Mutual Fund Flows:
A study of variables influencing investment
Ted Morrissey
November 20, 2001
QTM7010-61
Professor Sharpe
1
Introduction
Investment activities occur for many reasons. Companies invest their money into
assets which they hope will generate revenue. Individuals invest their money, hoping to
earn a return on their investment and obtain a more secure future. This analysis will
examine the flow of money into/out of US stock market mutual funds during the period
of 1984 to 1996. The objective of this case discussion is to examine what factors
determine the flow of money into and out of the US mutual funds.
Data
The Investment Company Institute tracked the money flowing into and out of US
stock market mutual funds on a monthly basis, from April 1984 until December 1996.
Other economic variables recorded during this period were: the stock market’s return %
on investment, interest rates on one-year certificates of deposits (CDs), US disposable per
capita income and gold prices/oz.. These economic variables were also recorded on a
monthly basis. (Sharpe, Ali and Potter, 2001)
Data Analysis
Scatter plot graphs were conducted to determine if any relationships appeared
present between these variables and mutual fund investment flows (Figures 1-4). Stock
market return % and disposable income appeared to have linear relationships with fund
flows. There appeared to be a curvilinear relationship between CD interest rates and fund
flows. A relationship between gold prices/oz. and fund flows was not visible during the
exploratory data analysis.
A correlation chart was constructed to determine the relationships, if any, which
these variables had with mutual fund investment flows (Table 1). Market return %, CD
interest rates and disposable income had p-values (less than a significance level of .05)
which pointed to a significant relationship between these variables and mutual fund
flows. Disposable income had the highest correlation value (.665) of these variables,
with CD interest rates having the second highest correlation value (.629) and market
return % in third (.204). Gold prices/oz. did not appear to have a significant relationship
with mutual fund flows. A potential area of concern was observed during the
examination of the correlation table. It appeared as though collinearity existed between
CD interest rates and disposable income, which in turn would lead to unstable
coefficients in the multiple regression model. Figure 5 suggested a negative linear
relationship between the two variables, indicating that when included in a multiple
regression equation together, they may cancel each other out, negating the other’s effect
on mutual fund flows.
Further analysis of these variables consisted of regression equation tables (Tables
2,3,4 &5). US disposable income (Table 4) had the highest coefficient of determination
(44.3), with a similar adjusted value (43.9). The relationship between fund flows and US
disposable income was as follows: For every dollar of US disposable income, 5.64
million dollars was invested into US stock market mutual funds (Table 4). CD interest
rates (Table 3) also had a high coefficient of determination in respect to its relationship
with fund flows (39.5). In examining the relationship of this equation’s residuals versus
fits (Figure 7), there appeared to be a pattern in the form of a curve. A linear equation
model did not sufficiently describe this relationship, for the residuals did not vary
2
randomly with each “x” value. This variable was initially hypothesized to have a
curvilinear relationship with fund flows. A transformation of this variable was conducted
(Table 8). The plot of residuals versus fits for this transformation (Figure 11) indicated
that this description satisfied an assumption necessary to describe the relationship
between fund flows and CD interest rate as curvilinear.
Multiple regression analysis (Table 6) for all the variables brought the coefficient
of determination to 57.7%, but collinearity was of concern, as well as the issue that the
CD interest rates variable, in original form, was not sufficient to provide description of its
relationship with fund flows (which also effected the plot of residuals vs. fits for this
equation: Figure 9). Market return % and disposable income (Table 7) provided a
coefficient of determination (48.6%) that was lower than other multiple regression
equations, yet more conservative in terms of collinearity. Therefore, this model was the
most reliable.
Due to previous data analysis (Mutual Fund Flows Case A: Sharpe, Ali and
Potter, 2001) in which the market return % provided different patterns on mutual fund
flows based upon time frame (i.e. 1984 – 1989 and 1990-1996), it was hypothesized that
different variables may have been either more or less significant, based upon the time
period that fund flows were analyzed. Therefore, regression analysis was conducted for
each time period (Tables 10-18).
From 1984 until 1989, the market return % appeared to be the most significant
factor in determining mutual fund flows, with the highest coefficient of determination
(38.7%; Table 11), as well as the highest correlation factor (.622; Table 10). An
interesting discovery made was that during this time period, an increase in disposable
income meant a decrease in money invested in mutual fund flows (Tables 10 & 12).
Once again, CD interest rates and disposable income appeared to be related (Table 10).
From 1984-1989, gold prices appeared to have a significant relationship with mutual fund
flows (Tables 10 & 13). In order to achieve a better coefficient of determination,
multiple regression analysis was conducted (Table 14). When all variables were taken
into consideration, gold price/oz. did not have as significant a relationship with fund flow
(Table 14).
These variables played a much different role in the mutual fund flows from 19901996 (Table 15). Disposable income had the highest correlation value (.655), while the
correlation of market return % to fund flows during this period (.282) was similar to that
of gold prices/oz. (.260). Collinearity between CD interest rates and disposable income
did not appear to be of concern for this period (Table 15; Figure 15). A multiple
regression equation involving all variables (Table 17) had a high coefficient of
determination (71.8), but once again, collinearity between the variables (disposable
income and gold prices/oz.) raised concern. To gain a more reliable model, gold prices
were excluded from the multiple regression analysis (Table 18), and a high coefficient of
determination was still obtained (68.2).
Conclusion
It makes sense that disposable income and market return % were the most
influential variables in fund flows. If people have money, they will want to watch it
grow, so they will invest it. If the market is providing a good return %, then they will
invest their money. Put these two variables together (Table 7), and one has money to
3
invest and a place to earn on investment. If other investment opportunities, such as CDs,
provide a better return on investment, then it would be wise to withdraw money out of the
mutual fund market and invest in a better return opportunity (Table 8). Another
relationship that would be interesting to examine would be that of the actual worth of a
mutual fund to the money flowing into it.
It was interesting to see the difference between the investment practices of two
different decades. The 1980s were more conservative, and the market return % had the
heaviest influence on money flowing into a mutual fund. The 1990s saw a booming
economy, and people were much more willing to invest their money in the market,
hoping to watch it grow. With the economy in its current state, it would be interesting to
examine mutual fund flows for this decade. Combined with the variable of a mutual
fund’s worth, a full analysis of mutual fund investment could be completed for the 1980s,
1990s and 2000s, providing a full realm of economic conditions and a better
understanding of when to invest in a mutual fund, and when to take that investment
elsewhere.
4
Bibliography:
McClave, James T., Benson, P. George and Sincich, Terry (2001),
Statistics for Business and Economics, 8th Edition. New Jersey: Prentice Hall.
Sharpe, N., Ali, A., and Potter, M.E. (2001), A Casebook for Business Statistics:
Laboratories for Decision Making. NY: John Wiley & sons, Inc.

All tables and graphs were constructed in the Minitab Program
5
Figure 1: Mutual Fund flows to Market Return % (Entire Sample)
Fund Flows ($millions)
30000
20000
10000
0
-10000
-20
-10
0
10
Market Return (%)
Figure 2: Mutual Fund Flows to CD Interest Rate (Entire Sample)
Fund Flows ($millions)
30000
20000
10000
0
-10000
2
7
12
CD_Interest_Rate
Figure 3: Mutual Fund Flows to US Disposable Income per Capita (Entire Sample)
Fund Flows ($millions)
30000
20000
10000
0
-10000
16000
17000
18000
19000
US Disposable Income per Capita
6
Figure 4: Mutual Fund Flows to Gold Price/oz. (Entire Sample)
Fund Flows ($millions)
30000
20000
10000
0
-10000
300
400
500
Gold price per oz.
Table 1: Correlation Chart (Entire Sample)
Fund Flows by:
Market Return %
CD Interest Rate
US Disposable Income
Gold Price/oz.
Market%
CD Rate
Dispos Inc.
0.204
0.011
-0.629
0.000
0.049
0.546
0.665
0.000
-0.006
0.941
-0.595
0.000
-0.071
0.386
-0.067
0.412
-0.005
0.955
0.188
0.020
Cell Contents: Correlation
P-Value
7
Figure 5: CD Interest Rate to US Disposable Income (Entire Sample)
CD_Interest_Rate
12
7
2
16000
17000
18000
19000
US_Disposable_Income_per_Capita
Table 2: Regression Analysis of Fund Flows by Market Return % (Entire Sample)
The regression equation is
Fund Flows ($millions) = 4589 + 310 Market Return (%)
Predictor
Constant
Market %
Coef
4589.1
310.2
S = 6145
StDev
523.3
121.1
R-Sq = 4.2%
T
8.77
2.56
P
0.000
0.011
R-Sq(adj) = 3.5%
Figure 6: Residuals of Market Return % v. Fits (Entire Sample)
Residuals Versus the Fitted Values
(response is Fund Flo)
Residual
20000
10000
0
-10000
0
5000
10000
Fitted Value
Table 3: Regression Analysis of Fund Flows by CD Interest Rate (Entire Sample)
The regression equation is
Fund Flows ($millions) = 16470 - 1761 CD Interest Rate
Predictor
Constant
CD Rate
S = 4882
Coef
16470
-1761.2
StDev
1219
177.3
R-Sq = 39.5%
T
13.51
-9.93
P
0.000
0.000
R-Sq(adj) = 39.1%
8
Figure 7: Residuals of CD Interest Rate vs. Fits (Entire Sample)
Residuals Versus the Fitted Values
(response is Fund Flo)
20000
Residual
10000
0
-10000
-5000
0
5000
10000
Fitted Value
Table 4: Regression Analysis of Fund Flows by US Disposable Income (Entire Sample)
The regression equation is
Fund Flows ($millions) = - 94972 + 5.64 US Disposable Income
Predictor
Constant
Disposable Income
S = 4686
Coef
-94972
5.6359
R-Sq = 44.3%
StDev
9140
0.5148
T
-10.39
10.95
P
0.000
0.000
R-Sq(adj) = 43.9%
Figure 8: Residuals of US Disposable Income vs. Fits (Entire Sample)
Residuals Versus the Fitted Values
(response is Fund Flo)
20000
Residual
10000
0
-10000
0
5000
10000
15000
Fitted Value
Table 5: Regression Analysis of Fund Flows by Gold Price/oz. (Entire Sample)
The regression equation is
9
Fund Flows ($millions) = 9384 - 11.6 Gold price/oz.
Predictor
Constant
Gold price
S = 6261
Coef
9384
-11.58
StDev
5058
13.32
R-Sq = 0.5%
T
1.86
-0.87
P
0.065
0.386
R-Sq(adj) = 0.0%
Table 6: Mutliple Regression Equation for Fund Flows (Entire Sample)
The regression equation is
Fund Flows ($millions) = - 55144 + 342 Market Return (%)
- 1054 CD Interest Rate + 3.75 US Disposable Income
Predictor
Constant
Market %
CD Rate
Disposable income
S = 4109
Coef
-55144
342.41
-1054.3
3.7513
R-Sq = 57.7%
StDev
10732
81.10
186.0
0.5617
T
-5.14
4.22
-5.67
6.68
P
0.000
0.000
0.000
0.000
R-Sq(adj) = 56.9%
Figure 9: Residuals vs. Fits of Multiple Regression Model (Entire Sample)
Residuals Versus the Fitted Values
(response is Fund Flo)
20000
Residual
10000
0
-10000
0
10000
Fitted Value
Table 7: Multiple Regression Model for Market Return & Disposable Income
(Entire Sample)
The regression equation is
Fund Flows ($millions) = - 95591 + 316 Market Return (%)
+ 5.65 US_Disposable_Income_per_Capita
Predictor
Constant
Market %
Disposable income
S = 4516
Coef
-95591
316.35
5.6466
R-Sq = 48.6%
StDev
8809
88.98
0.4960
T
-10.85
3.56
11.38
P
0.000
0.001
0.000
R-Sq(adj) = 47.9%
10
Figure 10: Residuals vs. Fits of Market Return & Disposable Income (Entire Sample)
Residuals Versus the Fitted Values
(response is Fund Flo)
20000
Residual
10000
0
-5000
0
5000
10000
15000
Fitted Value
Table 8: Regression Analysis for CD interest Rate (Adjusted Variable) (Entire Sample)
The regression equation is
Fund Flows ($millions) = 22899 - 3837 CD Interest Rate
+ 150 cd interest rate squared
Predictor
Constant
CD rate
CD rate squ.
Coef
22899
-3836.7
149.62
S = 4790
R-Sq = 42.2%
StDev
2730
811.1
57.11
T
8.39
-4.73
2.62
P
0.000
0.000
0.010
R-Sq(adj) = 41.4%
Figure 11: Residuals of Adjusted CD Rate vs. Fits (Entire Sample)
Residuals Versus the Fitted Values
(response is Fund Flo)
20000
Residual
10000
0
-10000
0
5000
10000
15000
Fitted Value
11
Table 9: Correlation Chart (Entire Data) with Adjusted Variable
Fund Flows by:
Market Return %
Market%
CD Rate
Dispos Inc.
0.204
0.011
CD Interest Rate
US Disposable Income
CD interest Rate Squared
-0.629
0.000
0.049
0.546
0.665
0.000
-0.006
0.941
-0.595
0.000
-0.579
0.000
0.038
0.639
0.977
0.000
Market%
CD Rate
-0.612
0.000
Table 10: Correlation Model (1984-1989)
Fund Flows by:
Market Return %
Dispos Inc.
0.622
0.000
CD Rate
-0.177
0.145
0.011
0.929
US Disposable Income
-0.290
0.016
0.019
0.874
-0.315
0.008
Gold price
-0.243
0.044
-0.121
0.322
-0.399
0.001
0.524
0.000
Table 11: Regression Analysis Fund Flows by Market Return % (1984-1989)
The regression equation is
Fund Flows ($millions) = 206 + 262 Market Return (%)
Predictor
Constant
Market %
S = 1630
Coef
205.9
261.50
StDev
206.2
40.23
R-Sq = 38.7%
T
1.00
6.50
P
0.322
0.000
R-Sq(adj) = 37.8%
12
Figure 12: Residuals of Market Return vs. Fits (1984-1989)
Residuals Versus the Fitted Values
(response is Fund Flo)
6000
Residual
4000
2000
0
-2000
-4000
-5000
0
5000
Fitted Value
Table 12: Regression Analysis of fund Flows by US Disposable Income (1984-1989)
The regression equation is
Fund Flows ($millions) = 20003 - 1.13 US Disposable Income
Predictor
Coef
Constant
20003
Disposable Income -1.1324
S = 1992
StDev
7825
0.4569
R-Sq = 8.4%
T
2.56
-2.48
P
0.013
0.016
R-Sq(adj) = 7.0%
Figure 13: Residuals of Disposable Income vs. Fits (1984-1989)
Residuals Versus the Fitted Values
(response is Fund Flo)
Residual
5000
0
-5000
0
500
1000
1500
Fitted Value
13
Table 13: Regression analysis of Fund Flows by Gold Price/oz.
(1984-1989)
The regression equation is
Fund Flows ($millions) = 4343 - 9.70 Gold _price_per_oz
Predictor
Constant
Gold price
S = 2019
Coef
4343
-9.701
StDev
1832
4.728
R-Sq = 5.9%
T
2.37
-2.05
P
0.021
0.044
R-Sq(adj) = 4.5%
Figure 14: Residuals of Gold Price/oz. Vs. Fits (1984-1989)
Residuals Versus the Fitted Values
(response is Fund Flo)
Residual
5000
0
-5000
0
500
1000
1500
Fitted Value
Table 14: Multiple Regression Model for Fund Flows (1984-1989)
The regression equation is
Fund Flows ($millions) = 28469 + 260 Market Return (%) - 407 CD
Interest Rate
- 1.35 US Disposable Income - 4.96 Gold _price_per_oz
Predictor
Coef
Constant
28469
Market R
259.57
CD Rate
-406.7
Disposable Income -1.3465
Gold price
-4.958
S = 1389
R-Sq = 57.5%
StDev
6182
34.71
106.7
0.3792
4.038
T
4.61
7.48
-3.81
-3.55
-1.23
P
0.000
0.000
0.000
0.001
0.224
R-Sq(adj) = 54.8%
14
Figure 14: Residuals of Multipe Regression Model vs. Fits (1984-1989)
Residuals Versus the Fitted Values
(response is Fund Flo)
5000
4000
Residual
3000
2000
1000
0
-1000
-2000
-3000
-5000
0
5000
Fitted Value
Table 15: Correlation Chart (1990-1996)
Fund Flows by:
Market %
0.282
0.009
Market%
CD Rate
-0.467
0.000
Dispos. Inc. 0.655
0.000
0.040
0.718
0.090
0.414
-0.041
0.708
Gold price
0.059
0.595
0.401
0.000
CD Rate
0.260
0.017
Dispos. Inc.
0.455
0.000
Figure 15: Matrix Plot of Fund Flows to Variables (1990-1996)
15
Scatter Plot Matrix
20395
Fund Flows ($millions)
4923
6.36125
Market Return (%)
-3.67425
6.985
CD_Interest_Rate
4.235
18768.5
US_Disposable_Income_per_Capita
18037.5
394.325
Gold _price_per_oz
350.475
49
23
20
39
5
67
- 3.
42
5
6 .3
61
25
4.2
35
6.9
85
18
03
7.5 68.5
7
18
35
75
25
0 .4 9 4 .3
3
Table 16: Regression Analysis of Fund flows by Disposable Income (1990-1996)
The regression equation is
Fund Flows ($millions) = - 165690 + 9.55 US Disposable Income
Predictor
Coef
Constant
-165690
Disposable Income 9.550
S = 4748
StDev
22241
1.218
R-Sq = 42.8%
T
-7.45
7.84
P
0.000
0.000
R-Sq(adj) = 42.1%
Figure 16: Residual of Disposable Income vs. Fits (1990-1996)
Residuals Versus the Fitted Values
(response is Fund Flo)
Residual
10000
0
-10000
2000
7000
12000
17000
Fitted Value
16
Table 17: Multiple Regression Analysis of Fund Flows (1990-1996)
The regression equation is
Fund Flows ($millions) = - 141998 + 458 Market Return (%)
- 2114 CD Interest Rate + 7.30 US Disposable Income
+ 74.7 Gold price/oz.
Predictor
Coef
Constant
-141998
Market R
457.9
CD Rate
-2113.8
Disposable Income 7.297
Gold _pr
74.74
S = 3400
StDev
16155
112.2
259.8
1.022
23.71
R-Sq = 71.8%
T
-8.79
4.08
-8.14
7.14
3.15
P
0.000
0.000
0.000
0.000
0.002
R-Sq(adj) = 70.3%
Figure 17: Residuals of Multiple Regression vs. Fits (1990-1996)
Residuals Versus the Fitted Values
(response is Fund Flo)
15000
Residual
10000
5000
0
-5000
0
10000
20000
Fitted Value
17
Table 18: Adjusted Multiple Regression Model (1990-1996)
The regression equation is
Fund Flows ($millions) = - 146414 + 458 Market Return (%)
- 1727 CD Interest Rate + 8.95 US Disposable Income
Predictor
Coef
Constant
-146414
Market R
457.6
CD Rate
-1727.3
Disposable Income 8.9542
S = 3585
StDev
16969
118.3
241.5
0.9246
R-Sq = 68.2%
T
-8.63
3.87
-7.15
9.68
P
0.000
0.000
0.000
0.000
R-Sq(adj) = 67.0%
Figure 18: Residuals of Adjusted Model and Fits (1990-1996)
Residuals Versus the Fitted Values
(response is Fund Flo)
Residual
10000
0
-10000
0
10000
20000
Fitted Value
18
19