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LIBRARY

OF THE

MASSACHUSETTS INSTITUTE

OF TECHNOLOGY

ALFRED P. SLOAN SCHOOL OF MANAGEMENT

FACTORS THAT AFFECT MUTUAL FUND GROWTH

256-67

F. B. Allderdice and D. E. Farrar

MASSACHUSETTS

INSTITUTE OF TECHNOLOGY

50 MEMORIAL DRIVE

CAMBRIDGE, MASSACHUSETTS 02139

FACTORS THAT AFFECT MUTUAL FUND GROWTH

F. B. Allderdice and D. E. Farrar

Sloan Fellow and Associate Professor of Finance, respectively, at the

Sloan School of Management, Massachusetts Institute of Technology.

WAY 01 ^'-^^^

M. I. T. UbWAKicb_

FACTORS THAT AFFECT MUTUAL FUND GROWTH

Introduction

The substantial growth of the mutual fund industry during the

last few years has attracted the attention of students of finance, eco-

nomics and public policy alike. Net assets managed by such funds have

grown from approximately $^50 million in 19'+0 to more than $38 billion

by June of 1966. During 1965 the mutual fund industry funneled some

$5.2 billion of new (primarily equity) funds into the capital markets;

more than twice the $2.3 billion in new equity raised by all non- financial

U. S. corporations during the year. Growth of the industry has not

been uniform, however, but has been concentrated among a relatively

small number of highly successful funds.

A portion of the industry's growth can be traced to apprecia-

tion in the market value of the securities under its management. Another

and far larger portion, however, represents net new investment by the

public in mutual fund shares. Reasons for the latter source of growth,

and especially for its uneven distribution among the industry's parti-

cipants, are examined in the present study.

Methodology

Broadly speaking, any of a wide variety of forces may be ex-

pected to have an impact on mutual fund growth. Some of these, such

Securities and Exchange Commission, Public Policy Implication of

Investment Company Growth, 89th Congress^ Second Session, House Report

#2337, U. S. Government Printing Office, Washington, D. C, I966.

â– x-x-

Ibid .

Ibid.

as growth in gross national product, stock prices, and disposable

personal income may be expected to be largely time- related phenomena,

and to bear relatively uniformly on all members of the industry. Others,

such as fund performance, sales effort, and size may be expected to

vary widely across funds in the industry. Cross-section analyses,

rather than the analysis of economic aggregates over time, are required

to detect the latter source of variation in mutual fund growth. By

using successive cross sections over time, however, an effort also is

made to control at least roughly for important, time-dependent phenomena.

Simple correlations between net, new money inflows and any of

a broad range of potential explanatory variables can be helpful in iso-

lating those factors that, in a statistical sense, appear most closely

related to mutual fund growth. Care must be taken, however, to avoid

confusing statistical association with causality. There is, clearly,

no fool-proof guarantee that such confusion may be avoided. By simul-

taneously examining the relationship between a dependent variable (such

as net new investment in mutual fund shares) and as broad a range as

possible of potential explanatory variables (such as performance, sales

effort and general economic growth), the danger of spurious association

can, at least, be reduced. Accordingly, a least squares regression

model that simultaneously measures partial relationships between depen-

dent and independent variables is employed in the present study.

Defining:

_Y as a vector of observations on net new money, the

variable whose behavior is to be explained.

X as a matrix of observations on a set of explanatory

variables thought to affect the flow of new funds

into an investment company,

_b as a vector of structural parameters that relates

expected values of _Y to X, and

U as a vector of stochastic error terms,

the basic relationship hypothesized can be summarized as

Y = X Jb + U.

Measures of estimation efficiency can be summarized through

numerous statistics. A common measure of an equation's explanatory

2

power, R , may be interpreted as the percentage of a dependent variable's

total variation that can be explained through a given set of explanatory

variables. Similarly, each independent variable's contribution to an

equation's explanatory power often is measured by the familiar t- ratio,

t = b/a^,

where b is the variable's regression coefficient, and ct, is the coeffi-

2

cient's sample standard deviation. Measures of R greater than .10

or .20 are sufficiently large to suggest the presence of significant

(non-zero) relationships between Y and X over cross sectional samples

such as those encountered here; while t-ratios greater than 1.0 or 2.0

generally are interpreted as identifying meaningful (non-zero) partial

relationships between dependent and independent variables. Squared

multiple correlation coefficients, regression coefficients, and t-

ratios, accordingly, are reported in the analyses that follow.

Scope of the Study

This study's â€” indeed any study's - scope can be defined

along at least three dimensions: its units of observation (in this

case mutual funds), the time period over which observations are col-

lected, and the variables by which each observation is charaterized.

The present study employs observations on I69 mutual funds,

approximately U5^ of the funds in existence during June, I966. A

better idea of the sample's significance in terms of the industry's

overall size, however, can be gained by noting that the companies

covered received some $3.2 billion in net new investment during 1965?

more than 60'^^ of the industry's new money during the year. In terms

of total assets managed, this sample contained $30-2 billion at the

end of 1965, or 79^ of the industry's total assets. Similarly, com-

panies covered by the present sample contain 5*9 million shareholder

accounts, or 88^ of the industry's accounts. By any measure, therefore,

the sample covers a significant portion of the investment company

industry.

Data is collected on each fund over a three-year period of

time, from 1963-65. Data limitations, especially regarding portfolio

turnover, constitute the primary constraint on the sample's coverage.

Data elements by which each fund and year are characterized

include percentage increases in gross national product, total personal

income, and Standard and Poor's 5OO Stock Security Price Index, plus

9 measures specific to each fund, summarized in Table I. Most of the

variables in the Table are self-explanatory. Total net assets and

numbers of shareholders constitute rough indications of a fund's size.

- 5 -

Table I

RAW DATA

Factor Description

Symbol

Total Wet Assets

TA

Net Asset Value

NAV

Portfolio Turnover Ratio

pro

Dividends

D

Capital Gains

CG

Shareholders

s

Expense Ratio

ER

Sales Charge

SO

Fund Objective

OBJ

- 6 -

Net asset value, dividends and capital gains distributions provide

the per-share data out of which various performance measures are formed.

Expense ratio is defined as the ratio of expenses actually paid by the

fund, as a per cent of total net assets. It includes management fees,

the salaries of fund employees, office expenses and other expenses not

provided by the fund's advisor. Expense ratio, however, does not in-

clude services provided to the fund or its advisor in return for broker-

age. Sales charge is defined as the maximian load, applicable to a

fund's smallest (non- contractual plan) investors. Portfolio turnover

is calculated by dividing the lesser of sales or purchases, excluding

government securities and other short-term obligations, by the average

of total net assets over a year; and. is the same as that reported to the

Securities and Exchange Commission on Form N-IR. Fund objective is

that adopted by Arthur Weisenburger and Company.

From the raw data described above, a series of working data

elements is developed for each observation, and summarized in Table II.

Certain variables - specifically, total gain, dividend yield, capital

gains distribution, unrealized gain, expense ratio and portfolio turn-

over - are lagged by one year to more closely approximate the informa-

tion available to an investor at the time of a fund purchase decision.

A complete set of raw and working data elements is summarized for a

single fund in Tfeble III.

Securities and Exchange Commission, Form N-IR, Annual Report of Registered

Management Investment Companies under the Investment Company Act of 19^0

and the Securities and Exchange Act of 193^, January 25, 1965; item 1.25(a).

Wessman, L., Editor, Investment Companies , Arthur Weisenburger and

Company, New York, I966.

- 7 -

Table II

Working Data

Variable Symbol

Net New Investment, as per cent of

total assets NNI^

Net New Investment, per cent, lagged

one year NNI^, ,

Percentage growth in Standard

and Poor 500 Stock Index SP

Dividend Yield, lagged one year ^\-l

Capital Gain Yield, lagged one year "^"^^-l

Unrealized Gain, lagged one year ^*^t-l

Total Gain, lagged one year '^t-1

Portfolio Turnover, lagged one year PTO, _,

Sales Charge SC

Expense Ratio, lagged one year ^^t-l

Total Assets, lagged one year

(in logarithms) "^t-l

Fund Objective OBJ

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- 9 -

Some of the variables described above may require further

comment. Although it would be desirable to characterize each fund and

year by a complete spectriom of the variables that affect net new money

inflows during the year, it must be recognized that any characteriza-

tion will, in fact, be incomplete. To reduce the danger of introducing

spurious relationships between measured variables and other character-

istics that should be, but are not included in an independent variable

set, an effort is made to proxy excluded characteristics (such as the

size and efficiency of a fund's sales force), by including in each

equation a lagged value of its dependent variable. The rationale

underlying such a variable's use may be traced to a belief that factors

excluded from a given year's set of independent variables are likely

to have been operative during the preceding year, as well. Analyses

of the relationships reported below, excluding this effect, indicate

the presence of serial correlation between observed residuals, and

*

accordingly, support such a variable's use.

A second broad class of measurement problems concerns the

quantification of variables, such as a fund's objective, that do not

lend themselves to continuous measurement. A fund either is a growth

fund or is not; or a maximum performance fund, or not; or an income

fund, or not, etc. To the ext.ent that labels possess sales appeal, an

ability to measure the appeal inherent in a fund's objective may be

desirable. Accordingly, a set of dummy variables is defined for each

of k Weinsenburger objectives: maximuiri gain, growth, growth- income.

For further discussion of this problem, see L. M. Koyck, Distributed Lags

and Investment Analysis , North Holland Publishing Company, Amsterdam, 195^;

and L. R. Klein"^ "The Estimation of Distributed Lags," Econometrica , 26,

^, 1958Â«

- 10 -

and income. Should a fund fall into one of these categories the vari-

able corresponding to the category assumes a value of 1.0, if not its

value is 0. Each fund, of course, falls into one and only one category.

To avoid singularity, of course, one objective (in this case the Growth-

Income- Stability amalgam; must be excluded from the set. Coefficient

estimates for included objectives, accordingly, are interpreted as

the difference between a given objective's sales appeal and that enjoyed

by a Growth- Income- Stability investment objective.

An effort also is made to reduce the enormous variation in

new money attributable only to fund size., by transforming total asset

measures to logarithms, and standardizing each equation's dependent

variable, net new investment, to a percentage of the fund's beginning-

of-year total assets.

Analyses

As indicated earlier, the study is designed to investigate

the relationship between percentage growth in investment company assets

through net new investment, and a wide variety of both general economic

conditions and specific fund characteristics. Broadly speaking, five

general categories of factors are investigated: economic conditions,

sales effort, fund performance, fund size, and fund objective. Initial

exploratory analyses eliminate percentage growth in such general economic

characteristics as gross national product and total personal income

See D. Suits, "Use of Dummy Variables in Regression Equations, " Journal

of the American Statistical Association, 52, 28, 1957.

11

from further consideration. An example of the type of finding uncovered

is summarized in Table IV, where all k68 usable observations on l69 mutual

funds are pooled in a single regression model. Four separate equations,

each employing a different measure of performance (total gain, dividend

yield, capital gains yield, and unrealized gain) are summarized. Regression

2

equations, t-ratios, R corrected for degrees of freedom, and sample size

are reported for each equation.

Each equation's statistical significance is considerable. Differ-

2

ences in R are trivial, leading to no preference for one equation, and

therefore one measure of performance, over another. Comparisons between

t-ratios for different parameters, however, highlight the overwhelming

importance of lagged net new investment as an explanatory variable; sug-

gesting the existence of both relevant, excluded, independent variables

and considerable stability in the forces that determine the distribution over

time of new money inflows between companies in the industry. The lagged

variable ' s considerable explanatory power also tends to reduce confidence

in the validity of equations (over this set of data) that do not contain

such a variable.

Portfolio turnover, fund size, expense ratio, and fund performance

also appear to be highly signficant determinants of the distribution of

net new investment between competing funds. Certain fund objectives such

as growth and grovrth- income also appear to have at least moderate investor

appeal. Market action, measured by percentage change in the Standard and

Thirty- nine missing data elements, primarily portfolio turnover, account

for the discreptancy between k68 useable observations and 3 x l69 = 507

expected data points for 169 funds over a three-year period of time.

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OF THE

MASSACHUSETTS INSTITUTE

OF TECHNOLOGY

ALFRED P. SLOAN SCHOOL OF MANAGEMENT

FACTORS THAT AFFECT MUTUAL FUND GROWTH

256-67

F. B. Allderdice and D. E. Farrar

MASSACHUSETTS

INSTITUTE OF TECHNOLOGY

50 MEMORIAL DRIVE

CAMBRIDGE, MASSACHUSETTS 02139

FACTORS THAT AFFECT MUTUAL FUND GROWTH

F. B. Allderdice and D. E. Farrar

Sloan Fellow and Associate Professor of Finance, respectively, at the

Sloan School of Management, Massachusetts Institute of Technology.

WAY 01 ^'-^^^

M. I. T. UbWAKicb_

FACTORS THAT AFFECT MUTUAL FUND GROWTH

Introduction

The substantial growth of the mutual fund industry during the

last few years has attracted the attention of students of finance, eco-

nomics and public policy alike. Net assets managed by such funds have

grown from approximately $^50 million in 19'+0 to more than $38 billion

by June of 1966. During 1965 the mutual fund industry funneled some

$5.2 billion of new (primarily equity) funds into the capital markets;

more than twice the $2.3 billion in new equity raised by all non- financial

U. S. corporations during the year. Growth of the industry has not

been uniform, however, but has been concentrated among a relatively

small number of highly successful funds.

A portion of the industry's growth can be traced to apprecia-

tion in the market value of the securities under its management. Another

and far larger portion, however, represents net new investment by the

public in mutual fund shares. Reasons for the latter source of growth,

and especially for its uneven distribution among the industry's parti-

cipants, are examined in the present study.

Methodology

Broadly speaking, any of a wide variety of forces may be ex-

pected to have an impact on mutual fund growth. Some of these, such

Securities and Exchange Commission, Public Policy Implication of

Investment Company Growth, 89th Congress^ Second Session, House Report

#2337, U. S. Government Printing Office, Washington, D. C, I966.

â– x-x-

Ibid .

Ibid.

as growth in gross national product, stock prices, and disposable

personal income may be expected to be largely time- related phenomena,

and to bear relatively uniformly on all members of the industry. Others,

such as fund performance, sales effort, and size may be expected to

vary widely across funds in the industry. Cross-section analyses,

rather than the analysis of economic aggregates over time, are required

to detect the latter source of variation in mutual fund growth. By

using successive cross sections over time, however, an effort also is

made to control at least roughly for important, time-dependent phenomena.

Simple correlations between net, new money inflows and any of

a broad range of potential explanatory variables can be helpful in iso-

lating those factors that, in a statistical sense, appear most closely

related to mutual fund growth. Care must be taken, however, to avoid

confusing statistical association with causality. There is, clearly,

no fool-proof guarantee that such confusion may be avoided. By simul-

taneously examining the relationship between a dependent variable (such

as net new investment in mutual fund shares) and as broad a range as

possible of potential explanatory variables (such as performance, sales

effort and general economic growth), the danger of spurious association

can, at least, be reduced. Accordingly, a least squares regression

model that simultaneously measures partial relationships between depen-

dent and independent variables is employed in the present study.

Defining:

_Y as a vector of observations on net new money, the

variable whose behavior is to be explained.

X as a matrix of observations on a set of explanatory

variables thought to affect the flow of new funds

into an investment company,

_b as a vector of structural parameters that relates

expected values of _Y to X, and

U as a vector of stochastic error terms,

the basic relationship hypothesized can be summarized as

Y = X Jb + U.

Measures of estimation efficiency can be summarized through

numerous statistics. A common measure of an equation's explanatory

2

power, R , may be interpreted as the percentage of a dependent variable's

total variation that can be explained through a given set of explanatory

variables. Similarly, each independent variable's contribution to an

equation's explanatory power often is measured by the familiar t- ratio,

t = b/a^,

where b is the variable's regression coefficient, and ct, is the coeffi-

2

cient's sample standard deviation. Measures of R greater than .10

or .20 are sufficiently large to suggest the presence of significant

(non-zero) relationships between Y and X over cross sectional samples

such as those encountered here; while t-ratios greater than 1.0 or 2.0

generally are interpreted as identifying meaningful (non-zero) partial

relationships between dependent and independent variables. Squared

multiple correlation coefficients, regression coefficients, and t-

ratios, accordingly, are reported in the analyses that follow.

Scope of the Study

This study's â€” indeed any study's - scope can be defined

along at least three dimensions: its units of observation (in this

case mutual funds), the time period over which observations are col-

lected, and the variables by which each observation is charaterized.

The present study employs observations on I69 mutual funds,

approximately U5^ of the funds in existence during June, I966. A

better idea of the sample's significance in terms of the industry's

overall size, however, can be gained by noting that the companies

covered received some $3.2 billion in net new investment during 1965?

more than 60'^^ of the industry's new money during the year. In terms

of total assets managed, this sample contained $30-2 billion at the

end of 1965, or 79^ of the industry's total assets. Similarly, com-

panies covered by the present sample contain 5*9 million shareholder

accounts, or 88^ of the industry's accounts. By any measure, therefore,

the sample covers a significant portion of the investment company

industry.

Data is collected on each fund over a three-year period of

time, from 1963-65. Data limitations, especially regarding portfolio

turnover, constitute the primary constraint on the sample's coverage.

Data elements by which each fund and year are characterized

include percentage increases in gross national product, total personal

income, and Standard and Poor's 5OO Stock Security Price Index, plus

9 measures specific to each fund, summarized in Table I. Most of the

variables in the Table are self-explanatory. Total net assets and

numbers of shareholders constitute rough indications of a fund's size.

- 5 -

Table I

RAW DATA

Factor Description

Symbol

Total Wet Assets

TA

Net Asset Value

NAV

Portfolio Turnover Ratio

pro

Dividends

D

Capital Gains

CG

Shareholders

s

Expense Ratio

ER

Sales Charge

SO

Fund Objective

OBJ

- 6 -

Net asset value, dividends and capital gains distributions provide

the per-share data out of which various performance measures are formed.

Expense ratio is defined as the ratio of expenses actually paid by the

fund, as a per cent of total net assets. It includes management fees,

the salaries of fund employees, office expenses and other expenses not

provided by the fund's advisor. Expense ratio, however, does not in-

clude services provided to the fund or its advisor in return for broker-

age. Sales charge is defined as the maximian load, applicable to a

fund's smallest (non- contractual plan) investors. Portfolio turnover

is calculated by dividing the lesser of sales or purchases, excluding

government securities and other short-term obligations, by the average

of total net assets over a year; and. is the same as that reported to the

Securities and Exchange Commission on Form N-IR. Fund objective is

that adopted by Arthur Weisenburger and Company.

From the raw data described above, a series of working data

elements is developed for each observation, and summarized in Table II.

Certain variables - specifically, total gain, dividend yield, capital

gains distribution, unrealized gain, expense ratio and portfolio turn-

over - are lagged by one year to more closely approximate the informa-

tion available to an investor at the time of a fund purchase decision.

A complete set of raw and working data elements is summarized for a

single fund in Tfeble III.

Securities and Exchange Commission, Form N-IR, Annual Report of Registered

Management Investment Companies under the Investment Company Act of 19^0

and the Securities and Exchange Act of 193^, January 25, 1965; item 1.25(a).

Wessman, L., Editor, Investment Companies , Arthur Weisenburger and

Company, New York, I966.

- 7 -

Table II

Working Data

Variable Symbol

Net New Investment, as per cent of

total assets NNI^

Net New Investment, per cent, lagged

one year NNI^, ,

Percentage growth in Standard

and Poor 500 Stock Index SP

Dividend Yield, lagged one year ^\-l

Capital Gain Yield, lagged one year "^"^^-l

Unrealized Gain, lagged one year ^*^t-l

Total Gain, lagged one year '^t-1

Portfolio Turnover, lagged one year PTO, _,

Sales Charge SC

Expense Ratio, lagged one year ^^t-l

Total Assets, lagged one year

(in logarithms) "^t-l

Fund Objective OBJ

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- 9 -

Some of the variables described above may require further

comment. Although it would be desirable to characterize each fund and

year by a complete spectriom of the variables that affect net new money

inflows during the year, it must be recognized that any characteriza-

tion will, in fact, be incomplete. To reduce the danger of introducing

spurious relationships between measured variables and other character-

istics that should be, but are not included in an independent variable

set, an effort is made to proxy excluded characteristics (such as the

size and efficiency of a fund's sales force), by including in each

equation a lagged value of its dependent variable. The rationale

underlying such a variable's use may be traced to a belief that factors

excluded from a given year's set of independent variables are likely

to have been operative during the preceding year, as well. Analyses

of the relationships reported below, excluding this effect, indicate

the presence of serial correlation between observed residuals, and

*

accordingly, support such a variable's use.

A second broad class of measurement problems concerns the

quantification of variables, such as a fund's objective, that do not

lend themselves to continuous measurement. A fund either is a growth

fund or is not; or a maximum performance fund, or not; or an income

fund, or not, etc. To the ext.ent that labels possess sales appeal, an

ability to measure the appeal inherent in a fund's objective may be

desirable. Accordingly, a set of dummy variables is defined for each

of k Weinsenburger objectives: maximuiri gain, growth, growth- income.

For further discussion of this problem, see L. M. Koyck, Distributed Lags

and Investment Analysis , North Holland Publishing Company, Amsterdam, 195^;

and L. R. Klein"^ "The Estimation of Distributed Lags," Econometrica , 26,

^, 1958Â«

- 10 -

and income. Should a fund fall into one of these categories the vari-

able corresponding to the category assumes a value of 1.0, if not its

value is 0. Each fund, of course, falls into one and only one category.

To avoid singularity, of course, one objective (in this case the Growth-

Income- Stability amalgam; must be excluded from the set. Coefficient

estimates for included objectives, accordingly, are interpreted as

the difference between a given objective's sales appeal and that enjoyed

by a Growth- Income- Stability investment objective.

An effort also is made to reduce the enormous variation in

new money attributable only to fund size., by transforming total asset

measures to logarithms, and standardizing each equation's dependent

variable, net new investment, to a percentage of the fund's beginning-

of-year total assets.

Analyses

As indicated earlier, the study is designed to investigate

the relationship between percentage growth in investment company assets

through net new investment, and a wide variety of both general economic

conditions and specific fund characteristics. Broadly speaking, five

general categories of factors are investigated: economic conditions,

sales effort, fund performance, fund size, and fund objective. Initial

exploratory analyses eliminate percentage growth in such general economic

characteristics as gross national product and total personal income

See D. Suits, "Use of Dummy Variables in Regression Equations, " Journal

of the American Statistical Association, 52, 28, 1957.

11

from further consideration. An example of the type of finding uncovered

is summarized in Table IV, where all k68 usable observations on l69 mutual

funds are pooled in a single regression model. Four separate equations,

each employing a different measure of performance (total gain, dividend

yield, capital gains yield, and unrealized gain) are summarized. Regression

2

equations, t-ratios, R corrected for degrees of freedom, and sample size

are reported for each equation.

Each equation's statistical significance is considerable. Differ-

2

ences in R are trivial, leading to no preference for one equation, and

therefore one measure of performance, over another. Comparisons between

t-ratios for different parameters, however, highlight the overwhelming

importance of lagged net new investment as an explanatory variable; sug-

gesting the existence of both relevant, excluded, independent variables

and considerable stability in the forces that determine the distribution over

time of new money inflows between companies in the industry. The lagged

variable ' s considerable explanatory power also tends to reduce confidence

in the validity of equations (over this set of data) that do not contain

such a variable.

Portfolio turnover, fund size, expense ratio, and fund performance

also appear to be highly signficant determinants of the distribution of

net new investment between competing funds. Certain fund objectives such

as growth and grovrth- income also appear to have at least moderate investor

appeal. Market action, measured by percentage change in the Standard and

Thirty- nine missing data elements, primarily portfolio turnover, account

for the discreptancy between k68 useable observations and 3 x l69 = 507

expected data points for 169 funds over a three-year period of time.

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