Journal of Financial Risk Management
2012. Vol.1, No.3, 33-37
Published Online September 2012 in SciRes (http://www.SciRP.org/journal/jfrm) http://dx.doi.org/10.4236/jfrm.2012.13006
Portfolio Risk Management Implications of Mutual Fund
Investment Objective Classifications
Larry J. Prather
Department of Accounting & Finance, Southeastern Oklahoma State University, Durant, USA
Received July 15th, 2012; revised August 22nd, 2012; accepted August 30th, 2012
I examine portfolio risk management implications of using hypothetical investment returns from a sample
of mutual funds in a variety of investment objective classifications to select mutual funds. While early re-
search supported this practice by showing that risk is homogeneous within investment objective groups
and heterogeneous between groups, more recent research suggests that earlier findings are no longer true.
Research also suggests that load and no-load funds may exhibit risk differences. I examine whether risk is
homogeneous within investment classification and heterogeneous between classes after controlling for
potential load effects. Results reveal that significant risk differences exist even after controlling for the
load structure of the fund and that those risk differences can have significant implications for portfolio
risk management.
Keywords: Mutual Funds; Investment Objectives; Mutual Fund Risk
Introduction
Finance theory suggests that risk and return are essential
elements in selecting investments. Utility theory further sug-
gests that understanding the risk and return of mutual funds is
crucial to investors in order to maximize the investors’ satisfac-
tion (utility) with an investment.
Many mutual funds exist from which investors can choose in
building their investment portfolio. Practitioners often assist
with the selection process by ascertaining the investors risk
tolerance and then providing hypothetical investment results of
suitable mutual funds that illustrate the return of various in-
vestment options. Investors then use the hypothetical invest-
ment results to compare the returns that would have been
achieved if an investment had been made in the selected funds.
This approach provides the investors with a benchmark that
they can use to assess the relative performance of their invest-
ments.
The above approach is suitable if the investment objectives
properly convey risk as suggested by Sharpe (1966) and Klem-
kosky (1976). However, for investment objectives to properly
convey risk, the objectives must be systematically related to a
quantitative measure of risk such as beta or volatility. Also, risk
must be homogeneous within investment objective and hetero-
geneous between classes. However, if the risks of funds within
an investment objective class differ, comparing returns alone is
insufficient to make utility maximizing investment decisions.
Unfortunately, Najand and Prather (1999) reported that risk is
heterogeneous within investment objective groups. Therefore,
the practice of comparing returns does not appear optimal.
I extend the work of Najand and Prather (1999) to incorpo-
rate the findings of Chordia (1996) that no-load fund portfolio
managers hold more cash to meet a higher level of uncertain
redemptions. This implies that systemic differences in risk be-
tween load and no-load funds may occur. Malhotra and
McLeod (1997) also reported that load and no-load funds may
have risk differences because they found that no-load funds
have a higher cash ratio. Chordia’s (1996) work suggests that
one factor that may drive the reported risk heterogeneity is that
risks differ systematically between load and no-load funds.
Chordia (1996) characterized no-load fund investors as less
loyal to a fund that performs poorly. Therefore, no-load fund
managers must be sensitive to performance. This is consistent
with the findings of Brown, Harlow and Starks (1996) that the
“tournament” effect that is strongest with no-load funds. If
more frequent switching by no-load fund investors causes
no-load fund portfolio managers to respond by holding more
cash to meet uncertain redemptions, that singular action could
cause no-load funds to have lower risk than load funds in the
same investment objective if investment constraints result in
similar portfolios of risky assets.
The remainder of the paper is organized as follows. The next
section, Data Sources and Methodology presents the data
sources that I use and the methods that I employ to conduct
statistical analysis. The Empirical Results section provides the
results of empirical tests of risk homogeneity of mutual funds
in five investment objectives classes. These results compare
systematic risk using three difference indices and also compare
total risk as well. My conclusions are presented in the Conclu-
sion section.
Data Sources and Methodology
Thirteen years of monthly return data was obtained from
CDA Investment Technology, Incorporated and screened using
a process similar to that of Grinblatt and Titman (1989, 1992,
1993, and 1994) and Najand and Prather (1999). Table 1 pre-
sents the sample size by the CDA investment objective classi-
fication.
CDA’s return data is also used for the risk-free proxy (90-
day T-bill return) while The Center for Research in Security
Prices (CRSP) return data is used for the CRSP equally weighted

L. J. PRATHER
Table 1.
Sample.
CDA Investment Objective Number of Funds
Aggressive Growth (AG) 43
Growth (G) 112
Growth and Income (GI) 66
Balanced (B) 36
Bond and Preferred Stock (BP) 66
Total 323
Note: Column one presents the CDA investment objective classification and colu-
mn two presents the sample size for that investment objective.
(EW) and value weighted (VW) indices. Return data for the
Morgan Stanley Capital International Perspective Index (MSCI)
is also used as a benchmark for globally diversified investors.
Because Brown and Brown (1987) and Lehmann and Modest
(1987) reported that the selection of the index can have sub-
stantial impact on performance evaluation, using multiple indi-
ces when computing risk measures helps ensure that the results
are robust with respect to the index.
Computation of Returns
Continuously compounded monthly net returns are computed
by taking the natural log of the change in wealth over each of
the 156-month holding periods as shown in Equation (1).

,,
ln
ititi iit
RNAVDVCGNAV ,1




(1)
where: Ri,t is the return on fund i during period t, NAVi,t is the
net asset value of fund i at time t, DVi is the dividend and inter-
est paid on fund i during the period, and CGi is the capital gain
distribution paid on fund i during the period. Index returns are
computed similarly.
Determination of Systematic Risk
Systematic risk is determined by using ordinary least squares
regression (OLS) and the Capital Asset Pricing Model (CAPM).
The model used is:


,,,
–αβ –ε
mfftmt ftt
RR RR  (2)
where Rmf is the return on the mutual fund, Rf is the return on
the risk-free asset (90-day T-bill), and Rm is the return on the
market proxy. β measures the systematic risk for each mutual
fund from the perspective of an investor that holds a portfolio
identical to the selected market proxy. If the investment objec-
ve classification conveys risk, the β’s for funds within each
investment objective classification should not differ signifi-
antly from one another for a given index, although it may dif-
fer for different indices.
Empirical Results
The mutual fund’s prospectus details specific constraints
about the investment composition of the fund and cannot be
changed without shareholder’s approval since it would alter the
basic characteristics of the investment. Based, at least in part,
on this information, funds are classified into an investment
objective. If investment constraints are binding and the invest-
ment objectives are good surrogates for risk, risk should be
homogeneous within an investment objective group and het-
erogeneous between groups. To examine the usefulness of in-
vestment objectives as risk proxies, the risks that investors
would experience had they invested in the funds are estimated.
Table 2 presents the results of estimating the systematic risk
or beta (β) for each fund over the 156-month period. Betas can
vary with the selected index since β = (Cov Ri,Rm)/ơm
2 there-
fore, three indices were utilized to ascertain the impact of index
selection on beta computation. The results suggest that the sys-
tematic risk of funds within each investment objective group
varies widely, despite the selected market proxy. The large
range in estimated systematic risk is consistent with the find-
ings of Najand and Prather (1999) and suggests that risk may
not be homogeneous within each investment objective classifi-
cation. Therefore, I now test the hypothesis that risk is homo-
geneous within investment objective groups to find out if these
differences are statistically significant or due solely to chance.
Systematic Risk Homogeneity Tests
To conduct statistical testing, βs are computed using monthly
data over rolling one-year periods for the thirteen-year period.
This provides a distribution of 144 βs for each of the 323 funds
for each of the five indexes. These βs are then compared using
One-way ANOVA to test the equality of βs within each in-
vestment objective group to learn if the average β for all funds
within the investment objective group are equal. Formally,
ANOVA will be utilized to test:
HO: ,1,, 2,, 3,, n , βββ β
iti titit


HA: not all βi are equal
where βi,1,t represents the estimated systematic risk (β) of fund 1
using index i during period t. The null hypothesis is that the
average systematic risk for each fund within the investment
objective group is equal. My methodology follows Klemkosky
(1976) and Najand and Prather (1999). The critical value of the
F statistic (F*) is computed using Equation (3)




*––
rf f
F
SSE RSSE FdfdfSSEFdf

 


 
(3)
where SSE (R) and SSE (F) are the explained sum of squares for
e 3 presents results of the one-way ANOVA F-test to
de
able 2.
stimated Betas.
Index (maximum/minimum)
the reduced and full models respectively, and dfr and dff are the
degrees of freedom for the reduced and full models respect-
tively.
Tabl
termine if the risk differences reported in Table 2 are statis-
tically significant or whether they can be attributed to chance.
Interestingly, statistical testing rejects the null hypothesis that
risk is homogeneous within investment objective classes for
most investment objective index combinations. Four of five
investment objectives exhibit heterogeneous risk with the
T
Range of E
Investment
Objective Number of Funds CR SP EW CRSP VWMSCI
AG 43 1.46/0.70 1.57/0.811.14/0.63
(G) 112 1.18/0.36 1.29/0.470.94/0.38
(GI) 66 0.93/0.25 1.06/0.250.80/0.19
(B) 36 0.88/0.30 0.99/0.320.73/0.25
(BP) 66 0.67/0.00 0.68/0.000.52/0.00
Note: C one provides thA invesine olumne CDtment objectve and colum two lists th
number of funds comprising the sample. Columns three and four are the estimated
systematic risk measures for domestic investors using the CRSP EW and CRSP
VW indices as market proxies, respectively. Column five is the estimated system-
atic risk for globally diversified investors using the MSCI index as a market proxy.
34

L. J. PRATHER
Table 3.
Homogeneity of Systematic Risk within CDA Investment Objective Cla-
Index (F value)
sses.
Investment Number of Funds CRSP EWMSCI
Objective CRSP VW
AG 43 3.135** 2.135** 0.506
(G) 112 1.094 0.995 0.94/0.38
(GI) 66 7.286** 9.962** 2.538**
(B) 36 4.752** 0.999 1.471*
(BP) 66 1.937** 2.585** 2.047**
Note: T presents reshe onOVto df
be

his tableults of te-way ANA F-test etermine i
risk differences observed in Table 2 are statistically significant or whether they
can be attributed to chance. Column one provides the CDA investment objective
and column two lists the number of funds comprising the sample. Columns three
and four are the ANOVA F-statistics for the tests of the null hypotheses that the
risk for domestic only investors is homogeneous within the investment objective
group. Column five is the ANOVA F-statistic for the test of the null hypothesis
that the risk for globally diversified investors (MSCI) is homogeneous within the
investment objective group. **,*Indicates significance at the 0.01 and 0.05 levels,
respectively.
CRSP EW index and three of the five investment objectives
exhibit heterogeneous risk with the CRSP VW and MSCI in-
dexes. Moreover, two of the five investment objective classes
exhibit heterogeneous risk with all three indexes and another two
of the five investment objective classes exhibit heterogeneous
risk with two of the three indexes.
Differences in Systematic Risk between Load
and No-Load Funds
Chordia (1996) and Malhotra and McLeod (1997) reported
that load funds hold less cash than no-load funds. Presumably,
this is due to a more stable clientele and redemptions that are
more predictable. The act of holding dissimilar amounts of cash
could cause systemic differences in risk between load and
no-load funds. If no-load funds hold more cash and fewer risky
assets, they would be less risky ceteris paribus because the
standard deviation of a portfolio (p) is equal to the product of
the weight in the risky asset (wr) and the standard deviation of
the risky asset (r) or p = wr (r). Therefore, as the propor-
tion of cash increases (wc), the proportion of the total invest-
ment in the risky portfolio (wr) decreases and so does the stan-
dard deviation of the portfolio (p). This would decrease the
systematic risk (β) as well since the beta of a portfolio (βp) can
be expressed as βp= ρ(σp /σm), where ρ is the correlation be-
tween the portfolio and the market and σp
and σm are the portfo-
lio and market variabilities, respectively. Alternatively, the beta
of a portfolio is the weighted sum of the beta of each asset
times the beta of the asset. Because the beta of cash is zero, a
portfolio with higher cash holdings would have a smaller beta
ceteris paribus.
Brown, Harlow, and Starks (1996) found that no-load fund
managers with a poor performance record in the first half of the
year alter risk in the second half of the year to improve per-
formance suggesting that no-load funds investors may be more
sensitive to performance. Chordia (1996) believes that is the
case and that switching costs create differences in loyalty be-
tween load and no-load fund investors. He believes that this
mitigates fund flows for load funds and therefore creates dif-
ferent effects for load and no-load portfolio managers. Therefo-
re, the load structure may explain the documented heterogene-
ous within group risk.
To test the hypothesis that systematic risk is homogeneous
tween the load and no-load funds for each investment objec-
tive, the sample was segmented into two groups, load funds and
no-load funds. This division provides a sample of 180 load
funds consisting of 21 aggressive growth (AG), 52 growth (G),
39 growth and income (GI), 22 balanced (B), and 46 bond and
preferred stock (BP). The remainder of the sample consists of
143 no-load funds broken down into 22 (AG), 60 (G), 27 (GI),
14 (B), and 20 (BP). The monthly returns from each group are
computed to provide an equally weighted 156-month index
return from each group. Using equally weighted indexes is
important since the objective is to determine the similarity of
risk between the average load fund and the average no-load
fund in a selected investment objective. Once the indices were
computed, a modified market model, Equation (4), was used to
determine the relative systematic risk.

–αβ
,, ,,
–ε
L
DItf tLDLDNLtf tt
RRR R


(4)
where RLDI,t is the return on the load fund index for
ble 4 columns two through four provide the sample size
fo
able 4.
ity of Systematic Risk between Load and No-load Funds.
a given
investment objective group during each month t of the 156-
month sample period, Rf,t is the risk-free rate of interest (90 day
US T-bills), RNLI,t is the return on the no-load fund index for a
given investment objective group during each month t of the
156-month sample period, and αLD and βLD are the estimated
excess risk-adjusted return and systematic risk coefficients of
the load fund index. This permits determining whether the av-
erage risk of load funds differs systematically from that of
no-load funds. If the risk of load and no-load funds is the same,
the estimated βLD coefficient should not differ statistically from
one.
Ta
r the total sample, the load fund sample, and the no-load fund
sample respectively. Column five provides the systematic risk
estimate generated by regressing the returns of the index of load
funds on the index of no-load funds and column six is the ad-
justed coefficient of determination of the model. A beta of one
would suggest equal risk whereas a beta with a confidence in-
terval that excludes one would suggest that risk is significantly
different between the two groups. Results suggest that systemic
differences exist and the differences in risk are significant at
the .05 level. These results are consistent with no-load portfo-
lio managers holding more cash (e.g., Chordia (1996), Mal-
hotra and McLeod (1997)) and having similar risky asset port-
folio compositions. At a minimum, these findings suggest that
T
Homogene
Number of Funds
Investment
Objective Total LoadLD R
2 No-load β
AG 43 21 22 1. 0.030*986
(G) 112 52 60 1.040* 0.991
(GI) 66 39 27 1.099* 0.989
(B) 36 22 14 1.066* 0.972
(BP) 66 46 20 1.099* 0.951
Note: Tle presentltsests of whether siffhis tabs the resu of tystemic derences in
risk exist between load and no-load funds. Column one is the CDA investment
objective group. Columns two through four provide the sample size for the total
sample, the load fund sample, and the no-load fund sample, respectively. Column
five provides the slope estimate generated by regressing the returns of the index
of load funds on the index of no-load funds over the 156-month sample period. A
beta of one would suggest equal risk whereas a beta with a confidence interval
that excludes one would suggest that risk is significantly different between the
two groups. The model below estimates betas:

αβ

,, ,,
ε
L
DItf tLDLDNLtf tt
RRR R

 
*Indicates that the .05 confidence interval does not include oe. n

L. J. PRATHER
comparing funds within investment objective classes without
considering the fee structure can be misleading.
Load Adjusted Systematic Risk Homogeneity
Tests
To determine if systemic differences in risk between load
d no-load funds were the sole cause of heterogeneous within
group risk, the sample was partitioned into load and no-load
sub samples and one-way ANOVA on betas was repeated for
each sub sample. To conduct statistical testing, betas are com-
puted using monthly data over rolling one-year periods for the
thirteen-year period. This provides a distribution of betas for
each fund. These betas are then compared using One-way AN-
OVA to test the equality of betas within each investment objec-
tive group for each load structure to learn if the average beta for
all funds within the investment objective group is then equal.
Table 5 panels A and B present results of the one-way
an
2
ANOVA F-test to determine if risk differences reported in Ta-
ble 3 remain after controlling for load effects for load and
no-load funds, respectively. Column one provides the CDA
investment objective and column two is the number of funds
comprising the sample. Columns three through five are the
ANOVA F-statistic p-values for the null hypothesis that the risk
for investors is homogeneous within the investment objective
group. Results suggest that risk homogeneity is rejected for all
five investment objective groups (for both the load and no-load
subsamples) when the CRSP VW index is used. When using
the CRSP EW index, risk homogeneity is rejected for two of
the five investment objective groups in both the load and
no-load subsamples. The MSCI index shows that for load funds,
risk homogeneity is rejected for four of the five investment
objective groups. No-load funds fare somewhat better but risk
homogeneity is rejected for three of the five investment objec
tive groups. Thus, while empirical results reveal that load funds
exhibit statically higher risk, segmenting funds by load struc-
ture does not correct systematic risk heterogeneity within ob-
jective classifications.
Examination of Total Risk
Najand and Prather (1999) question whether investment ob-
jectives may do a good job of capturing elements of risk that
are not captured by beta. Therefore, they examine the total
variability of fund returns within each investment objective
group. Since the number of degrees of freedom for each of the r
sample variances si
2 is equal, they use the Hartley test to deter-
mine whether differences in variance are significant. I also use
the Hartley test to examine total risk over the 156-month period.
Formally, Hartley is used to test:
22 2
HO:
12
σσ σ
r
HA: not all σi are equal.
Equation (5) is used to compute the Hartley test statistic




22
max min
i
Hs s
i
2
able 5.
ematic Risk Homogeneity after Controlling for Load.
Index (P value)
(5)
where H is the Hartley statistic, max si is the maximum sample
variance and min si
2 is the minimum sample variance. Critical
H values are from David (1952).
Table 6 presents the results of the Hartley test on the total
variance of funds within each of the CDA investment objective
classes. Columns one and two provide the investment objective
classification and the number of funds included in the sample,
respectively. Column three provides the variance of the funds in
the sample with the lowest variance and column four provides
the variance of the funds in the sample with the highest vari-
ance. Column five provides the Hartley statistic, which is used
to test whether the sample variances are significantly different.
Results are presented for the load fund sample and the no-load
fund sample in panels A and B, respectively. Hartley statistics
suggests that the total risk is heterogeneous within each of the
T
CDA Syst
Panel A. Load Fund Systematic Risk.
Investment
Objective Number of Funds CRSP EWMSCI CRSP VW
AG 21 0.9868 0.0004 0.1055
(G) 52 0.9943 0.0000 0.0000
(GI) 39 0.0389 0.0000 0.0000
(B) 22 0.2760 0.0000 0.0000
(BP) 46 0.0001 0.0000 0.0000
Panel load Fund Satic Ri
Index (P value)
B. No-ystemsk.
Investment
Objective Number of Funds CRSP EWMSCI CRSP VW
AG 22 0.9438 0.0000 0.0003
(G) 60 0.6063 0.0000 0.4859
(GI) 27 0.0000 0.0000 0.0000
(B) 14 0.0161 0.0000 0.4535
(BP) 20 0.0927 0.0016 0.0011
Note: T presents reshe onOVo deif
able 6.
ity of CDA Total Risk.
er of Minimum Maximum Hartley
his tableults of te-way ANA F-test ttermine
risk differences observed in Table 4 remain after controlling for load effects.
Panel A presents the results for load funds and Panel B presents the results for
no-load funds. Column one provides the CDA investment objective and column
two is the number of funds comprising the sample. Columns three and four are the
ANOVA F-statistic p-values for the tests of the null hypotheses that the risk for
domestic only investors is homogeneous within the investment objective group.
Column five is the ANOVA P-value for the test of the null hypothesis test that the
risk for globally diversified investors (MSCI) is homogeneous within the invest-
ment objective group.
T
Homogene
Panel A. (Load Funds).
Investment Numb
Objective Funds Variance Variance Statistic
AG 21 0.0017 0.0060 3.4509***
(G) 52 0.0013 0.0038 2.8406**
(GI) 39 0.0006 0.0023 3.6887***
(B) 22 0.0005 0.0022 3.9873***
(BP) 46 0.0002 0.0013 7.9669***
Panel Load).
umber of Minimum Maximum Hartley Sta-
B. (No-
Investment N
Objective Funds Variance Variance tistic
AG 22 0.0023 0.0049 2. 0695**
(G) 60 0.0009 0.0033 3.6717***
(GI) 27 0.0003 0.0024 8.4641***
(B) 14 0.0004 0.0013 3.2105***
(BP) 20 0.0000 0.0006 112.4264***
Note: Te presentsresults oley te totf his tabl the f the Hartst on theal variance o
funds within each of the eight CDA investment objectives. Columns one and two
provide the investment objective classification and the number of funds included
in the sample, respectively. Columns three and four provide the variances of the
funds in the sample with the lowest and highest variance over the 156-month
sample period, respectively. Column five provides the Hartley statistic, which is
used to test whether the sample variances are significantly different. ***, **Indi-
cates significance at the 0.01 and 0.05 levels, respectively.
36

L. J. PRATHER
For investors to maxi must be able to build
m
suggests that the total risk is heterogeneous within each of the
CDA investment objective groups after controlling for risk
differences between load and no-load funds. Because neither
systematic nor total risk is homogeneous with investment ob-
jective classes, even after correcting for load effects, investment
objectives are viewed as poor proxies for risk.
Conclusion
mize utility, they
utual fund portfolios that exhibit risk and return tradeoffs that
the individual finds most appealing from the array of mutual
funds available. After the investor determines their own risk
tolerance they need two additional pieces of information to
make utility maximizing choices—the return and risk of com-
peting mutual funds. While historical returns are readily avail-
able, the risk of funds is much less clear.
If investors believe the early research in the field that in-
vestment objectives are valid risk proxies, they may compare
raw returns of funds within an asset class and select the fund
with the highest return. However, if earlier findings are not
correct and if the risks of the funds within an investment object-
tive classification differ, the capital asset pricing model and
efficient market hypothesis would suggest that the investor may
be unwittingly selecting the higher risk fund and ending up
with lower utility.
I extend the findings of Najand and Prather (1999) to ascer-
tain whether the load structure of the funds may drive their
heterogeneous within class risk findings. If both load and
no-load fund managers within a given investment objective
class face similar constraints, the risk of the risky portfolio that
they select should be similar. However, recent literature, (e.g.,
Chordia (1996), Goetzmann and Peles (1997), Ippolito (1992),
Sirri and Tufano (1998)), suggests that agency problems may
cause load and no-load fund managers to hold differing per-
centages of cash to meet uncertain redemptions. Therefore, it is
possible that findings of risk heterogeneity are not due to lack-
ing regulation or inability to properly capture risk. Rather, it
may be a logical response by managers attempting to maximize
their own utility.
To examine risk, I conduct empirical testing on monthly re-
turns of more than 300 mutual funds over a thirteen-year period.
Results suggest that the average risks of load and no-load funds
differ statistically. After segmenting the sample into load and
no-load funds, I examine the risk homogeneity of funds within
investment objective classes using analysis of variance
(ANOVA). Results suggest that risk is not homogeneous within
investment objective classes and the risks of load and no-load
funds generally differ. Moreover, the result is robust with re-
spect to the selected market proxy.
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