Data and Return Computation

Data for the analysis of this essay comes from several sources. Initially a sample of all international mutual funds (both equity and bonds) was sorted using both Morningstar Principia Pro and CDA (Wiesenberger) Investment View mutual fund databases at the end of the period (October 2002). To be included in this study, the fund must have been in continuous operation during the period January 4, 1993 through October 31, 2002.26 _{Since open-end mutual funds are} permitted to change the objective if shareholders approve the change, I consult both Morningstar

and CDA to eliminate any international funds that changed objectives during the period of study. The purpose of eliminating these funds is to ensure, as much as possible, the homogeneity of funds representing each international fund category. This is important since I want to capture the uniqueness of the return properties of individual international fund in each investment category. Load and no load funds are segregated from one another to distinguish the differences (if any) of exploitable patterns. For multiple share classes within the same fund family, I use the share class, which was started (incepted) first. If the inception date is same for multiple share classes, I choose the share class alphabetically (usually A-share class).27

Once selected, I sort the international funds in terms of their Morningstar category. This allows me to use mutual fund samples from Far eastern to European and north/south American

26 _{The disappearance of some funds (survivorship bias) may not be a problem in this study. One reason for this} belief is that disappearing funds would likely be poor performing funds.

27 _{The sample includes funds that are closed to new investors (an indication of whether or not a security investment} has eligible shares for issue to new investors). It is important because one objective of this study is to develop trading strategies where investors may switch funds without any purchase constraints or limited purchase constraints. These funds are interesting as the prevailing investors can still use them by switching most of their money from these funds and keeping a small fraction of investment in these funds.

35

markets. The final sample consists of 2,479 daily returns of 117 international equity (stock) funds from the following Morningstar categories: Diversified Emerging market fund (4), Diversified Pacific/Asia fund (7), Europe fund (11), Foreign fund (56), Japan fund (4), Pacific/Asia excluding Japan fund (5), Latin America fund (1) and World fund (29). The sample also includes 21 International Bond funds and 6 International Hybrid funds (funds with stock holdings of greater than 20% but less than 70% of the portfolios, where 40% of the stocks and bonds are from foreign markets).28

Daily NAVs and distributions (dividends or capital gains or both) data for each of the selected funds during the sample period are obtained from Dial data. The original source of NAV of Dial data is NASD quotes services. To ensure the quality of the data I follow the screening procedure of Busse (1999).29

Continuously compounded daily returns are computed for each fund by taking the natural logarithm of the change in daily NAV for each day in the sample. Daily mutual fund returns are calculated by using the following formula:

1 , , , ln − = t i t i t i value value R (1)

where R_i,tis the return on fund i during the period t, value_i,t is the value of an investment in fund i at time t, value_i,t−1 is the net asset value of an investment in fund i at time t-1.

28 _{When I screen the sample international funds, which were actively traded on or before January 4, 1993 I found} more funds than my actual sample of this study. This is due to the difference between the inception dates and the data beginning dates of funds.

29 _{Missing NAVs and errors in distributions dates account for less than 1% of our Dial Data sample. For example,} distributions are sometimes recorded one day or two days before or after the actual distributions date (ex-dividend date). Following Busse (1999), I use Moody’s Dividend Record: Annual Cumulative Issue to verify and correct the missing NAVs for which distributions records are found in Moody’s Dividend Record.

36

After the returns for each international fund were computed, an equally weighted index return for each international fund category was computed by summing the returns of the individual funds (i) within the international fund category (c), and computing their average daily return using equation (2).

n

R

R

∑

=

where Rc,t is the average return on international fund category (c) during the period t. This resulted in developing equally weighted daily return indices (portfolio returns) for each international fund category.

It should be mentioned here that the NAV of equity mutual fund is reduced by the exact amount of dividends or capital gains distributions paid to the shareholders. When I calculate the returns of international equity mutual funds, I add the distributions back with the NAV of equity fund. However, for international bond mutual funds, distributions (or interest payments) are declared on a daily basis but are usually paid at the end of each month. However, the NAVs of international bond funds are not reduced by the amount distributions paid (i.e. the accrued interest is not included in calculating the NAVs of bond funds). The accrued interest is prorated over the month. Dial Data provides the distributions data of international bond funds on a particular day of each month when the bond fund distributes dividend income to its shareholders. I divide the amount of distributions paid in each month by the number of business days of that

37

month and accordingly adjust the NAVs and returns of international bond funds.30 This approximation spreads the monthly income distributions out over the month. This also eliminates the impression that a dividend capture strategy would be highly profitable.

This study uses both the US and foreign indices. The following major US indices are used to predict the US-based international mutual funds’ returns: the S&P 500, the Russell 1000, the Russell 2000, the Russell 3000, the Wilshire 5000, the Dow Jones Composite, the Dow Jones industrial and the Nasdaq indices.

I choose the corresponding foreign indices on the basis of the approximate regional or country composition of underlying shares of each sample international mutual fund. Funds for which the major underlying shares are located in a single country I use the corresponding country index. For example, I use the major Japanese indices (Nikkei 225, Topix 1st and 2nd sections) as benchmark indices for the US-based Japan funds. But I use different categories of the Morgan Stanley Capital International (MSCI) indices for most of the regional and diversified funds because the MSCI indices represent many countries and these indices possibly are the closest to the theoretical market index. The MSCI offers real-time data for the MSCI indices and

MSCI free indices. The difference between the MSCI indices and the MSCI free indices is that the MSCI free indices are the most appropriate benchmarks for regional or diversified

30 _{The prospectus of PIMCO foreign bond fund states, ‘Each fund intends to declare income dividends daily and}

distribute them monthly to shareholders of records’ (Page 40, date: 07-31-03). The prospectus also states that you begin earning dividends on fund shares the day after the Trust receives your purchase payment (page 40). I also talked to the industry people of some of the sample bond funds (for example, PIMCO, T. Rowe Price, Putnam, Credit Suisse etc.) and gathered that the international bond funds calculate dividend income (or interest) on a daily basis; but they do not pay interest everyday. Instead, the dividend income is accrued daily and usually paid at the end of the month. The accrued interest does not reduce the NAV of bond funds on ex-dividend date (when the distribution is actually paid). This makes the return calculation of bund mutual funds different from the returns calculation of equity mutual funds. However, the prospectuses of sample bond funds do not provide enough information about the common practices followed by the mutual fund industry in paying interest distributions. When I talked to the industry people, I understand that some funds follow business days and some funds follow calendar days to pay distributions. Even if they use calendar days, it is not clear whether they pay the three-days of accrued weekend interests on Friday or Monday. For simplicity, I use business days to divide the monthly distributions. Accordingly, the daily distribution is computed as a constant value and added with the NAV to calculate the return series of international bond funds.

38

international funds because the MSCI free indices exclude shares of companies that are not readily available for foreign investors. I use the MSCI free indices throughout this study and the MSCI free index data are obtained from DRI in terms of US dollars. The Japanese indices data are also obtained from DRI but in Japanese local currency.31 Continuously compounded daily returns for each foreign index are computed by taking the natural logarithm of the change in daily price (prior day’s close to today’s close). Table A-1 of appendix lists the details about sample funds of this study. The summary statistics of sample funds and the US and foreign indices used in this study are presented in Table 1.

31 _{Fluctuations in currency exchange rates may distort the value of foreign securities (and hence the return of the} fund) without a change in the intrinsic value of these securities. For example, if the value of Japanese stocks increased by 5% over the last one month and if the value of Japanese yen decreases by 5% during the same time, an investor will break-even. Some international mutual funds try to offset the currency exchange effect by hedging currency exposure with future contracts. NAVs of international funds are dollar denominated because the funds are traded in the USA. Prices of foreign securities are converted to US dollars by using appropriate exchange rate. Therefore NAVs include exchange rate effects. But returns to foreign market indices are in local currency. On a daily basis the market movement dominates the exchange rate movement, such that the exchange rate plays a small role in the relationship. In a more fundamental way, if one is interested in seeing how a foreign stock market influences mutual fund values based on that market, it is probably better not to adjust the foreign market for the exchange rate. The mutual fund is the one that actually adjusts for the exchange rate in calculating its NAV. If there had been no relation, then it might have been wise to see whether the mutual funds’ adjustment was the factor eliminating the relation. However, Varela (2002) finds high R-squares in his regressions even though the currencies are different for NAVs and foreign indices. But Zitzewitz (2003a) shows that his results for international mutual funds may be an underestimation if he takes care of exchange rate. An investor can trade on exchange rate movements by buying international funds from post-close exchange rate fluctuations. For example, investors may monitor the movement of foreign exchange rate especially after 12 PM ET since most funds convert local prices into dollars using 12 PM ET exchange rates. Some websites (for example, http://www.econofinance.com/xrate.htm; http://www.bloomberg.com/markets/currencies/fxc.html; http://www.oanda.com/convert/classic etc.) provide intra- day exchange rate fluctuations. However, some mutual funds also use 4 PM exchange rate or exchange rate after 12 PM. Bhargava, Bose and Dubofsky (1998) suggest that the currency prices that mutual funds use to determine the dollar values of funds’ underlying foreign securities are also stale. However, Karolyi and Stulz (1996) find that shocks to the Yen/Dollar foreign exchange rate and Treasury bill returns have no significant influence on the return correlations of the US and Japanese stocks. Copeland and Copeland (1998) suggest that the exchange rate is a significant and independent explanatory factor for both local-currency and dollar-denominated index returns; however they show that the exchange rate does not affect or bias their lead-lag results among the US and European or Asian countries. Most of these studies show a little or no effect of exchange rate in mutual fund’s NAV prediction.

39