portfolio volatility adjustment by canadian mutual funds
TRANSCRIPT
PORTFOLIO VOLATILITY ADJUSTMENT BY CANADIAN MUTUAL FUNDS*
HARBANS L. DHINGRA
INTRODUCTION
The impressive growth of mutual funds during the last two decades suggests that this investment medium enjoys the popular support and confidence of the invest- ing public. Recently numerous researchers (1 -7,9-11) have empirically evaluated mutual fund performance and they have presented many conflicting results. This may, perhaps, be due to the fact that mutual funds have a very wide spectrum of investment objectives, and thereby they pursue different policies and methods of investment; consequently they may be expected to produce different portfolio performance results.
Mutual funds which have set forth capital appreciation or growth as a primary objective are expected to be more aggressive or risk taking in their investments compared with those to whom stability of income is more important. Since there are many other different types of mutual funds which have mixes of different degrees of capital appreciation and stability of income as their objectives, these funds facilitate the placing of investment funds in different risk classes. Usually the investor, through the published objectives of mutual funds in their prospectuses, periodical reports to shareholders, or sales promotion literature, tries to find out which of them are likely to place him in his risk preference class. After considering the data on past performance of these funds and some other factors which may have some bearing on the final choice, the investor selects the specific fund(s1 for his investment purposes.
As one of the important functions served by a published statement of objectives of a mutual fund is to inform the investment community of the type of performance being sought (or being avoided) by its management, and since each mutual fund would like to strengthen the confidence of its clients as to its ability to perform according to its objectives, the managements of these funds promise a stability in their stated risk classes. Indeed, for this promised service they charge their clientele various kinds of fees.
This study empirically explores whether, by and large, Canadian mutual funds have been successful in achieving their stated objectives. In other words, the study *The author is Professor of Finance and Management Science at the Lkiversity of Saskatchewan. m e project was funded by the research gmnts from the University of Saskatchewan. The author acknowledges the computational assistance of Dan Hoodicoff. An earlier version of this paper was presented at the Annual Conference of the American Statistical Association, August, I9 77. (Paperreceived February 1978, revised July 1978)
Jownal of Business Finance t Accounting 5,4(1978) 305
investigates whether the portfolio composition of Canadian mutual funds is consistent with their committed risk posture, and whether the degree of risk is stable over time.
INVESTMENT RISK
Although the notion of risk is central in every investment decision as well as in portfolio analysis, there still exists a controversy about what constitutes the risk and how it should be quantified. However, in financial literature, risk is most often equated with dispersion in returns. Despite the many statistical methods available for measuring dispersion, the one that has proved to be most useful for both analytical and empirical purposes is the variance or its square root - the standard deviation of returns. The larger the variance (or standard deviation) of returns around the expected value of a security, the larger is the investor’s risk in that security. Sharpe [ 121 has proposed the following market model which dichotomises the total risk of a security into “systematic” and “unsystematic” risks:
where the tilde denotes random variable,
k,, R,,,,, Ci , ,
is the return on the ith security during the jth period, is the return on the market factor during the jth period, is the return on residual factors, other than market, of the ith security during the jth period such that
E(Pi , l ) = 0 V(Zi,j) = V(Ei,k ) = r&,
COV (Zi . j , zi, k) = 0
and
of returns on thc ith security is partitioned into two parts: a,, and pi are the regression coefficients of the ith security. The total variance
V(R,) = V(ai + /3i R, + t i ) = 0; V(R,,) t V(Pi) = Systematic variance + Unsystematic variance.
Systematic risk of a security is dependent upon the market return and is measured by its beta coefficient (the slope of the linear regression eqyation of security return on market return) times the standard deviation of market return. A similar
306 Harbans L. Dhirigra
model may be applied to returns from a portfolio of securities. As the standard deviation of market returns is common to all securities or portfolios, the beta coefficient is an appropriate measure of systematic risk. Unsystematic risk, also known as diversifiable risk, of a security is the standard deviation (qmm) of its res iual factors Pi, and previous research (6) suggests that this component of total risk can be considerably mitigated by mixing the security with other securities. Thus, as the diversification of a portfolio increases, the only relevant measure of investment risk is the systematic risk, sometimes called undiversifiable risk, market risk, or volatility, measured by the beta coefficient of a portfolio.
Since some investors by temperament are risk takers, whereas others are risk averters, different volatilities of investment funds, therefore, suit the preferences of different investors. Management of cach mutual fund, therefore, decides which particular investor objectives it intends to fulfill, and after publishing its objectives makes an effort to serve the needs of those investors whose risk preferences are aligned with its risk objectives. Thus, there is no u priori basis for calling a given magnitude of portfolio volatility of a mutual fund good or bad.
THE DATA
In order to meet the purposes of this study, a l l those Canadian mutual funds which have at least ten years (1966-75) of data reported in the annual publicat- ion entitled “The Financial Post Survey of Funds” were selected. The sample so selected consisted of 88 funds listed in Appendix A and constitutes 46 percent of the mutual funds listed in the 1976 edition of t h i s publication. For each of the selected funds, annual rates of return for a period of 10 years (1966-75) were obtained and, for some of these funds, annual rates of return also were collected for a period of 15 years (1961-75). The rates of return are based upon net assets per share and have been computed as the following:
where
% =
Vj =
vj- 1 =
4 =
Portfolio Volatili@ Adjustment 307
annual rate of return of the mutual fund for the jth year, the portfolio market value per share of the mutual fund at the end of the jth year,
the portfolio market value per share of the mutual fund at the beginning of the jth year, cash dividends paid per share to the investors during the jthyear.
The information on investment objectives, yearend composition of portfolios in terms of their common stock investments in various industries, and number of securities within each industry; annual portfolio turn-over in terms of additions of new securities and deletion of old securities; and the yearly market value of assets for the sample funds were also obtained from the Financial Post Survey of Funds. Yearly data were collected for two reasons. Firstly, mutual funds usually do not make substantial changes in their portfolio compositions in order to counterbalance the effect of expected future changes in market returns more often than once a year. Secondly, the Financial Post Survey of Funds provides data on investment funds only on annual basis and there is no other secondary source of such data either on a monthly or quarterly basis.
For some mutual funds, the Financial Post Survey of Funds presents a very imprecise set of objectives, as if the managements of these mutual funds, perhaps for some special reasons such as operational convenience, penetration into a wider market of institutional investors, protection from comparing their actual performance with their stated objectives, etc., had intentionally stated their investment objectives in only broad terms. Considering the reported objectives in various annual issues of the Survey of Funds, all the sample funds were classif- ied in one of the five mutually exclusive categories, namely, (a) growth, (b) growth and income, (c) income and growth, (d) income, and (e) balanced port- folio, arranged in descending order with respect to the expected degree of aggressiveness to investment risk. The objective code for each of the sample mutual funds is listed against the name of the fund in Appendix A.
The Industrial Index' of the Toronto Stock Exchange was taken as a proxy for the market, and annual rates of return on this index were computed for the period 1961-75. Regressions, of the market model form of the annual rates of each mutual fund on the annual rates of return of the Industrial index, were obtained for six overlapping decades (1961-70 to 1966-75).
EMPl R ICAL RESULTS
Of the 88 mutual finds 37 were classified as seeking growth, 13 seeking growth and income with emphasis on growth, 25 seeking income and growth with emphasis on income, 5 seeking income, and the remaining 8 seeking balanced portfolios or income stability. Moreover, of these funds for which data were available for ten years (1966-75), there were 68,61, 56,52, and 44 funds for which the data also were available for 1 1, 12, 13, 14, and 15 years, respectively.
The following Tables 1 ,2 , and 3 provide average values of beta coefficients, variances, and average rates of return of sample funds in each investment objective category for the six overlapping decades, 1961-70 to 1966-75.
308 Harbans L. Dhingra
A visual inspection of these tables does not suggest any pattern in the relationship between funds objectives (which are arranged in descending order of the degree of aggressiveness) and beta coefficients (measures of systematic risk), variances (measures of total risk), and average returns of the funds. However, during each of the time periods the coefficients of correlation, shown in Table 4, between average returns of funds on the one hand, and variances and beta coefficients of returns on the other, are positive and are statistically significant at the 0.05 level. In other words, the study provides empirical evidence that mutual funds which have consistently higher risks, whether total or systematic, have consistently realized high rates of return.
The funds which emphasize greater capital appreciation rather than a steady flow of income are generally expected to be relatively more aggressive in their invest- ment policies and thereby have a higher degree of risk exposure. This study fails to provide any consistent evidence about this proposition. Perhaps there are some errors in classification of mutual funds in appropriate objective categories, as some of the funds, for the reasons given earlier, have stated their objectives in very broad terms. If the funds are classified in two categories of objectives, namely growth, and income, rather than in five categories, there is less likelihood of a classification error. Tables 5,6, and 7 provide the data on average values of beta coefficients, variances, and average rates of return, respectively, when the funds are classified into two groups of objectives.
Tables 5 and 6 show that for each of the time periods, the average risk levels, both systematic risk and total risk, of mutual funds which have set forth capital appreciation or growth as their primary objective, have always been higher than of those funds which have stability of income as their primary objective. Similarly, Table 7 demonstrates that the average returns of growth oriented funds are considerably higher than the funds which are primarily income oriented.
A two-way analysis of variance was performed to test the null hypothesis of no significant differences between objective groups and time periods with respect to beta coefficients, variances, and average returns. The results are shown in Tables 8 , 9 , and 10. In each of these tables, the computed F-ratios exceed those required at the 0.05 and 0.01 levels of significance to reject the null hypothesis.
An analysis of variance relating to beta coefficients, and variances (i.e., systematic and total risk) suggests that with respect to risk exposure there are not only significant differences between mutual funds pursuing different objectives, but that there also are significant differences between time periods. Thus, the study suggests that, over time, mutual funds do not have a stable level of risk, and perhaps, by design, have changed their risk levels in accordance with changes in market conditions. But, if we compare beta coefficients or variances of the growth seeking funds with those of the income seeking funds, Tables 5 and 6 disclose
Portfolio Volatility Adjustment 309
TAB
LE 1
AV
ERA
GE
BETA
COEFFICIENTS
___-
9 P
LY
I’cr
iods
1966
-75
1965
-74
1964
-73
1963
-72
1962
-71
1961
7l
J A
v(: r
agc
Gro
wth
0.
5967
1.
0092
0.
7721
0.
9073
0.
9414
1 4
54
I (J
.850
2 G
row
th &
Inc
ome
0.71
90
1.01
12
0.96
03
1.08
33
1.1
340
I .07
51
0.98
37
Inco
me
&G
row
th
0.47
18
0.70
89
0.65
67
0.73
69
0.69
80
0.95
87
r~.6
693
lnco
mc
0.1
363
0.27
41
0.33
91
0.56
58
1 .I 2
09
0.56
01
(~.3
7(~
2
Bala
nced
0.
5774
0.
9723
0.
7144
0.
7889
0.
7890
0.
8255
0.
7671
A
vera
ge
0.55
70
0.89
1 8
0.74
81
0.86
84
0.89
50
0.98
1 5
0.79
76
TAB
LE 2
AVER
AGE
VA
RIA
NC
ES
Peri
ods
Obj
ectiv
es
1966
-75
1965
-74
1964
-73
1963
-72
1962
-71
1961
-70
Ave
rage
Gro
wth
42
2.01
36
0.67
30
6.83
24
2.98
22
5.27
30
6.83
32
5.16
G
row
th &
Inc
ome
499.
72
426.
74
320.
98
258.
80
261 .
I 6
292.
78
356.
57
Inco
me
&G
row
th
184.
75
178.
52
156.
71
134.
92
129.
90
170.
03
162.
11
inco
me
68.2
9 78
.99
108.
80
107.
98
106.
26
102.
37
92.0
8 Ba
lanr
vd
21 1.
71
180.
12
135.
84
126.
98
119.
38
143.
72
154.
58
Ave
rage
32
6.87
29
4.32
24
3.91
19
5.97
18
6.52
23
7.00
25
6.66
TAB
LE 3
AV
ERA
GE
AN
NU
AL
RET
UR
NS
(Per
cent
)
Obj
ectiv
es
Peri
ods
1966-75
1965-74
1964 -73
1963-72
1962-71
1961 -70
Ave
ragc
Gro
wth
G
row
th &
Inc
ome
Inco
me
&G
row
th
Inco
me
Balanced
Ave
rage
4.1911
3.3024
7.8444
10.6341
7.5525
9.6941
6.6607
4.3808
2.8956
6.5600
9.1900
6.51 I
1 7.4500
5.9258
4.0484
3.2219
6.0967
7.8033
6.1038
6.9200
5.4225
4.1200
3.0250
3.8500
4.5167
4.0167
3.4833
3.8238
4.0000
2.8571
6.5714
8.2857
5.7286
6.6500
5.6190
4.1571
3.1496
6.8774
9.0254
6.5606
7.8 I70
5.9459
TAB
LE 4
CO
EFFI
CIE
NTS
OF CORRELATION
BETW
EEN
Perio
d A
vera
ge R
etur
n an
d Variance
Ave
rage
Ret
urn and
Beta
Coe
ffic
ient
1966-75
1965- 74
1964-73
1963-72
1962-71
1961 -70
0.0990
0.1687
0.2754
0.6708
0.5486
0.7393
~ ~
~_
__
__
0.2097
0.0809a
0.1761
0.4155
0.2223
0.5670
1961-75
0.1503
0.2901
'Sig
nific
ant a
t the
Spe
rcen
t lev
el. A
ll o
ther
coef
ficie
nts a
re s
igni
fican
t at t
he I
perc
ent l
evel
.
2
%
a &
h
h,
TAB
LE 5
AV
ERA
GE
BETA
CO
EFFI
CIEN
TS
2 s? 3
Peri
ods
s' O
bjec
tives
19
66-7
5 19
65-7
4 19
64-7
3 19
63-7
2 19
62-7
1
1961
-70
Ave
ragc
Gro
wth
0.
5784
0.
9293
0.
7774
0.
8937
0.
9073
1.
0338
0.
8247
In
com
e 0.
4303
0.
6822
0.
6018
0.
7393
0.
8305
0.
7592
0.
6557
A
vcra
gc
0.55
67
0.89
18
0.74
81
0.86
84
0.89
50
0.98
50
0.79
76
TAB
LE 6
AV
ERAG
E V
AR
IAN
CES
Peri
ods
0bjc
r.t i
vcc
1966
- 75
1965
-74
1964
-73
1963
-7 2
19
62-7
1 19
61 -7
0 A
vera
gc
GI,
>\\
tll
356.
39
323.
45
266.
25
211.
86
203.
44
264.
53
281.
73
inL
.oiii
c 15
6.55
14
3 34
12
7.73
12
1.27
11
5.44
12
9 94
10
6.45
A
VI' 1 .
I+,
326.
87
294
32
243
91
195
91
186.
52
236
99
256.
66
-_-_
s TA
BLE
7
AV
ERA
GE
AN
NU
AL
RET
UR
NS
rf 8
Peri
od
b a
Gro
wth
4.
1764
3.
1942
7.
0932
9.
4234
6.
8809
8.
3884
6.
1 35
2 E
Inco
me
4.04
6 1
2.91
82
5.75
50
7.15
50
5.21
50
5.59
44
5.02
06
Obj
cctiv
cs
1966
-75
1965
-74
1964
-73
1963
-72
1962
-71
1961
-70
Avc
ragc
is” A
vera
ge
4.15
71
3.14
96
6.87
44
9.02
54
6.56
06
7.81
70
5.94
59
9 .) TA
BLE
8
AN
ALY
SIS
OF
VA
RIA
NC
E O
F BE
TA C
OEF
FIC
IEN
TS
Sour
ce o
f V
aria
tion
Sum
of S
quar
es
Deg
rees
of
Free
dom
M
ean
Squa
re
F Rat
io
1. 2. 3.
4. (B)
1.
2. 3.
4.
Obj
ectiv
es cl
assif
iied in
5 ca
tego
ries
B
etw
een
obje
ctiv
es
6.47
5 B
etw
een
peri
ods
7.20
1 In
tera
ctio
n 1.
458
Res
idua
l 33
.073
T
otal
48
.672
O
bjec
tives
clas
sifie
d in
2 ca
tego
ries
B
etw
een
obje
ctiv
es
1.52
7 B
etw
een
peri
ods
7.82
8 In
tera
ctio
n 0.
183
Res
idua
l 39
.296
Tot
al
48.6
72
4 5 20
324
353 1 5 5
342
35 3
1.61
9 1.
440
0.07
3 0.
538
1.52
7 1.
566
0.03
7 0.
115
15.8
58
14.1
08
0.71
4
13.2
93
13.6
25
0.31
8
TAB
LE 9
AN
ALY
SIS
OF
VA
RIA
NC
E O
F V
AR
IAN
CES
’’ So
iree o
f V
aria
tion
Sum
of
Squa
res
Deg
rees
of
3 Fr
eedo
m
Mea
n !3
quar
e F
Rat
io
(A)
1.
2.
3.
4. m
1.
2.
3.
4.
Obj
ectiv
es c
lass
ified
in 5
cat
egor
ies
Bet
wee
n ob
ject
ives
2,
484,
95 8.
00
Bet
wee
n pe
riod
s 97
3,58
9.94
In
tera
ctio
n 31
9,67
3.56
R
esid
ual
11,0
04,3
84.0
0 T
otal
14
,771
,575
.00
Obj
ectiv
es cl
assi
fied in
2 ca
tego
ries
Bet
wee
n ob
ject
ives
8a
4,7 2
9.50
B
etw
een
peri
ods
923,
216.
12
Inte
ract
ion
88,1
00.0
0 R
esid
ual
12,8
36,1
87.0
0
‘4 5 20
324
35 3 1 5 5
342
621,
239.
5 19
4,71
7.9
15,9
83.7
33
,964
.1
884,
729.
5 18
4,64
3.2
17,6
20.0
37
,532
.7
18.2
91
5.73
3 0.
471
23.5
72
4.92
0 0.
469
Tot
al
14,7
71,5
75.0
0 35
3
that both the systematic volatility and the total risk level of the former group are always higher than that of the latter group. In other words, the study reveals that although over time mutual funds have not had stable absolute levels of systematic or total risk, they have maintained fairly stationary relative risk levels.
Having seen that when mutual funds are classified into two broad categories of objectives they maintain their relative risk classes in accordance with the objectives which they profess to undertake, we now pose the question whether or not the portfolio compositions and turnovers of these funds are consistent with these objectives.
It is usually expected’ that mutual funds which emphasize growth rather than stability of income are exposed to relatively higher degrees of risk. This would mean that growth funds are expected to have a relatively higher concentration of their investment funds in securities of high risk industries, and their portfolio turnovers are also expected to be largely confined to these industries. The reverse is expected of the funds which have stability of income as their primary objective. To examine this proposition empirically, data on composition and turnover of portfolios of the sample funds were collected for four years, namely, 1961,1966, 1971, and 1975, from the Financial Post Survey of Funds. Unfortunately, the appropriate information is not available for some of the sample mutual funds cove red.
Like individual securities or portfolios, industries also have their own risk characteristics, and these characteristics may be classified into different risk groups. The total, systematic, and unsystematic risks of industries are measured in the same way as those of securities or portfolios. Using monthly data on rates of return of industry indexes as dependent variable, and monthly rates of return of market index (i.e., Toronto Stock Exchange Industrial Index) as independent variable, simple linear regressions for 18 industries were obtained for four non-overlapping time periods, namely 1956-60,1961-65,1966-70, and 1971-75. Beta coefficients of these industries by period are given in Appendix B. Undertaking one-way analyses of variance of average monthly returns, variances of returns, and beta coefficients with independent variable as time periods, Tables 11-13 suggest that, except for average returns, no significant differences were observed for variances and beta coefficients at the 0.05 level. Thus, the mean rates of return of industries are not stationary over time whereas their risk measures, both total and systematic, are stable over time.
Further, within each time period, as well as for all time periods taken together, one-way analyses of variance of mean returns, variances, and beta coefficients were also undertaken with respect to industries. The analysis’ suggests that, except for beta coefficients, there are no significant differences between industries at the 0.05 level. In other words, the empirical evidence indicates that the industries
Portfolio Volatility Adjustment 315
TAB
LE 1
0
Q 5 P
9'
sour
ce o
f V
aria
tion
Sum
of S
quar
es
Deg
rees
of
Mea
n F.
Rat
io
3 Fr
eedo
m
Squa
re
ANALYSIS OF VA
RIAN
CE OF AV
ERAG
E AN
NUAL
RET
UR
NS
% 9 Fa
(A)
1.
2.
3.
4.
(B)
1.
2,. 3.
4.
Obj
ectiv
es c
lass
ified
in 5
cat
egor
ies
Betw
een
obje
ctiv
es
242.
976
Bet
wee
n pe
riod
s 1,
595.
907
Inte
ract
ion
172.
491
Res
idua
l 3,
035.
354
Tot
al
5,04
8.35
2
Obj
ectiv
es c
lass
ified
in 2
cate
gori
es
Betw
een
obje
ctiv
es
95.8
98
Betw
een
peri
ods
1,61
8.38
9 In
tera
ctio
ns
36.3
99
Res
idua
l 3.
31 8.
527
Tot
al
5.04
8.35
2
4 5 20
324
353 1 5 5
342
35 3
60.7
45
319.
1 81
8.
625
9.36
8
95.8
98
323.
618
7.28
0 9.
703
6.48
4 34
.070
0.
921
9.88
3 33
.357
0.
750
TAB
LE 1
1
AN
ALY
SIS
OF
VA
RIA
NC
E O
F AV
ERAG
E R
ETU
RN
S O
F IN
DU
STR
IES
Sum
of S
quar
es
Deg
rees
of
Free
dom
F. R
atio
Tot
al
17.0
341
58
TAB
LE 1
2
AN
ALY
SIS O
F V
AR
IAN
CE
OF
VA
RIA
NC
ES O
F R
ETU
RN
S O
F IN
DU
STR
IES
Sour
ce o
f V
aria
tion
Sum
of S
quar
es
Deg
rees
of
Free
dom
M
ean
Squa
re
F. R
atio
1.
Bet
wee
n pe
riod
s 4,
837.
75
2.
Res
idua
l 11
4,59
3.31
Tot
al
119,
431.
06
3 55
58
1.61
2.5
8 2,
083.
51
0.77
4
2
Q
9
TAB
LE 1
3
ANAL
YSIS
OF
VA
RIA
NC
E O
F BE
TA C
OEF
FICI
ENTS
OF
IND
UST
RIE
S
$ El
~ou
rcc u
f V
aria
tion
Sum
of
Squa
res
Deg
rees
of
Mea
n F.
Rat
io
P
Free
dom
Sq
uare
$ 1.
Bct
wee
n pc
riod
s 0.
0114
6 3
0.03
82
0.56
2
3 2.
R
esid
ual
3.73
88
55
0.06
80
b
Tota
l 3.
8534
TAB
LE 1
4 PE
RCEN
T O
F TO
TAL
INVE
STM
ENTS
IN
COM
MON
STO
CKS
OF
DIF
FER
ENT
INDUSTRY RISK C
LASS
ES A
ND
OTH
ER IN
VEST
MEN
TS
Year
s
(Per
cent
ages
) In
dust
ry R
isk C
lass
19
75
1971
19
66
1961
1.
Low
Risk
'2
. M
ediu
m R
isk
3.
Hig
h R
isk
13.5
7 13
.83
9.59
7.
74
17.4
6 23
.43
29.6
0 31
.37
43.1
7 41
.20
47.4
8 46
.19
Tota
l Com
mon
Sto
cks
84.2
0 78
.46
86.6
7 85
.30
Oth
er I
nves
tmen
ts
15.8
0 21
.54
13.3
3 14
.70
Tota
l 10
0.00
10
0.00
10
0.00
10
0.00
N
umbe
r of
fun
ds:
73
47
36
46
differ ammg themselves with respect to their systematic risk levels but not with respect to their mean returns or total risk.
Using average values of beta coefficients of industries for the four time periods, three risk categories, namely low .risk, medium risk and high risk, were developed with average beta values of less than 0.5, between 0.5 to 1 .O, and more than 1 .O, respectively.
Table. 14 gives industrywise composition of common stock investments of mutual funds for the years 1975,1971,1966, and 1961, and suggests that within a risk class industry, the proportion of their total investments held in common stocks are stable over time; moreover, mutual funds have a relatively high proportion of their investments in high risk industries.
Further, for each of the four years, data on variables such as (i) average proport- ion of investments in common stocks, (ii) average number of securities held, (iii) average number of additions of new securities, (iv) average number of deletions of old securities, (v) average. percent of additions of new securities to total securities held, and (vi) average percent of deletions of old securities to total securities held, were classified industrywise and fundwise in Tables IS to 20 respectively.
A one-way analysis of variance was undertaken for each of these variables to examine whether or not there were significant differences between the funds pursuing different objectives. For each of the above variables, the analysis‘ suggests that there is no significant association between the funds’ objectives and the variable. This suggests that within each industry risk group, both the magnitude of diversification (in terms of securities held and percent of the total common stock investments held) and the portfolio turnover,(in terms of absolute and relative additions and/or deletions of securities) are the same for each fund irrespective of its investment objective. But a visual inspection of the data suggests that within each year these variables generally have high values for high risk industries and low values for low risk industries. An analysis of variance’ of the data has confirmed this observation at the 5 percent level of significance. Further, within each industry risk group, no significant differences were noticed in the average values of these variables from year to year. This suggests that these variables are fairly stationary over time within each industry risk group.
SUMMARY AND CONCLUSIONS
This study, based upon a sample of 88 Canadian mutual funds, has examined empirically whether over time these funds have been maintaining their risk levels consistent with their published objectives. The data relating to funds’ objectives, returns and risk measures, diversification and turnover of portfolios, etc., relate to
Portfolio Volatiliry Adjustment 319
h
TAB
LE 1
5
AVER
AGE
PERC
ENT INVESTMENT IN
COM
MON
STOCKS
!?-
9' Ye
am
1975
1971
1966
1961
;;I I
nd
us
tr
y G
ro
up
s
1 2
3 1
2 3
1 2
3 1
2 3
Obj
ectiw
s Pe
rcen
t Inv
estm
ent
A.
1 2 3 4 5 Av
erag
C B.
1 2
Ave
rage
16.13
25.50
45.76
11.53
21.67
36.81
10.13
30.51
45.37
6.74
32.40
41.86
11.14
26.61
39.90
19.63
30.17
42.M)
10.40
19.00
55.25
1.70
27.16
47.78
13.44
31.16
39.24
15.43
20.93
44.43
10.80
24.1
0 56.60
1.75
37.23
31.97
2.30
27.90
64.20
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0 .o
12.80
31.75
33.10
10.47
22.87
43.53
3.00
47.40
41.80
6.85
30.05
43.70
13.57
27.46
43.17
13.82
23.43
41.20
9.59
29.59
47.48
7.74
31.31
46.19
14.21
27.05
43.07
14.6
23.56
40.57
10.25
28.11
47.96
7.89
31.56
46.52
9.30
30.47
43.93
10.47
22.17
43.94
3.00
47.40
41.80
6.15
30.05
43.70
13.57
27.46
43.17
13.12
23.43
41.20
9.59
29.59
47.41
7.74
31.31
46.19
Indu
stry
Gro
ups:
1.
Low
Risk
2.
Med
ium
Ris
k 3.
Hig
hRis
k O
bjec
tives
A.
1. Growth
2. Growth a
nd I
ncom
e 3.
In
com
e and
Growth
4. In
com
e 5.
Balanced
B.
1.
Growth
2. In
com
e
TAB
LE 1
6
AVER
AGE NU
MBER
OF
SECU
RITI
ES H
ELD
0': fi 3
Year
s 19
75
1971
19
66
1961
In
du
st
ry
G
ro
up
s
b
Q
4 2
1 2
3 1
2 3
1 2
3 1
2 3
r: 3 O
bjec
tives
N
umbe
r of S
ecur
ities
-+ +-
A
1 6.
59
15.6
4 21
.17
6.14
15
.73
26.1
2 4.
94
14.0
5 23
.75
2.67
11
.80
20.0
5 2
10.5
7 30
.71
36.0
0 8.
70
17.1
0 22
.90
6.92
16
.06
16.6
3 3.
76
13.9
0 19
.90
3 6.
57
21.0
0 26
.29
5.91
14
.54
20.7
3 5.
73
14.9
3 21
.00
4.17
14
.63
22.2
5 4
. 200
14.0
0 38
.00
2.00
13
.00
26.0
0 0.
0 0.
0 0.
0 0.
0 0.
0 0.
0 5
10.0
0 26
.75
30.2
5 10
.67
26.6
7 27
.63
5.33
16
.50
23.1
7 5.
00
13.0
0 17
.33
Ave
r=
6.54
21
.63
27.8
4 7.
90
17.4
9 24
.31,
5.
61
15.0
6 22
.56
3.67
12
.95
20.0
4
B 1
6.58
21
.36
27.0
8 7.
60
15.7
5 23
.71
5.73
14
.67
22.5
0 3.
40
12.9
5 20
.46
2 8.
40
24.2
0 31
.85
9.43
26
.42
27.5
7 6.
33
16.5
0 23
.17
5.00
13
.00
17.3
3 Av
erag
e 6.
54
21.6
3 27
.84
7.90
17
.49
24.3
1 5.
61
15.0
6 22
.56
3.67
12
.95
20.0
4
Indu
stry
Gro
upQ
: 1.
Lo
wR
islr
2.
Med
ium
Rirk
3,
Hig
hRhk
O
bjec
tives
A.
1.
Gro
wth
2.
G
row
th an
d ln
wm
e 3.
Inco
me
and
Gro
wth
4.
Income
5.
Eah
ced
B.
1.
Gro
wth
2.
Income
TABL
E 17
iF
AVER
AGE NU
MBER
OF
AD
DIT
ION
S OF
NEW
SEC
URIT
IES
(0 P
--
9
Yea
s 1975
1971
1966
1961
In
du
st
ry
Gr
ou
ps
1 2
3 1
2 3
1 2
3 1
2 3
Obj
ectiv
es
Num
ber o
f A
dditi
ons
A.
1 2 3 4 5 Av
erag
e
9.
1 2 A
vpg
e
3.29
5.00
5.11
3.82
4.09
6.88
3.00
4.06
2.83
6.57
8.71
2.25
3.67
6.56
3.50
7 .00
3.50
6.00
7.50
1.50
2.20
5.60
2.17
5.08
0.0
0.0
0.0
0.0
1.00
4.00
0.0
0.0
2.33
5.25
8.75
4.25
5.60
5.00
1.01
3.17
3.00
5.74
7.19
3.07
3.81
6.19
2.65
4.80
3.13
5.84
6.91
2.88
3.56
6.44
2.96
5.05
2.33
5.25
8.75
4.25
4.83
4.86
1.00
3.17
3.00
5.74
4.19
3.07
3.81
6.19
2.62
4.80
8.80
6.00
7.85
0.0
3 .O
7.22
7.78
3.00
7.22
1.75
2.76
4.75
1 .00
3.29
4.63
1 .00
3.00
6.00
0.0
0.0
0.0
1 .oo
280
1.67
1.27
2.91
4.37
1.43
2.93
4.118
1 .oo
2.80
1.67
1.27
2.91
4.37
Indu
stry
Gro
ups:
1.
Low
Ris
k 2.
Med
ium
Risk
3.
Hig
hRw
r O
bjec
tives
A
1.
Gro
wth
2.
G
row
thm
dlnc
ome
3. In
com
emdC
row
th
4.
Inco
me
5. B
alan
ced
B 1.
Gro
wth
2
lnco
mc
TAB
LE 1
8
AVER
AGE
NUM
BER
OF
DELE
TIO
NS O
F O
LD SE
CURI
TIES
Year
s 1975
1971
1966
1961
In
du
st
ry
Gr
ou
ps
I 2
3 1
2 3
I 2
3 I
2 3
Ob
jCC
tiW
N
umbe
r of Deletions
A 1
2.40
4.50
2.11
3.20
5.54
7.00
2.38
6.89
11.80
2.13
4.21
6.05
2 2.25
6.57
8.67
4.14
5.44
9.80
2.86
5.20
5.75
1.50
4.57
4.67
3 1.50
6.00
4.85
2.25
3.57
4.20
1.60
3.33
6.21
3.00
2.00
5.60
4 0.0
0.0
0.0
0.0
0.0'
2.00
0.0
0.0
0.0
0.0
0.0
0.0
5. 0.0
4.67
2.33
2.25
5.60
7.40
1.50
3.67
4.67
1.50
2.17
3.60
Ave
rage
2.15
5.48
4.48
3.16
5.12
6.93
2.15
5.17
8.08
1.93
3.52
5.21
B I
0.0
5.60
4.77
3.33
5.03
7.00
233
5-40
8.52
2.09
3.81
5.61
2 0.0
4.67
2.33
2.25
5.60
6.50
1.50
3.67
4.67
1.50
2.17
3.00
Ave
rage
0.0
5.48
4.48
3.16
5.12
6.93
215
5.17
8.08
1.93
3.52
5.21
Indu
stry
Gro
ups:
1.
Low
Ris
k 2.
-Mtd
ium
-Risk
3.
Hig
hRbk
ob
ject
ivca
A.
1. G
row
th
2. G
row
thm
dInc
ome
3.
Inw
mca
nd
clo
wth
4.
Inco
me
5. Ba
lana
d B.
1. G
row
th
2.
Inco
me.
TAB
LE 1
9
AV
ERA
GE
PER
CEN
T A
DD
ITIO
NS
OF
NEW
SEC
UR
ITIE
S
P-
S'
Yea
rs:
1975
19
71
1966
19
61
In
du
st
ry
Gr
ou
ps
1
2 3
1
2 3
1 2
3 1
2 3
Objectives
Perc
ent A
dditi
ons
A.
1 7.
18
10.3
1 13
.22
7.02
7.
79
14.3
2 8.
63
10.1
3 21
.40
6.90
9.
31
15.4
6 11
.71
2 4.
98
9.51
11
.34
4.63
8.
08
13.9
2 6.
48
14.4
2 3
5.30
10
.16
12.4
5 4.
28
5.60
14
.54
5.67
12
.95
19.1
0 1.
80
5.90
'1
1.60
4 0.
0 0.
0 0.0
0.
0 2.4
0 9.
80
0.0
0 .o
0.0
0.0
0.0
0.0
5 2.
83
8.35
12
.20
5.50
7.
60
7.28
2.
30
8.00
6.
98
3.40
9.
92
5.20
A
vera
ge
5.17
9.
70
12.3
8 5.
63
7.32
13
.20
6.48
11
.49
17.4
5 4.
39
8.55
12
.64
B.
1 6.
05
9.98
12
.41
5.65
7.
46
14.2
8 7.
28
12.0
1 18
.84
4.96
8.
31
14.0
4 2
2.83
8.
35
12.2
0 5.
50
6.73
7.
64
2.30
8.
00
6.98
3.
40
9.92
5.
20
Aw
ge
5.
52
9.69
12
.38
5.63
7.
32
13.2
0 6.
48
11.4
9 17
.45
4.39
8.
55
12.6
4
14.3
1 2.
65
7.26
Indu
stry
Gro
ups:
1.
Lo
w Risk
2. M
ediu
m R
isk
3.
Hig
h Ri
rk
Obj
ectiv
es A
. 1.
Gro
wth
2.
Gro
wth
and
Inco
me
3. ln
com
e an
d G
row
th
4.
lnco
me
5. B
akna
d B.
1.
G
row
th
2. In
com
e
TAB
LE 2
0
AVER
AGE
PERC
ENT
DELE
TIO
NS O
F OLD
SECU
RITI
ES
% 5 8
8
Yea
rs:
1975
19
71
1966
19
61
In
du
st
ry
G
ro
up
s
1 2
3 1
2 3
1 2
3 1
2 3
Obj
ectiv
es
Rra
nt
Del
etio
ns
A.
1 4.
72
9.56
4.
46
6.11
11
.01
16.2
5 6.
31
12.3
4 26
.76
7.21
11
.25
22.3
8 2
2.60
7.
96
6.65
6.
16
10.8
9 21
.27
4.83
10
.13
14.0
6 4.
70
12.5
1 12
.22
3 2.
70
9.56
6.
71
6.10
10
.04
11.3
1 4.
13
6.73
16
.51
5.40
5.
23
12.0
4 4
0.0
0.0
0.0
0.0
0.0
4.90
0.
0 0.
0 0.
0 0.
0 0.
0 0.
0
5 0.
0 5.
23
3.23
2.
96
7.06
9.
50
3.15
7.
97
10.5
8 4.
66
6.70
9.
67
Am
age
3.56
8.
56
6.42
6.
16
10.2
0 15
.22
4.99
10
.30
19.0
7 6.
08
9.60
16
.79
B. I
0.0
9.03
6.
88
6.79
10
.74
16.2
7 5.
24
10.6
7 20
.20
6.59
10
.24
18.0
s
Aw
rrge
0.
0 636
6.42
6.
18
10.2
0 15
.22
4.99
10
.30
19.0
7 6.
06
9.60
16
.79
2 0.
0 5.
23
3.23
2.
96
7.06
6.
73
3.15
7.
97
10.5
6 4.
66
6.70
9.
87
Indu
NyG
roup
s:
1. L
owR
isk
2.
Med
lum
Rkk
3.
H
ighR
kk
Obj
ectiv
es A
. 1.
G
row
th
2.
Growth an
d In
com
e 3.
In
com
eand
Gro
wth
4.
Income
5. B
alan
a B.
1.
G
row
th
2.
Inco
me
the period 1961-75. Correlation and regression analysis, and andysis of variance have been used. In this study the major findings are:
1. When mutual funds were classified into five categories according to their investment objectives, namely, (i) growth, (ii) growth and income, (iii) income and growth, (iv) income, and (v) balanced portfolio, no particular patterns of relationship between the funds’ objectives, and their average returns and risk levels (both total and systematic risk) were observed for the six overlapping ten-year periods. However, when two categories of objectives, namely, (i) growth, and (ii) income were adopted, there were systematic and consistent relationships between the funds’ objectives, and their average returns and risk measures, for each of the time periods.
2. Average returns and risk measures of mutual funds were positively and signif- icantly correlated within each of the time periods as if risk and return of mutual funds always go hand-in-hand.
3. Within each investment objective group, average return and risk level of mutual funds were not stationary over time. But the degree of risk exposure of mutual funds pursuing growth was consistently higher than that of funds which have income as their primary objective.
4. No significant differences were observed between funds pursuing different investment objectives with respect to either their portfolio compositions in terms of investments in different risk class industries, or portfolio turnovers in terms of additions and deletions of securities of different risk class industries.
The implications of these findings are that since growth oriented Canadian mutual funds have average returns and risk levels consistently higher than those of income oriented funds, the funds in general have not only been operating but also have been adjusting portfolio volatilities over time in accordance with their published objectives.
326 Harbans L. Dhingra
b P 3
3 s B ' A
PP
EN
DIX
A
? N
ame of M
utua
l Fun
d O
bjec
tive
Cod
e 4 9
1.
Inve
stor
s Mut
ual o
f Ca
nada
5
$ 3.
U
nite
d A
ccum
ulat
ive
Fund
1
$ 5.
A
mer
ican
Gro
wth
Fun
d 2
2.
Inve
stor
s Gro
wth
Fun
d of
Can
ada
1
4.
Cana
dian
Inw
stm
ent
Fund
3
6.
Inve
stor
s Int
erna
tiona
l Mut
ual F
und
1 7.
h
ton
Com
mon
wea
lth F
und
2 8.
Ca
nadi
an G
as &
Ene
rgy
Fund
1
9. M
utua
l Acc
umul
atin
g Fu
nd
1 10
. Ea
ton
Leve
rag
Fund
2
11.
Row
dent
Mut
ual F
und
5.
12.
AllC
anad
ian
Evid
ent F
und
3 13
. Be
aubr
an C
orpo
ratio
n 2
14.
NW G
row
th F
und
2 15
. Fo
nds
Des
jard
ins I
nter
natio
nal
1 16
. N
atur
al R
esou
rces
Gro
wth
Fun
d 1
17.
Gro
uped
Inc
ome
Shar
es
3 18
. IT
CO
lnve
stm
ent F
und
1 19
. Ca
nada
Gro
wth
Fun
d 1
20.
Fond
s D
esja
rdin
s Qna
dien
3
21
Cor
pora
te ln
vert
on
2 22
. M
ontre
al T
rust
Com
pany
Con
soli-
da
ted
Inve
stm
ent p
lan
(Equ
ity)
1 23
. D
omin
ion
Equi
ty I
nves
tmen
ts
3 24
. Ca
nadi
an S
ecur
ity G
row
th F
und
1
MUTU
AL F
UN
D B
ETA
COEF
FICI
ENTS
Perio
ds
66-7
5 65
-14
64-7
3 63
-72
0.49
11
0.59
30
0.44
96
0.57
77
0.55
92
0.38
77
0.73
84
0.36
78
0.52
23
0.72
66
0.53
50
62-7
1 61
-70
0.75
29
0.89
22
0.81
51
0.83
70
1.15
92
0.94
65
1.07
28
0.89
03
0.82
45
1.38
51
0.85
46
0.55
98
0.70
45
0.92
23
0.62
14
0.74
19
0.42
78
1.00
95
0.1
159
0.88
13
1.20
92
0.66
31
0.63
60
0.80
43
1.08
94
0.69
70
0.93
59
0.60
22
1 .I 3
93
0.23
61
0.96
62
1.39
53
0.74
06
0.37
90
0.76
29
0.62
82
0.81
41
0.66
10
0.89
81
0.79
37
0.86
28
0.00
00
0.79
40
0.89
00
1.06
84
0.18
77
0.71
92
0.59
83
0.81
78
0.70
91
0.91
89
0.47
27
0.49
80
0.78
99
1.09
34
1.10
04
1.29
05
0.68
43
0.99
43
0.74
20
0.81
43
0.42
67
1.10
75
0.87
61
0.99
91
0.60
50
0.99
54
0.79
19
0.83
41
0.74
93
0.96
70
0.77
41
0.81
45
0.69
38
0.94
01
1.01
77
1.08
39
0.98
46
1.26
97
1.17
41
1.27
68
0.72
37
1.07
10
0.72
21
0.80
61
0.67
58
0.73
94
0.93
43
0.95
94
1.22
00
1.24
83
0.69
71
0.84
10
1.41
83
1.24
06
1.01
68
NA
1.
2190
1.
0534
0.
2843
0.
7628
0.
9579
1.
0269
1.
5610
1.
3898
0.
7510
N
A
1.03
65
1.09
45
0.82
18
0.86
23
1.37
03
1.05
84
1.03
10
1.20
95
0.51
80
o.Si8
0 1.
1957
1.
0477
0.
8058
1.
1560
1.
0462
0.
7291
0.
7292
0.
9154
0.
7718
0.
8283
1.00
16
0.73
57
0.98
01
1.01
14
NA
NA
Nam
e of
Mut
ual F
und
Obj
ectiv
e Pe
riods
Co
de
66-7
5 65
-74
64-7
3 63
-72
62-7
1 61
-70
25.
2 26
. 3'
27.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
41.
42.
43.
44.
45.
46.
47.
48.
49.
SO.
2 28
.
Colle
ctiv
e M
utua
l Fun
d N
atru
sco
Com
mon
Sha
res F
und
Gua
rant
y Tr
ust I
nves
tors
Fun
d Pl
anne
d R
esou
rces
Fun
d R
ever
t M
utua
l Fun
d V
icto
ria k G
rey
Trus
t Co.
RSP
A
ssoc
iate
Inve
stor
s Ca
nadi
an A
naes
thet
ists
' Mut
ual
Acc
umul
atin
g Fu
nd
Dom
inio
n C
ompo
und
Fund
Ea
ton
Gro
wth
Fun
d Ex
ecut
ive
Fund
of
Cana
da
Trad
ex I
nves
tmen
t Fun
d G
row
th E
quity
Fun
d G
uard
ian
Gro
wth
Fun
d N
atio
nal T
rust
Co.
RSP
Mon
trcal
Tru
st C
o. R
SP
The
Met
ropo
titan
Tru
st C
o.
Inve
stmen
t Fun
ds (
Gro
wth
) NW C
anad
ian
Trus
t Pa
cific
Div
iden
d Fu
nd
Pens
ion
Mut
ual F
und
Phill
ips.
Haw
& N
orth
Fun
d St
erlin
g Eq
uity
Fun
d Ta
urus
Fun
d G
uara
nty
Trus
t Co.
Man
ager
R
etire
men
t Sav
ings
Fun
d Tr
ansC
anad
a Sh
ares
"C"
Uni
vers
al Saving
Equi
ty F
und
2 0.
6352
1
0.75
18
2 0.
5520
1
0.57
37
5 0.
8527
5
0.69
72
3 01
6984
1 0.
7912
1
0.66
76
1 0.
3655
3
0.69
39
1 0.
6959
2
1.20
40
1 0.
5298
2
0.85
18
2 0.
8264
3 0.
8589
1
1.18
13
3 0.
5475
2
0.64
38
1 0.
0000
1
0.60
1 7
1 0.
4525
3 0.
6424
5
0.82
89
2 0.
4807
1.09
82
1.09
32
1.07
49
0.83
79
0.85
14
0.94
54
1.39
23
1.35
25
1.10
42
0.83
03
0.94
91
0.87
03
0.94
75
1.07
21
1.08
44
0.63
64
0.91
91
0.72
24
0.98
94
0.77
59
0.79
98
0.91
17
NA
N
A
NA
N
A
0.65
79
0.86
30
1.13
32
0.90
50
1.15
67
1.24
06
1.10
10
0.74
88
1.63
19
NA
N
A
NA
0.
7880
N
A
0.92
1 8
NA
1.
0103
0.
6151
N
A
NA
NA
N
A
1.19
48
0.99
15
0.83
09
NA
1.24
88
NA
1.
0542
N
A
0.93
20
0.93
17
1.16
16
0.97
62
0.77
78
0.90
58
0.99
80
NA
N
A
1.09
63
0.99
63
1.31
75
NA
N
A
NA
N
A
NA
0.
7302
N
A
NA
1.
0724
N
A
NA
N
A
1.01
99
NA
0.
9398
0.
8069
1.
1718
0.82
29
0.73
81
0.89
38
1.00
44
NA
N
A
1.38
40
0.90
56
1.11
80
NA
N
A
NA
N
A
NA
0.
8979
N
A
NA
0.
9787
N
A
NA
N
A
NA
N
A
0.89
86
0.77
37
1.14
46
0.76
66
0.90
14
1 .I 3
69
1.10
45
NA
'
NA
2.
3534
0.
8858
1.
2819
NA
N
A
NA
N
A
NA
0.
8641
N
A
NA
0.
9915
N
A
Nam
e of
Mut
ual
Fund
O
bjcc
tivc
Pcrio
dr
Cod
e 66
-75
65 -7
4 64
-13
63 -
72
62-7
1 61
70
51.
52.
53.
54.
55.
56.
57.
58.
59.
60.
61.
62.
63.
64.
65.
66.
67.
68.
69.
70.
71.
72.
73.
Cdn
ddld
n Tr
u\tc
c\ l
nwni
c t
und
3 Fo
nd5
Dcs
jard
ins H
ypot
hequ
es
4 In
tern
atio
nal h
com
e Fu
nd
4 G
nada
Tru
st l
nvcs
tmcn
t run
d 3
(Inc
omc)
C
anad
a Tr
ust C
o. R
SP (I
ncom
e)
5 Crown
Trus
t Co.
RSP
3
Fond
s hs
jard
ins H
ypot
hequ
es
4 G
uara
nty
Trus
t Co.
Inv
csto
rs F
und
3 G
uara
nty
Trus
t Co.
Man
aged
R
ctir
cmcn
t Sav
ings
I-un
d 3
Can
adia
n M
cdic
al A
ssoc
iatio
n RS
P 3
Savi
ngs
and
Inve
stm
ent
Cor
p M
utua
l Fun
d of C
anad
a 5
Car
nbrid
gc G
row
th F
und
1 C
apita
l Gro
wth
Fun
d 1
Dyn
amic
Fun
d of
Can
ada
1 G
uard
ian
Ente
rpri
se F
und
of
Can
ada
1 In
dust
rial
Div
iden
d Fu
nd
3 M
ariti
me
Equi
ty F
und
1 Te
mpl
eton
Gro
wth
Fun
d 1
Tran
sCan
ada
Shar
es “B”
3 W
este
rn G
row
th F
und
1 G
uard
ian
Secu
rity
Inco
me
Fund
3
ba
da
Perm
anen
t Tru
st R
etir
emen
t 5
Smm
gs F
unds
(Fi
xed)
Fo
nds
Sous
Ces
tion
du T
rust
G
ener
al “B”
4
0.19
72
0.1
I30
0.38
02
0.00
00
-0.0
480
-0.0
600
0.00
00
0.04
43
0.00
00
0.83
30
0.63
13
0.64
47
0.78
83
0.90
62
0.47
53
0.79
61
0.58
03
1.32
03
0.85
79
0.51
80
0.63
08
-0.0
339
-0.0
235
0.27
86
0.23
78
0.56
22
0.11
18
0.0000
-0.0
388
0.05
63
0.1 1
04
NA
NA
0.97
80
NA
1.
0603
1.
2458
0.85
13
1.06
25
NA
1.
8933
N
A
0.72
89
o.oo
00
NA
NA
NA
0.
0645
1.
007 I
0.
2379
0.09
1 1
0.13
84
NA
0.
0355
N
A
NA
0.99
46
NA
1.01
78
-0.2
051
0.72
60
NA
1.
9207
N
A
0.03
46
NA
0.~
95
0.5a
i7
NA
NA
N
A
1.05
22
0.29
77
0.14
45
0.15
99
NA
0.
0391
N
A
NA
1.06
52
NA
0.
8886
1.
1153
NA
0.
8525
N
A
2.03
45
NA
N
A
0.04
92
NA
NA
NA
N
A
I .I 2
09
0.47
63
0.32
57
0.32
81
NA
-0
.019
9 N
A
NA
1.04
53
NA
0.
8392
N
A
NA
0.
8299
N
A
I .66
35
NA
N
A
-0.0
440
NA
NA
NA
0.
0310
1.
1512
0.
6681
0.52
60
NA
N
A
NA
N
A
NA
1.02
39
NA
0.
9604
N
A
NA
0.
8013
N
A
1.20
00
NA
N
A
NA
N
A
NA
Obj
ectiv
e Pe
riods
N
ame
of M
utua
l Fun
d Co
de
66-7
5 65
-74
64-7
3 63
-72
62-7
1 61
-70
5: B g
74.
CI t*
75.
3
77.
76.
78.
79.
80.
81.
82.
83.
84.
85.
86.
87.
88.
3
Linc
oln
Trus
t Co.
Ret
irem
ent
Savings F
und
3 Th
e M
etro
polit
an T
rust
Company
Inve
st,m
ent F
unds
(Inc
ome)
3
Mon
treal
Tru
st C
o. R
SP (I
ncom
e)
Vic
toria
&G
rey
Trus
t Co. R
SP
(Inc
ome)
3
Cana
da P
erm
anen
t Inv
estm
ent
Fund
3
Cana
da P
erm
anen
t Tru
st R
etire
men
t 1
Savi
ngs
Fund
s (Eq
uity
) Ca
nada
Tru
st In
vest
men
t Fun
d
4
(Equ
ity)
3 Ca
nada
Tru
st R
SP (E
quity
) 1
Clo
wn
Trus
t Ret
irem
ent S
avings
1 Fu
nds
(Equ
ity)
Fond
s Des
jard
ins Q
uebe
c 1
Fond
s So
us C
estio
n du
Tru
st G
ener
al "
A"
Linc
oln
Trus
t RS
P (E
quity
) 1
Mon
treal
Tru
st C
ompa
ny C
onso
ti-
1
date
d In
vestm
ent
Plan
(In
tern
atio
nal)
Roya
l Tru
st M
anag
ed F
unds
"A
" 1
Roya
l Tru
st Managed
Fund
s "C"
3 1
-0.1
335
0.10
37
0.07
55
0.00
00
-0.1
576
0.49
68
0.83
49
0.69
94
0.71
15
0.61
76
0.45
40
0.61
56
0.08
81
0.20
74
0.78
60
NA
0.15
78
0.13
23
NA
N
A
0.81
64
1.14
45
0.98
54
0.89
98
0.98
67
NA
NA
N
A
NA
N
A
NA
NA
0.
0748
NA
N
A
0.85
40
0.97
22
0.78
07
0.79
1 2
NA
N
A
NA
N
A
NA
N
A
NA
NA
0.
0795
NA
N
A
0.96
17
1.03
16
0.89
2%
0.86
44
NA
N
A
NA
N
A
NA
N
A
NA
NA
NA
NA
N
A
0.92
80
0.68
87
0.93
79
0.90
62
NA
N
A
NA
N
A
NA
N
A
NA
NA
N
A
NA
N
A
NA
NA
0.
9307
N
A
NA
N
A
NA
N
A
NA
N
A
!A =
Not
Ava
ikbl
e 3b
jecr
ive
Cod
es
1.
Gro
wth
2.
Gro
wth
& In
com
e 3.
ln
wm
e &
Gro
wth
4.
In
com
e 5.
B
alan
cedF
und
La B 3
3 A
PP
EN
DIX
B
F
INDU
STRY
BETA
COEFFICIENTS
B b
Cod
e
5’ 1.
Banks
2 0.
9098
1.
1680
0.
8701
0.
9521
0.
9750
8
2. Be
vera
ges
3 15
599
0.97
66
i.ooo
a 0.
6838
1.
0551
3.
chcmi&
2 0.
9560
1.
1015
0.
9910
0.
9318
0.
995
1 2
4. am
mun
icat
irm
r 2
0.83
76
0.96
57
NA
NA
0.
901 7
5.
Con
stru
ctio
n &
Mat
eria
ls 2
1.07
56
0.93
59
0.87
92
0.89
35
0.94
61
6.
Food
Roo
essi
ng
2 0.
7397
0.
7074
0.
6594
0.
5255
0.
6573
7.
Gen
eral
Ifla
nufa
ctur
ing
3 0.
9804
1.
031 9
1.
2281
0.
8484
1.
0222
8.
Indu
stria
l Mining
3 1.
2610
0.
9666
1.
4139
1.
1923
1.
2085
9.
Mer
chan
disin
g 2
1.14
59
0.71
06
1.10
76
0.83
63
0.95
01
IO.O
il& R
efm
ing
3 1.
1162
1.
0180
0.
6955
1.
1766
1.
0016
11
.Pap
er &
For
est R
odua
s 2
1.07
07
0.97
58
0.82
14
1.08
58
0.98
84
12.P
ipe
Line
s 2
0.93
97
1 ,00
06
0.80
11
1.08
82
0.95
74
13.R
ed E
stat
e 3
1.16
18
NA
NA
N
A
1.16
18
14.S
teel
3
1.14
52
1.24
52
1.17
49
1.36
62
1.23
29
15.T
extil
es &
Clo
thin
g 1
4.13
33
NA
N
A
NA
-0
.133
3 16
.Trm
spor
tatio
n 1
0.01
61
NA
N
A
NA
0.
0161
17
.Tnr
st &
Lopn
3 0.
7959
0.
9736
1.
3010
0.
9533
1.
0060
18
. Util
ities
1
0.35
19
0.63
96
0.58
60
0.06
17
0.40
98
2
Nam
e of
Ind
ustr
y Ri
sk C
lass
71
-75
66-7
0 61
-65
56-6
0 A
vera
ge
NA
=
Not
Ava
ilabl
e Ri
sk Class C
ode
1. L
ower
Risk
(Be
ta v
alue
s less than
0.5)
2.
Medium
Risk
(Be
ta v
alues
bet
wen
0.5
to 1
.0)
3. High R
A (Beta d
ues
grea
ter t
han
1.0)
ul 2
NOTES
The new TSE 3000 Composite Index is a better- proxy for the market but data on this mdex were not available at the time this work wps being done.
This study provides empirical evidence on this proposition.
In order to save space the tables of analysis of variance are omitted
In order to save space the tables of analysis of v a r i a n ~ are omitted
In order to save space the tables of analysis of variance are omitted
REFERENCES
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Bogle, J.C. “Mutual Fund Performance Evaluation”, Financial Analyst Journal (November-December, 1970), pp.25 -33.
Brown, F.E., and Vickers, D. “Mutual Fund Portfolio Activity, Performance, and Market Impact”, The Journalof Finance, (May, 1963). pp. 377-391.
Carlson, R. “Aggregate Performance of Mutual Funds, 1948-1967”, Journal of Quantitative and Financial Analysis (March, 1970). pp. 11 -32.
Cohen, K. and Pogue, J.A. “Some Comments Concernin Mutual Fund Versus Random Portfolio Performance ” Journalof Business, ?AM, 19681, pp. 180-190.
Evan, J. and Archer, S. “Diversification and the Reduction of Dispersion: An Empirical Analysis”, Journal o f Finance (December, 1968). pp. 761-761.
Friend, 1. and Blume, M. “Measurement of Portfolio Performance Under Uncertainty”, The American Economic Review (September, 1970), pp. 561-575.
Jensen, M. “The Performance of Mutual Funds in the Period 1945-1964”, The Journal ofFieance (May, 1968), pp. 389-416.
Jensen, M. “Risk, The Pricing of Capital Assets, and the Evaluation of Investment Portfolios”, Journal of Business (April 1969), pp. 167-247.
Klemkosky, R.C. “Additional Evidence on the Risk Level Discriminatory Powcrs of the Weisenberger Classifications”, The Journal of Business (January, 1976), pp.48-50.
Reins, W.W., and Vandenberg, P.A. “A Comment on the Risk Level Discriminatory Powers of the Wiesenberger Classification”, The Journal of Business (April, 1973). pp. 270-283.
Sharpe, W. “A Simplified Model for Portfolio Analysis”, Management Science January, 1963), pp. 277-293.
Sharpe, W. “Mutual Fund Performance”, Journal of Business (JanGary 1966), pp. 119-1 38.
Harbans L. Dhingra
14) Treynor, J . “How to Rate Management of Investment Funds”, H m a r d Business Review (January-February, 196% pp.63-75.
Treynor, J.L., and Mauy, K. “Can Mutual Funds Outguess the Market?” Harvmd BusinessReview (July, August, 19661, pp. 131-136.
West, R.W. “Mutual Fund Performance and the Theory of Capital Asset Pricing: Some Comments”, The Journal of Business (April, 1 9 6 0 , pp. 230-236.
15)
‘16)
Portfolio Volatility Adjustment 333