Another Puzzle: The Growth In Another Puzzle: The Growth In Actively Managed Mutual Actively Managed Mutual

FundsFunds

Professor Martin J. GruberProfessor Martin J. Gruber

2

Bibliography

• Modern Portfolio Analysis and Investment AnalysisEdwin J. Elton, Martin J. Gruber, Stephen Brown and William Goetzmann, John Wiley and Sons, Sixth Edition, 2003

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• The Performance of Publicly Offered Commodity FundsEdwin J. Elton, Martin J. Gruber and Joel C. Rentzler, Financial Analysts Journal, July-August 1990

• New Public Offerings, Information, and Investor Rationality: The Case of Publicly Offered Commodity FundsEdwin J. Elton, Martin J. Gruber and Joel C. Rentzler, Journal of Business, January 1989

• Professionally Managed Publicly Traded Commodity FundsEdwin J. Elton, Martin J. Gruber and Joel C. Rentzler, Journal of Business, April 1987

4

• Efficiency With Costly Information: A Reinterpretation of Evidence From Managed PortfoliosEdwin J. Elton, Martin J. Gruber, Sanjiv Das and Matthew Hlavka, The Review of Financial Studies, 1993

• The Performance of Bond Mutual FundsChristopher R. Blake, Edwin J. Elton and Martin J. Gruber, Journal of Business, July 1993

• Fundamental Economic Variables, Expected Returns, and Bond Fund PerformanceEdwin J. Elton, Martin J. Gruber and Christopher R. Blake, Journal of Finance, September 1995

• Survivorship Bias and Mutual Fund PerformanceEdwin J. Elton, Martin J. Gruber and Christopher R. Blake, The Review of Financial Studies, Winter 1996

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• The Persistence of Risk-adjusted Mutual Fund PerformanceEdwin J. Elton, Martin J. Gruber and Christopher R. Blake, Journal of Business, April 1996

• Another Puzzle: the Growth in Actively Managed Mutual FundsMartin J. Gruber, Journal of Finance, June 1996

• Do Investors Care About Sentiment?Edwin J. Elton, Martin J. Gruber and Jeff Busse, Journal of Business, October 1998

• Common Factors in Mutual Funds ReturnsEdwin J. Elton, Martin J. Gruber and Christopher R. Blake, European Finance Review, November 1999

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• Spiders: Where Are the Bugs?Edwin J. Elton, Martin J. Gruber George Comer and Kai Li, Journal of Business, June 2002

• A First Look at the Accuracy of the CRSP Mutual Fund Database and Comparison With Morningstar Data Edwin J. Elton, Martin J. Gruber and Christopher R. Blake, Journal of Finance, December 2001

• Incentive Fees and Mutual FundsEdwin J. Elton, Martin J. Gruber and Christopher R. Blake, Journal of Finance, April 2003

• Are Investors Rational: Choices Among Index FundsEdwin J. Elton, Martin J. Gruber and Jeff Busse, Journal of Finance, February 2004

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U.S. Mutual Funds by Type (market value)

Fixed Income16%

Money Market24%

Equity60%

Based on 1/30/05 Assets Total $8.00 Trillion

8

19701973

19761979

19821985

19881991

19941997

20002003

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

Bill

ions

of U

.S. D

olla

rGrowth of Mutual Funds by Type

Bond & Income Money Market Equity

9

10

Growth of U.S. Mutual Funds by Type(Market Value)

7413411912412053200363922995112522722002

80004800130019002004

697537659252285200170194363811184520006843442380816121999446826857241059199728201269798753199510672463234981990496117135244198513444147619804738541975

TotalEquityBond & Income

Money MarketYear

5 year avg. 8.7% 10.0% 1.6% 3.2%

11

Growth of U.S. Mutual Funds by Type(Market Value)

7413411912412053200363922995112522722002

80004800130019002004

697537659252285200170194363811184520006843442380816121999446826857241059199728201269798753199510672463234981990496117135244198513444147619804738541975

TotalEquityBond & Income

Money MarketYear

5 year avg. 8.7% 10.0% 1.6% 3.2%

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Percent of U.S. Households Owning Mutual Funds

6%

11% 12%

20%

24%25%

27%

31%

37%

44%

49%

52%50%

48% 48%

0%

10%

20%

30%

40%

50%

60%

1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2001 2002 2003 2004

Inside employees sponsored plans 32.5%Outside employee sponsored plans 35.1%

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• Average Performance

• Index Funds

• Closed End Funds

• The Persistence Of Performance

• Expenses

• What Accounts For Cash Flow

• How Well Do Investors Do

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• Customer Services – including record keeping, the ability to move money around among funds, and daily valuation

• Low Transaction Costs

• Low Cost Diversification

• Professional Management (security diversification)

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Open end mutual funds sell at the net asset value.

If “good management” exists, a fund which has superior management will sell at net asset vale. If “bad management” exists, a fund which has inferior management will sell at net asset value.

Management is not pricedManagement is not priced.

Counter argument.

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iFMMiiFi eRRRR +−+=− )(βα

Ri

RF

αi

M

βi

( ) ( )( ) ( ) iFBBiVGGi

LSSiFMMiiFi

eRRRRRRRRRR

+−+−+−+−+=−

ββββα

iMi RR α=−

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Return Per Year

11.1%10.9%18.4%1996-2000

24.4%24.5%14.8%1991-95

1.0%0.6%13.1%1986-90

19.2%18.8%14.7%1981-85

36.1%37.4%13.9%1976-80

0.8%0.6%3.2%1971-75

Manager CManager BManager AYears

18

Random+

+

+

+

+

+=

Index BondonReturn

Excess

Index Bond to

ySensitivit

Index ValueMinusGrowth

onReturn

Growth to

ySensitivit

Index LargeMinus SmallonReturn

Size toySensitivit

P&Son Return

Excess

P&S toySensitivit

ConstantFund

OnReturn Excess

Return Based Style Analysis

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Average Performance

0.7100.929-4.200-5.184Non-surviving

0.8100.963-1.560-1.944Open End

ρβMαRi-RM

0.095

0.090

βB

0.290

0.229

βG

0.8010.3910.781-2.748Non-surviving

0.8860.3140.850-0.648Open End

ρ2βSβMα

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Average Performance

0.8100.978-1.572-1.848Growth

0.8400.829-0.876-2.556Growth and Income

0.7801.073-2.184-1.500Maximum Capital Gains

ρβMαRi-RM

0.8860.0770.2640.3060.860-0.540Growth

0.108

0.092

βB

-0.031

0.433

βG

0.8780.1750.796-1.056Growth and Income

0.8970.4660.889-0.420Maximum Capital Gains

ρ2βSβMα

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Index Funds

1985 3 S&P Funds 1.24%1 Small Stock 0.88%No Growth, Value, or Bond Fund

1994 Over 100 Index Funds44 S&P Funds 0.19-1.35%

Good Tracking (R2 = .997)Low Cost

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Closed end funds sell at an average discount of 10%

Investors are only willing to pay 90 cents for $1 in assets under management

Why will they pay $1 for $1 under management in open end?

Management is not priced in open end fundsManagement is not priced in open end funds

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Ranked By Previous 1-Year Alpha

3.408*Top – Bottom 0.891* *Spearman Rank

0.816Top 10-0.15690.06080.5287

-0.4686-0.2405-0.5284-0.4443-1.0802-2.592Bottom 1

1 year alphaDecile

* Significant at 1% level** Significant at 5% level

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Ranked By Previous Expense Ratio

1.620*Low – High 0.552Spearman Rank -0.096Low-0.21690.15680.56470.1206-0.0245-0.0124-0.8283-0.9482-1.716High

1 year alphaDecile

* Significant at 1% level

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Realized Annual Three Year Four Index Alpha Predicted By 3 Year Alpha

3.564*Top – Bottom 0.903*Spearman Rank 0.876Top 100.69690.06080.1327-0.3726-0.1565-0.6844-0.3123-0.5282-2.676Bottom 1

3 year alphaDecile

* Significant at 1% level

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Realized Annual Three Year Four Index Alpha Predicted By Expense Ratio

1.620* Low – High 0.552Spearman Rank -0.096Low-0.21690.15680.56470.1206-0.0245-0.0124-0.8283-0.9482-1.716High

Exp Ratio†Decile

† Expense ratios are reported from high to low* Significant at 1% level

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Expense Ratios for Deciles Formed on the Basis of Four Index Alphas:

1.063

1.0481.0371.0530.9980.9701.0290.9841.0311.0681.413t+2

1.078

1.0581.0551.0801.0070.9671.049.09981.0641.0841.415t+3

1.039

1.0421.0271.0350.9730.9550.9710.9601.0181.0501.357

t

1.0891.049Mean

1.0571.052101.0281.04391.1191.01681.0500.98670.9590.96261.0640.99451.0240.96841.1151.00731.0721.06121.4001.4051t+4t+1Decile (t)

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Annual Cash Flows for Deciles Formed on the Basis of Four Index Alphas in the Year Following Formation

1.620*Top – Bottom1.00*Spearman Rank 29.01012.896.684.57-2.46-3.75-5.04-5.13-11.22-15.41

% Change in Cash FlowDecile

* Significant at 1% level

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Annual Realized Cash Flow Weighted Alpha

0.0660

0.0984

0.0396

3 Years

0.2652

0.2244

0.2892

1Year

0.5280

0.8544

0.3516

1Quarter

Holding Period

Negative

Weighted Avg.

Positive

Return on Cash Flows

Buy at End of Quarter

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- 0. 60%

- 0. 40%

- 0. 20%

0. 00%

0. 20%

0. 40%

0. 60%

0. 80%

0 6 12 18 24 30 36

Months

Ann

ual A

vera

ge A

lpha

L. Zheng

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1. Index funds outperform actively managed funds of the same riskActive funds 65b.p. below indexes.Charge fee of 130 b.p.Bring information worth 65b.p. but charge 130b.p.

2. Funds that charge higher fees tend to do worse that funds that charge lower fees

3. Funds that perform well have a slight tendency to continue to perform wellFunds that perform really badly tend to continue to perform really badly

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4. Investors seem to be aware of this.Funds that perform well have higher subsequent cash flows.Funds that perform badly have high cash out flows.

5. The result of this is that new investment and disinvestment earns a risk adjusted return slightly above that which would be earned on a set of index funds with the same risk.

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A. A sophisticated clientele.

B. A disadvantaged clientele.

1. Unsophisticated investors

2. Institutionally disadvantaged investors

3. Tax disadvantaged investors