Attribution. Which sectors drove performance? Why did you perform better or worse than the benchmark? Excess Return Arithmetic vs. Geometric?

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1 Types of Attribution Absolute Attribution Attribution Which sectors drove performance? Contribution to Return Weights * Return, Weights = Denominator Relative Attribution Why did you perform better or worse than the benchmark? Excess Return Arithmetic vs. Geometric?

2 Absolute Attribution: Contribution to Return Sectors Return Weight CTR Apt 2.37% 26.30% 0.62% Hot 1.79% 1.93% 0.03% Ind 3.28% 13.79% 0.45% Land 3.80% 0.47% 0.02% Off 2.73% 38.28% 1.05% Other 4.84% 2.29% 0.11% Ret 2.67% 16.93% 0.45% Total 2.74% % 2.74% Math for single time period is easy. What math is used for multi-periods?

3 Relative Attribution Your return compared to a benchmark Under- vs. Out- Performance Excess Return How is Excess Return defined? Arithmetic vs. Geometric

4 Arithmetic Attribution Manager A s return is 30% and the Benchmark return is 20% Manager B s return is 10% and the Benchmark is 1% Excess Return Manager A = 30% - 20% = 10% Manager B = 10% - 1% = 9% Using Arithmetic Attribution Manager A did better than Manager B

5 Geometric Attribution Manager A s 30% vs. Benchmark 20% Manager B s 10% vs. Benchmark 1% Manager A (1+30%) / (1+20%) 1 Excess Return is 8.33% Manager B (1+10%) / (1+1%) 1 Excess Return is 8.91% Using Geometric Attribution Manager B did better than Manager A

6 Arithmetic vs. Geometric Manager A s return on $100 initial investment 30% vs. Benchmark 20% Arithmetic How well you did compared to starting point Excess return is $10 $10 / $100 = 10% Excess Return Geometric How well you did compared to ending point (as if you were invested in the Benchmark) Excess return is $10 $10 / $120 = 8.33% Excess Return

7 Which Attribution do you use? Arithmetic (primarily used in U.S.) Intuitive Higher than geometric in an up market Lower than geometric in a down market Geometric (primarily used in Europe) Not as intuitive, but proportional Lower than arithmetic in an up market Higher than arithmetic in a down market

8 Relative Attribution The Concept Manager adds value in two ways: Choosing superior investments Executing a superior strategy SELECTION ALLOCATION Superior selection contributions involve: Value added by transactions team Superior asset/property management practices Executing an effective disposition policy Superior allocation contributions involve: Buying/selling in the right markets at the right times Buying/selling in the right property types at the right times Investment Choices and Strategy Both Matter!

9 Two Primary Relative Attribution Models (1985,1985,1991) Brinson-Hood-Beebower (BHB ) This is the one we used in the previous examples. Brinson-Fachler (BF) This is a variation of BHB The way the allocation portion of the analysis is calculated is modified for each sector in a way that the total allocation impact for the fund is the same. But the allocation for a particular sector will be positive if the manager has over-weighted a sector that has a benchmark return for that sector higher than the total benchmark return.

10 Relative Attribution the Basic Math For an individual sector: R f R b W f W b Fund return for sector i Benchmark return for sector i Fund proportion of sector i Benchmark proportion of sector i There are four key terms for each sector: W f R f W b R b W b R f W f R b Sector i contribution to total fund return Sector I contribution to total benchmark return Fund proportion of sector i Benchmark proportion of sector i

11 Relative Attribution the Basic Math (cont d) Now, if we add up all of the sectors we get: F = W f R f B = W b R b NS = W b R f NA = W f R b Fund total return Benchmark total return Fund return if diversified like the benchmark (Notional Selection) Benchmark return if diversified like the fund (Notional Allocation) Here is a tabular form of the above: Fund weights Benchmark weights Fund returns F = W f R f NS = W b R f Benchmark returns NA = W f R b B = W b R b

12 Relative Attribution Brinson Hood Beebower F B = NS B W b (R f -R b ) NA B F NS NA B Total excess return Selection effects (W f -W b ) R b Allocation effects (W f -W b ) (R f -R b ) Cross product terms Benchmark weight applied to return difference Benchmark return applied to weight difference Difference in weights x difference in returns

13 Relative Attribution Brinson Fachler F B = NS B W b (R f - R b ) Total excess return Selection effects Benchmark weight applied to return difference NA B F NS NA B (W f - W b ) (R b B) Allocation effects (W f - W b ) (R f - R b ) Cross product terms Benchmark return difference from total benchmark return applied to weight difference Difference in weights x difference in returns Note: (W f - W b ) (R b B) = (W f - W b ) R b so total Allocation is the same as BHB

14 Attribution Absolute vs. Relative Absolute is Contribution to Return Relative is Excess Return combined with contribution to return Single Period = math adds up Multi-period = need to deal with time or compounding residuals

15 Properties of Attribution Models Intuitive, transparent, robustness, absence of residuals Commutative vs. Order dependent Causality vs. A-Causality

16 Methods to Allocate Residual in Arithmetic Relative Attribution GRAP Institute (1997) Uses G factor to smooth Carino (1999, 2002) Logs & continuous compound, uses K factor Menchero (2000, 2002, 2004) Uses A factor based on geometric compounding Davies & Laker (2001, 2005) The exact multi-period Brinson attribution Frongello (2002, 2003) Scales prior period effects separately David (2006) CNP method

17 Multi-period Absolute Attribution A B C D E F G 2 Weights Returns CTR Formula 3 Q1 Retail 40.0% 2.00% 0.80% =D3*E3 4 Office 60.0% 1.50% 0.90% =D4*E4 5 Total 100.0% 1.70% 1.70% =SUM(F3:F4) 6 7 Q2 Retail 50.0% 2.50% 1.25% =D7*E7 8 Office 50.0% 1.25% 0.63% =D8*E8 9 Total 100.0% 1.88% 1.88% =SUM(F7:F8) Q1&Q2 Retail??? 12 Office??? 13 Total 100.0% 3.61% 3.61% =(1+E5)*(1+E9)-1

18 Link the Quarters? A B C D E F G 2 Weights Returns CTR Formula 3 Q1 Retail 40.0% 2.00% 0.80% =D3*E3 4 Office 60.0% 1.50% 0.90% =D4*E4 5 Total 100.0% 1.70% 1.70% =SUM(F3:F4) 6 7 Q2 Retail 50.0% 2.50% 1.25% =D7*E7 8 Office 50.0% 1.25% 0.63% =D8*E8 9 Total 100.0% 1.88% 1.88% =SUM(F7:F8) Link then Retail 45.3% 4.55% 2.06% =(1+F3)*(1+F7)-1 21 Sum? Office 55.3% 2.77% 1.53% =(1+F4)*(1+F8)-1 22 Total 100.6% 3.61% 3.59% =F20+F21 23 Residual 0.02% =F13-F22

19 Add the Quarters? A B C D E F G 2 Weights Returns CTR Formula 3 Q1 Retail 40.0% 2.00% 0.80% =D3*E3 4 Office 60.0% 1.50% 0.90% =D4*E4 5 Total 100.0% 1.70% 1.70% =SUM(F3:F4) 6 7 Q2 Retail 50.0% 2.50% 1.25% =D7*E7 8 Office 50.0% 1.25% 0.63% =D8*E8 9 Total 100.0% 1.88% 1.88% =SUM(F7:F8) Retail?? 2.05% =F3+F7 Add? 16 Office?? 1.53% =F4+F8 17 Total 100.0% 3.61% 3.58% =F5+F9 18 Residual 0.03% =F13-F17

20 Average the Quarters? A B C D E F G 2 Weights Returns CTR Formula 3 Q1 Retail 40.0% 2.00% 0.80% =D3*E3 4 Office 60.0% 1.50% 0.90% =D4*E4 5 Total 100.0% 1.70% 1.70% =SUM(F3:F4) 6 7 Q2 Retail 50.0% 2.50% 1.25% =D7*E7 8 Office 50.0% 1.25% 0.63% =D8*E8 9 Total 100.0% 1.88% 1.88% =SUM(F7:F8) Average Retail 45.00% 2.25% 2.04% =(1+D25*E25)^ then Sum? Office 55.00% 1.38% 1.52% =(1+D26*E26)^ Total % 3.63% 3.55% =F25+F26 28 Residual 0.05% =F13-F28

21 CNP -Two Quarters A1 B C D E F G 3 =C =E*(1+ C7) =D+F 4 Description 2014q1 Cum Sum 2014q2 Linked Cum Sum 5 Retail 0.80% 0.80% 1.25% 1.27% 2.07% 6 Office 0.90% 0.90% 0.63% 0.64% 1.54% 7 Total 1.70% 1.70% 1.88% 1.91% 3.61% 8 1+Fund Return % 9 Sum down = linked across

22 CNP - Two more Quarters A1 B G H I J K L M From previous slide 3 =D+F =H*(1 +G7) =G+I =K*(1+ J7) =J+L 4 Description Cum Sum 2014q3 Linked Cum Sum 2014q4 Linked Cum Sum 5 Retail 2.07% 1.30% 1.35% 3.42% 1.36% 1.44% 4.86% 6 Office 1.54% 0.70% 0.73% 2.27% 0.80% 0.85% 3.11% 7 Total 3.61% 2.00% 2.07% 5.68% 2.16% 2.28% 7.97% 8 1+Fund Return 3.61% % % 9 Sum down = linked across Sum down = linked across Sum down = linked across

23 CNP - Three more Quarters A1 B M N O P Q R S T U V From previous slide 3 =J+L =N*(1+ M7) =M+O =Q*(1 +P7) =P+R =T*(1+ S7) =S+U 4 Descrip tion Cum Sum 2015q 1 Linked Cum Sum 2015q 2 Linked Cum Sum 2015q 3 Linked Cum Sum 5 Retail 4.86% 1.90% 2.05% 6.91% 2.50% 2.80% 9.71% -1.50% -1.76% 7.95% 6 Office 3.11% 2.00% 2.16% 5.27% 2.20% 2.47% 7.74% -0.50% -0.59% 7.15% 7 Total 7.97% 3.90% 4.21% 12.18% 4.70% 5.27% 17.45% -2.00% -2.35% 15.10% 8 1+Fund Return 7.97% % % % 9 Sum down = linked across Sum down = linked across Sum down = linked across Sum down = linked across

24 CNP 2 Year Example A1 B V W X Y Z AA AB From previous slide 3 =S+U =W*(1+ V15) =V+X =(1+Y)^(1/2 )-1 =Z8 =Y*AA 4 Description Cum Sum 2015q4 Linked Cum Sum Annualized Ratio Adjusted Annualized 5 Retail 7.95% -2.00% -2.30% 5.65% 2.78% 48.73% 2.75% 6 Office 7.15% -1.80% -2.07% 5.08% 2.51% 48.73% 2.48% 7 Total 15.10% -3.80% -4.37% 10.73% 5.23% 48.73% 5.23% Fund Return 15.10% % Sum is 5.29% 48.73% 5.23% Sum down = linked across =Z7/Y8' Sum down = linked across Residual Diff -.07% Sum down = linked across