Investments

Academic Year 2004 - 2005

Lectures n° 9 & 10

Performance Measurement

& Commenting Mutual Funds Strategies & Performance

Performance Assessment

• Performance Measurement• Benchmarks• Performance Attribution• AIMR Norms• Operational risks in private banking• Cases and exercises

1. Performance Measurement

Absolute return• Return = total proceeds/initial investment• Which average to use? – Arithmetic Average : for future expected performance– Geometric Average : for past performance

• Example : +10% in year 1 and –10% in year 2 =>arithmetic average = 0

geometric average = %50.01%)101%)(101( 2/1

1. Performance Measurement

Returns compared to risk – Which risk?– Performance of investment funds is usually estimated by

comparing gross returns of funds with similar risk characteristics (equity growth, equity world, high-yield bond,…) .

– Then funds are ranked comparatively to one another within the same “investment universe”.

– This way you can rank financial institutions or funds managers.

Example : Ranking system Micropal from S&P

– It ranks the investment funds by comparing them to one another within the same category : same types of assets, currency, geographical zones, industries, etc.

– A single type of performance measure is not suitable for all types of portfolio.

1. Performance Measurement

Sharpe ratio : unit of excess return per unit of risk

good for the performance of an entire portfolio, or to compare with other portfolios, and to the market portfolio the higher the better if negative : value destruction (an investment in cash

would have been better)

p

fp rr

Information ratio : unit of excess return over the benchmark per unit of risk

same concept as the Sharpe ratio used by practitioners, highly dependant of the benchmark chosen, the higher the better if negative : a passive strategy would have been better

p

bp rr

1. Performance Measurement

Treynor ratio : unit of excess return per unit of systematic risk

suited when a well diversified portfolio is mixed with others

allows to compare the performances of several managers of a well diversified portfolio

the higher the better if negative : value destruction

p

fp rr

1. Performance Measurement

Appraisal ratio : unit of Jensen’s alpha return per unit of non systematic risk

suited for parts of portfolios suited for concentrated portfolios measure the benefit-to-cost of a not well diversified

portfolio capture the benefits of an active stock selection if negative : a passive strategy would have been better

)( p

p

e )( fMPfPP rrrr

1. Performance Measurement

Sharpe ratio of a composite portfolio : unit of excess return per unit of risk for a composite portfolio (C) made of an active part (P) and a passive part (M).

2

22

)(

P

PMC e

SS

1. Performance Measurement

Key performances measures - 3. Example :

Portfolio P Portfolio Q Market PortfolioSharpe 0.45 0.51 0.19Alpha 1.63 5.28 0.00Beta 0.69 1.40 1.00Treynor 4.00 3.77 1.63(e) 2.37 8.98 0.00Appraisal ratio 0.84 0.59 0.00R2 0.91 0.64 1.00

Which one is : Riskier ? Better diversified ? Outperforming the market? Better if a single fund? Better if part of a larger passive fund? Of an active fund?

1. Performance Measurement

1. Performance Measurement

• Limits to the reliability of performance results : – Changing portfolio composition

• Practical difficulty in performance measurement : – large number of observations required for statistical

significance,– but changing pattern of risk in case of active portfolio

management.

• A help : – keep track of portfolio composition and changes (in µ and

s),– keep a data series of coherent ratio measurement.

1. Performance Measurement

• Statistical significance – Number of observations required for statistical

significance : increased by the noise in return data (due to external random effects)

– If N is the required number of observations to perform a significant test at 5% over the non-zero value of α with σ(e) being the sample estimate of nonsystematic risk, we have :

e

Nt

ˆ

)ˆ(

At 5% level of significance, t = 1.96. If monthly α = 0.2% and (e)=2%, then N =....

1. Performance Measurement

• N = 384 months = 32 years !

• In case of low significativity of the results (on alphas, for instance), how to tell ability (or disability) from luck (or bad luck)?

• Or flat results from low alphas?

Quite impossible.

• This is one of the reasons why performance of portfolio managers seems to be so erratic through the years.

2. Benchmarks

• Benchmark : reference portfolio - Characteristics:– Representative of the funds’s investment strategy

and risk level– Or, representative of the client’s demanded return (in

private banking only)– Can be external : reference index, per market, per

geographical zone, even per sector. External benchmarks are preferable whenever possible, both for independence and methodological reasons

– Index vendors : Moody’s, JPM, S&P…– Can be internal : built by the asset management itself

(even by the client, sometimes, in private banking).

2. Benchmarks

• Key roles of the benchmarks – In asset management :

Managers work in relative terms, based on the benchmark

More and more systematic use of benchmarks– In performance measurement :

Benchmarks used a departure point for assessing performance (see further)

2. Benchmarks

• Key roles of the benchmarks – In risk management

Basis for establishing various management goals or limits:

– targeted surperformance rates, – tracking errors limits (difference between the return

of the portfolio and the benchmark, in %), – stop-loss procedures.

– In Marketing and Communication

help clarify and communicate the investment objective of a fund to the clients

Performance attribution = decomposition of the performance of a portfolio into its various components, in order to identify the decisions that caused the sur- or subperformance of the overall portfolio.

• Useful when it fits the investment process, following the top-down procedure of the decisions taken by the management.

• For global portfolios, performance attribution starts from the broadest asset allocation choices and progressively focus on ever-finer details portfolio choices.

3. Performance Attribution

3. Performance Attribution

• Example of attribution system for fixed-income portfolio :– overall duration– market allocation :

currency markets maturity segments credit classes

– issue selection : sector and rating– currency allocation :

FX transactions within a same type of issue

• Example of attribution system for a mixed fund:– asset allocation decisions : bonds - equity - cash,– sector choices between each market,– security selection within each sector.

3. Performance Attribution

• Performance Attribution – Equations : – If return of the benchmark portfolio:

where wBi is the weight of the asset class i in the benchmark portfolio,

and rBi is the return of that asset class over the period.

– And return of the active portfolio:

– The difference in returns writes :

n

iBiBiB rwr

1

n

iPiPiP rwr

1

n

iBiBiPiPi

n

iBiBi

n

iPiPiBP rwrwrwrwrr

111

)(

3. Performance Attribution

• Performance Attribution – Equations : – If can be rewritten as:

Contribution from asset allocationBiBiPi rww )(

+ Contribution from security selection )( BiPiPi rrw = Total Contribution from asset class i )( BiBiPiPi rwrw

3. Performance Attribution

4. AIMR Norms

• Performance Evaluation Standards : – Returns must be total returns (income + capital gain).– Annual returns reported for all years individually, and

longer periods. – Time-weighted average rates of return and geometric

average linked returns.– Performance reported before fees.– Composite results reflect the record of the firm, not of

individual managers.– Composite returns reported for at least a 10-year

period.– Risk measures such as beta, duration, or standard

deviation are encouraged.

5. Operational Risk in Private Banking

Operational risk is the risk of loss resulting from inadequate or failed internal processes, people, and systems or from external events.

Categories of OR events

• Execution, Delivery & Process Management (processing error,

information transfer, data coding,...)

• Clients, Products & Business Practices (clients misinformation,

complaints and discounts due to errors, products

misspecification...)

• Internal fraud (thefts and frauds by employees)

• External fraud (hold-up, thefts,..)

• Employment practices & workplace safety (contract

termination, disputes with employees...)

• Damage to physical assets

• Business disruption & system failures (IT break-down,

hacking...)

5. Operational Risk in Private Banking

• Main risks– Clients, Products & Business Practices :

Inappropriate advice to the clients leading to clients claims

Inappropriate clients protection and delegation contracts

At the verge of legal risk – huge risk in private banking and asset management activities

2. Execution, Delivery & Process Management : Errors in back-office procedures : buy – sell confusion, wrong

asset bought, … « Commercial interventions » : cut-off in price and rebates

allowed by front office manager to clients, either to hide a mistake, or for pure commercial reason : could be uncontrolled

3. Internal fraud : Cash-flow embezzlement, at the detriment of one client, to

another, or to the employee himself

6. Cases and Exercises

• Please refer to the mutual funds summaries enclosed and comment:– The active strategies used in this portfolio– The type of client it should suit / it would not suit at all– Comment the performance results– What would you change if it were your own portfolio?