Evolution of Performance Attribution Methodologies. Carl Bacon Round-Table Performance Attribution Zurich, 23 rd June 2004

Transcription

1 Evolution of Performance Attribution Methodologies Carl Bacon Round-Table Performance Attribution Zurich, 23 rd June 2004

2 What is Performance Measurement? What Calculation of Portfolio Return, Benchmark and Peer Group comparison Maintenance of performance track records Distribution Why Performance Attribution Risk Analysis Forensic Analysis How Feedback into Investment Decision Process Structural Issues 2 2

3 What is Performance Attribution? Definition: Performance attribution is a technique used to quantify the excess returns of a portfolio against it s benchmark into the active decisions of the investment management process. 3 3

4 Why is Attribution Important? Key management tool Analysts Portfolio Managers Senior Management Consultants Clients 4 4

5 Performance Analyst Allows: The measurer to add value Participate in the Investment process Act as a control function and raises the profile of the Performance Measurement Function 5 5

6 Evolution of Performance Attribution Methodologies Fama Decomposition Brinson, Hood & Beebower Brinson & Fachler Arithmetic Geometric Multi-currency 6 6

7 Evolution of Performance Attribution Methodologies Arithmetic Geometric Multi-currency Manchero Allen Carino Ankrim & Hensel GRAP Davies& Laker Karnosky & Singer Burnie, Teder & Knowles Geometric Bain Multi-currency geometric 7 7

8 Fama Decomposition 972 A Return Net Selectivity Total Excess Return from Selectivity Return from Return A 2 Benchmark A 3 Diversification Manager s Risk Return from Investor s risk I P F Systematic Risk 8 8

9 Attribution - Brinson Model (985, 986 & 99) Portfolio Performance n Benchmark Performance r b n PW PR IW IR Intermediate Notional Funds: b S n PW IR Allocation r S n IW PR Selection 9 9

10 Brinson Model Quadrant Portfolio Return Quadrant 2 Allocation Return r n PW PR b S n PW IR Quadrant 3 Quadrant 4 r S Selection Return n IW PR b Benchmark Return n IW IR 0 0

11 Brinson attribution Excess Return Quadrant Quadrant 4 Asset Allocation Quadrant 2 Quadrant 4 Stock Selection Quadrant 3 Quadrant 4 Interaction Quadrant Quadrant 3 Quadrant 2 + Quadrant 4

12 Brinson Fachler Asset Allocation n PW IR n IW OR IR n ( PW IW ) IR Brinson Hood Beebower Since n n PW IW n ( PW IW ) ( IR b) 2 2

13 3 3 Brinson Brinson Fachler Fachler Stock Selection Interaction ( ) n n n IR PR IW IR IW PR IW ( ) ( ) + n J n n n n IR PR IW PW IR IW PR IW IR PW PR PW

14 Arithmetic Worked Example (Asset allocation) Portfolio Benchmark Portfolio Index Weight Weight Return Return UK 40% 40% Japan 30% 20% US 30% 40% Total 00% 00% Total Excess Return Asset (or country) Allocation UK [40%-40%] x ( ) 0 JAPAN [30%-20%] x ( ) -.04 US [30%-40%] x ( ) -0.6 TOTAL

15 Example (Stock Selection) Portfolio Benchmark Portfolio Index Weight Weight Return Return UK 40% 40% Japan 30% 20% US 30% 40% Total 00% 00% Total Excess Return Stock Selection UK [40%] x ( ) 4.0 JAPAN [20%] x ( ) -0.2 US [40%] x ( ) -0.8 TOTAL

16 Example (Interaction) Portfolio Benchmark Portfolio Index Weight Weight Return Return UK 40% 40% Japan 30% 20% US 30% 40% Total 00% 00% Total Excess Return Interaction UK [40%-40%] x ( ) 0 JAPAN [30%-20%] x ( ) -0. US [30%-40%] x ( ) 0.2 TOTAL TOTAL

17 Brinson Model Quadrant Portfolio Return Quadrant 2 Allocation Return r n PW PR b S n PW IR Quadrant 4 b Benchmark Return n IW IR 7 7

18 Stock Selection including Interaction Excess Return Quadrant Quadrant 4 Asset Allocation Quadrant 2 Quadrant 4 Stock Selection Quadrant Quadrant 2 8 8

19 Brinson Model r Step III Portfolio Return n PW PR b S Step II Semi-Notional n PW IR b Step I Benchmark Return n IW IR 9 9

20 Brinson Fachler Stock Selection n PW PR n PW IR n PW ( PR IR ) No Interaction 20 20

21 Example (Stock Selection with Interaction) Portfolio Benchmark Portfolio Index Weight Weight Return Return UK 40% 40% Japan 30% 20% US 30% 40% Total 00% 00% Total Excess Return Stock Selection UK [40%] x ( ) 4.0 JAPAN [30%] x ( ) -0.3 US [30%] x ( ) -0.6 TOTAL

22 Excess Return Arithmetic Arithmetic excess return is the profit in excess of a notional or benchmark fund expressed as a percentage of the initial amount invested Geometric Geometric Excess return is the profit in excess of the benchmark fund expressed as a percentage of the final value of the benchmark fund

23 Excess Return Example Arithmetic Market Start Value,000,000 Market End Value,070,000 Hence Profit 70,000 and a return of 7% Benchmark return 5% Hence value of notional fund,050,000 and profit of 50,000 Added value 70,000-50,000 20,000 or 7% - 5% 2% or 20,000/,000,000 Geometric Added value 20,000/,050,000.9% or %

24 Arithmetic or Geometric? Arithmetic Easier to understand Larger absolute values in rising markets More widely and traditionally used Geometric Compoundable Convertible Proportionate 24 24

25 Compoundable Since actual performance is chain-linked and expressed as : ( + r ) ( + r ) ( + r ) KKK ( + rn ) ( + R) 2 3 K and similarly for benchmark performance ( + b ) ( + b ) ( + b ) KKK ( + bn ) ( + B) 2 3 K then the geometric outperformance over the total period can be expressed as: ( + G ) ( ) ( + R) ( + B) ( + R ) ( + B ) ( + r ) ( + b ) ( + r2 ) ( + b ) 2 ( + r3 ) ( + b ) 3 KKKK ( + rn ) ( + b ) ( + g ) ( + g ) ( + g ) KKK ( ) 2 3 K + G + n g n 25 25

26 Convertible In US Dollars Portfolio Benchmark Arithmetic Difference In Sterling Portfolio Benchmark Arithmetic Difference in Deutschemarks Portfolio Benchmark Arithmetic Difference Geometric Difference

27 Proportionate Which is the better excess return? 5% v 50% or % v 0% Arithmetically both +% Geometrically: % %

28 Excess Return Geometric Excess return: + + r b + + r b + + b b r + b b Hence Geometric Excess return is simply the Arithmetic Excess return divided by the wealth ratio of the benchmark %.05.9% 28 28

29 Geometric Attribution (Various 990 s) Total Portfolio performance r n PW PR and benchmark performance Rename semi-notional fund b (Index returns applied to actual portfolio weights) b S n n IW IR PW IR Now Expanding ( + g) ( + g) ( + r) ( + b) ( + r) ( + b ) ( + bs ) ( b) S + Stock Market Selection Selection 29 29

30 30 30 Geometric Attribution Geometric Attribution Asset Allocation Stock Selection + + ) ( b IR IW PW i i i S i i i i b IR IR PR PW

31 Geometric Worked Example (Asset Allocation) Portfolio Benchmark Portfolio Index Semi- Weight Weight Return Return Notional UK 40% 40% Japan 30% 20% US 30% 40% Total 00% 00% Total Excess Return Asset (or country) Allocation UK.0 [ 40 % 40% ] JAPAN 0.96 [ 30% 20% ] US.08 [ 30% 40% ] TOTAL or alternatively

32 Example (Stock Selection) Portfolio Benchmark Portfolio Index Semi- Weight Weight Return Return Notional UK 40% 40% Japan 30% 20% US 30% 40% Total 00% 00% Stock Selection UK.20.0 [ 40%] JAPAN [ 30%] US [ 30 %] TOTAL or alternatively

33 Geometric Performance Attribution Excess Return Country X Stock 33 33

34 Excess Return Attribution? Preferences: Arithmetic Excess Return Arithmetic Attribution Methodology Geometric Excess Return Geometric Attribution Methodology 34 34

35 Smoothing Algorithms Natural consequence of using arithmetic excess returns! Two approaches: Genuine Smoothing algorithms Square pegs into round holes Excess return reinvestment Arithmetic factors restated 35 35

36 Carino Smoothing (999) Using logs (or continuous compounding) ( ) ln + R ln( + R ) + ln( + R2 ) + KKK + ln( + T R ) Excess Return: ( ) ln + R ln( + B) ln( + R ) ln( + B ) + KKK + ln( + R T ) ln( + B T ) 36 36

37 37 37 Introduce the term k t Then Carino Smoothing ( ) t t t t t B R B R k + + ) ln( ln ( ) + + T t t t t B R k B R ) ln( ) ln(

38 Carino Smoothing Divide by K K [ ln( + R ) ln( + B )] ( R B ) New Multi-period arithmetic Factor Old Single period Arithmetic Factor K t K 38 38

39 Manchero Smoothing (2000) Clearly: R B ( R t B ) t Need factor A that satisfies: R B A T ( R ) t B t t A Average Arithmetic Difference Geometric Mean Difference or ( R B ) T / T ( + R ) ( I + B ) A [ ] T 39 39

40 40 40 A still leaves a residual Create Corrective term t so that: ( ) ( ) t t T t t B R A B R + ( ) ( ) t t T T t B R B R B R A B R 2 ) ( Manchero Smoothing

41 4 4 New Multi-period arithmetic Factor Old Single period Arithmetic Factor Manchero Smoothing ) + t A ( ( ) [ ] ) ) ( ) (( ) ( / T T B R B R T A + + ( ) ( ) t t T T t B R B R B R A B R 2 ) ( ( ) B R ( ) ( ) ( ) T T R A + ( ) B R

42 GRAP Institute Method (997) Let E i be the arithmetic excess return in period i then: R B + E and R 2 B2 + E2 Thus the total excess return is: + R ( ( ( ( B B B + + B ) + E E )( + B E )( + )( + 2 ) + B B ( + B E + E 2 ) ) + ( + ( + B ) + ( + 2 R B + ) E 2 E ) + ( + ) E R 2 ) E 2 E E ( + E + B 2 ) + ( R )

43 GRAP Institute Method We can generalised for n periods: E n T E T T ( ) t t + R n t T + ( + B t ) 43 43

44 Frongello Linking Algorithm (2002) F it A it t t ( + R t ) + B t t t F it 44 44

45 Geometric Linking Geometric Excess Return Stock selection Market allocation it follows: ( + G ) ( + S) ( + M) ( + G ) ( + S ) ( + M ) ( + R ) ( + B ) ( + R ) ( + B SN ) ( + B SN ) ( + B ) By definition no residuals ( + G ) ( + S ) ( + S )... ( + S ) ( + M ) ( + M )... ( + ) 2 n 2 M n 45 45

46 Main Differences in Approach Interaction Arithmetic or Geometric Interest rate differentials Transactions Residuals Smoothing algorithms Daily v s monthly 46 46

47 Other Forms of Attribution Stock level attribution Multi-currency attribution Trading attribution Risk adusted attribution Risk attribution (ex-ante) Fixed income attribution Style analysis: growth value large cap - small cap 47 47

48 Transaction Analysis Part of the Investment Decision Process Dealing function Transaction Costs Market Impact Standard Attribution All transaction cost in Stock Selection Notional transfer Buy/hold analysis 48 48

49 Buy/Hold Attribution Holdings Based Attribution: Performance return attribution calculated with reference to holdings data only Monthly, weekly or daily Transaction Based Attribution Performance return attribution calculated from holdings and transaction data

50 Holdings based Advantages: Easy to implement Can use alternative pricing sources Disadvantages Will not reconcile to performance return Can t be used as an operational tool Residual might overwhelm over factors Errors won t be spotted 50 50

51 Transaction based Advantages: Reconciles to performance return Identifies all sources of excess return Can be used as a operational tool Disadvantages More difficult to implement Data must be complete & accurate Back office inefficiencies highlighted 5 5

52 Does Accuracy Matter? Internal Controls no residuals Complete Picture Confidence in data Operational improvements (Investment data is poor) Daily calculation not analysis 52 52

53 Is the error term a problem? Depends: Manager Activity Asset Category (Liquidity) IPOs Price Sources Cashflow Residuals - Commonly single largest factor - Can invalidate entire analysis 53 53

54 Buy/hold concerns We are ignoring the active decision in the investment process Holding based attribution is least useful when we need it most I.e. when we have a problem Are we letting the back office off the hook? 54 54

55 Currency Attribution Market returns compound with currency returns Assets denominated in currencies other than country of origin Forward contracts generate unrealised gains and losses Local returns cannot be achieved 55 55

56 Karnosky & Singer (994) r i n PW PR + i n i Li i i PW i c i b i n IW IR + i n i Li i i IW i c i *Continuously compounded returns 56 56

57 Karnosky & Singer r i n PW i n ( PR x ) + PW ( c + x ) i Li i i i i i i b i n IW i n ( IR x ) + IW ( c + x ) i Li i i i i i i 57 57

58 Karnosky & Singer Excess Return r b i n PW Local Attribution i n ( PR x ) IW ( IR x ) i Li i i i Quadrant Quadrant 2 i Li i i n PW Currency Attribution i n ( c + x ) IW ( c + x ) i i i i i Quadrant Quadrant 2 i i i Quadrant 3 Quadrant 4 Quadrant 3 Quadrant

59 Currency Returns - Definitions Base Return Return in base currency of portfolio Local Return Weighted average local return Currency return Currency Forward return Forward Premium S t + S S t t+ F t t S t Spot rate at time t F t Forward rate at time t for conversion at time t+ F S t 59 59

60 Currency - Portfolio Portfolio Local Portfolio Currency Weight Return Return ( ) Return UK 40% Japan 30% US 30% Total 00% Currency Return %

61 Currency Benchmark Benchmark Local Benchmark Currency Weight Return Return ( ) Return UK 40% Japan 20% US 40% Total 00% Currency Return 9.92 %

62 Naïve Currency Attribution Portfolio Currency Return Benchmark Currency Return % 62 62

63 Currency Attribution Assume currency allocation is independent Must be achieved by forward currency contracts Therefore exposed to interest rate differentials Forward Premium Karnosky & Singer 63 63

64 Currency Allocation Semi- Portfolio Benchmark Notional Benchmark Weight Weight Currency Currency UK 40% 40% Japan 30% 20% US 30% 40% Total 00% 00% Sterling Yen.0 [ 40 % 40 % ] % 20 % 0..0 [ ] Dollar TOTAL.78.0 [ 30% 40% ] or alternatively

65 Currency Timing Portfolio Portfolio Index Currency Semi Weight Return Return Return Notional UK 40% Japan 30% US 30% Total 00% Sterling Yen Dollar [ 40%] 0.0% [ 30%] 0.03% [ 30%] 0.2% TOTAL or alternatively 0.24%

66 Cost of Hedging (asset allocator s perspective) Portfolio Benchmark Semi Hedged Weight Weight Notional to Neutral UK 40% 40% Japan 30% 20% US 30% 40% Total 00% 00% Sterling Yen Dollar.0.0 [ 40% 40%] 0.0% [ 30% 20%] 0.0% [ 30% 40%] 0.9% TOTAL % Semi-Notional Hedged to Neutral or alternatively 0.0%

67 Revised Country Allocation Portfolio Benchmark Index Hedged Weight Weight Return Index UK 40% 40% Japan 30% 20% US 30% 40% Total 00% 00% Revised Asset (or country) Selection Sterling [ 40 % 40% ] 0 Yen [ 30% 20% ] Dollar TOTAL [ 30% 40% ] or alternatively

68 Currency Benchmark Benchmark Local Benchmark Currency Weight Return Return ( ) Return UK 40% Japan 20% US 40% Total 00% Currency Return Sterling 40% X 0.0% 0.0% % Yen 20% X 0.0% 2.0% Dollar 40% X 20% 8.0% Total 0.0% currency return 68 68

69 Currency Compounding (Benchmark) Benchmark Local Benchmark Currency Weight Return Return ( ) Return UK 40% Japan 20% US 40% Total 00% Currency Return Sterling Yen [ 40%] 0.0% 0.0% [ 20%] 0.0%.80%.064 Dollar.08 [ 40%] 20.0% 8.2%.064 TOTAL % % 69 69

70 Benchmark Compounding Benchmark Benchmark Adusted Weight Currency Currency UK 40% Japan 20% US 40% Total 00% Benchmark compounding Sterling Yen Dollar [ 40%] 0.0% [ 20%] 0.8% [ 40%] 0.% TOTAL or alternatively %

71 Currency Compounding (Portfolio) Portfolio Local Portfolio Currency Weight Return Return ( ) Return UK 40% Japan 30% US 30% Total 00% Currency Return Sterling Yen %.20 [ 40%] 0.0% 0.0% [ 30%] 0.%.083 Dollar.06 [ 30%] 20.8%.083 TOTAL % % 6.09% 7 7

72 Portfolio Compounding Portfolio Portfolio Adusted Weight Currency Currency UK 40% Japan 30% US 30% Total 00% Portfolio compounding Sterling Yen Dollar [ 40%] 0.0% [ 30%] 0.34% [ 30%] 0.2% TOTAL or alternatively %

73 Currency Attribution Currency Timing Cost of Hedging Currency perspective Currency Allocation Cost of Hedging Country perspective Portfolio Compounding Benchmark Compounding Portfolio Currency Cost of Hedging X Benchmark Currency 73 73

74 Currency Attribution Currency +r L +b SNH +b SNL +r +b * * * * L +b SNL +b L +b SNH +r L +b Stock Country Cost of Hedging 74 74

75 Currency Attribution Currency Stock Country Cost of Hedging Portfolio Currency Benchmark Currency (Inverted) 75 75

76 Geometric Attribution Excess Return Market selection X Security selection X Currency 76 76

77 Fixed Interest Attribution Very different to Equity attribution! - Fixed Income managers are more concerns about yield curve effects - Parallel shift, steepening or flattening yield curve - Credit spreads Daily attribution Essential for active managers Hedged to Neutral Critical for Global Bond portfolios Emerging debt 77 77

78 Fixed Income Attribution Three Types Yield Curve Decomposition Aggregated Decomposition Regression Method 78 78

79 Single Currency Yield Curve Attribution Attribute Time Effect Parallel Shift Slope (or twist) (between two maturities) Other Curve reshape ( Yield curve must be input) Spread effects Pricing 79 79

80 Where next? Integrated Performance Attribution & Risk Integrated Balanced Attribution Complete Investment Process Transactions Research Attribution Standards 80 80

81 Attribution Standards No generic attribution methodology Fit the Investment Process Purpose? Performance tool Operational tool Portfolio Management tool Risk control tool Geometric v Arithmetic Multiple smoothing algorithms 8 8

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