݁݅ݐ݅ݎݑܿ݁ݏ݂݋ܸܯ‬ℎܽ‫ݐ݊݁ݏ݁ݎ݌݁ݎܽݐ‬
൤
൨
ܾ݅݊‫ݐ݋‬ℎ‫ݐ‬ℎܾ݁݁݊ܿℎ݉ܽ‫݋݈݅݋݂ݐݎ݋݌݀݊ܽ݇ݎ‬
ܶ‫ݐ݂݋ܸܯ݈ܽݐ݋‬ℎ݁‫݋݈݅݋݂ݐݎ݋݌‬
Low coverage indicates that the benchmark is
poor.

Turnover

Positive Active Positions

% of the benchmark’s MV that is
purchased/sold for the purpose of periodic
rebalancing.
Passively managed portfolio ⇒low benchmark
turnover.

Large no. of +ve active positions ⇒ good custom
security based benchmark has to be constructed.

5.7 Hedge Funds and Hedge Fund Benchmarks

Long only benchmark is inappropriate to
evaluate HF performance due to short
positions.
Due to zero net position or –ve net position
traditional methods to calculate return does
not yield reliable results.
Hedge Fund Benchmarks

Following three are appropriate:
Value added return.
‫ݎ‬௩ = ‫ݎ‬௉ − ‫ݎ‬஻
Construct separate long & short benchmarks.
Limitation ⇒ not appropriate if rapidly changing leveraged
positions.
Sharpe ratio.
Limitations ⇒ assume normal distribution.

6. PERFORMANCE ATTRIBUTION

Macro attribution ⇒ conducted at the fund sponsor level
(total fund performance).
Micro attribution ⇒ carried out at the investment
manager level (performance of individual portfolios).

Copyright © FinQuiz.com. All rights reserved.

2018 Study Session # 17, Reading # 33

6.1 Impact Equals Weight Times Return
Impact = weight × return.
Select superior performing assets.
Overweight superior performing assets relative to
benchmark.

6.2 Macro Attribution Overview
6.3 Macro Attribution Inputs

Policy Allocations

Benchmark Portfolio Returns

Fund sponsor determines the broad allocation to the
fund & individual managers.
Policy allocations depend on:
Fund sponsor’s risk tolerance & liabilities.
Sponsor’s long term expectations.

Fund sponsor selects:
Broad market indexes as benchmark for asset
category.
Specific benchmark for manager’s style.

Fund Returns, Valuations, and External CF

Rate-of-Return Metric

Value Metric

Computing fund return at individual manager level to
evaluate decision regarding manager selection.

Requires A/C valuation & external CF data to compute
accurate rate of return.
To evaluate the impact of the fund sponsor’s investment
decision-making on the fund’s performance.

6.4 Conducting a Macro Attribution Analysis

Six components of investment policy decision making with
increasing order of volatility & complexity.
Based on incremental return of each investment strategy &
contribution of each level to the overall return of the fund.

Macro Attribution Components

Net Contributions

These include additions to the portfolio.
These CF are invested at zero rate of return.
∆ in the value of fund = total amount of net
contributions.
Ending value = beginning value + net contributions.

Risk-Free Asset

Conservative strategy involving all fund’s assets invested
at RF.
∆In fund’s value = ending value under RF investment
strategy-beginning value.

Copyright © FinQuiz.com. All rights reserved.


2018 Study Session # 17, Reading # 33

Macro Attribution Components

Asset Category

Benchmarks

Fund’s beginning value & external CF are invested
passively based on policy allocations.
Pure index fund approach.
Return –metric perspective ‫ݎ‬஺஼ = ∑஺௜ୀ ‫ݓ‬௜ × ൫‫ݎ‬௖௜ −‫ݎ‬௙ ൯
where
‫ݎ‬஺஼ = return contribution of asset category
‫ݎ‬௖௜ = return on ith asset category.
‫ݓ‬௜ = weight of asset category i.

Assume that the fund’s beg value & net external CF are
invested in manager’s benchmark.
Pure index fund approach.
From a return-metric perspective

஺

௜ୀଵ ௝ୀଵ

Value – metric perspective:
sum (each manger’s policy proportion of the total fund’s
beg value + net external CF)× (manager’s benchmark
return – return of the manager’s asset category).

Investment Managers

Allocation Effects

Assumes that the fund sponsor has invested in each of
the manager according to the manager’s policy
allocation.
Return to the investment managers level = sum (active
managers’ return – their benchmark return).
Return metric perspective:
஺

ெ

‫ݎ‬௜௦ = ෍ ෍ ‫ݓ‬௜ × ‫ݓ‬௜௝ × ൫‫ݎ‬஻௜௝ − ‫ݎ‬௖௜ ൯

Allocation effects incremental contribution= fund’s
ending value-value calculated at the investment
manager’s level.
Allocation effect results when fund sponsors slightly
deviate from their policy allocation.

ெ

‫ݎ‬ூெ = ෍ ෍ ‫ݓ‬௜ × ‫ݓ‬௜௝ × ൫‫ܣݎ‬௜௝ − ‫ܤݎ‬௜௜ ൯
௜ୀଵ ௝ୀଵ

6.5 Micro Attribution Overview

Security-by-security analysis:
௡

‫ݎ‬௉ = ෍
௜ୀଵ

ൣ൫ܹ௣௜ − ܹ஻௜ ൯ × ሺ‫ݎ‬௜ − ‫ݎ‬஻ ሻ൧

Manager can add value by overweighting outperforming securities.
Limitation ⇒ as the no. of securities in a portfolio the impact of any individual security becomes insignificant.
Micro attribution using factor model of returns:
Allocating the value added return to various sources of systematic return.
Market model is a type of factor model.

6.6 Sector Weighting/Stock Selection Micro Attribution

Holding Based Attributions
‫ݎ‬௉ = ∑ௌ௝ୀଵ ‫ݓ‬௉௝ ‫ݎ‬௉௝ − ∑ௌ௝ୀଵ ‫ݓ‬஻௝ ‫ݎ‬஻௝
Advantage ⇒ only holdings & their returns
are required to perform attribution analysis.
Limitation ⇒ ignores the impact of
transactions.

Transaction Based Attribution

Mostly used in actively managed accounts with high turnover.
Three components:
Pure sector allocation:
ௌ

෍൫ܹ௣௝ − ܹ஻௝ ൯ ൫‫ݎ‬஻௝ − ‫ݎ‬஻ ൯
௝ୀଵ

Within sector selection:
ௌ

෍ ܹ஻௃ ൫‫ݎ‬௣௝ − ‫ݎ‬஻௝ ൯
௝ୀଵ

assumes same sector weight in portfolio as in benchmark.
Allocation selection interaction:
ௌ

෍൫ܹ௣௝ − ܹ஻௝ ൯ ൫‫ݎ‬௣௝ − ‫ݎ‬஻௝ ൯
௝ୀଵ

Copyright © FinQuiz.com. All rights reserved.


2018 Study Session # 17, Reading # 33

6.7 Fundamental Factor Model Micro Attribution

Combines economic sector factors with other fundamental factors.
Following are steps to perform fundamental factor model:
Identify the fundamental factors.
Determine the portfolio & benchmark sensitivity to the fundamental factors
at the beginning of evaluation period.
Specify a valid benchmark for portfolio to determine the performance of each
of the factors.

6.8 Fixed-Income Attribution

Major determinants of F.I account returns include:
∆ in general level of IR.
∆ in sector, credit quality, individual security differentials to the Y.C.

Factors That Contribute to Total Return of F.I Portfolio

External I.R Effect

Management Effect

is estimated using a term structure
analysis.
Manager has no control over external
IR environment.
External IR environment can be
separated into expected & unexpected
return.

Estimated by a series of repricing.

Four components:
IR management effect.
Sector/quality effect.
Security selection effect.
Trading actively.

7. PERFORMANCE APPRAISAL

Performance appraisal ⇒evaluation of investment skill of managers & to make
decisions regarding retaining or modifying portion of investment program.
Level & magnitude of the value-added return should be used to determine
manager’s skill.

7.1 Risk-Adjusted Performance Appraisal Measures

Jensen’s Alpha

Measures the excess of the portfolio’s return over
that predicted by CAPM.
ߙ = ‫ݎ‬௉ − ൣ‫ݎ‬௙ + ߚ௉ ൫‫ݎ‬௠ − ‫ݎ‬௙ ൯൧
Direct measure of performance.

Treynor Measure

ܶ஺ =

ோ஺ ି௥ಷ
෡ಲ
ఉ

Represents the slope of the line b/w RF & the point
representing the avg return &β for the security.

Copyright © FinQuiz.com. All rights reserved.


2018 Study Session # 17, Reading # 33
7.1 Risk-Adjusted Performance Appraisal Measures

M2

Sharpe Ratio

ܵ஺ =

ோಲ ି௥೑

Avg. incremental return over a market index of a
hypothetical portfolio that is created by combining
the account with borrowing or lending at Rf. so that
its SD is identical to the market index.

ఙಲ

Benchmark k is based on ex-post CML.
Like Treynor ratio, greater slope indicates a better
risk return trade off.

‫ܯ‬஺ଶ = ‫ݎ‬௙ + ቂ

ோಲ ି௥೑
ఙ
ෝಲ

ቃ ߪො௠

Information Ratio

‫ܴܫ‬஺ =

ோಲ ିோಳ
ఙ
ෝಲಳ

+ve (-ve) IR indicates that the manager
outperforms (underperforms) the benchmark.

7.2 Quality Control Charts

Effective & useful way of presenting performance appraisal data.
Assumptions:
Null hypothesis ⇒ manager has no investment skill.
Value added returns are independent.
Manager’s investment process is consistent.
Confidence band ⇒indicates the range within which the
manager’s value added returns are expected to fall.
Confidence range is only for one time period.

7.3 Interpreting the Quality Control Chart

If value-added returns are distributed more or less randomly
around the horizontal line ⇒ deviations from the benchmark are
purely random.
We fail to reject the null hypothesis when investment results of a
manager fall within the confidence band.

8. THE PRACTICE OF PERFORMANCE EVALUATION

Sponsors use qualitative & quantitative factors to
evaluate investment managers.

8.1 Noisiness of Performance Data

Past performance is not a good evaluation tool.
Long evaluation period must be used to
determine truly superior performance.

Copyright © FinQuiz.com. All rights reserved.


2018 Study Session # 17, Reading # 33

8.2 Manager Continuation Policy

Hiring new managers & firing old managers involves a significant
cost in terms of money & time.
MCP ⇒ to the costs of manager’s turnover & to deal
appropriately with future poor performance.
MCP is used to minimize manager turnover & to consistently apply
procedures to overall managers.

MCP is a two part process.
Manager monitoring.
Manager reviews.

8.3 Manager Continuation Policy as a Filter

MCP can be used as a statistical filter to remove-ve value add
managers & retain +ve value added mangers.
Null hypothesis ⇒ manager has no investment skill.
Alternative hypothesis ⇒ managers are not zero value added
managers.
Type I error ⇒rejecting the null hypothesis when it is true.
Type II error ⇒ not rejecting the null when it is incorrect.
When the width of the confidence band is widened, type I error
type II error .

Copyright © FinQuiz.com. All rights reserved.

&