Intermediate Performance Calculations: Attribution

Transcription

1 Intermediate Performance Calculations: Attribution Monday, October 20, 2008 Public Pension Financial Forum John D. Simpson, CIPM The Spaulding Group, Inc.

2 What we l do today We l now complement our earlier return & risk discussion with attribution Performance Atribution, while not new, is stil an evolving discipline. Gary Brinson, FAJ, July/Aug 1986 Focus on ideas & concepts not the math Again, we have a fair amount to cover and limited time Feel free to ask questions

3 Contribution Analysis AbsoluteAtribution Return Total Return Portfolio

4 Is Contribution a form of Attribution? And the survey says Money Managers: 77% Plan Sponsors: 89% Investment Consultants: 100% Said yes! We suggest the term absolute atribution for contribution

5 Contribution A process to assess how individual securities / sectors contribute to the return Contribution = Weight * Return Weight = the relative market value

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

7 Contribution Rules 1. The sum of the contribution effects should equal the portfolio s return n i1 CE However, depending on volatility, this may not happen 2. Include effect of cash (when cash is included in the return) i R

8 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

9 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%

10 What if our absolute attribution and performance measurement 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 Transaction-based attribution

11 Day-Weighting Factor End-of-day Start-of-day* W CD D i CD i W CD D i CD i 1 Cash flow on 3 rd day of a 31-day month: 31 W i % W i %

12 Advantages of Contribution The math is quite simple Easy to comprehend Easy to explain Often, it s what managers initialy mean when they say they want attribution Usually, we look at the top 5 or top 10, and bottom 5 or bottom 10 holdings Could also calculate for the index

13 Disadvantages of Contribution How to calculate when portfolio makeup changes over time Fine for a static portfolio But what if you ve sold/bought something between the start and end of the month? A transaction-based approach generally helps

14 Now that we ve discussed absolute attribution We l move onto relative atribution

15 Relative attribution: where did the excess return come from? Relative Atribution Excess Return Returns The portfolio beat the benchmark - why? Portfolio Benchm ark

16 The Top-Down Approach Economic Data (CPI, Unemployment Stats, Production Figures, Interest Rate) Also, Political & World Data (Candidate polls, world events)

17 An example of how politics can influence the markets

18 The Top-Down Approach (cont d) Econom ic Data (CPI, Unem ploym ent Stats, Production Figures, Interest Rate) Also, Political & World Data (Candidate polls, world events) Predict the impact on Industry Sectors (example: will help Technology and hurt Banking; therefore bullish on Tech, bearish on Banks) Security Selection Decisions / Strategy Index Tech 4% Banks 5% We will want to assess the Allocation decisions and the Selection decisions Allocation Decision/Strategy Overweight Tech; Underweight Banks

19 Is it possible to beat every sector and still under perform the index? Yes? But How? Returns 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%

20 We will introduce 2 laws!

21 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 equity model for a fixed income portfolio (more on this later)

22 Notation we l use Portfolio Return n i1 R w r i i Benchmark Return (with overbar) n i1 R w r i i

23 The Second Law of Performance Attribution The sum of the attribution effects must equal the excess return. n i1 AE R R i

24 Note: there may be a residual In order to achieve the second law, it s possible that there may be a residual 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 model when there s portfolio turnover (probably the most common source) This is a single-period residual Multi-period residuals: use geometric model or smoothing algorithm

25 Performance Attribution: measuring the success/failure of 3 weighting decisions Active Return 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?

26 Brinson, Hood & Beebower (BHB) Model Actual Selection Passive Tim ing Actual Passive (IV) Actual Portfolio Return (III) Policy and Security Selection Return (II) Policy and Tim ing Return (I) Policy Return (Passive Portfolio Benchm ark)

27 Quadrant Meanings Quadrant I (Policy):Reflects the fund s long-term asset alocation plan. The fund s benchmark return goes here. Policy identifies the plan s normal portfolio. The result of the plan sponsor s investment policy. Quadrant II(Policy and timing s return efects): 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 actual return. This is the result of the segment weights and returns.

28 BHB Quadrant Formulas Quadrant I = Quadrant II = Quadrant III = Quadrant IV = w r i i i n 1 w r i i i n 1 w r i i i n 1 w r i i i n 1

29 Calculating the BHB Attribution Effects: Timing (Allocation): II I n w r w r i i i1 i1 n i1 r w w Other : (interaction) IV-III-II+I n i1 n i i i i w w r r i i i i i Stock selection: III I n Total: IV-I n i1 w r w r i i i1 i1 n i1 n w r r i i i w r w r i i i i i i

30 Trying to reconcile the excess return BM Portfolio Where did this excess come from? Weight Benchmark Contribution BM Portfolio Return

31 Visualizing the effects Weight BM Portfolio Allocation Effect Benchm ark Contribution Interaction Effect Selection Effect BM Portfolio Return

32 Interaction Some models, like the BHB, have an other or interaction efect So, what is interaction? Various interpretations Error term The interaction between two or more efects (e.g., allocation and selection) In fixed income, can mean effects too small to account for individualy ( residual is a beter term)

33 The interaction formula shows where it comes from n i1 w w r r i i i i From differences between the portfolio and benchmark s weights and returns If the diferences are slight, we l have zero or minimal interaction As the differences increase, the interaction will grow Also, from investing in securities or sectors that aren t in the index

34 Some examples n i1 w w r r i i i i 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%

35 BHB example ROR Weight 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%

36 Let s begin with Basic Materials ROR Weight Portfolio Index Portfolio Index Basic Mat'ls 0.25% 0.15% 10% 11% AllocEffect r w w % i i i SelEffect w r r % i i i InteractionEffect w w r r i i i i % Do these results make sense?

37 The BHB applied to the entire portfolio ROR Weight Effects Portfolio Benchmk Portfolio Benchmk Allocation Stk Sel Interaction Total Basic Mat'ls 0.25% 0.15% 10% 11% % 0.011% % 0.009% Industrials 0.50% 0.51% 11% 9% 0.010% % 0.000% 0.009% Cons Cyc 1.00% 1.01% 8% 7% 0.010% % 0.000% 0.009% Utilities -0.80% -0.75% 12% 13% 0.008% % 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% % % 0.001% % Telecom -0.20% -0.21% 13% 10% % 0.001% 0.000% % Cons, Non-Cyc -0.50% -0.52% 9% 14% 0.026% 0.003% % 0.028% Portfolio 0.29% 0.19% 100% 100% 0.100% 0.001% 0.000% 0.102% Do the portfolio s results make sense?

38 Fixed income: Fong, et al Return decomposition using the Fong-Pearson-Vasicek framework for fixed income attribution: Total return Effect of External Interest Environment Contribution of Management Process 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 security selection Return from trading activity

39 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

40 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 I C R = total return I = effect of external interest rate environment, beyond the manager s control C = contribution of the manager s process

41 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 Treasury issues

42 Dissecting the external interest rate environment contribution The external interest rate environment (beyond the manager s control) could be further broken 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 If interest rates don t change, this return wil be the same forall securities in the treasury index This is the most neutral forecast; referred to as the market implicit forecast

43 Dissecting the external interest rate environment contribution (2) The external interest rate environment (beyond the manager s control) could be further broken 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 index minus the return under the market implicit forecast

44 Expressing the external interest rate environment mathematically Expressing this relationship mathematically: I E U I = the external interest rate environment E = return on default free securities under the marketimplicit assumption (no changes in forward rates); i.e., expected return U = return attributable to actual changes in forward rates; i.e., unexpected return

45 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 M S B C = the management contribution M = return from maturity management S = return form spread/quality management B = return attributable to the selection of specific securities

46 Adding value through maturity management Maturity management (duration management) is typically where the manager has the largest impact on performance Maturity management measures the 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 will have a negative impact on performance

47 Adding value through sector/quality management Sector and quality management measures the manager s alocation decision to alternative 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 manager

48 Adding value through security selection Bond selection management measures the manager s ability to hold bonds that outperform the average performance of their given sector and quality group

49 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 Subtract the return of the Treasury index (contribution I ) from the repriced portfolio to obtain M

50 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 diference the bond s actual yield 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 components I and M

51 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 other components ( I, M, S )

52 The micro decomposition of bond portfolio performance Based on the approach, we have decomposed bond returns into the following micro level contributions: R E U M S B 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

53 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) E+U+M+S+B is the actual portfolio return

54 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

55 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) Value (i.e., in money terms)

56 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 Fund returns, valuations and external cash flows

57 Policy allocations These are the normal weightings to asset categories in the fund the weights the fund sponsor would hold to satisfy long-term objectives These weights reflect the fund sponsor s risk tolerance, long-term expectations of risk and reward and liabilities fund must satisfy

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

59 Benchmark Returns Broad market indices (or other benchmarks) are used for the asset categories Manager benchmarks are used for each manager s within asset categories If managers have style biases, the benchmarks should reflect managers style

60 Example benchmark assignment with returns Asset Type Stocks Style A Style B Bonds Style C Style D Total Fund Benchmark S&P 600 S&P 600 Smallcap Growth S&P 600 Smallcap Value SalomonGov t Index Salomon 1-3 Yr Gov tindex Salomon YrGov tindex Return 7.02% 7.45% 4.75% 2.09% 2.15% 1.75% 6.74%

61 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 allows statement of results in a value-metric

62 Example fund data for our macro attribution analysis Asset Category Starting Value Ending Value Net Cash Flows Fund Return Benchmark Return Stocks $7,500,000 $8,864,200 $700, % 7.02% Manager A $3,500,000 $4,097,030 $329, % 7.45% Manager B $4,000,000 $4,767,170 $371, % 4.75% Bonds $2,500,000 $2,675,000 $300, % 2.09% Manager C $625,000 $675,000 $75, % 2.15% Manager D $1,875,000 $2,000,000 $225, % 1.75% Total Fund $10,000,000 $11,539,200 $1,000, % 6.74% 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

63 Macro Attribution Analysis Components From the plan sponsor s viewpoint, we wil break 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 necessarily the only methodology that could be used

64 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 of each 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

65 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 $10,000,000 to $11,000,000

66 Attribution effects scoreboard Incremental Return Contribution Incremental Value Contribution Decision-Making Level Cumulative Return 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

67 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. For simplicity, we l assume in the example that al 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 contribution (value metric)

68 Attribution effects scoreboard Incremental Return Contribution Incremental Value Contribution Decision-Making Level Cumulative Return 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

69 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

70 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 r AC A i1 w i * r c i r f

71 Asset Category calculations Excess return over RFR r AC A i 1 w i * r c i r f rac. 70 * ( ).30 * ( ) 5.29 % Policy weights vac 7,700,000*( ) 3,300,000*( ) 582,010 Value of weights plus cash flows

72 About the Asset Category Contribution This is typically where the most value is added to the plan sponsor s program, often much larger than the contribution from style bias and active management

73 Attribution effects scoreboard Incremental Return Contribution Incremental Value Contribution Decision-Making Level Cumulative Return 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

74 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 r IS A M i 1 j 1 w i * w ij r B ij r C i

75 Benchmark calculations Excess return over asset category benchmarks r IS A M i1 j 1 w i * w ij r B ij r C i Style Areturn Style Breturn. 70*.47*( ). 70*.53*( ) StyleCreturn Style Dreturn. 30*.25*( ). 30*.75*( )

76 Benchmark calculations Excess return over asset category benchmarks r IS A M i1 j 1 w i * w ij r B ij r C i Style Avalue (3,619,000*.0043) Style Bvalue Style Cvalue Style Dvalue ( 4,081,000*(.0227)) (825,000*.0006) ( 2,475,000*(.0034))

77 Benchmark calculations Excess return over asset category benchmarks r IS A M i1 j 1 w i * w ij r B ij r C i ris. 70*.47*( ).70*.53*( ).30*.25*( ).30*.75*( ) 0.77% vis ( 3,619,000*.0043) (4,081,000*(.0227)) (825,000*.0006) (2,475,000*(.0034)) 84,997

78 About the Benchmark Contribution It is important for the plan sponsor to distinguish value added from choice of managers/styles (within the sponsor s direct control) and managers active management (outside sponsor s direct control) Benchmark misfit that is large indicates there is uncompensated risk that should be minimized If plan wants no style bias, benchmark contribution should be minimized to be close to zero

79 Attribution effects scoreboard Incremental Return Contribution Incremental Value Contribution Decision-Making Level Cumulative Return 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

80 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 r IM A M i1 j 1 w i * w ij r A ij r B ij

81 Investment managers calculations Excess return over manager benchmarks r IM A M i1 j 1 w i * w ij r A ij r B ij Manager Areturn Manager Breturn Manager Creturn Manager Dreturn. 70*.47*( ). 70*.53*( ). 30*.25*((.0357).0215). 30*.75*((.0476).0175)

82 Investment managers calculations Excess return over manager benchmarks r IM A M i1 j 1 w i * w ij r A ij r B ij Manager Manager Avalue Bvalue ( 3,619,000*(.0045)) (4,081,000*.0431) Manager Manager Cvalue Dvalue ( 825,000*(.0572)) ( 2,475,000*(.0651))

83 Investment managers calculations Excess return over manager benchmarks r IM A M i1 j 1 w i * w ij r A ij r B ij ris. 70*.47*( ).70*.53*( ).30*.25*((.0357).0215).30*.75*((.0476).0175) 0.44% vis ( 3,619,000*(.0045)) (4,081,000*.0431) (825,000*(.0572)) (2,475,000*(.0651)) 48,707

84 Attribution effects scoreboard Incremental Return Contribution Incremental Value Contribution Decision-Making Level Cumulative Return 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

85 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

86 Macro attribution results Incremental Return Contribution Incremental Value Contribution Decision-Making Level Cumulative Return 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

87 Questions? John D. Simpson