Intermediate Performance Calculations: Attribution

Intermediate Performance

Calculations: Attribution

Monday, October 20, 2008

Public Pension Financial Forum

John D. Simpson, CIPM

What

we’

l

l

do

t

oday



We’

l

l

now

compl

ement

our

ear

l

i

er

r

et

ur

n

&

r

i

sk

discussion with attribution

“Per

f

or

mance

At

t

r

i

but

i

on,

whi

l

e

not

new,

i

s

st

i

l

l

an

evol

vi

ng

di

sci

pl

i

ne.

”

Gary Brinson, FAJ, July/Aug 1986



Focus

on

i

deas

&

concept

s…

not

t

he

mat

h



Again, we have a fair amount to cover and limited

time

Contribution Analysis

“Absolute

At

t

r

i

but

i

on”

Total Return Portfolio R e tu rn

Is Contribution a form of

Attribution?



And

t

he

sur

vey

says…



Money Managers: 77%



Plan Sponsors: 89%



Investment Consultants: 100%

Sai

d

“

yes

”!



We

suggest

t

he

t

er

m

“absol

ut

e

at

t

r

i

but

i

on”

Contribution

A process to assess how

individual securities / sectors

contribute to the return

Contribution = Weight * Return

Weight = the relative market value

Visualizing contribution

Weight ROR Utilities 42% 3.70% 1.55% Consumer 26% 6.20% 1.61% Technology 8% -10.30% -0.82% Banks 24% 7.30% 1.75% Totals 100% 4.09% 4.09% Portfolio Sector Contribution

Contribution Rules

1.

The sum of the

contribution effects

should

equal

t

he

por

t

f

ol

i

o’

s

r

et

ur

n

However, depending on volatility, this may not happen

2.

Include effect of cash (when cash is

included in the return)

CE

_i

R

i

n







1

Security Contribution

Contribution = Weight x Return

Security ROR Weight Contribution A 1.50% 11.00% 0.17% B 1.80% 12.00% 0.22% C 2.00% 1.20% 0.02% D 0.50% 1.50% 0.01% E 0.70% 22.00% 0.15% F -1.10% 1.30% -0.01% G -0.30% 11.00% -0.03% H 1.00% 20.00% 0.20% I 2.50% 13.00% 0.33% Cash 0.20% 7.00% 0.01% Portfolio 1.06% 100% 1.06% Find Security I’s Contribution

Security Contribution

Solution

Security ROR Weight Contribution

A 1.50% 11.00% 0.17% B 1.80% 12.00% 0.22% C 2.00% 1.20% 0.02% D 0.50% 1.50% 0.01% E 0.70% 22.00% 0.15% F -1.10% 1.30% -0.01% G -0.30% 11.00% -0.03% H 1.00% 20.00% 0.20% I 2.50% 13.00% 0.33% Cash 0.20% 7.00% 0.01% Portfolio 1.06% 100% 1.06%

What if our absolute attribution and

per

f

or

mance

measur

ement

don’

t

jibe?



Previous formula assumes buy-and-hold

A

holdings-based

approach to contribution



We can improve by taking into consideration

the intra-period cash flows:

BMV + Weighted Flows will improve accuracy



This would be a

transaction-based

approach

to contribution

Day-Weighting Factor

End-of-day

Start-of-day

*

Cash flow on 3

rd

_{day of a 31-day month:}

W

CD

D

CD

i i





W

CD

D

CD

i i





1

W_i 31 3    31 28 31 .9032 90 32%. Wi       31 3 1 31 29 31 .9355 9355%.

Advantages of Contribution



The math is quite simple



Easy to comprehend



Easy to explain



Of

t

en,

i

t

’

s

what

manager

s

i

ni

t

i

al

l

y

mean

when they say they want

attribution



Usually, we look at the

top 5

or

top 10,

and

bottom 5

or

bottom 10

holdings

Disadvantages of Contribution

How to calculate when portfolio makeup

changes over time



Fine for a static portfolio



But

what

i

f

you’

ve

sol

d/

bought

somet

hi

ng

between the start and end of the month?

Now

t

hat

we’

ve

di

scussed

absolute attribution

Relative attribution: where did

the

excess return

come from?

Excess Return

Portfolio _{Benchm ark}

R

e

tu

rn

s The portfolio beat

the benchm ark -w hy?

“Relative

The Top-Down Approach

Economic Data

(CPI, Unemployment Stats, Production Figures, Interest Rate)

Also, Political & World Data

An example of how politics can

influence the markets

The Top-Down Approach

(

cont

’

d)

Econom ic Data

(CPI, Unem ploym ent Stats, Production Figures, Interest Rate)

Predict the impact on Industry Sectors

(example: will help Technology and hurt Banking; therefore

bullish on Tech,bearish on Banks)

Index Tech 4% Banks 5% Allocation Decision/Strategy Overweight Tech; Underweight Banks Security Selection Decisions / Strategy W e w ill w ant to assess the Allocation decisions and the Selection

decisions

Also, Political & World Data

Is it possible to beat every sector

and still under perform the index?

Yes?

But

How?

Sum of Portfolio Index Differences Basic Mat'ls 0.25% 0.15% 0.10% Industrials 1.02% 0.51% 0.51% Cons Cyc 1.05% 1.04% 0.01% Utilities -0.71% -0.78% 0.07% Energy 2.08% 2.04% 0.04% Fin'l -0.20% -0.36% 0.16% Healthcare 0.84% 0.79% 0.05% Technology 0.56% 0.54% 0.02% Telecom -0.19% -0.21% 0.02% Cons, Non-Cyc -0.50% -0.52% 0.02% Total 0.23% 0.46% 1.00% Returns

The First Law of

Performance Attribution

The attribution model

should conform with the investment style

or approach of the firm

i.e., it should make sense relative to

the way the firm manages money

Example:

don’

t

use

an

equi

t

y

model

f

or

a

f

i

xed

income portfolio (more on this later)

Not

at

i

on

we’

l

l

use



Portfolio Return



Benchmark Return

(with overbar)

R

w

_i

r

_i i n









1

R

w

i

r

i i n









1

The Second Law

of Performance Attribution

The sum of the attribution effects

must equal the excess return.

AE

_i

R

R

i

n

 

1

Note: there may be a residual



I

n

or

der

t

o

achi

eve

t

he

second

l

aw,

i

t

’

s

possi

bl

e

t

hat

t

her

e

may

be

a

“r

esi

dual

”



The residual may arise because of:

 The use of a multi-factor model that does not take into

account all the factors

 The use of a transaction-based system where pricing

differences may occur (bigger problems than residual)

 Using a holdings-based modelwhen there’s portfolio

turnover (probably the most common source)



This is a single-period residual



Multi-period residuals: use geometric model or

Performance Attribution: measuring

the success/failure of 3 weighting

decisions

Sector

Allocation

Issue Selection

Currency

Allocation

What was the effect of overweighting individual

sectors?

Within sectors, how well did the manager pick securities?

What was the effect of currency hedging / fluctuations? A c ti v e R e tu rn

Brinson, Hood & Beebower (BHB)

Model

(IV) Actual Portfolio Return (II) Policy and Tim ing Return (III) Policy and Security Selection Return (I) Policy Return (Passive Portfolio Benchm ark) Actual Passive A c tu a l P a s s iv e

Selection

T

im

in

g

Quadrant Meanings

Quadrant I (Policy): Reflects the fund’s long-term asset allocation plan.The fund’s benchmark return goes here. Policy identifies the plan’s normal portfolio. The result of the plan sponsor’s investmentpolicy.

Quadrant II (Policy and timing’s return effects):Timing is the strategic decisions regarding the variation in asset

class weightings relative to the normal weight. Decisions that result in adjustments to these weights are made to achieve a higher return and/or lower risk.

Quadrant III (Policy and security selection returns):

Security selection deals with the active selection of investments within an asset class.

Quadrant IV (Actual): Holds the fund’s actualreturn.This is the result of the segment weights and returns.

BHB Quadrant Formulas



Quadrant I

=



Quadrant II

=



Quadrant III

=



Quadrant IV

=

w

_i

r

_i i n







1

w

_i

r

_i i n







1

w

_i

r

_i i n







1

w

_i

r

_i i n







1

Calculating the BHB

Attribution Effects:

Timing (Allocation):

II –I

“Ot

her

”:

(

i

nt

er

act

i

on)

IV-III-II+I

Stock selection: III–I

Total: IV-I





w r w r r w w i i i n i _i i n i _i i i n         







1 1 1



w

_i

r

_i

 

w

i

r

i



i n

 







1

 

w

r

w

r

w

r

r

i _i i n i _i i n i _i i i n

 

 

 

  







1 1 1



w

_i

w

i

  

r

_i

r

i i n



 





1

Trying to reconcile the excess

return

Where did this excess come from? Benchmark Contribution Return W e ig h t BM B M P o rt fo li o Portfolio

Visualizing the effects

Benchm ark Contribution Selection Effect Allocation Effect Interaction Effect Return BM Portfolio W e ig h t B M P o rt fo li o

Interaction



Some models, like the BHB, have an

“ot

her

”

or

“i

nt

er

act

i

on”

ef

f

ect



So, what is interaction?



Various interpretations



Error term



The

“i

nt

er

act

i

on”

bet

ween

t

wo

or

mor

e

ef

f

ect

s

(e.g., allocation and selection)



In fixed income, can mean effects too small to

account

f

or

i

ndi

vi

dual

l

y

(

“r

esi

dual

”

i

s

a

bet

t

er

term)

The interaction formula shows

where it comes from



From differences between the portfolio and

benchmar

k’

s

wei

ght

s

and

r

et

ur

ns

 Ifthe differences are slight,we’llhave zero orminimal interaction

 As the differences increase, the interaction will grow



Also, from investing in securities or sectors that

ar

en’

t

i

n

t

he

i

ndex



w

_i

w

i

  

r

_i

r

i i n



 





1

Some

examples

Wp Wb Rp Rb Interaction Stock Selection (Benchmark Wt) Stock Selection (Portfolio Wt) 6% 5% 3.2% 3.0% 0.00% 0.01% 0.01% 7% 5% 3.2% 3.0% 0.00% 0.01% 0.01% 6% 5% 3.4% 3.0% 0.00% 0.02% 0.02% 7% 5% 3.4% 3.0% 0.01% 0.02% 0.03% 8% 5% 3.2% 3.0% 0.01% 0.01% 0.02% 8% 5% 3.4% 3.0% 0.01% 0.02% 0.03% 8% 5% 4.0% 3.0% 0.03% 0.05% 0.08% 8% 5% 5.0% 3.0% 0.06% 0.10% 0.16% 5% 8% 6.0% 3.0% -0.09% 0.24% 0.15% 8% 5% 6.0% 3.0% 0.09% 0.15% 0.24%



w

_i

w

i

  

r

_i

r

i i n



 





1

BHB example

Portfolio Benchmk Portfolio Benchmk Basic Mat'ls 0.25% 0.15% 10% 11% Industrials 0.50% 0.51% 11% 9% Cons Cyc 1.00% 1.01% 8% 7% Utilities -0.80% -0.75% 12% 13% Energy 2.00% 1.95% 7% 5% Fin'l -0.30% -0.31% 6% 8% Healthcare 0.80% 0.79% 15% 13% Technology 0.60% 0.70% 9% 10% Telecom -0.20% -0.21% 13% 10% Cons, Non-Cyc -0.50% -0.52% 9% 14% Portfolio 0.29% 0.19% 100% 100% ROR Weight

Let

’

s

begi

n

wi

t

h

Basi

c

Materials

Portfolio Index Portfolio Index

Basic Mat'ls 0.25% 0.15% 10% 11% ROR Weight









AllocEffect  r_i w_i wi 0 0015.  010. 0 11. 0 002%.

 





SelEffect wi  r_i ri 011.  0 0025 0 0015.  . 0 011%.



  



 



InteractionEffect  w_i wi  r_i ri      010. 011. 0 0025 0 0015. . 0 001%.

The BHB applied

to the entire portfolio

Portfolio Benchmk Portfolio Benchmk Allocation Stk Sel Interaction Total Basic Mat'ls 0.25% 0.15% 10% 11% -0.002% 0.011% -0.001% 0.009% Industrials 0.50% 0.51% 11% 9% 0.010% -0.001% 0.000% 0.009% Cons Cyc 1.00% 1.01% 8% 7% 0.010% -0.001% 0.000% 0.009% Utilities -0.80% -0.75% 12% 13% 0.008% -0.007% 0.001% 0.001% Energy 2.00% 1.95% 7% 5% 0.039% 0.003% 0.001% 0.043% Fin'l -0.30% -0.31% 6% 8% 0.006% 0.001% 0.000% 0.007% Healthcare 0.80% 0.79% 15% 13% 0.016% 0.001% 0.000% 0.017% Technology 0.60% 0.70% 9% 10% -0.007% -0.010% 0.001% -0.016% Telecom -0.20% -0.21% 13% 10% -0.006% 0.001% 0.000% -0.005% Cons, Non-Cyc -0.50% -0.52% 9% 14% 0.026% 0.003% -0.001% 0.028% Portfolio 0.29% 0.19% 100% 100% 0.100% 0.001% 0.000% 0.102%

ROR Weight Effects

Fixed income: Fong, et al

Return decomposition using the Fong-Pearson-Vasicek framework for fixed income attribution:

Total return

Effect of External

Interest Environment Management ProcessContribution of

Return on default-free benchmark assuming no

change in forward rates

Return due to change in Forward rates

Return from Interest rate management

Return from sector/ Quality management

Return from

Describing the approach

The Fong, et al, approach explains return in

terms of its macro sources, and then further

breaks down the macro sources into micro

components

The macro sources of return

The first level of decomposition distinguishes

between the effect of the external interest

rate environment and the management

contribution. Mathematically:



R = total return



I = effect of external interest rate environment,

beyond

t

he

manager

’

s

cont

r

ol



C

=

cont

r

i

but

i

on

of

t

he

manager

’

s

pr

ocess

C

I

Observations at the macro

level



In the absence of management, the return would

be simply I

 A proxy for this passive portfolio is the set of (most)

default-free bonds, best approximated by outstanding U.S. Treasuries

 Inclusion of any other type of bond (corporate,

municipal, agency) constitutes an element of risk; higher yields would be expected for accepting that risk

 These risk allocations would be elements of C (manager

contribution)



We can think of this portfolio as an index of

Dissecting the external interest

rate environment contribution

The external interest rate environment (beyond the

manager

’

s

cont

r

ol

)

coul

d

be

f

ur

t

her

br

oken

down

into two components or sources of return:

 Interest rate level: the return that would be realized if

interest rates in the market did not change

 Spot rates are yields on pure discount bonds

 Return comes from the spot rate compounded for the holding

period

 Ifinterestrates don’tchange,this return willbe the same forall

securities in the treasury index

 This is the most neutral forecast; referred to as the market

Dissecting the external interest

rate environment contribution (2)

The external interest rate environment (beyond the

manager

’

s

cont

r

ol

)

coul

d

be

f

ur

t

her

br

oken

down

into two components or sources of return:

 Interest rate change: the return that comes from actual

changes in interest rates in the Treasury market

 This contribution is calculated as the return on the Treasury

Expressing the external interest

rate environment mathematically

Expressing this relationship mathematically:

 I = the external interest rate environment

 E = return on default free securities under the

market-implicit assumption (no changes in forward rates); i.e., expected return

 U = return attributable to actual changes in forward

rates; i.e., unexpected return

U

E

Decomposing the

management contribution

We can obtain the management contribution by subtracting the return on the Treasury index from the actual portfolio

return. This can be decomposed into three principal management skills:

 C = the management contribution

 M = return from maturity management

 S = return form spread/quality management

 B = return attributable to the selection of specific securities

B

S

M

Adding value through maturity

management



Maturity management (duration management) is

typically where the manager has the largest impact

on performance



Mat

ur

i

t

y

management

measur

es

t

he

manager

’

s

ability to anticipate interest rate changes

 Holding long duration portfolios during periods of

decreasing interest rates will typically add value

 Holding short duration portfolios during periods of rate

increases will also typically add value

 Being short when rates decline or long when rates go up

Adding value through

sector/quality management

Sector and quality management measures the

manager

’

s

al

l

ocat

i

on

deci

si

on

t

o

al

t

er

nat

i

ve

bond

sectors and quality groups

 Concentrating the portfolio in bond sectors (municipal,

corporate, agency, foreign) or ratings categories (AAA, AA, BBB, etc.) that perform favorably compared to other sector and/or ratings categories is the goal of the

Adding value through security

selection

Bond

sel

ect

i

on

management

measur

es

t

he

manager

’

s

ability to hold bonds that outperform the average

Measuring the return due to

management decisions

The return of each component of management

contribution is calculated using security repricing

 Maturity management

 Assume each bond in the actual portfolio is a Treasury bond

priced on the term structure

 The default-free price of the given security is the present value

of its payments discounted by spot rates corresponding to the maturity of the payment

 Subtractthe return ofthe Treasury index (contribution “I”)from

Measuring the return due to

management decisions

The return of each component of management

contribution is calculated using security repricing

 Sector/quality management

 Reprice each security in the actual portfolio as if it were exactly

in line with its own sector/quality group (i.e., no security specific return)

 Base the repricings on the term structure of U.S. Treasuries, plus

spreads based on the difference the bond’s actualyield and the

default-free bond’s yield

 The average spread for the sector/quality group is added to the

yield implied by the Treasury term structure, and the corresponding price is calculated

 From this total portfolio value, subtract the return from

Measuring the return due to

management decisions

The return of each component of management

contribution is calculated using security repricing

 Security selection contribution

 This contribution is simply the actual portfolio return minus all

The micro decomposition of

bond portfolio performance

Based on the approach, we have decomposed bond returns into the following micro level contributions:

 R = total return

 E = return on default free securities under the market-implicit

assumption (no changes in forward rates); i.e., expected return

 U = return attributable to actual changes in forward rates; i.e.,

unexpected return

 M = return from maturity management

 S = return form spread/quality management

 B = return attributable to the selection of specific securities

B S M U E R     

An alternate view of these

definitions

We can look at these various contributions in another way that may add meaning, by looking at the incremental value

added by each component:

 E is the expected return on a randomly selected portfolio of

Treasuries, assuming no change in interest rates

 E+U is the actual return on the randomly selected portfolio of

Treasuries

 E+U+M is the return on the actual portfolio as if all securities were

Treasuries priced on the term structure (no sector/quality effects and no specific returns)

 E+U+M+S is the return on actual portfolio as if all securities were

priced according to their issuing sector and quality (no specific returns)

Comparing the actual portfolio

to a benchmark



The approach decomposes returns for a portfolio

using a Treasury index as the starting source for

return contributions



We can perform the same analysis on a given

benchmark the manager is using



The attribution for the manager may then be

calculated as the relative contributions (portfolio

minus benchmark) for each component

Macro Attribution Overview



Macro attribution is executed at the fund sponsor

level for the total fund



The fund sponsor makes broad-level allocation

decisions (e.g., asset class level)



Sponsor hires a team of managers for the fund,

making secondary allocation decisions to investment

styles and managers



We will look at macro attribution in two metrics:

 Rate of return (i.e., as a percentage)

Inputs for Macro Attribution

Analysis

In order to carry out macro attribution analysis,

we need three sets of input data



Policy allocations



Benchmark portfolio returns

Policy allocations



These

ar

e

t

he

“nor

mal

”

wei

ght

i

ngs

t

o

asset

categories in the fund –the weights the fund

sponsor would hold to satisfy long-term objectives



These

wei

ght

s

r

ef

l

ect

t

he

f

und

sponsor

’

s

r

i

sk

tolerance, long-term expectations of risk and reward

and liabilities fund must satisfy

Example Policy Allocation

100% Total Fund 75% of 30% 75% Style D 25% of 30% 25% Style C 30% Bonds 53% of 70% 53% Style B 47% of 70% 47% Style A 70% Stocks Asset Type Allocation Style Allocation Asset Type

Benchmark Returns



Broad market indices (or other benchmarks) are

used for the asset categories



Manager

benchmar

ks

ar

e

used

f

or

each

manager

’

s

within asset categories

 If managers have style biases, the benchmarks should

Example benchmark assignment

with returns

6.74% Total Fund 1.75% Salomon 10-30 Yr Gov’tIndex Style D 2.15% Salomon 1-3 Yr Gov’tIndex Style C 2.09% Salomon Gov’t Index Bonds 4.75% S&P 600 Smallcap Value Style B 7.45% S&P 600 Smallcap Growth Style A 7.02% S&P 600 Stocks Return Benchmark Asset Type

Fund Returns, Valuations and

External Cash Flows



Stating the attribution results using a return-only

metric only requires fund returns



The addition of market values and external cash

Example fund data for our macro

attribution analysis



Our objective:

 Explain how the fund grew $1,539,200 over the period

 Explain how the sponsor’s decisions led to 490 bps (4.90%) of return

Asset Category Starting Value

Ending Value

Net Cash

Flows Fund Return

Benchmark Return Stocks $7,500,000 $8,864,200 $700,000 8.10% 7.02% Manager A $3,500,000 $4,097,030 $329,000 7.00% 7.45% Manager B $4,000,000 $4,767,170 $371,000 9.06% 4.75% Bonds $2,500,000 $2,675,000 $300,000 -4.46% 2.09% Manager C $625,000 $675,000 $75,000 -3.57% 2.15% Manager D $1,875,000 $2,000,000 $225,000 -4.76% 1.75% Total Fund $10,000,000 $11,539,200 $1,000,000 4.90% 6.74%

Macro Attribution Analysis

Components

 From the plan sponsor’s viewpoint,we willbreak down the

attribution analysis according to the following hierarchy:

 Net Contributions  Risk-free asset  Asset Categories  Benchmarks  Investment Managers  Allocation Effects

 Note: These decision variables may be typical, but are not

About the Macro Attribution

Approach

 Each level of the hierarchy represents an investment

alternative for the plan sponsor (i.e., an investment strategy)

 The attribution analysis assesses the incremental

contribution ofeach strategy to the fund’s change in value over the evaluation period

 Each component represents an unambiguous, appropriate

and specified investment alternative  a valid benchmark

 Strategies are ordered by increasing risk and complexity  Thus, the attribution analysis calculates the incremental

contribution of each strategy component to

 Period return for the fund  Change in fund value

Net Contributions

 This component of the analysis simply calculates the sum of

external cash flows

 In our example, the net external cash flows sum to

$1,000,000 –this is the incremental value contribution

 Note: since these amounts represent flows, there is no

return contribution (i.e., return = 0.00%)

 Net contributions cause the fund to increase in value from

Attribution effects scoreboard

Decision-Making Level Incremental Return Contribution Cumulative Return Incremental Value Contribution Cumulative Fund Value Beginning Value $10,000,000 Net Contributions 0.00% 0.00% $1,000,000 $11,000,000 Risk-Free Asset Asset Category Benchmarks Investment Managers Allocation Effects Total Fund 4.90% $11,539,200

Risk-Free Asset

 Assumes the fund sponsor invests all assets at the risk-free

rate (e.g., 90 day Treasury bills)

 The assumed invested amount is the fund starting value plus

net contributions. Dates of external cash flows should be considered.

 Forsimplicity,we’llassume in the example thatall

contributions occurred at the start of the month and the RFR is 0.25%

 0.25% is our return metric

 $11,000,000 invested at the RFR $27,500 as the incremental value

Attribution effects scoreboard

Decision-Making Level Incremental Return Contribution Cumulative Return Incremental Value Contribution Cumulative Fund Value Beginning Value $10,000,000 Net Contributions 0.00% 0.00% $1,000,000 $11,000,000 Risk-Free Asset 0.25% 0.25% $27,500 $11,027,500 Asset Category Benchmarks Investment Managers Allocation Effects Total Fund 4.90% $11,539,200

About the Net Contributions and

Risk-Free Asset Strategies

 The fund sponsor is unlikely to pursue a strategy that only

includes net contributions, but this strategy provides a baseline for the rest of the analysis

 The risk-free asset strategy represents a strategy that will

consistently produce a positive return over time

The remaining strategies reflect the willingness of the plan sponsor to accept some degree of risk

Asset Category

 Calculates a contribution based on the fund sponsor

following the policy weights; i.e., passive investment in the designated asset category benchmarks

 Investing along policy lines amounts to a pure index fund

approach

 Return is based on benchmark rate in excess of risk free

rate

 Value metric assumes investment of starting value plus

external cash flows

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Asset Category calculations

% 29 . 5 ) 0025 . 0209 (. * 30 . ) 0025 . 0702 (. * 70 .      AC r

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010 , 582 ) 0025 . 0209 (. * 000 , 300 , 3 ) 0025 . 0702 (. * 000 , 700 , 7      AC v Policy weights

Value of weights plus cash flows

About the Asset Category

Contribution

This is typically where the most value is added to the plan

sponsor’s program,often much largerthan the contribution from style bias and active management

Attribution effects scoreboard

Decision-Making Level Incremental Return Contribution Cumulative Return Incremental Value Contribution Cumulative Fund Value Beginning Value $10,000,000 Net Contributions 0.00% 0.00% $1,000,000 $11,000,000 Risk-Free Asset 0.25% 0.25% $27,500 $11,027,500 Asset Category 5.29% 5.54% $582,010 $11,609,510 Benchmarks Investment Managers Allocation Effects Total Fund 4.90% $11,539,200

Benchmark contribution (investment

style, aka benchmark misfit)

 Calculates a contribution based on the managers’

investment styles (distinct from policy and active management)

 Investing along policy lines amounts to a pure index

fund approach

 Return is based on style benchmark rate in excess of

broad benchmark rate

 Value metric assumes investment of starting value plus

external cash flows

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Benchmark calculations

) 0702 . 0745 (. * 47 . * 70 .   return A Style

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Excess return over asset category benchmarks ) 0702 . 0475 (. * 53 . * 70 .   return B Style ) 0209 . 0215 (. * 25 . * 30 .   return C Style ) 0209 . 0175 (. * 75 . * 30 .   return D Style

Benchmark calculations

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Benchmark calculations

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About the Benchmark

Contribution

 It is important for the plan sponsor to distinguish value

added from choice ofmanagers/styles (within the sponsor’s directcontrol)and managers’active management(outside sponsor’s directcontrol)

 Benchmark misfit that is large indicates there is

uncompensated risk that should be minimized

 If plan wants no style bias, benchmark contribution should be

Attribution effects scoreboard

Decision-Making Level Incremental Return Contribution Cumulative Return Incremental Value Contribution Cumulative Fund Value Beginning Value $10,000,000 Net Contributions 0.00% 0.00% $1,000,000 $11,000,000 Risk-Free Asset 0.25% 0.25% $27,500 $11,027,500 Asset Category 5.29% 5.54% $582,010 $11,609,510 Benchmarks -0.77% 4.77% -$84,997 $11,524,513 Investment Managers Allocation Effects Total Fund 4.90% $11,539,200

Contribution from Investment

Managers

 Calculates a contribution based on the managers’active

management (distinct from policy and investment style)

 Return is based on actual fund rates in excess of style

benchmark rates

 Value metric assumes investment of starting value plus

external cash flows

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Investment managers

calculations

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Excess return over manager benchmarks

) 0745 . 0700 (. * 47 . * 70 .   return A Manager ) 0475 . 0906 (. * 53 . * 70 .   return B Manager ) 0215 . ) 0357 . (( * 25 . * 30 .    return C Manager ) 0175 . ) 0476 ((. * 75 . * 30 .   return D Manager

Investment managers

calculations

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Excess return over manager benchmarks

)) 0045 . ( * 000 , 619 , 3 (   value A Manager ) 0431 . * 000 , 081 , 4 (  value B Manager )) 0572 . ( * 000 , 825 (   value C Manager )) 0651 . ( * 000 , 475 , 2 (   value D Manager

Investment managers

calculations

% 44 . 0 ) 0175 . ) 0476 . (( * 75 . * 30 . ) 0215 . ) 0357 . (( * 25 . * 30 . ) 0475 . 0906 (. * 53 . * 70 . ) 0745 . 0700 (. * 47 . * 70 .            IS r 707 , 48 )) 0651 . ( * 000 , 475 , 2 ( )) 0572 . ( * 000 , 825 ( ) 0431 . * 000 , 081 , 4 ( )) 0045 . ( * 000 , 619 , 3 (         IS v

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Attribution effects scoreboard

Decision-Making Level Incremental Return Contribution Cumulative Return Incremental Value Contribution Cumulative Fund Value Beginning Value $10,000,000 Net Contributions 0.00% 0.00% $1,000,000 $11,000,000 Risk-Free Asset 0.25% 0.25% $27,500 $11,027,500 Asset Category 5.29% 5.54% $582,010 $11,609,510 Benchmarks -0.77% 4.77% -$84,997 $11,524,513 Investment Managers -0.44% 4.33% -$48,707 $11,475,806 Allocation Effects Total Fund 4.90% $11,539,200

Contribution from Allocation

Effects



Calculates the residual effect –i

.

e.

,

what

’

s

left over –after all of the previous effects



Arises from fund sponsor deviations in policy

allocations at asset category (broad market)

and manager (investment style) levels

Macro attribution results

Decision-Making Level Incremental Return Contribution Cumulative Return Incremental Value Contribution Cumulative Fund Value Beginning Value $10,000,000 Net Contributions 0.00% 0.00% $1,000,000 $11,000,000 Risk-Free Asset 0.25% 0.25% $27,500 $11,027,500 Asset Category 5.29% 5.54% $582,010 $11,609,510 Benchmarks -0.77% 4.77% -$84,997 $11,524,513 Investment Managers -0.44% 4.33% -$48,707 $11,475,806 Allocation Effects 0.57% 4.90% $63,394 $11,539,200 Total Fund 4.90% $11,539,200

Questions?

John D. Simpson

[email protected]

1.310.500.9640