Directory UMM :Data Elmu:jurnal:J-a:Journal Of Banking And Finance:Vol25.Issue2.2001:
Journal of Banking & Finance 25 (2001) 339±354
www.elsevier.com/locate/econbase
A note on fair value pricing of mutual funds
Rahul Bhargava a, David A. Dubofsky
a
b
b,*
College of Business Administration, University of Nevada at Reno, Reno, NV 89557, USA
Department of Finance, Insurance, and Real Estate, Virginia Commonwealth University,
P.O. Box 844000, 1015 Floyd Ave., Richmond, VA 23284-4000, USA
Received 3 May 1990; accepted 5 October 1999
Abstract
Mutual funds claim that they employ fair value pricing to prevent active investors
from trading on their beliefs that the fundsÕ net asset values are stale. Our results
support the fundsÕ assertions. We estimate the returns from the following active strategy: buy international open end mutual funds that do not employ fair value pricing on
days that the S&P500 index rises by a large amount, and/or sell them on days that the
S&P500 index declines by a large amount. These active strategies signi®cantly outperform pure buy-and-hold strategies. We conclude that international mutual funds should
make greater use of fair value pricing. Ó 2001 Elsevier Science B.V. All rights reserved.
JEL classi®cation: G20
Keywords: Mutual funds; Fair value pricing; Investments
1. Introduction
Rule 22c-1 of the Investment Company Act of 1940 requires open-end
mutual funds to adopt ``forward pricing'' procedures. Under such procedures,
a fund must ®ll an order to buy or redeem shares based on the net asset value of
its shares next calculated after receipt of the order. The net asset value is
*
Corresponding author. Tel.: +1-804-828-1620; fax: +1-804-828-3972.
E-mail address: [email protected] (D.A. Dubofsky).
0378-4266/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved.
PII: S 0 3 7 8 - 4 2 6 6 ( 9 9 ) 0 0 1 2 6 - 0
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R. Bhargava, D.A. Dubofsky / Journal of Banking & Finance 25 (2001) 339±354
computed using market quotations to value the securities in the fundÕs portfolio. If a market quotation for a security is not readily available, then it must
be valued at its fair value as determined in good faith by the fundÕs board of
directors. Historically, this latter rule was implemented for valuing non-treasury bonds, thinly traded stocks that did not trade during the prior 24 hours
and which had no bid or oer quote available, and shares in which trading had
been halted prior to the marketÕs close.
In 1981, the SEC ruled that a fund may (but is not required to) value securities that trade in foreign markets at their fair values, when an event has
occurred after the close of the foreign market that may have aected their
values. With this ruling, the SEC basically permitted funds to employ fair value
pricing even when it has last-trade prices of foreign securities available.
Fair value pricing only recently became a controversial issue. On 28 October
1997, Asian stocks plummeted in value; in particular the Hang Seng Index of
stocks trading in Hong Kong fell 14%. This occurred prior to the commencement of 28 October trading in the US. If a US-based mutual fund did not
utilize fair value pricing, it would have reduced the value of the average Hong
Kong-traded stock held in its portfolio by 14%. But later on 28 October, an
event occurred which aected these stocksÕ values in the opinion of some
mutual funds: US stocks, as measured by the Dow Jones Industrial Average,
rose by 4.71%. Instead of reporting a large decline in their net asset values
(NAV) due to their holdings of Asian stocks, funds that employed fair value
pricing instead reported increases in their NAVs.
Many investors, unaware that their mutual funds could employ fair value
pricing, were upset by this move, even though the fundsÕ prospectuses stated
that they could take these actions (see Gasparino, 1997; Wyatt, 1997). These
investors expected to buy shares of international mutual funds that invested in
Asian stocks at much lower prices than what they actually paid.
The purpose of this paper is to examine the potential for abuse that exists
when a mutual fund family does not use fair value pricing. The ability to trade
at known and stale prices permits some active investors to exploit the other
passive owners of international mutual funds. Fair value pricing preserves the
intent of Rule 22c-1 of the Investment Company Act of 1940, as it attempts to
result in investors trading open end mutual fund shares at the next NAV that is
computed after the trade order has been entered.
2. The problem
Suppose that there are only three stock markets in the world, in Tokyo,
London, and New York City. Trading day t begins in the Far East. At 9 AM
(Tokyo time), equity trading begins in Tokyo, and ends at 3 PM. 3 PM Tokyo
time is 6 AM in London. Equity trading does not begin in London until 9 AM.
R. Bhargava, D.A. Dubofsky / Journal of Banking & Finance 25 (2001) 339±354
341
Thus, there are 3 hours in which there is no trading of stocks. When British
equity trading ceases at 4:30 PM on day t, it is 11:30 AM in New York City.
Equity trading began 2 hours earlier in New York, so that there is overlap of 2
hours during which trading is taking place both in London and New York.
Trading ends at 4 PM in New York, at which time it is 6 AM on day t 1 in
Tokyo. 1 Thus, 3 hours remain until day t 1 trading commences.
Now consider a US-based mutual fund that invests in foreign securities, and
de®ne all times as those in New York (Eastern Standard Time). Any order to
trade the fund that is received between 4 PM on day t ÿ 1 and 3:59 PM on day t
is ®lled at the fundÕs NAV on day t. That NAV is the dierence between the
values of all the fundÕs assets, and all of its liabilities, where both asset and
liability values are measured at 4 PM on day t. The value of an asset is generally the last trade price, or the average of its last bid and oer quotes.
The problem is that, in the absence of fair value pricing, the last trade price
of a foreign security that does not trade in the US is stale, and there is no
opportunity to update its value at 4 PM. This situation exists even when new
information, relevant for the foreign securityÕs valuation, has been revealed
since the foreign market closed on day t. Investors have knowledge of the information and can assess its expected impact on the securityÕs true value.
However the information cannot be impounded in its price because it trades
only in its home market. By purchasing shares in international funds which do
not employ fair value pricing, investors have the opportunity to purchase these
foreign securities at the stale day t prices, and subsequently realize a gain when
foreign market trading commences on day t 1.
Fair value pricing should eliminate the potential for investor abuse. A fund
using fair value pricing could either make its own assessment about the impact
of the newly revealed information on the values of its foreign securities, or
implement a plan by which the fundÕs NAV on day t is determined by the prices
and quotes that exist at the start of trading on day t 1.
We wish to estimate the potential rewards for investors who exploit the
failure to employ fair value pricing. Of course, it is dicult to de®ne what
represents relevant information that would likely aect the values of foreign
securities. As a proxy, we use the percentage rate of return on the S&P500
index on day t. Basically, we assume that on average, a signi®cant portion of a
large change in the S&P500 can be attributed to global valuation factors. Thus,
a large increase (decrease) in the S&P500 on day t signals that foreign stock
markets will rise (fall) on day t 1. Under this assumption, investing in an
international fund at the close of trading on day t, after a large increase in the
S&P500, will be pro®table, as will selling an international fund just before the
close of trading on a day that the S&P declines signi®cantly. Investors will
1
All of these are standard times.
342
R. Bhargava, D.A. Dubofsky / Journal of Banking & Finance 25 (2001) 339±354
likely capture a positive return in the former case, and avoid a negative return
in the latter case.
Recent research has supported the conclusions that the correlations between
the returns in foreign stock markets are positive and increasing (see, for example, Koch and Koch, 1991). Considerable other research has concluded that
the US market aects subsequent changes in foreign stock prices more than
foreign markets aect the US. (Eun and Shim, 1989; Bailey and Stulz, 1990;
Hamao et al., 1990; Becker et al., 1990; Jeon and Von Furstenberg, 1990; Lin et
al., 1994), and that correlations increase as volatility increases (King and
Wadhwani, 1990; Neumark et al., 1991; Longin and Solnik, 1995, 1998;
Karolyi and Stulz, 1996). Volatile markets increase the correlations. In fact,
Ramchand and Susmel (1997) conclude that correlations between US and
foreign stock markets are on average 2±3.5 times higher when the US market is
highly volatile as compared to when it is experiencing low volatility.
3. Data
Our data consists of three Vanguard International Equity Index Funds: the
European, Paci®c and Emerging Markets portfolios. We use these funds as
proxies for typical international mutual funds. 2 We also use the actual S&P
stock market index (not a mutual fund) to measure the returns realized by an
investor when he or she is in US stocks. 3 The data for the European and
Paci®c mutual funds begin on 18 July 1990. The data for the Emerging Markets mutual fund begin on 4 May 1994. All data end on 31 December 1996.
Vanguard veri®ed, via a phone conversation, that the funds never used fair
value pricing during this time period.
We examine the results from two similar strategies. The ®rst takes the
perspective of an investor primarily interested in domestic (US) equities. Funds
are transferred from the S&P500 index into an international mutual fund at the
close of trading on any day on which the daily rate of return of the S&P500
index exceeds its mean daily return (estimated using the past 40 days of returns)
by more than 1.5 times its standard deviation. 4 Thus, the benchmark is the
rate of return realized on the S&P500 index on the day after the one-day in-
2
Sesit (1998) suggests that actively managed international mutual funds outperform indexes
(and hence international index funds).
3
In the period 1990±1996, the Vanguard 500 index mutual fund, which attempts to track the
performance of the S&P500 index, underperformed the index by an average of 18.6 basis points per
year.
4
The 1:5r parameter was arbitrarily chosen in order to generate about one trade each month.
However, our results are unaected by using either 1.25 standard deviations or 1.75 standard
deviations as a signal to trade.
R. Bhargava, D.A. Dubofsky / Journal of Banking & Finance 25 (2001) 339±354
343
vestment in the international fund. The second strategy incorporates the perspective of an investor who is normally invested in an international mutual
fund. This investor sells his or her fund and buys the S&P500 index whenever
the S&P500 daily rate of return is more than 1.5 standard deviations below its
mean. Here, the benchmark is the foregone one-day return that would have
been realized on the international mutual fund.
This trading scheme determines an estimated upper bound of what an investor can eectively steal from passive investors in a mutual fund family that
does not employ fair value pricing. It is an upper bound because of several
factors:
· We assume that an investor knows the daily rate of return of the S&P500
index prior to its realization. In other words, to precisely implement this
trading scheme, an investor would have to observe the spot S&P500 index
at 4 PM ± e, and then instantaneously make all of the required trades.
· We ignore all transaction costs. The Vanguard mutual funds used in this study
assess transaction fees on all purchases: 0.5% for the Paci®c portfolio, 1% for
the European portfolio, and 1.5% for the Emerging Markets portfolio.
· Funds vary in their methods by which shares can be bought or sold. For example, the Vanguard funds permit index fund trades only by mail or by wire.
Moreover, even if a fund family allows telephone or internet exchanges,
there is no guarantee that on busy days an investor will be able to ``get
through'' to a telephone representative or to the internet site.
· Some funds place restrictions on the number of exchanges that can be made
during some stated calendar period, or add fees to the trades of active traders.
Thus, in practice, an investor who tries to exploit the fundsÕ practice of using
last trade prices would inject some noise into the results by trading on the
information available several minutes prior to the marketÕs close at 4 PM. He
would have to utilize true no-load funds. He would trade actively managed
mutual funds, rather than the index funds (or the index, in the case of the
S&P500) that we analyze. He would have to move his capital from one family
of funds to another in order to circumvent the limits that many fund families
have placed on the number of exchanges per period. While these factors represent real costs, and they create real (though small) risks, we believe that the
active strategy described above is still feasible.
4. Results
4.1. Sell the S&P and buy the international fund after the S&P rises
The mean percentage increase in the S&P500 index that triggers the decision
to switch from the S&P500 to the Vanguard European or Paci®c Funds is
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R. Bhargava, D.A. Dubofsky / Journal of Banking & Finance 25 (2001) 339±354
1.356%; the median return is 1.234%. These means are for the 115 signals over
a 6.54 year period from 18 June 1990 through 31 December 1996.
The results that could be realized under ideal trading conditions are presented in Table 1. On the day that the hypothetical investor is in the international fund, the mean rate of return foregone on the S&P500 index is 0.2042%.
The median return foregone is 0.0784%. However, the rates of return on each
of the three Vanguard international index funds are signi®cantly higher than
that dayÕs return on the S&P. For example, the European portfolioÕs mean
(median) return is 0.5046% (0.4838%). The incremental mean return realized by
switching funds (from the S&P to the European portfolio) is 0.3003%; the tstatistic for the paired dierence between means test is 3.46, which is signi®cant
at the 1% level. Similar statistically signi®cant results are realized by switching
to the Paci®c and Emerging Markets portfolios. 75 of the 115 trading signals
proved to be pro®table for the European portfolio, and the binomial z-statistic
of 3.171 is signi®cantly dierent from zero. The binomial z-statistic for the
Paci®c portfolio is 1.306, which is the only insigni®cant ®gure for the relevant
tests.
The values of corr(S&P(t), fund(t 1)) are 0.22, 0.36, and 0.11 for the
European, Paci®c and Emerging Market funds, respectively. However, because
the observed values of S&P(t) are not normally distributed (all of the observations are positive), we also compute the SpearmanÕs rank correlation coef®cients, and they are 0.10, 0.23, and 0.074 for the European, Paci®c and
Emerging Market funds, respectively. These correlations are computed using
the 115 one-day observations for the European and Paci®c funds, and the 48
one-day observations for the Emerging Markets fund. 5
The results are suggestive of an upper bound of what failure to employ fair
value pricing might cost the passive investors of a mutual fund. Suppose that
active investors (who exploit funds that do not employ fair value pricing) own
1% of an international fundÕs assets at the start of the year. The international
fund has $1 billion invested in international stocks. Capturing an extra return
of 0.3% per day would lead to an excess return of 5.41% per year, if 17.58 trade
signals per year are received. This represents $54.1 million that is eectively
stolen each year from the international mutual fund investors who own the
remaining 99% of its shares.
We also examine the results that an active investor could realize by employing a slightly dierent trading strategy that exploits the lack of fair value
pricing. As before, the investor sells his/her initial investment in the S&P500
index portfolio and purchases shares in the international mutual fund at the
5
For the entire period studied, corr(S&P(t), fund(t 1)) is 0.22, 0.26, and 0.36 for the European,
Paci®c and Emerging Markets funds, respectively. The corresponding values of SpearmanÕs rank
correlations are 0.24, 0.20, and 0.35.
# Observations
Mean return (%)
t-Statistic
Median return (%)
Min return (%)
Max return (%)
# Positive
# Negative
z-Statistic
a
S&P
Euro
Paci®c
S&P
Emerging
S&P-Euro
S&P-Pac
S&P-Emer
115
0.2042
3.00b
0.0784
)1.857
3.1877
67
48
1.679d
115
0.5046
5.91b
0.4838
)2.031
4.8193
88
27
5.595b
115
0.5770
3.89b
0.4779
)3.735
9.8143
79
36
3.917b
48
0.1642
2.26c
0.091
)0.7624
1.9184
31
17
1.876d
48
0.6880
6.82b
0.5892
)0.3268
3.0097
42
6
5.052b
115
0.3003
3.46b
0.2421
)1.943
4.6298
75
40
3.171b
115
0.3727
2.49c
0.2741
)3.9546
9.7286
65
50
1.306
48
0.5237
4.89b
0.4142
)0.8819
2.0484
37
11
3.608b
This table presents the returns on the day after a signal to sell the S&P500 and buy the international fund is received. A signal is a return on the
S&P500 index that is 1:5r greater than the mean S&P500 rate of return during the previous 40 trading days. The ®gures in the columns labeled ``S&P''
are the returns that are foregone. The returns in the columns labeled ``Euro'', ``Paci®c'', and ``Emerging'' are realized. The dierential returns, shown in
the last three columns, represent excess returns that can be realized by domestically-oriented (US) aggressive traders in mutual fund families that do not
use fair value pricing.
b
Signi®cantly dierent from zero at the 1% level of con®dence.
c
Signi®cantly dierent from zero at the 5% level of con®dence.
d
Signi®cantly dierent from zero at the 10% level of con®dence.
R. Bhargava, D.A. Dubofsky / Journal of Banking & Finance 25 (2001) 339±354
Table 1
Results realized by selling the S&P500 and investing international index funds after a large rise in the S&P500: one-day holding perioda
345
346
R. Bhargava, D.A. Dubofsky / Journal of Banking & Finance 25 (2001) 339±354
close of trading on any day on which the daily rate of return of the S&P500
index exceeds its mean return by more than 1.5 standard deviations. But now,
the investment capital remains in the international fund until the close of
trading of the next subsequent day that the S&P500 index declines, at which
time the international fund is sold and the S&P500 index portfolio is re-purchased. Thus, this strategy typically keeps the investorÕs investment capital in
the international funds longer than one day. 6 The investor captures the high
return from the international fund that typically follows a high S&P500 return,
and also avoids the last day S&P500 negative return, which triggers the decision to switch back to the S&P.
Table 2 presents the results. The three panels illustrate the results from
switching into the European, Paci®c, and Emerging Markets mutual funds.
The results are presented in each panel by year (column 1). Columns 2 and 3
show the number of switches per year, and the number of switches in which
performance was improved by switching (i.e., the international fund outperformed the S&P500 during the switch period). Column 4 contains the binomial
z-test results for the null hypothesis that the percentage of pro®table switches is
50%. The mean number of days that investment capital was in the international
mutual fund, per switch, is in column 5. The next three columns show the mean
daily S&P500 return while the investor is in the international fund (i.e., the
S&P500 return foregone), the mean daily international fund rate of return
while the investor is invested in the international fund, the dierence between
the S&P500 and the international fund returns, and the t-statistic that tests for
daily mean dierences. The last two columns show the mean dierence per
switch, and the t-statistic that tests for mean dierences per switch.
To illustrate how the data presented in Table 2 should be interpreted,
consider the European fund (Panel A) for 1996. There were 13 times that the
daily S&P return exceeded its previous mean by more than 1.5 standard deviations. These 13 trading signals led to pro®table switches seven times, and the
binomial z-statistic is 0.0. On an average, funds were invested in the international funds for exactly two days. While in the international funds, the mean
daily S&P500 rate of return was 0.1485%. But the mean daily return for the
European mutual fund during these times was 0.2734%. The daily dierence is
0.1249%, but with a t-statistic of 0.829, the dierence between daily mean returns is statistically insigni®cant. The mean dierence per switch is 0.2469%
(the investorÕs return is increased by keeping her investment capital in the
6
There are 42 out of 97 trade signals (1:5r) beginning 18 June 1990 that result in only a one day
transfer of investment capital from the S&P into the European and Paci®c funds. In 15 of the 43
trade signals in the period commencing 4 May 1994, investment capital resided in the Emerging
Markets fund only one day. There are more trade signals reported in Table 1 than in Table 2
because we treated two consecutive one-day signals as two observations when employing the
strategy described in Table 1; these would be only one signal in Table 2.
Table 2
Results realized by selling the S&P500 and investing in international index funds after a large rise in the S&P500: longer holding perioda
Year
Switches
Positive
z-Stat
Mean
days
Mean
daily S&P
return (%)
Mean
daily
strategy
return (%)
Mean di
per day
(%)
t-Stat
Mean di
per switch
(%)
t-Stat
0.894
1.336
0.555
1.455
1.871d
0.918
0.000
2.800
1.570
3.150
2.000
1.750
2.630
2.000
0.7221
0.0668
0.2359
0.0455
0.0234
0.1361
0.1485
1.1587
0.2478
0.1815
0.3170
0.4544
0.2859
0.2734
0.4366
0.1810
)0.0544
0.2715
0.4310
0.1498
0.1249
1.303
0.662
)0.148
1.969c
3.926b
1.645d
0.829
1.2687
0.2827
)0.2319
0.5427
0.7573
0.3954
0.2469
1.410
0.806
)0.407
2.761b
4.090b
1.727d
0.866
All (1.50)
97
66
3.452b
2.217
0.1587
0.3443
0.1856
2.107c
0.4057
3.075b
All (1.25)
All (1.75)
137
68
93
45
4.101b
2.118c
2.255
2.118
0.1637
0.1385
0.3178
0.3057
0.1541
0.1672
2.268c
1.960c
0.3430
0.3530
3.046b
2.291c
Panel B: Paci®c portfolio
1990
5
1991
14
1992
13
1993
17
1994
16
1995
19
1996
13
4
5
10
13
11
14
10
0.894
)1.336
1.664d
1.940d
1.250
1.835d
1.664d
2.800
1.570
3.150
2.000
1.750
2.630
2.000
0.7221
0.0668
0.2359
0.0455
0.0234
0.1361
0.1485
1.7300
0.0543
0.5686
0.3258
0.5311
0.5112
0.3536
1.0080
)0.0125
0.3327
0.2803
0.5077
0.3750
0.2051
1.281
)0.039
1.235
1.555
2.153c
2.023c
1.059
2.8396
)0.0250
1.0658
0.5595
0.8950
0.9879
0.4104
2.553c
)0.058
1.572
1.905d
1.964d
2.234c
1.020
All (1.5)
97
67
3.655b
2.217
0.1587
0.5090
0.3503
3.385b
0.7798
4.011b
All (1.25)
All (1.75)
137
68
88
47
3.247b
3.032b
2.255
2.118
0.1637
0.1385
0.4497
0.5064
0.2860
0.3679
3.577b
3.127b
0.6427
0.8620
4.286b
3.368b
347
Panel A: European portfolio
1990
5
4
1991
14
10
1992
13
8
1993
17
12
1994
16
13
1995
19
12
1996
13
7
R. Bhargava, D.A. Dubofsky / Journal of Banking & Finance 25 (2001) 339±354
Number
348
Number
Year
Switches
Positive
z-Stat
Mean
days
Mean
daily S&P
return (%)
Mean
daily
strategy
return (%)
Mean di
per day
(%)
t-Stat
Mean di
per switch
(%)
t-Stat
Panel C: Emerging markets portfolio
1994
11
10
1995
19
15
1996
13
10
2.412c
2.294c
1.664d
1.910
2.630
2.000
0.0400
0.1361
0.1485
0.7736
0.4245
0.3509
0.7336
0.2884
0.2023
3.918b
2.815b
1.531
1.4122
0.7614
0.4042
3.389b
2.584b
1.514
All (1.50)
43
35
3.965b
2.260
0.1186
0.4803
0.3617
4.633b
0.8199
4.196b
All (1.25)
All (1.75)
55
31
43
25
4.045b
3.233b
2.364
2.161
0.1362
0.1058
0.4360
0.4475
0.2998
0.3418
4.281b
3.737b
0.7124
0.7410
4.319b
3.940b
a
This table presents the results of a trading strategy in which an investor initially is invested in the S&P500 index. Investment capital is transferred into
one of three international mutual funds at the close of trading of any day on which the S&P rises by 1.5r times the mean daily return. Investment
capital remains in the international mutual fund until the close of trading on the next day that the S&P500 index declines.
b
Signi®cantly dierent from zero at the 1% level of con®dence.
c
Signi®cantly dierent from zero at the 5% level of con®dence.
d
Signi®cantly dierent from zero at the 10% level of con®dence.
R. Bhargava, D.A. Dubofsky / Journal of Banking & Finance 25 (2001) 339±354
Table 2 (Continued)
R. Bhargava, D.A. Dubofsky / Journal of Banking & Finance 25 (2001) 339±354
349
European fund until the day that the S&P declined; note that the investor is
foregoing this decline in the S&P on the last day). The t-statistic that tests
whether the mean dierence per switch is dierent from zero is 0.866, which is
insigni®cant.
While the results for any single year and any single international portfolio
exhibit a great deal of variability, overall, they indicate that a pro®table trading
strategy exists. For example, 66 of the 97 trading signals were associated with
higher returns from the European portfolio than the S&P500; the z-statistic of
3.452 rejects the null hypothesis that the trading signals lead to pro®table
switches in 50% of the observations. The mean excess return from investing in
the European portfolio is 0.1856% per day; the t-statistic of 2.107 is signi®cantly dierent from zero at the 5% level of con®dence. The excess return is
0.4057% per switch, as the mean number of days per switch is 2.217; this return
dierential per switch is statistically signi®cant at the 1% level, as the t-statistic
is 3.075.
Similar conclusions are drawn from analyzing the data for any of the three
international mutual funds. Furthermore, the results are not changed when we
use a trading signal of 1.25 standard deviations from the mean or 1.75 standard
deviations from the mean.
Table 3 illustrates other summary results from this strategy. In Panel A of
Table 3, the mean daily rate of return, standard deviation of daily returns,
coecient of variation, and geometric mean rate of return are presented.
They show that each ``switching strategy'' provides a higher daily mean rate
of return and higher daily geometric mean rate of return, than investing
only in the international fund or investing only in the S&P500. For example,
the arithmetic (geometric) daily mean rate of return for the S&P500 is
0.0467% (0.0442%). The arithmetic (geometric) daily mean rate of return for
the European portfolio is 0.0446% (0.04%). However, by actively switching
investment capital into international funds after a large increase in the
S&P500 index, the arithmetic (geometric) daily mean rate of return is
0.0705% (0.0672%). The coecient of variation of 11.49 is lower for the
switching strategy; the coecient of variation is 15.32 for an investment only
in the S&P500 index and 21.45 for an investment only in the European
fund.
Panel B of Table 3 illustrates how an initial $10 000 investment in each
fund, and in each trading strategy, would have fared by the end of the
period of analysis. The strategies of switching investments yield much higher
rates of return than a buy-and-hold strategy. The active strategies provide
terminal values of $43 162 (Paci®c) and $30 392 (European), compared to the
passive strategies of remaining invested in the S&P500 ($20 756), the Paci®c
portfolio ($11 169) and the European portfolio ($19 389). The same conclusion is drawn over a shorter time period for the Emerging Markets
portfolio.
350
R. Bhargava, D.A. Dubofsky / Journal of Banking & Finance 25 (2001) 339±354
Table 3
Other summary performance statistics realized by selling the S&P500 and investing in international
index funds after a large rise in the S&P500: longer holding perioda
Panel A
Portfolio
Mean daily
return (%)
Standard deviation
of daily returns (%)
C.V.
Geometric mean
return (%)
S&P500
European
European + S&P
Paci®c
Paci®c + S&P
Emerging Markets
Emerging + S&P
0.0467
0.0446
0.0705
0.0150
0.0923
0.0360
0.1276
0.7155
0.9572
0.8100
1.2950
0.8755
0.8266
0.6702
15.32
21.45
11.49
86.09
9.49
22.95
5.25
0.0442
0.0400
0.0672
0.0067
0.0885
0.0326
0.1253
on 18/6/90
on 4/5/94
on 31/12/96
Annual yield (%)
$10 000
$10 000
$10 000
$20 756.00
$11 169.36
$43 161.96
$19 389.17
$30 391.51
$16 398.21
$12 451.81
$23 233.57
11.82
1.71
25.07
10.66
18.54
20.43
8.59
37.29
Panel B
S&P500
Paci®c
Paci®c + S&P
European
European + S&P
S&P500
Emerging Markets
Emerging + S&P
$10 000
$10 000
$10 000
$10 000
$10 000
a
This table presents the summary statistics for a trading strategy that exploits a typical international mutual fund that does not use fair value pricing. The mean daily rates of return, standard
deviation, coecient of variation (C.V.), and geometric mean daily rates of return are shown in
panel A. Panel B shows what a $10 000 investment would have grown to by the end of our study
period, and the associated annualized rate of return. The results are presented for each individual
fund, the S&P500 index, and the trading strategy in which investment capital is transferred from the
S&P500 index to the indicated international mutual fund whenever the S&P500 rises by more than
1.5 standard deviations times the previous mean return. The international fund is sold, and the
proceeds re-invested in the S&P500 on the next day that the S&P500 index declines.
4.2. Sell the international fund and buy the S&P when the S&P declines
The mean percentage decline in the S&P500 index that triggers the decision
to switch out of the Vanguard European or Paci®c Funds into the S&P500 is
)1.333%; the median return is )1.232%. These means are for the 108 signals
over a 6.54-year period from 18 June 1990 through 31 December 1996. When
using one-day holding period data for these 108 sell signal (49 sell signals for
the Emerging Markets fund), corr(S&P(t), fund(t 1)) is )0.0087, 0.14, and
0.22 for the European, Paci®c, and Emerging Markets funds, respectively.
SpearmanÕs rank correlations are 0.059, 0.19, and 0.051 for the European,
Paci®c, and Emerging Markets funds, respectively.
R. Bhargava, D.A. Dubofsky / Journal of Banking & Finance 25 (2001) 339±354
351
The results for the strategy in which funds are transferred from the international fund into the S&P500 index for just one day are presented in Table 4.
The incremental returns that can be realized by selling the international funds
when a sell signal (the S&P500 declines by a large amount) is received are very
similar in magnitude and signi®cance to those realized from buying international funds when a buy signal is received (as shown in Table 1). The mean
dierential one-day returns are 0.3623%, 0.4252% and 0.5285% for the European, Paci®c and Emerging Markets portfolios, respectively. All of the paired
dierence t-statistics are signi®cant. The dierential data are shown in the last
three columns of Table 4.
We also examined the strategy that led to Tables 2 and 3, i.e., we estimated
the yearly performance by switching out of the European, Paci®c and
Emerging Markets Index Funds just before 4 PM on days when the S&P500
declines by more than 1.5 standard deviations times its estimated mean daily
return. The proceeds from the sales of the international funds are invested in
the S&P500. The investment is switched back to the international funds on the
next subsequent day that the S&P500 index rises (in order to pro®t from the
anticipated overnight increase in foreign markets). We ®nd that the added
returns achievable by investors who exploit the lack of fair value pricing are
statistically signi®cant at the 1% level of con®dence. The mean dierences per
switch are 0.5268%, 0.7000%, and 0.7424% for the European, Paci®c, and
Emerging Markets portfolios, respectively. The results are robust to the usage
of 1:25r and 1:75r of the mean daily return. We conclude that switching out of
the any of the three funds outperforms both a buy-and-hold investment in the
international fund, and a buy-and-hold investment in the S&P index. The tables for this strategy that are analogous to Tables 2 and 3 are available from
the authors.
5. Conclusions
This paper analyzes how active investors can exploit international mutual
funds that do not employ fair value pricing procedures when computing their
net asset values. Fair value pricing is a procedure by which mutual funds estimate the values of the securities in their portfolios, rather than use actual last
trade prices or quotes.
Past research has found that international stock markets are becoming
increasingly correlated, correlations are higher when markets are volatile,
and the US stock market aects subsequent foreign market returns more
than foreign stock markets aect subsequent US returns. Thus, one way to
exploit the nonexistence of fair value pricing is to switch investment capital
from the US market to international mutual funds on days when the US
stock market rises by a substantial amount and/or to switch out of inter-
352
# Observations
Mean return (%)
t-Statistic
Median return (%)
Min return (%)
Max return (%)
# Positive
# Negative
z-Statistic
a
S&P
Euro
Paci®c
S&P
Emerging
S&P-Euro
S&P-Pac
S&P-Emer
108
)0.0634
)0.802
0.0218
)3.024
2.135
55
53
0.096
108
)0.4257
)3.78b
)0.3047
)7.822
2.179
31
77
4.330b
108
)0.4886
)3.47b
)0.5009
)6.164
3.830
39
69
2.791b
49
0.0200
0.208
)0.0722
)1.180
1.381
22
27
0.571
49
)0.5085
)3.67b
)0.4562
)2.938
1.775
15
34
2.571c
108
0.3623
3.28b
0.3310
)2.830
5.460
71
37
3.175b
108
0.4252
3.04b
0.3672
)4.826
5.010
69
39
2.791b
49
0.5285
3.58b
0.4815
)1.180
3.706
33
16
2.286b
This table presents the returns on the day after a signal to sell the international fund and buy the S&P500 is received. A signal is a return on the
S&P500 index that is more than 1.5r below the mean S&P500 rate of return during the previous 40 trading days. The ®gures in the columns labeled
``S&P'' are the returns that are realized. The returns in the columns labeled ``Euro'', ``Paci®c'', and ``Emerging'' are foregone. The dierential returns
represent excess returns that can be realized by internationally-oriented aggressive investors in mutual fund families that do not use fair value pricing.
b
Signi®cantly dierent from zero at the 1% level of con®dence.
c
Signi®cantly dierent from zero at the 5% level of con®dence.
R. Bhargava, D.A. Dubofsky / Journal of Banking & Finance 25 (2001) 339±354
Table 4
Results realized by selling the international index funds and investing in the S&P500 after a large decline in the S&P500: one-day holding perioda
R. Bhargava, D.A. Dubofsky / Journal of Banking & Finance 25 (2001) 339±354
353
national mutual funds on days when the US stock market declines substantially.
We examine a hypothetical investor who switches from the S&P500 index
into one of three Vanguard International index mutual funds at the close of
trading on a day on which the S&P500 index rises by more than 1.5 standard
deviations times the mean daily rate of return of the S&P. The rate of return
from this strategy is signi®cantly higher than those available from other investments. This indicates the potential for abuse by active traders. Similar high
returns are obtained by switching from any of the three international index
funds into the S&P500 when the S&P500 index declines by more than 1:5r
times its estimated daily mean return.
In March 1998, the SEC did announce one change regarding the use of fair
value pricing. Now, if a mutual fund has a policy that utilizes fair value pricing
under special circumstances (e.g., when an event occurs after the close of the
foreign exchange on which its portfolio securities are principally traded that is
likely to have changed the value of the securities), it must provide a brief explanation of the circumstances and the eects of this policy. In addition, the
discussion must be stated in clear and unambiguous terms.
Our results imply that international funds implement fair value pricing more
frequently. Perhaps fair value pricing should be used whenever US markets
experience a ``big'' move up or down, as de®ned in our paper (any percentage
change exceeding 1.5 standard deviations times an indexÕs mean return). As
markets become more global, the problem will disappear. In a world of continuous, 24 hour trading of all securities, with dealers oering quotes on all
securities, regardless of their home market, fair value pricing will not be
needed. But until then, a change in the pricing policies of international mutual
funds is needed.
Acknowledgements
We thank David Harless for helpful comments. We are also grateful to other
participants in the Virginia Commonwealth University ®nance±economics
workshop for their suggestions.
References
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stock markets. Journal of Portfolio Management 16, 57±61.
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Eun, C.S., Shim, S., 1989. International transmission of stock market movements. Journal of
Financial and Quantitative Analysis 24, 241±256.
Gasparino, C., 1997. ÔFair-valueÕ pricing for shares in funds to be reviewed by SEC. 3 November,
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international stock markets. Review of Financial Studies 3, 281±307.
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indexes. Quarterly Review of Economics and Business 30, 15±30.
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Wyatt, E., 1997. WhatÕs fair in setting fund value. 9 November, New York Times, Section 3, p. 12.
www.elsevier.com/locate/econbase
A note on fair value pricing of mutual funds
Rahul Bhargava a, David A. Dubofsky
a
b
b,*
College of Business Administration, University of Nevada at Reno, Reno, NV 89557, USA
Department of Finance, Insurance, and Real Estate, Virginia Commonwealth University,
P.O. Box 844000, 1015 Floyd Ave., Richmond, VA 23284-4000, USA
Received 3 May 1990; accepted 5 October 1999
Abstract
Mutual funds claim that they employ fair value pricing to prevent active investors
from trading on their beliefs that the fundsÕ net asset values are stale. Our results
support the fundsÕ assertions. We estimate the returns from the following active strategy: buy international open end mutual funds that do not employ fair value pricing on
days that the S&P500 index rises by a large amount, and/or sell them on days that the
S&P500 index declines by a large amount. These active strategies signi®cantly outperform pure buy-and-hold strategies. We conclude that international mutual funds should
make greater use of fair value pricing. Ó 2001 Elsevier Science B.V. All rights reserved.
JEL classi®cation: G20
Keywords: Mutual funds; Fair value pricing; Investments
1. Introduction
Rule 22c-1 of the Investment Company Act of 1940 requires open-end
mutual funds to adopt ``forward pricing'' procedures. Under such procedures,
a fund must ®ll an order to buy or redeem shares based on the net asset value of
its shares next calculated after receipt of the order. The net asset value is
*
Corresponding author. Tel.: +1-804-828-1620; fax: +1-804-828-3972.
E-mail address: [email protected] (D.A. Dubofsky).
0378-4266/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved.
PII: S 0 3 7 8 - 4 2 6 6 ( 9 9 ) 0 0 1 2 6 - 0
340
R. Bhargava, D.A. Dubofsky / Journal of Banking & Finance 25 (2001) 339±354
computed using market quotations to value the securities in the fundÕs portfolio. If a market quotation for a security is not readily available, then it must
be valued at its fair value as determined in good faith by the fundÕs board of
directors. Historically, this latter rule was implemented for valuing non-treasury bonds, thinly traded stocks that did not trade during the prior 24 hours
and which had no bid or oer quote available, and shares in which trading had
been halted prior to the marketÕs close.
In 1981, the SEC ruled that a fund may (but is not required to) value securities that trade in foreign markets at their fair values, when an event has
occurred after the close of the foreign market that may have aected their
values. With this ruling, the SEC basically permitted funds to employ fair value
pricing even when it has last-trade prices of foreign securities available.
Fair value pricing only recently became a controversial issue. On 28 October
1997, Asian stocks plummeted in value; in particular the Hang Seng Index of
stocks trading in Hong Kong fell 14%. This occurred prior to the commencement of 28 October trading in the US. If a US-based mutual fund did not
utilize fair value pricing, it would have reduced the value of the average Hong
Kong-traded stock held in its portfolio by 14%. But later on 28 October, an
event occurred which aected these stocksÕ values in the opinion of some
mutual funds: US stocks, as measured by the Dow Jones Industrial Average,
rose by 4.71%. Instead of reporting a large decline in their net asset values
(NAV) due to their holdings of Asian stocks, funds that employed fair value
pricing instead reported increases in their NAVs.
Many investors, unaware that their mutual funds could employ fair value
pricing, were upset by this move, even though the fundsÕ prospectuses stated
that they could take these actions (see Gasparino, 1997; Wyatt, 1997). These
investors expected to buy shares of international mutual funds that invested in
Asian stocks at much lower prices than what they actually paid.
The purpose of this paper is to examine the potential for abuse that exists
when a mutual fund family does not use fair value pricing. The ability to trade
at known and stale prices permits some active investors to exploit the other
passive owners of international mutual funds. Fair value pricing preserves the
intent of Rule 22c-1 of the Investment Company Act of 1940, as it attempts to
result in investors trading open end mutual fund shares at the next NAV that is
computed after the trade order has been entered.
2. The problem
Suppose that there are only three stock markets in the world, in Tokyo,
London, and New York City. Trading day t begins in the Far East. At 9 AM
(Tokyo time), equity trading begins in Tokyo, and ends at 3 PM. 3 PM Tokyo
time is 6 AM in London. Equity trading does not begin in London until 9 AM.
R. Bhargava, D.A. Dubofsky / Journal of Banking & Finance 25 (2001) 339±354
341
Thus, there are 3 hours in which there is no trading of stocks. When British
equity trading ceases at 4:30 PM on day t, it is 11:30 AM in New York City.
Equity trading began 2 hours earlier in New York, so that there is overlap of 2
hours during which trading is taking place both in London and New York.
Trading ends at 4 PM in New York, at which time it is 6 AM on day t 1 in
Tokyo. 1 Thus, 3 hours remain until day t 1 trading commences.
Now consider a US-based mutual fund that invests in foreign securities, and
de®ne all times as those in New York (Eastern Standard Time). Any order to
trade the fund that is received between 4 PM on day t ÿ 1 and 3:59 PM on day t
is ®lled at the fundÕs NAV on day t. That NAV is the dierence between the
values of all the fundÕs assets, and all of its liabilities, where both asset and
liability values are measured at 4 PM on day t. The value of an asset is generally the last trade price, or the average of its last bid and oer quotes.
The problem is that, in the absence of fair value pricing, the last trade price
of a foreign security that does not trade in the US is stale, and there is no
opportunity to update its value at 4 PM. This situation exists even when new
information, relevant for the foreign securityÕs valuation, has been revealed
since the foreign market closed on day t. Investors have knowledge of the information and can assess its expected impact on the securityÕs true value.
However the information cannot be impounded in its price because it trades
only in its home market. By purchasing shares in international funds which do
not employ fair value pricing, investors have the opportunity to purchase these
foreign securities at the stale day t prices, and subsequently realize a gain when
foreign market trading commences on day t 1.
Fair value pricing should eliminate the potential for investor abuse. A fund
using fair value pricing could either make its own assessment about the impact
of the newly revealed information on the values of its foreign securities, or
implement a plan by which the fundÕs NAV on day t is determined by the prices
and quotes that exist at the start of trading on day t 1.
We wish to estimate the potential rewards for investors who exploit the
failure to employ fair value pricing. Of course, it is dicult to de®ne what
represents relevant information that would likely aect the values of foreign
securities. As a proxy, we use the percentage rate of return on the S&P500
index on day t. Basically, we assume that on average, a signi®cant portion of a
large change in the S&P500 can be attributed to global valuation factors. Thus,
a large increase (decrease) in the S&P500 on day t signals that foreign stock
markets will rise (fall) on day t 1. Under this assumption, investing in an
international fund at the close of trading on day t, after a large increase in the
S&P500, will be pro®table, as will selling an international fund just before the
close of trading on a day that the S&P declines signi®cantly. Investors will
1
All of these are standard times.
342
R. Bhargava, D.A. Dubofsky / Journal of Banking & Finance 25 (2001) 339±354
likely capture a positive return in the former case, and avoid a negative return
in the latter case.
Recent research has supported the conclusions that the correlations between
the returns in foreign stock markets are positive and increasing (see, for example, Koch and Koch, 1991). Considerable other research has concluded that
the US market aects subsequent changes in foreign stock prices more than
foreign markets aect the US. (Eun and Shim, 1989; Bailey and Stulz, 1990;
Hamao et al., 1990; Becker et al., 1990; Jeon and Von Furstenberg, 1990; Lin et
al., 1994), and that correlations increase as volatility increases (King and
Wadhwani, 1990; Neumark et al., 1991; Longin and Solnik, 1995, 1998;
Karolyi and Stulz, 1996). Volatile markets increase the correlations. In fact,
Ramchand and Susmel (1997) conclude that correlations between US and
foreign stock markets are on average 2±3.5 times higher when the US market is
highly volatile as compared to when it is experiencing low volatility.
3. Data
Our data consists of three Vanguard International Equity Index Funds: the
European, Paci®c and Emerging Markets portfolios. We use these funds as
proxies for typical international mutual funds. 2 We also use the actual S&P
stock market index (not a mutual fund) to measure the returns realized by an
investor when he or she is in US stocks. 3 The data for the European and
Paci®c mutual funds begin on 18 July 1990. The data for the Emerging Markets mutual fund begin on 4 May 1994. All data end on 31 December 1996.
Vanguard veri®ed, via a phone conversation, that the funds never used fair
value pricing during this time period.
We examine the results from two similar strategies. The ®rst takes the
perspective of an investor primarily interested in domestic (US) equities. Funds
are transferred from the S&P500 index into an international mutual fund at the
close of trading on any day on which the daily rate of return of the S&P500
index exceeds its mean daily return (estimated using the past 40 days of returns)
by more than 1.5 times its standard deviation. 4 Thus, the benchmark is the
rate of return realized on the S&P500 index on the day after the one-day in-
2
Sesit (1998) suggests that actively managed international mutual funds outperform indexes
(and hence international index funds).
3
In the period 1990±1996, the Vanguard 500 index mutual fund, which attempts to track the
performance of the S&P500 index, underperformed the index by an average of 18.6 basis points per
year.
4
The 1:5r parameter was arbitrarily chosen in order to generate about one trade each month.
However, our results are unaected by using either 1.25 standard deviations or 1.75 standard
deviations as a signal to trade.
R. Bhargava, D.A. Dubofsky / Journal of Banking & Finance 25 (2001) 339±354
343
vestment in the international fund. The second strategy incorporates the perspective of an investor who is normally invested in an international mutual
fund. This investor sells his or her fund and buys the S&P500 index whenever
the S&P500 daily rate of return is more than 1.5 standard deviations below its
mean. Here, the benchmark is the foregone one-day return that would have
been realized on the international mutual fund.
This trading scheme determines an estimated upper bound of what an investor can eectively steal from passive investors in a mutual fund family that
does not employ fair value pricing. It is an upper bound because of several
factors:
· We assume that an investor knows the daily rate of return of the S&P500
index prior to its realization. In other words, to precisely implement this
trading scheme, an investor would have to observe the spot S&P500 index
at 4 PM ± e, and then instantaneously make all of the required trades.
· We ignore all transaction costs. The Vanguard mutual funds used in this study
assess transaction fees on all purchases: 0.5% for the Paci®c portfolio, 1% for
the European portfolio, and 1.5% for the Emerging Markets portfolio.
· Funds vary in their methods by which shares can be bought or sold. For example, the Vanguard funds permit index fund trades only by mail or by wire.
Moreover, even if a fund family allows telephone or internet exchanges,
there is no guarantee that on busy days an investor will be able to ``get
through'' to a telephone representative or to the internet site.
· Some funds place restrictions on the number of exchanges that can be made
during some stated calendar period, or add fees to the trades of active traders.
Thus, in practice, an investor who tries to exploit the fundsÕ practice of using
last trade prices would inject some noise into the results by trading on the
information available several minutes prior to the marketÕs close at 4 PM. He
would have to utilize true no-load funds. He would trade actively managed
mutual funds, rather than the index funds (or the index, in the case of the
S&P500) that we analyze. He would have to move his capital from one family
of funds to another in order to circumvent the limits that many fund families
have placed on the number of exchanges per period. While these factors represent real costs, and they create real (though small) risks, we believe that the
active strategy described above is still feasible.
4. Results
4.1. Sell the S&P and buy the international fund after the S&P rises
The mean percentage increase in the S&P500 index that triggers the decision
to switch from the S&P500 to the Vanguard European or Paci®c Funds is
344
R. Bhargava, D.A. Dubofsky / Journal of Banking & Finance 25 (2001) 339±354
1.356%; the median return is 1.234%. These means are for the 115 signals over
a 6.54 year period from 18 June 1990 through 31 December 1996.
The results that could be realized under ideal trading conditions are presented in Table 1. On the day that the hypothetical investor is in the international fund, the mean rate of return foregone on the S&P500 index is 0.2042%.
The median return foregone is 0.0784%. However, the rates of return on each
of the three Vanguard international index funds are signi®cantly higher than
that dayÕs return on the S&P. For example, the European portfolioÕs mean
(median) return is 0.5046% (0.4838%). The incremental mean return realized by
switching funds (from the S&P to the European portfolio) is 0.3003%; the tstatistic for the paired dierence between means test is 3.46, which is signi®cant
at the 1% level. Similar statistically signi®cant results are realized by switching
to the Paci®c and Emerging Markets portfolios. 75 of the 115 trading signals
proved to be pro®table for the European portfolio, and the binomial z-statistic
of 3.171 is signi®cantly dierent from zero. The binomial z-statistic for the
Paci®c portfolio is 1.306, which is the only insigni®cant ®gure for the relevant
tests.
The values of corr(S&P(t), fund(t 1)) are 0.22, 0.36, and 0.11 for the
European, Paci®c and Emerging Market funds, respectively. However, because
the observed values of S&P(t) are not normally distributed (all of the observations are positive), we also compute the SpearmanÕs rank correlation coef®cients, and they are 0.10, 0.23, and 0.074 for the European, Paci®c and
Emerging Market funds, respectively. These correlations are computed using
the 115 one-day observations for the European and Paci®c funds, and the 48
one-day observations for the Emerging Markets fund. 5
The results are suggestive of an upper bound of what failure to employ fair
value pricing might cost the passive investors of a mutual fund. Suppose that
active investors (who exploit funds that do not employ fair value pricing) own
1% of an international fundÕs assets at the start of the year. The international
fund has $1 billion invested in international stocks. Capturing an extra return
of 0.3% per day would lead to an excess return of 5.41% per year, if 17.58 trade
signals per year are received. This represents $54.1 million that is eectively
stolen each year from the international mutual fund investors who own the
remaining 99% of its shares.
We also examine the results that an active investor could realize by employing a slightly dierent trading strategy that exploits the lack of fair value
pricing. As before, the investor sells his/her initial investment in the S&P500
index portfolio and purchases shares in the international mutual fund at the
5
For the entire period studied, corr(S&P(t), fund(t 1)) is 0.22, 0.26, and 0.36 for the European,
Paci®c and Emerging Markets funds, respectively. The corresponding values of SpearmanÕs rank
correlations are 0.24, 0.20, and 0.35.
# Observations
Mean return (%)
t-Statistic
Median return (%)
Min return (%)
Max return (%)
# Positive
# Negative
z-Statistic
a
S&P
Euro
Paci®c
S&P
Emerging
S&P-Euro
S&P-Pac
S&P-Emer
115
0.2042
3.00b
0.0784
)1.857
3.1877
67
48
1.679d
115
0.5046
5.91b
0.4838
)2.031
4.8193
88
27
5.595b
115
0.5770
3.89b
0.4779
)3.735
9.8143
79
36
3.917b
48
0.1642
2.26c
0.091
)0.7624
1.9184
31
17
1.876d
48
0.6880
6.82b
0.5892
)0.3268
3.0097
42
6
5.052b
115
0.3003
3.46b
0.2421
)1.943
4.6298
75
40
3.171b
115
0.3727
2.49c
0.2741
)3.9546
9.7286
65
50
1.306
48
0.5237
4.89b
0.4142
)0.8819
2.0484
37
11
3.608b
This table presents the returns on the day after a signal to sell the S&P500 and buy the international fund is received. A signal is a return on the
S&P500 index that is 1:5r greater than the mean S&P500 rate of return during the previous 40 trading days. The ®gures in the columns labeled ``S&P''
are the returns that are foregone. The returns in the columns labeled ``Euro'', ``Paci®c'', and ``Emerging'' are realized. The dierential returns, shown in
the last three columns, represent excess returns that can be realized by domestically-oriented (US) aggressive traders in mutual fund families that do not
use fair value pricing.
b
Signi®cantly dierent from zero at the 1% level of con®dence.
c
Signi®cantly dierent from zero at the 5% level of con®dence.
d
Signi®cantly dierent from zero at the 10% level of con®dence.
R. Bhargava, D.A. Dubofsky / Journal of Banking & Finance 25 (2001) 339±354
Table 1
Results realized by selling the S&P500 and investing international index funds after a large rise in the S&P500: one-day holding perioda
345
346
R. Bhargava, D.A. Dubofsky / Journal of Banking & Finance 25 (2001) 339±354
close of trading on any day on which the daily rate of return of the S&P500
index exceeds its mean return by more than 1.5 standard deviations. But now,
the investment capital remains in the international fund until the close of
trading of the next subsequent day that the S&P500 index declines, at which
time the international fund is sold and the S&P500 index portfolio is re-purchased. Thus, this strategy typically keeps the investorÕs investment capital in
the international funds longer than one day. 6 The investor captures the high
return from the international fund that typically follows a high S&P500 return,
and also avoids the last day S&P500 negative return, which triggers the decision to switch back to the S&P.
Table 2 presents the results. The three panels illustrate the results from
switching into the European, Paci®c, and Emerging Markets mutual funds.
The results are presented in each panel by year (column 1). Columns 2 and 3
show the number of switches per year, and the number of switches in which
performance was improved by switching (i.e., the international fund outperformed the S&P500 during the switch period). Column 4 contains the binomial
z-test results for the null hypothesis that the percentage of pro®table switches is
50%. The mean number of days that investment capital was in the international
mutual fund, per switch, is in column 5. The next three columns show the mean
daily S&P500 return while the investor is in the international fund (i.e., the
S&P500 return foregone), the mean daily international fund rate of return
while the investor is invested in the international fund, the dierence between
the S&P500 and the international fund returns, and the t-statistic that tests for
daily mean dierences. The last two columns show the mean dierence per
switch, and the t-statistic that tests for mean dierences per switch.
To illustrate how the data presented in Table 2 should be interpreted,
consider the European fund (Panel A) for 1996. There were 13 times that the
daily S&P return exceeded its previous mean by more than 1.5 standard deviations. These 13 trading signals led to pro®table switches seven times, and the
binomial z-statistic is 0.0. On an average, funds were invested in the international funds for exactly two days. While in the international funds, the mean
daily S&P500 rate of return was 0.1485%. But the mean daily return for the
European mutual fund during these times was 0.2734%. The daily dierence is
0.1249%, but with a t-statistic of 0.829, the dierence between daily mean returns is statistically insigni®cant. The mean dierence per switch is 0.2469%
(the investorÕs return is increased by keeping her investment capital in the
6
There are 42 out of 97 trade signals (1:5r) beginning 18 June 1990 that result in only a one day
transfer of investment capital from the S&P into the European and Paci®c funds. In 15 of the 43
trade signals in the period commencing 4 May 1994, investment capital resided in the Emerging
Markets fund only one day. There are more trade signals reported in Table 1 than in Table 2
because we treated two consecutive one-day signals as two observations when employing the
strategy described in Table 1; these would be only one signal in Table 2.
Table 2
Results realized by selling the S&P500 and investing in international index funds after a large rise in the S&P500: longer holding perioda
Year
Switches
Positive
z-Stat
Mean
days
Mean
daily S&P
return (%)
Mean
daily
strategy
return (%)
Mean di
per day
(%)
t-Stat
Mean di
per switch
(%)
t-Stat
0.894
1.336
0.555
1.455
1.871d
0.918
0.000
2.800
1.570
3.150
2.000
1.750
2.630
2.000
0.7221
0.0668
0.2359
0.0455
0.0234
0.1361
0.1485
1.1587
0.2478
0.1815
0.3170
0.4544
0.2859
0.2734
0.4366
0.1810
)0.0544
0.2715
0.4310
0.1498
0.1249
1.303
0.662
)0.148
1.969c
3.926b
1.645d
0.829
1.2687
0.2827
)0.2319
0.5427
0.7573
0.3954
0.2469
1.410
0.806
)0.407
2.761b
4.090b
1.727d
0.866
All (1.50)
97
66
3.452b
2.217
0.1587
0.3443
0.1856
2.107c
0.4057
3.075b
All (1.25)
All (1.75)
137
68
93
45
4.101b
2.118c
2.255
2.118
0.1637
0.1385
0.3178
0.3057
0.1541
0.1672
2.268c
1.960c
0.3430
0.3530
3.046b
2.291c
Panel B: Paci®c portfolio
1990
5
1991
14
1992
13
1993
17
1994
16
1995
19
1996
13
4
5
10
13
11
14
10
0.894
)1.336
1.664d
1.940d
1.250
1.835d
1.664d
2.800
1.570
3.150
2.000
1.750
2.630
2.000
0.7221
0.0668
0.2359
0.0455
0.0234
0.1361
0.1485
1.7300
0.0543
0.5686
0.3258
0.5311
0.5112
0.3536
1.0080
)0.0125
0.3327
0.2803
0.5077
0.3750
0.2051
1.281
)0.039
1.235
1.555
2.153c
2.023c
1.059
2.8396
)0.0250
1.0658
0.5595
0.8950
0.9879
0.4104
2.553c
)0.058
1.572
1.905d
1.964d
2.234c
1.020
All (1.5)
97
67
3.655b
2.217
0.1587
0.5090
0.3503
3.385b
0.7798
4.011b
All (1.25)
All (1.75)
137
68
88
47
3.247b
3.032b
2.255
2.118
0.1637
0.1385
0.4497
0.5064
0.2860
0.3679
3.577b
3.127b
0.6427
0.8620
4.286b
3.368b
347
Panel A: European portfolio
1990
5
4
1991
14
10
1992
13
8
1993
17
12
1994
16
13
1995
19
12
1996
13
7
R. Bhargava, D.A. Dubofsky / Journal of Banking & Finance 25 (2001) 339±354
Number
348
Number
Year
Switches
Positive
z-Stat
Mean
days
Mean
daily S&P
return (%)
Mean
daily
strategy
return (%)
Mean di
per day
(%)
t-Stat
Mean di
per switch
(%)
t-Stat
Panel C: Emerging markets portfolio
1994
11
10
1995
19
15
1996
13
10
2.412c
2.294c
1.664d
1.910
2.630
2.000
0.0400
0.1361
0.1485
0.7736
0.4245
0.3509
0.7336
0.2884
0.2023
3.918b
2.815b
1.531
1.4122
0.7614
0.4042
3.389b
2.584b
1.514
All (1.50)
43
35
3.965b
2.260
0.1186
0.4803
0.3617
4.633b
0.8199
4.196b
All (1.25)
All (1.75)
55
31
43
25
4.045b
3.233b
2.364
2.161
0.1362
0.1058
0.4360
0.4475
0.2998
0.3418
4.281b
3.737b
0.7124
0.7410
4.319b
3.940b
a
This table presents the results of a trading strategy in which an investor initially is invested in the S&P500 index. Investment capital is transferred into
one of three international mutual funds at the close of trading of any day on which the S&P rises by 1.5r times the mean daily return. Investment
capital remains in the international mutual fund until the close of trading on the next day that the S&P500 index declines.
b
Signi®cantly dierent from zero at the 1% level of con®dence.
c
Signi®cantly dierent from zero at the 5% level of con®dence.
d
Signi®cantly dierent from zero at the 10% level of con®dence.
R. Bhargava, D.A. Dubofsky / Journal of Banking & Finance 25 (2001) 339±354
Table 2 (Continued)
R. Bhargava, D.A. Dubofsky / Journal of Banking & Finance 25 (2001) 339±354
349
European fund until the day that the S&P declined; note that the investor is
foregoing this decline in the S&P on the last day). The t-statistic that tests
whether the mean dierence per switch is dierent from zero is 0.866, which is
insigni®cant.
While the results for any single year and any single international portfolio
exhibit a great deal of variability, overall, they indicate that a pro®table trading
strategy exists. For example, 66 of the 97 trading signals were associated with
higher returns from the European portfolio than the S&P500; the z-statistic of
3.452 rejects the null hypothesis that the trading signals lead to pro®table
switches in 50% of the observations. The mean excess return from investing in
the European portfolio is 0.1856% per day; the t-statistic of 2.107 is signi®cantly dierent from zero at the 5% level of con®dence. The excess return is
0.4057% per switch, as the mean number of days per switch is 2.217; this return
dierential per switch is statistically signi®cant at the 1% level, as the t-statistic
is 3.075.
Similar conclusions are drawn from analyzing the data for any of the three
international mutual funds. Furthermore, the results are not changed when we
use a trading signal of 1.25 standard deviations from the mean or 1.75 standard
deviations from the mean.
Table 3 illustrates other summary results from this strategy. In Panel A of
Table 3, the mean daily rate of return, standard deviation of daily returns,
coecient of variation, and geometric mean rate of return are presented.
They show that each ``switching strategy'' provides a higher daily mean rate
of return and higher daily geometric mean rate of return, than investing
only in the international fund or investing only in the S&P500. For example,
the arithmetic (geometric) daily mean rate of return for the S&P500 is
0.0467% (0.0442%). The arithmetic (geometric) daily mean rate of return for
the European portfolio is 0.0446% (0.04%). However, by actively switching
investment capital into international funds after a large increase in the
S&P500 index, the arithmetic (geometric) daily mean rate of return is
0.0705% (0.0672%). The coecient of variation of 11.49 is lower for the
switching strategy; the coecient of variation is 15.32 for an investment only
in the S&P500 index and 21.45 for an investment only in the European
fund.
Panel B of Table 3 illustrates how an initial $10 000 investment in each
fund, and in each trading strategy, would have fared by the end of the
period of analysis. The strategies of switching investments yield much higher
rates of return than a buy-and-hold strategy. The active strategies provide
terminal values of $43 162 (Paci®c) and $30 392 (European), compared to the
passive strategies of remaining invested in the S&P500 ($20 756), the Paci®c
portfolio ($11 169) and the European portfolio ($19 389). The same conclusion is drawn over a shorter time period for the Emerging Markets
portfolio.
350
R. Bhargava, D.A. Dubofsky / Journal of Banking & Finance 25 (2001) 339±354
Table 3
Other summary performance statistics realized by selling the S&P500 and investing in international
index funds after a large rise in the S&P500: longer holding perioda
Panel A
Portfolio
Mean daily
return (%)
Standard deviation
of daily returns (%)
C.V.
Geometric mean
return (%)
S&P500
European
European + S&P
Paci®c
Paci®c + S&P
Emerging Markets
Emerging + S&P
0.0467
0.0446
0.0705
0.0150
0.0923
0.0360
0.1276
0.7155
0.9572
0.8100
1.2950
0.8755
0.8266
0.6702
15.32
21.45
11.49
86.09
9.49
22.95
5.25
0.0442
0.0400
0.0672
0.0067
0.0885
0.0326
0.1253
on 18/6/90
on 4/5/94
on 31/12/96
Annual yield (%)
$10 000
$10 000
$10 000
$20 756.00
$11 169.36
$43 161.96
$19 389.17
$30 391.51
$16 398.21
$12 451.81
$23 233.57
11.82
1.71
25.07
10.66
18.54
20.43
8.59
37.29
Panel B
S&P500
Paci®c
Paci®c + S&P
European
European + S&P
S&P500
Emerging Markets
Emerging + S&P
$10 000
$10 000
$10 000
$10 000
$10 000
a
This table presents the summary statistics for a trading strategy that exploits a typical international mutual fund that does not use fair value pricing. The mean daily rates of return, standard
deviation, coecient of variation (C.V.), and geometric mean daily rates of return are shown in
panel A. Panel B shows what a $10 000 investment would have grown to by the end of our study
period, and the associated annualized rate of return. The results are presented for each individual
fund, the S&P500 index, and the trading strategy in which investment capital is transferred from the
S&P500 index to the indicated international mutual fund whenever the S&P500 rises by more than
1.5 standard deviations times the previous mean return. The international fund is sold, and the
proceeds re-invested in the S&P500 on the next day that the S&P500 index declines.
4.2. Sell the international fund and buy the S&P when the S&P declines
The mean percentage decline in the S&P500 index that triggers the decision
to switch out of the Vanguard European or Paci®c Funds into the S&P500 is
)1.333%; the median return is )1.232%. These means are for the 108 signals
over a 6.54-year period from 18 June 1990 through 31 December 1996. When
using one-day holding period data for these 108 sell signal (49 sell signals for
the Emerging Markets fund), corr(S&P(t), fund(t 1)) is )0.0087, 0.14, and
0.22 for the European, Paci®c, and Emerging Markets funds, respectively.
SpearmanÕs rank correlations are 0.059, 0.19, and 0.051 for the European,
Paci®c, and Emerging Markets funds, respectively.
R. Bhargava, D.A. Dubofsky / Journal of Banking & Finance 25 (2001) 339±354
351
The results for the strategy in which funds are transferred from the international fund into the S&P500 index for just one day are presented in Table 4.
The incremental returns that can be realized by selling the international funds
when a sell signal (the S&P500 declines by a large amount) is received are very
similar in magnitude and signi®cance to those realized from buying international funds when a buy signal is received (as shown in Table 1). The mean
dierential one-day returns are 0.3623%, 0.4252% and 0.5285% for the European, Paci®c and Emerging Markets portfolios, respectively. All of the paired
dierence t-statistics are signi®cant. The dierential data are shown in the last
three columns of Table 4.
We also examined the strategy that led to Tables 2 and 3, i.e., we estimated
the yearly performance by switching out of the European, Paci®c and
Emerging Markets Index Funds just before 4 PM on days when the S&P500
declines by more than 1.5 standard deviations times its estimated mean daily
return. The proceeds from the sales of the international funds are invested in
the S&P500. The investment is switched back to the international funds on the
next subsequent day that the S&P500 index rises (in order to pro®t from the
anticipated overnight increase in foreign markets). We ®nd that the added
returns achievable by investors who exploit the lack of fair value pricing are
statistically signi®cant at the 1% level of con®dence. The mean dierences per
switch are 0.5268%, 0.7000%, and 0.7424% for the European, Paci®c, and
Emerging Markets portfolios, respectively. The results are robust to the usage
of 1:25r and 1:75r of the mean daily return. We conclude that switching out of
the any of the three funds outperforms both a buy-and-hold investment in the
international fund, and a buy-and-hold investment in the S&P index. The tables for this strategy that are analogous to Tables 2 and 3 are available from
the authors.
5. Conclusions
This paper analyzes how active investors can exploit international mutual
funds that do not employ fair value pricing procedures when computing their
net asset values. Fair value pricing is a procedure by which mutual funds estimate the values of the securities in their portfolios, rather than use actual last
trade prices or quotes.
Past research has found that international stock markets are becoming
increasingly correlated, correlations are higher when markets are volatile,
and the US stock market aects subsequent foreign market returns more
than foreign stock markets aect subsequent US returns. Thus, one way to
exploit the nonexistence of fair value pricing is to switch investment capital
from the US market to international mutual funds on days when the US
stock market rises by a substantial amount and/or to switch out of inter-
352
# Observations
Mean return (%)
t-Statistic
Median return (%)
Min return (%)
Max return (%)
# Positive
# Negative
z-Statistic
a
S&P
Euro
Paci®c
S&P
Emerging
S&P-Euro
S&P-Pac
S&P-Emer
108
)0.0634
)0.802
0.0218
)3.024
2.135
55
53
0.096
108
)0.4257
)3.78b
)0.3047
)7.822
2.179
31
77
4.330b
108
)0.4886
)3.47b
)0.5009
)6.164
3.830
39
69
2.791b
49
0.0200
0.208
)0.0722
)1.180
1.381
22
27
0.571
49
)0.5085
)3.67b
)0.4562
)2.938
1.775
15
34
2.571c
108
0.3623
3.28b
0.3310
)2.830
5.460
71
37
3.175b
108
0.4252
3.04b
0.3672
)4.826
5.010
69
39
2.791b
49
0.5285
3.58b
0.4815
)1.180
3.706
33
16
2.286b
This table presents the returns on the day after a signal to sell the international fund and buy the S&P500 is received. A signal is a return on the
S&P500 index that is more than 1.5r below the mean S&P500 rate of return during the previous 40 trading days. The ®gures in the columns labeled
``S&P'' are the returns that are realized. The returns in the columns labeled ``Euro'', ``Paci®c'', and ``Emerging'' are foregone. The dierential returns
represent excess returns that can be realized by internationally-oriented aggressive investors in mutual fund families that do not use fair value pricing.
b
Signi®cantly dierent from zero at the 1% level of con®dence.
c
Signi®cantly dierent from zero at the 5% level of con®dence.
R. Bhargava, D.A. Dubofsky / Journal of Banking & Finance 25 (2001) 339±354
Table 4
Results realized by selling the international index funds and investing in the S&P500 after a large decline in the S&P500: one-day holding perioda
R. Bhargava, D.A. Dubofsky / Journal of Banking & Finance 25 (2001) 339±354
353
national mutual funds on days when the US stock market declines substantially.
We examine a hypothetical investor who switches from the S&P500 index
into one of three Vanguard International index mutual funds at the close of
trading on a day on which the S&P500 index rises by more than 1.5 standard
deviations times the mean daily rate of return of the S&P. The rate of return
from this strategy is signi®cantly higher than those available from other investments. This indicates the potential for abuse by active traders. Similar high
returns are obtained by switching from any of the three international index
funds into the S&P500 when the S&P500 index declines by more than 1:5r
times its estimated daily mean return.
In March 1998, the SEC did announce one change regarding the use of fair
value pricing. Now, if a mutual fund has a policy that utilizes fair value pricing
under special circumstances (e.g., when an event occurs after the close of the
foreign exchange on which its portfolio securities are principally traded that is
likely to have changed the value of the securities), it must provide a brief explanation of the circumstances and the eects of this policy. In addition, the
discussion must be stated in clear and unambiguous terms.
Our results imply that international funds implement fair value pricing more
frequently. Perhaps fair value pricing should be used whenever US markets
experience a ``big'' move up or down, as de®ned in our paper (any percentage
change exceeding 1.5 standard deviations times an indexÕs mean return). As
markets become more global, the problem will disappear. In a world of continuous, 24 hour trading of all securities, with dealers oering quotes on all
securities, regardless of their home market, fair value pricing will not be
needed. But until then, a change in the pricing policies of international mutual
funds is needed.
Acknowledgements
We thank David Harless for helpful comments. We are also grateful to other
participants in the Virginia Commonwealth University ®nance±economics
workshop for their suggestions.
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