1

The Fundamental Indexing Conundrum

Gaetan “Guy” Lion

April 2010

2

Introduction on Fundamental Indexing

• Robert D. Arnott develops fundamental indexes that weigh companies based on: 1) Sales (avg. over 5 years), 2) Cash flow (avg. over 5 years), 3) Book value (most recent), and 4) Dividends (avg. over 5 years).

• He starts an investment firm, Research

Affiliates that launches with PowerShares several ETFs using his indexing methodology.

• The basic rational is to reduce exposure to bubbling stocks that are overweighed within a market cap index.

3

Thoughts…

• Fundamental indexes, being defensive, to fare better than market cap ones during Bear markets.

• Market cap indexes to fare better in Bull markets because they capture upward momentum.

• Over long cycles both approaches to generate similar returns.

4

Back testing

Robert Arnott back-tests his (RAFI) indexes over decades. And, discloses his results (shown below) within his book:

Large U.S. EquitiesAnnual returns over the 1962 to 2007 period

Bull BearOverall Markets Markets

RAFI U.S. Large 12.30% 20.30% -18.10%S&P 500 10.30% 19.60% -23.90%Advantage 2.00% 0.70% 5.80%

Small U.S. EquitiesAnnual returns over the 1979 to 2007 period

Bull BearOverall Markets Markets

RAFI U.S. Small 16.40% 33.10% -26.70%Russell 2000 12.90% 30.80% -31.90%Advantage 3.50% 2.30% 5.20%All RAFI index returns earned with nearly exact samelevel of volatility as traditional market cap indexes.

5

The Debate

• Some say it is just Value investing.• Others state this approach is flawed. A

company with rising earnings of $5, $10, and $15 over past 3 years would have same weighing as one experiencing declining earnings of $15, $10, and $5.

• Proponents state it avoids market inefficiencies with specific sectors bubbling.

6

Empirical investigation

• Arnott launched his main fundamental index funds PowerShares FTSE RAFI US 1000 (large cap) and PowerShares FTSE RAFI US 1500 (small & mid cap) just a year before the 2007 Crash.

• This recent Bear market is a good test for the fundamental index approach.

• We will review the performance of both funds during the recent Crash and Recovery phases of the stock market.

7

Large Cap indexes correlation

The large cap fundamental index (PRF) is slightly more correlated with value oriented indexes. We will compare PRF’s performance to the other indexes.

Name of index fund or index Acronym Correl.PowerShares FTSE RAFI US 1000 PRFS&P 500 ^GSPC 0.972Russell 1000 Index ^RUI 0.930Russell 1000 Index - Value ^RLV 0.978Vanguard Value Index (Large cap.) VIVAX 0.977

8

PRF vs S&P 500 in the recent Crash

30

40

50

60

70

80

90

100

110

7/13/07

8/13/07

9/13/07

10/13/07

11/13/07

12/13/07

1/13/08

2/13/08

3/13/08

4/13/08

5/13/08

6/13/08

7/13/08

8/13/08

9/13/08

10/13/08

11/13/08

12/13/08

1/13/09

2/13/09

PRF

S&P 500

The Crash (7/13/07 = 100): PRF vs S&P 500

9

PRF vs S&P 500 in the current Recovery

The Recovery (3/09/09 = 100): PRF vs S&P 500

80

100

120

140

160

180

200

220

3/9/09

4/9/09

5/9/09

6/9/09

7/9/09

8/9/09

9/9/09

10/9/09

11/9/09

12/9/09

1/9/10

2/9/10

3/9/10

PRF

S&P 500

10

PRF vs S&P 500 since onsetSince onset (12/20/05 = 100). PRF vs S&P 500

40

50

60

70

80

90

100

110

120

130

140

12/2

0/05

3/20

/06

6/20

/06

9/20

/06

12/2

0/06

3/20

/07

6/20

/07

9/20

/07

12/2

0/07

3/20

/08

6/20

/08

9/20

/08

12/2

0/08

3/20

/09

6/20

/09

9/20

/09

12/2

0/09

PRF

S&P 500

% Difference: (PRF - S&P 500)/PRF

-10%

-5%

0%

5%

10%

15%

20%

12

/20

/05

3/2

0/0

6

6/2

0/0

6

9/2

0/0

6

12

/20

/06

3/2

0/0

7

6/2

0/0

7

9/2

0/0

7

12

/20

/07

3/2

0/0

8

6/2

0/0

8

9/2

0/0

8

12

/20

/08

3/2

0/0

9

6/2

0/0

9

9/2

0/0

9

12

/20

/09

11

PRF vs Russell 1000 (RUI)

30

40

50

60

70

80

90

100

110

7/13/2007

8/13/2007

9/13/2007

10/13/2007

11/13/2007

12/13/2007

1/13/2008

2/13/2008

3/13/2008

4/13/2008

5/13/2008

6/13/2008

7/13/2008

8/13/2008

9/13/2008

10/13/2008

11/13/2008

12/13/2008

1/13/2009

2/13/2009

PRF

RUI

The Crash (7/13/07 = 100): PRF vs RUI The Recovery (3/09/09 = 100): PRF vs RUI

80

100

120

140

160

180

200

220

3/9/2009

4/9/2009

5/9/2009

6/9/2009

7/9/2009

8/9/2009

9/9/2009

10/9/2009

11/9/2009

12/9/2009

1/9/2010

2/9/2010

3/9/2010

PRF

RUI

Since onset (12/20/05 = 100). PRF vs RUI

40

50

60

70

80

90

100

110

120

130

140

12/2

0/20

05

3/20

/200

6

6/20

/200

6

9/20

/200

6

12/2

0/20

06

3/20

/200

7

6/20

/200

7

9/20

/200

7

12/2

0/20

07

3/20

/200

8

6/20

/200

8

9/20

/200

8

12/2

0/20

08

3/20

/200

9

6/20

/200

9

9/20

/200

9

12/2

0/20

09

PRF

RUI

% Difference: (PRF - RUI)/PRF

-10%

-5%

0%

5%

10%

15%

20%

12/

20/2

005

3/2

0/20

06

6/2

0/20

06

9/2

0/20

06

12/

20/2

006

3/2

0/20

07

6/2

0/20

07

9/2

0/20

07

12/

20/2

007

3/2

0/20

08

6/2

0/20

08

9/2

0/20

08

12/

20/2

008

3/2

0/20

09

6/2

0/20

09

9/2

0/20

09

12/

20/2

009

12

PRF vs Russell 1000 Value

30

40

50

60

70

80

90

100

110

7/13/2007

8/13/2007

9/13/2007

10/13/2007

11/13/2007

12/13/2007

1/13/2008

2/13/2008

3/13/2008

4/13/2008

5/13/2008

6/13/2008

7/13/2008

8/13/2008

9/13/2008

10/13/2008

11/13/2008

12/13/2008

1/13/2009

2/13/2009

PRF

RLV

The Crash (7/13/07 = 100): PRF vs RLV The Recovery (3/09/09 = 100): PRF vs RLV

80

100

120

140

160

180

200

220

3/9/2009

4/9/2009

5/9/2009

6/9/2009

7/9/2009

8/9/2009

9/9/2009

10/9/2009

11/9/2009

12/9/2009

1/9/2010

2/9/2010

3/9/2010

PRF

RLV

Since onset (12/20/05 = 100). PRF vs RLV

40

50

60

70

80

90

100

110

120

130

140

12/2

0/20

05

3/20

/200

6

6/20

/200

6

9/20

/200

6

12/2

0/20

06

3/20

/200

7

6/20

/200

7

9/20

/200

7

12/2

0/20

07

3/20

/200

8

6/20

/200

8

9/20

/200

8

12/2

0/20

08

3/20

/200

9

6/20

/200

9

9/20

/200

9

12/2

0/20

09

PRF

RLV

% Difference: (PRF - RLV)/PRF

-5%

0%

5%

10%

15%

20%

25%

12/

20/2

005

3/2

0/2

006

6/2

0/2

006

9/2

0/2

006

12/

20/2

006

3/2

0/2

007

6/2

0/2

007

9/2

0/2

007

12/

20/2

007

3/2

0/2

008

6/2

0/2

008

9/2

0/2

008

12/

20/2

008

3/2

0/2

009

6/2

0/2

009

9/2

0/2

009

12/

20/2

009

13

PRF vs Vanguard Value (VIVAX)

30

40

50

60

70

80

90

100

110

7/13/2007

8/13/2007

9/13/2007

10/13/2007

11/13/2007

12/13/2007

1/13/2008

2/13/2008

3/13/2008

4/13/2008

5/13/2008

6/13/2008

7/13/2008

8/13/2008

9/13/2008

10/13/2008

11/13/2008

12/13/2008

1/13/2009

2/13/2009

PRF

VIVAX

The Crash (7/13/07 = 100): PRF vs VIVAX The Recovery (3/09/09 = 100): PRF vs VIVAX

80

100

120

140

160

180

200

220

3/9/2009

4/9/2009

5/9/2009

6/9/2009

7/9/2009

8/9/2009

9/9/2009

10/9/2009

11/9/2009

12/9/2009

1/9/2010

2/9/2010

3/9/2010

PRF

VIVAX

Since onset (12/20/05 = 100). PRF vs VIVAX

40

50

60

70

80

90

100

110

120

130

140

12/2

0/20

05

3/20

/200

6

6/20

/200

6

9/20

/200

6

12/2

0/20

06

3/20

/200

7

6/20

/200

7

9/20

/200

7

12/2

0/20

07

3/20

/200

8

6/20

/200

8

9/20

/200

8

12/2

0/20

08

3/20

/200

9

6/20

/200

9

9/20

/200

9

12/2

0/20

09

PRF

VIVAX

% Difference: (PRF - VIVAX)/PRF

-15%

-10%

-5%

0%

5%

10%

15%

12/

20/2

005

3/2

0/2

006

6/2

0/2

006

9/2

0/2

006

12/

20/2

006

3/2

0/2

007

6/2

0/2

007

9/2

0/2

007

12/

20/2

007

3/2

0/2

008

6/2

0/2

008

9/2

0/2

008

12/

20/2

008

3/2

0/2

009

6/2

0/2

009

9/2

0/2

009

12/

20/2

009

14

Table Summary for Large Cap

The fundamental index fund (PRF) beat out handsomely the other benchmarks over the entire period by 2.3 to 5.1 percentage points in annual return. But, it did it by fairing poorly in the 2007 Crash and extraordinarily well in the 2009 Recovery.

Level of risk (daily volatility) is similar.

Name of index fund or index Acronym Crash Recovery Since onsetPowerShares FTSE RAFI US 1000 PRF -43.5% 110.8% 1.4%S&P 500 Index ^GSPC -39.4% 69.1% -2.2%Russell 1000 Index ^RUI -39.5% 71.4% -1.9%Russell 1000 Index - Value ^RLV -44.3% 75.8% -3.7%Vanguard Value Index (Large cap.) VIVAX -41.9% 77.6% -0.8%

Pow. FTSE RAFI US 1000 advantage Crash Recovery Since onsetS&P 500 Index ^GSPC -4.0% 41.7% 3.7%Russell 1000 Index ^RUI -4.0% 39.3% 3.3%Russell 1000 Index - Value ^RLV 0.9% 34.9% 5.1%Vanguard Value Index (Large cap.) VIVAX -1.6% 33.1% 2.3%

Volatility of daily returns over entire period (since 12/20/2005).PowerShares FTSE RAFI US 1000 PRF 1.76%S&P 500 Index ^GSPC 1.64%Russell 1000 Index RUI 1.72%Russell 1000 Index - Value ^RLV 1.79%Vanguard Value Index (Large cap.) VIVAX 1.77%

Annualized return

Annualized return difference

15

Large Cap: Back Testing vs Actual

The relative performance of the RAFI large cap was very different during the two periods. While in the 45 years of back testing, it excelled at besting the S&P 500 in Bear markets while recording only a small advantage in Bull markets; in the actual 4.25 years it faired poorly in the Crash of 2007. But, did extremely well in the Recovery of 2009.

Large U.S. Equities.

Back testing 1962 to 2007 periodBull Bear

Overall Markets MarketsRAFI U.S. Large 12.30% 20.30% -18.10%S&P 500 10.30% 19.60% -23.90%Advantage 2.00% 0.70% 5.80%

Actual annualized results 12/20/2005 - 3/10/2010Bull Bear

Overall Market MarketRAFI U.S. Large 1.43% 110.75% -43.46%S&P 500 -2.22% 69.09% -39.42%Advantage 3.65% 41.66% -4.05%

16

Small Cap indexes correlation

Fundamental index (PRFZ) correlation to value index or regular ones are equally high.

Name of index fund or index Acronym Correl.PowerShares FTSE RAFI US 1500 Small-Mid PRFZiShares Russell 2000 Index IWM 0.96Vanguard Small Cap Value Index VISVX 0.97Vanguard Mid-Cap Value Index VMVIX 0.95

17

PRFZ vs Russell 2000 (IWM)

30

40

50

60

70

80

90

100

110

7/13/07

8/13/07

9/13/07

10/13/07

11/13/07

12/13/07

1/13/08

2/13/08

3/13/08

4/13/08

5/13/08

6/13/08

7/13/08

8/13/08

9/13/08

10/13/08

11/13/08

12/13/08

1/13/09

2/13/09

PRFZ

IWM

The Crash (7/13/07 = 100): PRFZ vs IWM VISVX (7/13/2007): PRFZ vs

The Recovery (3/09/09 = 100): PRFZ vs IWM

80

100

120

140

160

180

200

220

240

260

3/9/09

4/9/09

5/9/09

6/9/09

7/9/09

8/9/09

9/9/09

10/9/09

11/9/09

12/9/09

1/9/10

2/9/10

3/9/10

PRFZ

IWM

Since onset (9/20/06 = 100). PRFZ vs IWM

40

50

60

70

80

90

100

110

120

130

140

9/20

/06

11/2

0/06

1/20

/07

3/20

/07

5/20

/07

7/20

/07

9/20

/07

11/2

0/07

1/20

/08

3/20

/08

5/20

/08

7/20

/08

9/20

/08

11/2

0/08

1/20

/09

3/20

/09

5/20

/09

7/20

/09

9/20

/09

11/2

0/09

1/20

/10

PRFZ

IWM

% Difference: (PRFZ - IWM)/PRFZ

-10%

-5%

0%

5%

10%

15%

20%

9/20

/06

11/2

0/06

1/20

/07

3/20

/07

5/20

/07

7/20

/07

9/20

/07

11/2

0/07

1/20

/08

3/20

/08

5/20

/08

7/20

/08

9/20

/08

11/2

0/08

1/20

/09

3/20

/09

5/20

/09

7/20

/09

9/20

/09

11/2

0/09

1/20

/10

18

PRFZ vs Vanguard Small Cap Value (VISVX)

30

40

50

60

70

80

90

100

110

7/13/07

8/13/07

9/13/07

10/13/07

11/13/07

12/13/07

1/13/08

2/13/08

3/13/08

4/13/08

5/13/08

6/13/08

7/13/08

8/13/08

9/13/08

10/13/08

11/13/08

12/13/08

1/13/09

2/13/09

PRFZ

VISVX

The Crash (7/13/07 = 100): PRFZ vs VISVX VISVX (7/13/2007): PRFZ vs

The Recovery (3/09/09 = 100): PRFZ vs VISVX

80

100

120

140

160

180

200

220

240

260

3/9/09

4/9/09

5/9/09

6/9/09

7/9/09

8/9/09

9/9/09

10/9/09

11/9/09

12/9/09

1/9/10

2/9/10

3/9/10

PRFZ

VISVX

Since onset (9/20/06 = 100). PRFZ vs VISVX

40

50

60

70

80

90

100

110

120

130

140

9/20

/06

11/2

0/06

1/20

/07

3/20

/07

5/20

/07

7/20

/07

9/20

/07

11/2

0/07

1/20

/08

3/20

/08

5/20

/08

7/20

/08

9/20

/08

11/2

0/08

1/20

/09

3/20

/09

5/20

/09

7/20

/09

9/20

/09

11/2

0/09

1/20

/10

PRFZ

VISVX

% Difference: (PRFZ - VISVX)/PRFZ

-5%

0%

5%

10%

15%

20%

9/2

0/0

6

11

/20

/06

1/2

0/0

7

3/2

0/0

7

5/2

0/0

7

7/2

0/0

7

9/2

0/0

7

11

/20

/07

1/2

0/0

8

3/2

0/0

8

5/2

0/0

8

7/2

0/0

8

9/2

0/0

8

11

/20

/08

1/2

0/0

9

3/2

0/0

9

5/2

0/0

9

7/2

0/0

9

9/2

0/0

9

11

/20

/09

1/2

0/1

0

19

PRFZ vs Vanguard Midcap Value (VMVIX)

30

40

50

60

70

80

90

100

110

7/13/07

8/13/07

9/13/07

10/13/07

11/13/07

12/13/07

1/13/08

2/13/08

3/13/08

4/13/08

5/13/08

6/13/08

7/13/08

8/13/08

9/13/08

10/13/08

11/13/08

12/13/08

1/13/09

2/13/09

PRFZ

VMVIX

The Crash (7/13/07 = 100): PRFZ vs VMVIX VISVX (7/13/2007): PRFZ vs

The Recovery (3/09/09 = 100): PRFZ vs VMVIX

80

100

120

140

160

180

200

220

240

260

3/9/09

4/9/09

5/9/09

6/9/09

7/9/09

8/9/09

9/9/09

10/9/09

11/9/09

12/9/09

1/9/10

2/9/10

3/9/10

PRFZ

VMVIX

Since onset (9/20/06 = 100). PRFZ vs VMVIX

40

50

60

70

80

90

100

110

120

130

140

9/20

/06

11/2

0/06

1/20

/07

3/20

/07

5/20

/07

7/20

/07

9/20

/07

11/2

0/07

1/20

/08

3/20

/08

5/20

/08

7/20

/08

9/20

/08

11/2

0/08

1/20

/09

3/20

/09

5/20

/09

7/20

/09

9/20

/09

11/2

0/09

1/20

/10

PRFZ

VMVIX

% Difference: (PRFZ - VMVIX)/VMVIX

-10%

-5%

0%

5%

10%

15%

20%

9/2

0/06

11/2

0/0

6

1/2

0/07

3/2

0/07

5/2

0/07

7/2

0/07

9/2

0/07

11/2

0/0

7

1/2

0/08

3/2

0/08

5/2

0/08

7/2

0/08

9/2

0/08

11/2

0/0

8

1/2

0/09

3/2

0/09

5/2

0/09

7/2

0/09

9/2

0/09

11/2

0/0

9

1/2

0/10

20

Table Summary for Small Cap

The fundamental index fund (PRFZ) beat out the other benchmarks over the entire period by 7.2 to 8.0 percentage points in annual return. But, it did it by fairing poorly in the Crash and extraordinarily well in Recovery.

PRFZ bears similar level of risk.

Name of index fund or index Acronym Crash Recovery Since onsetPowerShares FTSE RAFI US 1500 Small-Mid PRFZ -44.6% 155.2% 6.3%iShares Russell 2000 Index IWM -41.5% 98.7% -1.7%Vanguard Small Cap Value Index VISVX -43.9% 116.2% -1.7%Vanguard Mid-Cap Value Index VMVIX -43.4% 107.7% -0.9%

Pow. FTSE RAFI US 1500 Small-Mid dvantage Crash Recovery Since onsetiShares Russell 2000 Index IWM -3.1% 56.5% 8.0%Vanguard Small Cap Value Index VISVX -0.6% 39.0% 8.0%Vanguard Mid-Cap Value Index VMVIX -1.2% 47.5% 7.2%

Volatility of daily returns over entire period (since 9/20/2006).PowerShares FTSE RAFI US 1500 Small-Mid PRFZ 2.14%iShares Russell 2000 Index IWM 2.10%Vanguard Small Cap Value Index VISVX 2.18%Vanguard Mid-Cap Value Index VMVIX 2.02%

Annualized returns

Annualized returns difference

21

Small Cap: Back Testing vs Actuals

The relative performance of the RAFI small cap was very different during the two periods. While in the 28 years of back testing, it excelled at besting the Russell 2000 in Bear markets while recording a smaller advantage in Bull markets; in the actual 3.5 years it faired poorly in the Crash of 2007. But, did extremely well in the Recovery of 2009.

Small U.S. Equities.

Back testing 1979 to 2007 periodBull Bear

Overall Markets MarketsRAFI U.S. Small 16.40% 33.10% -26.70%Russell 2000 12.90% 30.80% -31.90%Advantage 3.50% 2.30% 5.20%

Actual annualized results 9/20/2006 - 3/10/2010Bull Bear

Overall Markets MarketsRAFI U.S. Small 6.30% 155.17% -44.59%Russell 2000 (IWM) -1.73% 98.65% -41.48%Advantage 8.03% 56.51% -3.10%

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A couple of questions…

• Why did the RAFI U.S. 1000 Large Cap did poorly in the Crash of 2007?

• Why did the same fund do so much better than its counterparts in the Recovery of 2009?

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Explanation for poor performance in 2007 Crash: Growth vs Value…

• Large Value oriented index funds (including the RAFI funds) performed worse than traditional index funds during the Crash of 2007.

• Investigating the performance of a growth index fund vs a value index one may be interesting. Let’s look at Vanguard Growth Index (VIGRX) and Vanguard Value Index (VIVAX) that have long historical data going back to 1993.

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Growth vs Value – the Overall Picture

Growth (VIGRX) vs Value (VIVAX) (March 93 = 100)

0

100

200

300

400

500

600

Growth (VIGRX)

Value (VIVAX)

Growth Value

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The Dot.com bust

A Value index being less exposed to the hi-tech sector with high P/E ratio performed much better than a Growth index.

The Dot.com Bust: Growth (VIGRX) vs Value (VIVAX) (March 2000 = 100)

40

60

80

100

120

Growth

Value

Value

Growth

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The 2007 Credit Crash

The 2007 Credit Crash: Growth (VIGRX) vs Value (VIVAX) (October 2007 = 100)

40

60

80

100

120

Growth

Value

Value

Growth

Now, the Value index performed marginally worse. This credit crisis emerged from the financial sector (banks, insurance) that is more prevalent within a Value index including the RAFI US 1000 fund.

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Why did RAFI US 1000 do well in Recovery? Let’s look at sector allocations

VanguardRAFI US Russell Value

1000 1000 VIVAXAs of 12/31/2009 12/31/2009 9/30/2009

Financial services 27.2% 14.4% 25.7%Industrial materials 11.9% 11.0% 14.3%Consumer goods 11.6% 10.6% 8.4%Energy 9.1% 11.2% 16.7%Consumer services 9.1% 8.7% 3.3%Healthcare 5.8% 11.7% 10.3%Hardware 5.3% 11.0% 2.9%Business services 5.1% 4.2% 1.9%Telecommunication 4.8% 5.7% 5.7%Media 4.0% 2.8% 3.5%Utilities 3.3% 3.9% 7.0%Software 2.3% 4.8% 0.2%

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3 key sector allocation differences and performances during the recovery

Sectors in the Recovery (3/09/09 = 100)

100

125

150

175

200

225

250

275Energy

Healthcare

Financials

Healthcare

Energy

Financials

RAFI US 1000 is more heavily invested in Financials that did extremely well and less invested in Energy and Healthcare that did not do as well.

VanguardRAFI US Russell Value

Sector 1000 1000 VIVAXFinancials 27.2% 14.4% 25.7%Energy 9.1% 11.2% 16.7%Healthcare 5.8% 11.7% 10.3%

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Parting thoughts

• The RAFI 1000 Large cap performed poorly during the 2007 Credit Crisis because of its large exposure to Financials. This same exposure to Financials caused it to fare extremely well in the 2009 Recovery.

• Investing in the RAFI 1000 Large cap may entail chronic sector bets including being overweighed in Financials (low P/E sector) and underweighed in Hi tech (high P/E). Such a fund will do well in any hi-tech bubble burst, but not so well in any financial/credit crisis.

• The RAFI 1000 Large cap has a steadier sector allocation than its market cap counterparts because it prevents specific sectors from bubbling.

• So far, there seems to be more than just a Value orientation to such funds.

• A longer actual record will prove informative in fully assessing the relative performance of RAFI funds.

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Reference

Appell, Douglas. (2007). “Fundamental indexing superiority disputed.” Pensions & Investments. April 30, 2007. Available on Internet.

Arnott, Robert D. (2008). “The Fundamental Index.” John Wiley & Sons. Available at public libraries.

Arnott, Robert D. (2005). “Fundamental Indexation.” Financial Analyst Journal. March/April 2005. Available on Internet.

Kaplan, Paul. (2008). “Let’s Not All Become Fundamental Indexers Just Yet.” Morningstar Advisor. Spring 2008. Available on Internet.

Perold, Andre F. (2007). “Fundamentally Flawed Indexing.” Financial Analyst Journal. November/December 2007. Available on Internet.