A note on fair value pricing of mutual funds
Rahul Bhargava
a, David A. Dubofsky
b,*a
College of Business Administration, University of Nevada at Reno, Reno, NV 89557, USA b
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 fundsÕassertions. We estimate the returns from the following active strat-egy: 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 outper-form pure buy-and-hold strategies. We conclude that international mutual funds should make greater use of fair value pricing.Ó2001 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
Journal of Banking & Finance 25 (2001) 339±354
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*Corresponding author. Tel.: +1-804-828-1620; fax: +1-804-828-3972. E-mail address:[email protected] (D.A. Dubofsky).
computed using market quotations to value the securities in the fundÕs port-folio. 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-trea-sury 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 se-curities 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 com-mencement 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 doesnotuse 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 thenextNAV that is computed after the trade order has been entered.
2. The problem
Thus, there are 3 hours in which there is no trading of stocks. When British equity trading ceases at 4:30 PM on dayt, 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 dayt1 in Tokyo.1Thus, 3 hours remain until dayt1 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 daytÿ1 and 3:59 PM on dayt
is ®lled at the fundÕs NAV on dayt. 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 dayt. The value of an asset is gen-erallythe 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 dayt. Investors have knowledge of the in-formation 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 daytprices, and subsequently realize a gain when foreign market trading commences on dayt1.
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 daytis determined by the prices and quotes that exist at the start of trading on dayt1.
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 dayt. 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 tsignals that foreign stock markets will rise (fall) on day t1. Under this assumption, investing in an international fund at the close of trading on dayt, 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
1All of these are standard times.
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 ex-ample, 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.2We 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 Mar-kets 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.4Thus, 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.
4The 1
:5rparameter was arbitrarily chosen in order to generate about one trade each month.
vestment in the international fund. The second strategy incorporates the per-spective 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 deviationsbelowits 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 in-vestor can eectively steal from passive inin-vestors 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
ex-ample, 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 trad-ers.
Thus, in practice, an investor who tries to exploit the fundsÕpractice 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 rep-resent 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
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 pre-sented in Table 1. On the day that the hypothetical investor is in the interna-tional 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%; thet -statistic 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 binomialz-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(t1)) 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 obser-vations 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 em-ploying 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
5For the entire period studied, corr(S&P(
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
S&P Euro Paci®c S&P Emerging S&P-Euro S&P-Pac S&P-Emer
# Observations 115 115 115 48 48 115 115 48
Mean return (%) 0.2042 0.5046 0.5770 0.1642 0.6880 0.3003 0.3727 0.5237 t-Statistic 3.00b 5.91b 3.89b 2.26c 6.82b 3.46b 2.49c 4.89b Median return (%) 0.0784 0.4838 0.4779 0.091 0.5892 0.2421 0.2741 0.4142 Min return (%) )1.857 )2.031 )3.735 )0.7624 )0.3268 )1.943 )3.9546 )0.8819 Max return (%) 3.1877 4.8193 9.8143 1.9184 3.0097 4.6298 9.7286 2.0484
# Positive 67 88 79 31 42 75 65 37
# Negative 48 27 36 17 6 40 50 11
z-Statistic 1.679d 5.595b 3.917b 1.876d 5.052b 3.171b 1.306 3.608b aThis table presents the returns on the dayaftera 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 1:5rgreater 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
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-pur-chased. Thus, this strategy typically keeps the investorÕs investment capital in the international funds longer than one day.6The 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 deci-sion 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 outper-formed 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 thet-statistic that tests for daily mean dierences. The last two columns show the mean dierence per switch, and thet-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 de-viations. These 13 trading signals led to pro®table switches seven times, and the binomialz-statistic is 0.0. On an average, funds were invested in the interna-tional funds for exactly two days. While in the internainterna-tional 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 at-statistic of 0.829, the dierence between daily mean re-turns 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
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
Number Mean
1990 5 4 0.894 2.800 0.7221 1.1587 0.4366 1.303 1.2687 1.410
1991 14 10 1.336 1.570 0.0668 0.2478 0.1810 0.662 0.2827 0.806
1992 13 8 0.555 3.150 0.2359 0.1815 )0.0544 )0.148 )0.2319 )0.407
1993 17 12 1.455 2.000 0.0455 0.3170 0.2715 1.969c 0.5427 2.761b
1994 16 13 1.871d 1.750 0.0234 0.4544 0.4310 3.926b 0.7573 4.090b
1995 19 12 0.918 2.630 0.1361 0.2859 0.1498 1.645d 0.3954 1.727d
1996 13 7 0.000 2.000 0.1485 0.2734 0.1249 0.829 0.2469 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) 137 93 4.101b 2.255 0.1637 0.3178 0.1541 2.268c 0.3430 3.046b All (1.75) 68 45 2.118c 2.118 0.1385 0.3057 0.1672 1.960c 0.3530 2.291c
Panel B: Paci®c portfolio
1990 5 4 0.894 2.800 0.7221 1.7300 1.0080 1.281 2.8396 2.553c
1991 14 5 )1.336 1.570 0.0668 0.0543 )0.0125 )0.039 )0.0250 )0.058
1992 13 10 1.664d 3.150 0.2359 0.5686 0.3327 1.235 1.0658 1.572
1993 17 13 1.940d 2.000 0.0455 0.3258 0.2803 1.555 0.5595 1.905d
1994 16 11 1.250 1.750 0.0234 0.5311 0.5077 2.153c 0.8950 1.964d
1995 19 14 1.835d 2.630 0.1361 0.5112 0.3750 2.023c 0.9879 2.234c
1996 13 10 1.664d 2.000 0.1485 0.3536 0.2051 1.059 0.4104 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) 137 88 3.247b 2.255 0.1637 0.4497 0.2860 3.577b 0.6427 4.286b All (1.75) 68 47 3.032b 2.118 0.1385 0.5064 0.3679 3.127b 0.8620 3.368b
Table 2 (Continued)
1994 11 10 2.412c 1.910 0.0400 0.7736 0.7336 3.918b 1.4122 3.389b 1995 19 15 2.294c 2.630 0.1361 0.4245 0.2884 2.815b 0.7614 2.584b
1996 13 10 1.664d 2.000 0.1485 0.3509 0.2023 1.531 0.4042 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) 55 43 4.045b 2.364 0.1362 0.4360 0.2998 4.281b 0.7124 4.319b All (1.75) 31 25 3.233b 2.161 0.1058 0.4475 0.3418 3.737b 0.7410 3.940b aThis 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 1.5rtimes 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.
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; thez-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 thet-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 con-clusion is drawn over a shorter time period for the Emerging Markets portfolio.
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(t1)) 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.
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 0.0467 0.7155 15.32 0.0442
European 0.0446 0.9572 21.45 0.0400
European + S&P 0.0705 0.8100 11.49 0.0672
Paci®c 0.0150 1.2950 86.09 0.0067
Paci®c + S&P 0.0923 0.8755 9.49 0.0885
Emerging Markets 0.0360 0.8266 22.95 0.0326
Emerging + S&P 0.1276 0.6702 5.25 0.1253
Panel B
on 18/6/90 on 4/5/94 on 31/12/96 Annual yield (%)
S&P500 $10 000 $20 756.00 11.82
Paci®c $10 000 $11 169.36 1.71
Paci®c + S&P $10 000 $43 161.96 25.07
European $10 000 $19 389.17 10.66
European + S&P $10 000 $30 391.51 18.54
S&P500 $10 000 $16 398.21 20.43
Emerging Markets $10 000 $12 451.81 8.59
Emerging + S&P $10 000 $23 233.57 37.29
aThis table presents the summary statistics for a trading strategy that exploits a typical
The results for the strategy in which funds are transferred from the inter-national 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 interna-tional 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 Euro-pean, Paci®c and Emerging Markets portfolios, respectively. All of the paired dierencet-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 1:25rand 1
:75rof 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 ta-bles for this strategy that are analogous to Tata-bles 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 es-timate the values of the securities in their portfolios, rather than use actual last trade prices or quotes.
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
S&P Euro Paci®c S&P Emerging S&P-Euro S&P-Pac S&P-Emer
# Observations 108 108 108 49 49 108 108 49
Mean return (%) )0.0634 )0.4257 )0.4886 0.0200 )0.5085 0.3623 0.4252 0.5285 t-Statistic )0.802 )3.78b )3.47b 0.208 )3.67b 3.28b 3.04b 3.58b Median return (%) 0.0218 )0.3047 )0.5009 )0.0722 )0.4562 0.3310 0.3672 0.4815 Min return (%) )3.024 )7.822 )6.164 )1.180 )2.938 )2.830 )4.826 )1.180
Max return (%) 2.135 2.179 3.830 1.381 1.775 5.460 5.010 3.706
# Positive 55 31 39 22 15 71 69 33
# Negative 53 77 69 27 34 37 39 16
z-Statistic 0.096 4.330b 2.791b 0.571 2.571c 3.175b 2.791b 2.286b aThis table presents the returns on the dayaftera 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 1.5rbelow 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)
national mutual funds on days when the US stock market declines sub-stantially.
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 in-vestments. 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 ex-planation 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 con-tinuous, 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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