Effective fair pricing of international mutual funds

Available online at www.sciencedirect.com

Journal of Banking & Finance 32 (2008) 2307–2324 www.elsevier.com/locate/jbf

Effective fair pricing of international mutual funds Choong Tze Chua a,*, Sandy Lai a, Yangru Wu b,c a

Lee Kong Chian School of Business, Singapore Management University, 50 Stamford Road, Singapore 178899, Singapore b Rutgers Business School – Newark and New Brunswick, Rutgers University, China c Chinese Academy of Finance and Development, Central University of Finance and Economics, China Received 17 October 2006; accepted 21 June 2007 Available online 11 January 2008

Abstract We propose a new methodology to provide fair prices of international mutual funds by adjusting prices at the individual security level using a comprehensive and economically relevant information set. Stepwise regressions are used to endogenously determine the stockspecific optimal set of factors. Using 16 synthetic funds whose characteristics are extracted from 16 corresponding actual US-based Japanese mutual funds, we demonstrate that our method estimates fund prices significantly more accurately than existing methods. Although existing fair-pricing methods provide an improvement over the current practice of simply using Japanese market closing prices, they are still highly vulnerable to exploitation by market-timers. By contrast, our method is the most successful in preventing such strategic exploitation since no competing method can profit from our stated prices. Ó 2008 Elsevier B.V. All rights reserved. JEL classification: G10; G12; G15 Keywords: Stale pricing; Fair pricing; International mutual funds; Stepwise regression

1. Introduction International mutual funds are a convenient instrument for investors to make cross-border investments. To provide daily liquidity, an international fund allows investors to buy and sell shares of the fund at its net asset value (NAV), typically estimated using the daily foreign market close prices of the constituent foreign stocks of the fund. If US trading hours do not coincide with foreign hours, the NAV estimated by the stale prices of the stocks will not reflect the true value of the fund at US market close. An investor can use new information that arrives between foreign close and US close to guide his buy/sell decisions. The issue that stale pricing can be subject to the possibility of price exploitation by market timers has been discussed by previous researchers. See Bhargava et al. (1998), Boudoukh et al. (2002), Chalmers et al. (2001), Goetzmann *

Corresponding author. E-mail addresses: [email protected] (C.T. Chua), sandylai@smu. edu.sg (S. Lai), [email protected] (Y. Wu). 0378-4266/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jbankfin.2007.06.014

et al. (2001), Greene and Hodges (2002), and Zitzewitz (2003).1 While one way to deal with stale pricing is to impose fees and transaction costs on all fund investors, the literature generally agrees that fair pricing of mutual fund shares (at US market close) offers a superior solution.2 However, how to best price fund shares remains an unsettled issue. This paper offers an effective new approach for the fair pricing of international mutual fund shares. 1 This issue has recently captured much regulatory attention. For instance, on April 13, 2004, the SEC voted to adopt disclosure requirements for mutual funds to explain in their prospectuses both the circumstances under which they will use fair value pricing and the effects of using fair value pricing. 2 Fees will necessarily create economic distortions because they impose costs on all investors. In addition, as long as funds use the wrong price, there is room for market timers to exploit passive investors. Transaction restrictions can create a deadweight loss due to the loss in liquidity. Purchases and redemptions on the basis of the next-day NAV are also not welcomed because they create additional price uncertainty in investors’ decision making. See, e.g. Investment Company Institute (2002) and Zitzewitz (2003) for detailed descriptions of these alternative ways to reduce market timing and the analysis of their shortcomings.

2308

C.T. Chua et al. / Journal of Banking & Finance 32 (2008) 2307–2324

Our approach is motivated by the international finance literature on the linkages between domestic and foreign stock prices. In particular, Fama and French (1998) and Rouwenhorst (1998) provide evidence that global components are present in individual countries’ market, value/ growth and momentum factors that describe individual stock returns. In addition, Beckers et al. (1996) show that global industry factors have residual explanatory power over international stock returns. From the perspective of US investors, given that international stocks are exposed to common global factors, the (observed) US factors should help estimate the (unobserved) foreign security prices at US market close. Furthermore, in discussing the effects of market integration on security prices, Errunza and Losq (1985) and Eun and Janakiramanan (1986) argue that the pricing of international securities is dependent on their respective degree of integration with the world market. Multinational firms or firms that are more integrated with the world market are likely to be affected by world factors, whereas local firms are likely to be more vulnerable to country-specific shocks. Consequently, the relative importance of global and country factors in stock returns varies across securities. In summary, the existing literature suggests an economically relevant set of factors to be taken into account in the estimation of the fair price of international mutual fund shares. Furthermore, since the extent of exposures to these factors differs across securities, fair pricing is likely to be more effective at the security level rather than at the fund level. Following the above intuition, we design an empirical methodology to price international mutual fund shares at the security level with an economically relevant set of factors suggested by the literature. In our empirical experiment, we use 16 synthetic funds whose characteristics are extracted from 16 corresponding actual US-based mutual funds investing exclusively in Japanese stocks. We include in our information set the US market portfolio, size, book-to-market, and momentum factors, and twelve US industry portfolios to proxy for global factors. In addition, we consider the Nikkei 225 futures3, Japanese ETF, and composite Japanese ADR index as the proxy for the country factor for Japan, and compare the relative effectiveness of these proxies. We also include individual ADRs in our information set to take into account stock-specific effects. The effect of exchange rate movements on the share value of mutual funds is also considered. We use the information contained in these factors observed at US market close to estimate the fair price of fund shares. To use information efficiently, we employ a simplified stepwise regression to endogenously determine the parsimonious security-specific optimal set of factors to be included in estimating the price of each stock under investigation. In our preliminary analysis, we demonstrate that our candidate explanatory variables have significantly different explana3

Craig et al. (1995) provide evidence that the US-traded Nikkei futures contract provides complete information about contemporaneous overnight return on the Nikkei index in Japan.

tory power for stock returns across different types of firms. By adjusting prices at the individual security level rather than at the fund level as proposed by existing methods, we are able to incorporate the effects of dynamic factor loadings due to portfolio turnover. Furthermore, our design of the empirical model allows us to use the most relevant interval possible for the dependent variable, thereby avoiding introducing additional noise into the model. The reduction in noise relative to signal allows us to estimate our regression parameters more efficiently than the existing approaches. We compare the performance of our method with existing methods using the 16 synthetic funds. The ideal performance criterion is one which measures how accurately one method estimates the (unobserved) fund price at US close. However, this is not feasible since the true prices of Japanese stocks at US close are unobserved. As an alternative performance criterion, we measure the performance of each method by how accurately the method predicts the prices at next-day Japan open. In an efficient market, one would not be able to use information available at US close to forecast asset prices at next-day Japan open. Hence, the alternative performance criterion gives us the same rankings of estimation methods as the ideal but infeasible criterion. The results show that our approach yields significantly lower root mean squared errors (RMSE) in estimating fund prices than the alternatives. Moreover, the fair prices estimated using existing approaches remains highly vulnerable to exploitation by market timers. In contrast, the fair prices estimated using our approach are not significantly exploitable. In addition, given the estimated fair prices from the existing approaches, our method can profit from them significantly, from between 12% and 37% annually.4 The remainder of the paper is organized as follows. Section 2 describes our method of estimating fair prices of international mutual funds and compares it with the existing methods. Section 3 describes the data and presents some preliminary analysis of our stepwise regression. The design of our study is discussed in Section 4. Empirical results are reported in Section 5. Section 6 conducts a number of simulations to check for robustness and the final section concludes. 2. The proposed fair-pricing approach: a comparison with the existing approaches Inspired by the literature on cross-border linkage of securities returns, we propose to use an economically relevant set of variables to estimate the fair value of international mutual fund shares at the security level. Specifically, to estimate the unobserved prices of Japanese securities at US market close, we use the following regression model: X F bi RF ;t1 þ li;t ; ð1Þ ri;t ¼ ai þ F 4 Our method can profitably exploit other methods by between 0.092% per trade (alternative method 3) and 0.296% per trade (alternative method 4). In a typical year, there would be approximately 125 trades. The annualized profit is therefore between 12% and 37%.

C.T. Chua et al. / Journal of Banking & Finance 32 (2008) 2307–2324

2309

Panel A. Time Frame in Security-Level Regression ri , t

U.S. close day t-2

4pmEST

Japan close day t-1

U.S. close day t-1

Japan open day t

Japan close day t

1amEST

4pmEST

7pmEST

1amEST

U.S. close day t

4pmEST

RF , t -1 Panel B. Time Frame in Portfolio-Level Regression RtFX

RKStock ,t

U.S. close day t-2

4pmEST

Japan close day t-1

1amEST

U.S. close day t-1

4pmEST

Japan open day t

Japan close day t

7pmEST

1amEST

U.S. close day t

4pmEST

RM, t-1 Fig. 1. Time frame in regression design. Panel A displays the time frame in our regression setup, while Panel B draws the time frame in the regression of estimating fair price by Goetzmann et al. (2001). ri,t is the return in dollar terms on Japanese stock i from Japan close on day (t  1) to Japan open on day t, and RF,t1 is the return on factor F from US close on day (t  2) to US close on day (t  1). Rstock K;t is the percentage change in fund K’s underlying stock is the percentage appreciation of the yen from US close on day (t  1) to value in yen terms from Japan close on day (t  1) to Japan close on day t, RFX t US close on day t, and RM,t1 is the return on index M from US close on day (t  2) to US close on day (t  1).

where the lower case ri,t refers to the return in dollar terms on Japanese stock i from Japan close on day (t  1) to Japan open on day t; F refers to the factors that we use to estimate the returns on Japanese securities5, which are observed at US market close; RF,t1 are the returns of F from US close on day (t  2) to US close on day (t  1). For clarity, we present the time frame of the above variables in Panel A of Fig. 1. Once the regression coefficients are estimated, security i’s price at US close on day t is then estimated by its unadjusted dollarP price measured at Japan ^F RF ;t Þ, where ai is igclose on date t multiplied by ð1 þ F b i nored since it is empirically small and insignificant. A fund’s price can then be calculated as the value-weighted average price of its constituent stocks. Although all the factors being considered can potentially affect stock returns, including all of them in every regression introduces estimation error and affects the quality of the resulting coefficients. Therefore, we employ a stepwise regression to endogenously select only those factors that are significant at the 1% level for each security. We implement the 5 The economic and empirical relevance of each factor that we consider is well documented and will be discussed in Section 3.

forward selection procedure in which we start with the intercept. Variables are then added one at a time, and the variable that gives the highest partial F-statistic at each step is chosen. The choice of variables is finalized when the next best variable is not significant at the predetermined 1% significance level6 (see Draper and Smith, 1998, pp. 335–344) for details regarding stepwise regression and the forward selection procedure). We estimate all the regressions by OLS.7 In comparison to our method which adjusts prices at the security level, the existing literature, represented by Goetzmann et al. (2001), adjusts the price of US-based international fund shares at the fund level using the following regression model: RK;t ¼ aK þ

X

bM K RM;t1 þ lK;t ;

ð2Þ

M 6 It is important to note that since the stepwise regression is mechanically applied to the in-sample data without regard to the out-of-sample performance, there is no data mining in this exercise. 7 Burns et al. (1998) propose an asynchronous GARCH model to estimate returns and volatilities of foreign indices at US close. Since our focus is on returns rather than volatilities, other than the heavy computational burden, there is no obvious added benefit from using GARCH rather than OLS regression.

2310

C.T. Chua et al. / Journal of Banking & Finance 32 (2008) 2307–2324

where RK,t refers to the percentage change in fund K’s unadjusted NAV in dollar terms measured at US close from day (t  1) to day t. Because the unadjusted NAV is computed using stale prices, RK,t in fact compounds the return in yen terms of Japanese stocks from Japan close on day (t  1) to Japan close on day tðRstock K;t Þ and the return in the yen exchange rate from US close on day (t  1) to US close on day t ðRFX t Þ. RM,t1 denotes the return on index M from US close on day (t  2) to US close on day (t  1), where M can be the S&P500 index and/or other market-wide information such as the Nikkei225 or the Japan exchange traded fund (ETF). For clarity, we present the time frame of these variables in Panel B of Fig. 1. Once the regression coefficients are estimated, one can estimate the fair price of the fund shares by multiplying the unadjusted NAV available at US close on day t (which is computedPusing stale stock prices at Japan close on day t) by ^M RM;t Þ. ð1 þ M b K Compared to the existing fair-pricing methods described above, our approach offers a more effective way to fairly price international mutual fund shares. First, our approach offers a better matching of the measurement period for the explanatory variables and the dependent variable. As a result, we can avoid introducing unnecessary noise into our regression model. The increased signal to noise ratio in the model enables us to obtain a more efficient estimation of parameters. Second, our approach adjusts the price of international mutual fund shares at the security level using an economically relevant set of factors suggested by the literature. By contrast, the existing approaches focus on a smaller information set and adjust the price of fund shares at the fund level, ignoring potential differences across securities and the effects of dynamic factor loadings due to portfolio turnover. As we will demonstrate in Section 5, using the fund-based approach can result in the exploitation by investors. Finally, our method is most relevant from the perspective of mutual fund firms setting fair prices to avoid strategic exploitation. As we will demonstrate later, if a fund company does not estimate the fair price accurately (say it uses only the S&P500 index to estimate the fair price at the fund level), it is likely that a simple strategy such as the one that relies only on signals from the Nikkei225 index can profitably exploit the fund. 3. Relevant information set and preliminary analysis This section discusses the information set, describes the data and presents preliminary analysis of our stepwise regression at the security level. We only consider information that has been shown in the literature to be economically and empirically relevant in affecting security returns. 3.1. Relevant information set International asset pricing theory (e.g. Errunza and Losq, 1985; Eun and Janakiramanan, 1986) suggests that if the Japanese market is fully or partially integrated with the world, the

US market index (which is the major component of the world market factor) and the Japanese market index would have their own distinctive predictive power on the overnight returns of Japanese securities. Campbell and Hamao (1992) suggest that the US and Japanese markets are at least partially integrated. Hence, we include both the S&P500 and Nikkei225 in our information set. We also consider the Japan ETF and the equally-weighted Japanese ADR index as alternative proxies for the Japanese market portfolio. The extant literature (e.g. Fama and French, 1998; Hou et al., 2006) also suggests that size, book-to-market, and momentum factors help explain international stock returns and that a common global component exists in these factors. Furthermore, Beckers et al. (1996) show that global industry factors have additional explanatory power for security returns beyond global market and country-specific effects. In our empirical analysis, we use US factors to proxy for the global factors and include them in our information set. Jorion (1990), Dumas and Solnik (1995), and He and Ng (1998) suggest that exchange rate movements affect firm value and that exchange rate risk is priced in stock returns. Hence, we include the daily change in the Japanese yen exchange rate in our information set. Finally, we include all Japanese ADRs in our information set. We do so because an ADR may contain relevant information for not only its underlying firm but also for closely related firms. For firms with ADRs traded in the US, we may include not only their ADRs but also the aforementioned factors in the information set. This is because although in theory, the price movement of an ADR should mimic that of its underlying home country security, Froot and Dabora (1999) and Chan et al. (2003) show that a security’s price is substantially affected by the investor sentiment of the country where the security is traded. Hence, it can be useful to include other factors to estimate the price of ADR stocks. 3.2. Data and preliminary analysis We obtain the daily return8, market capitalization, fiscal year-end book-to-market ratios, and industry classification of Japanese securities from the Pacific-Basin Capital Market database (PACAP), which covers all securities traded on the Tokyo Stock Exchange. In addition, we obtain the daily settlement prices of the S&P500 futures and Nikkei225 futures from the Chicago Mercantile Exchange. The returns on the S&P500 and Nikkei225 futures are calculated as the percentage price changes in the respective futures contracts nearest to maturity. Returns on Japan ETF and ADRs and US T-bill rates are from CRSP. 8 Since the unadjusted close-to-open returns are complicated by the effects of dividend payouts and stock splits that may have occurred between the close of the previous day to the open of any given day, we construct a time-series of adjusted close-to-open returns for each stock, which are used throughout the paper wherever applicable. The adjusted close-to-open returns are calculated as the day’s close-to-close returns (which are provided and are adjusted for dividends and stock splits) minus the day’s open-to-close returns.

C.T. Chua et al. / Journal of Banking & Finance 32 (2008) 2307–2324

Returns on the yen–dollar exchange rate are acquired from the foreign exchange data vendor Olsen Associates. The daily US momentum factor and size and book-to-market factors are from Jeffrey Busse’s and Kenneth French’s websites, respectively. We define the size membership of Japanese securities in a similar manner to that in Fama and French (1996).9 We also construct 12 US industry portfolios following the methodology described in Fama and French (1997) and then calculate daily value-weighted returns in excess of S&P returns for each portfolio to obtain a set of industry factors which is orthogonal to S&P returns.10 We start our sample period from January 2, 1991 to incorporate the data from Nikkei 225 futures, which does not trade in the US until the fourth quarter of 1990. Our sample period ends on December 31, 2001 because more recent data for Japanese securities are not available from PACAP, as the database only makes the historical data available with several years’ lag. Panel A of Table 1 reports the mean return, standard deviation, and cross correlation of the factors included in our information set. The correlation structure suggests that these factors are only moderately correlated except for Nikkei225, Japan ETF and ADRs. However, multi-collinearlity is not generally a concern in our empirical model because in cases where one of the three Japanese indices is chosen, the other two are rarely chosen at the same time, due to the use of a stepwise regression approach. Panel B reports the proportion of times each factor is selected into the final regression model using the stepwise regression methodology. We estimate the stepwise regression each day from January 6, 1993 to on December 31, 2001, where the past two years’ data are used to conduct the estimation for the first day. Then, the regression is rolled over daily with an accumulative window as a new observation becomes available.11 In Panel B, Column (1) reports the averages across all firms. It is not surprising that the dollar–yen exchange rate is selected most often (94% of the time) because the dependent variable of our regression model is the US dollar return of a Japanese security from Japan close to the next-day Japan open, and as a result movements on the 9 Specifically, at the beginning of July each year, we sort all Japanese stocks in PACAP in descending order by their market-cap as at the end of June. The top 30% are classified as large-cap stocks, the middle 40% as mid-cap, and the bottom 30% as small-cap. The book-to-market memberships of Japanese securities are defined analogously. The daily portfolio returns are calculated from July 1 to June 30 of the following year. 10 To make the number of industries manageable, we use a twelve rather than forty-eight-industry classification as in Fama and French (1997). The details of our industry classification and the list of Japanese ADRs are provided in the Appendix. 11 As will be discussed in Sections 3 and 4, to avoid data mining we use an accumulative estimation window for our fair-pricing method, while allowing the competing methods to use their respective optimal windows. Specifically, for competing methods using the S&P500 and the Nikkei225 indices alone, the optimal window is the accumulative window, while for the competing method using the S&P500 and Nikkei225 combined, the optimal window is the 360-day fixed moving window. These respective optimal window sizes are used in all regressions throughout the paper.

2311

dollar–yen rate would have a direct impact on the dependent variable. It is interesting to note that the Nikkei225 and S&P500 futures are selected 66.2% and 42.9% of the time, respectively, suggesting that both indices contain material information about the overnight returns of Japanese securities with the former somewhat more important than the latter. The Japan ETF is selected only 8.3% of the time, suggesting that the Nikkei225 futures index may be superior to the Japan ETF as a proxy for the Japanese market portfolio. ADRs, size, industry, book-to-market and momentum factors also help estimate the price of Japanese securities. They are selected into the regression model 4.5%, 2.1%, 2.0%, 1.9%, and 1.8% of the time, respectively. Columns (2)–(11) report the proportion of times the factors are selected in our stepwise regressions for different types of firms. Overall, the US and Japan country factors, as well as the US SMB, HML, momentum, and industry factors are all more useful to the estimation of the prices of (Japanese) index than non-index stocks (columns (2) and (3)), ADR than non-ADR stocks (columns (4) and (5)), and large- than small-cap stocks (columns (6) and (8)). It is not surprising that the global factors (proxied by the US factors) are less important to the pricing of non-index, non-ADR, and small-cap stocks because these stocks tend to be more affected by country-specific factors. The finding that Nikkei225 is also chosen more often by index, ADR, and large-cap stocks than their counterparts, however, reflects that these stocks tend to be part of the index itself. Interestingly, we also find that the effect of the S&P500 outweighs the Nikkei225 for index and ADR stocks, while the opposite holds true for non-index and non-ADR stocks. This might be because index and ADR stocks are more integrated with the world market, and hence the world market factor, which is dominated by the US market factor, is more important than the country factor in explaining the returns of these stocks. Furthermore, index and ADR stocks may be more susceptible to the influence of the US investor sentiment because a larger proportion of their shares are held by US and international investors relative to non-index and non-ADR stocks. Consistent with our priors, ADRs are chosen more often by ADR stocks (7.8%) than by non-ADR stocks (4.4%). Finally, columns (9)–(11) suggest that differences among firms with different book-to-market equity ratios are small. Overall, the results presented in Table 1 show that the candidate explanatory variables have significantly different explanatory power for stock returns across different types of firms in our sample, further justifying our approach of estimating fair prices at the security level.

4. Design of experiment To evaluate the effectiveness of various fair-pricing approaches, we design an experiment comparing the outof-sample forecast accuracy and exploitability of competing

2312

Table 1 Information set, summary statistics, and stepwise regressions Explanatory variables

Mean return

Standard deviation

Explanatory variables

All (1)

Index (2)

Nikkei225 futures

Japan ETF

Dollar– yen rate

SMB factor

HML factor

Momentum factor

Industry portfolio

ADRs

0.41 1.00

0.43 0.75 1.00

0.08 0.06 0.31 1.00

0.32 0.07 0.06 0.01 1.00

0.60 0.27 0.31 0.03 0.23 1.00

0.09 0.00 0.02 0.00 0.08 0.16 1.00

0.18 0.07 0.08 0.01 0.11 0.18 0.04 1.00

0.33 0.70 0.79 0.24 0.01 0.24 0.02 0.05 1.00

Non-index (3)

ADR (4)

Panel B. Proportion of time variables are selected in the stepwise regressions S&P500 futures 42.9 92.2 36.0 87.4 Nikkei 225 futures 66.2 84.4 63.3 82.5 Japan ETF 8.3 9.1 8.1 5.2 Dollar–yen rate 94.0 99.3 92.5 98.2 SMB factor 2.1 1.9 2.1 2.7 HML factor 1.9 2.8 1.7 4.4 Momentum factor 1.8 2.7 1.6 1.2 Industry portfolios 2.0 2.6 1.9 3.8 ADRs 4.5 5.3 4.3 7.8

Non-ADR (5)

Large (6)

Medium (7)

Small (8)

Value (9)

Blend (10)

Growth (11)

41.8 65.5 8.3 93.2 2.0 1.8 1.8 2.0 4.4

74.7 77.4 9.1 97.3 2.7 2.6 2.2 2.4 4.5

42.0 69.8 7.5 93.8 2.1 1.9 1.4 1.8 4.2

11.4 49.1 8.3 89.0 1.4 1.1 1.8 1.8 4.8

31.0 63.0 8.2 94.4 2.1 1.3 1.9 1.8 4.5

45.5 68.7 7.6 94.3 1.9 1.5 1.5 1.9 4.3

50.9 65.1 9.0 91.4 2.2 2.8 1.9 2.4 4.6

Panel A provides daily means, standard deviations (both in percent) and cross correlations of the variables included in our information set, which are used as the explanatory variables in our stepwise regressions. The correlations with the industry portfolios (ADRs) represent the average of all industries (ADRs). Panel B reports the proportion of times (in percent) that a particular explanatory variable is selected into the final regression model. Column 1 reports the average across all stocks. Columns 2–5 report the average for index (the Nikkei225 index), non-index, ADR, and non-ADR stocks, respectively. Columns 6–8 report the average for large-, medium-, and small-cap stocks, respectively, while columns 9–11 report the average for high (value), medium (blend), and low (growth) book-to-market ratio stocks, respectively. The daily returns on the dollar–yen rate are measured from Japan close to US close. For the rest of factors, returns are measured from US close to the next-day US close. The sample period is from January 2, 1991 to December 31, 2001.

C.T. Chua et al. / Journal of Banking & Finance 32 (2008) 2307–2324

Panel A. mean, standard deviation, and correlation matrix S&P500 futures 0.040 1.032 Nikkei 225 futures 0.023 1.536 Japan ETF 0.027 1.795 Dollar–yen rate 0.012 0.608 SMB factor 0.003 0.570 HML factor 0.018 0.628 Momentum factor 0.047 0.732 Industry portfolios 0.002 0.814 ADRs 0.028 3.164

Cross correlations

C.T. Chua et al. / Journal of Banking & Finance 32 (2008) 2307–2324

fair-pricing methods using simulated daily holdings of Japanese funds. 4.1. Simulation of fund holdings: actual vs. synthetic fund Because we are not able to obtain fund holding data on a daily basis, we simulate the daily holdings of 16 synthetic funds whose key characteristics are extracted from the actual mutual funds.12 Specifically, we obtain the portfolio composition and turnover ratio information of 16 USbased Japanese funds as of March 2004 from Morningstar.13 Table 2 reports the sample statistics of these funds. The majority of the funds follow a ‘‘large-cap” style (10 out of 16) and ‘‘growth” style (9 out of 16), as defined by Morningstar. The number of stocks in a fund varies greatly across funds, ranging from 33 for the Japan Smaller Companies fund and Matthews Japan fund to 973 for the Dimensional Japan Small Company fund. The annual turnover ratio also varies substantially across funds, ranging from 39% for the Japan Smaller Companies fund to 797% for the JP Morgan Fleming Japan fund. Upon obtaining the 2004 portfolio composition of these funds, we match each fund’s constituent stocks with the securities in PACAP. If a stock is not identifiable in PACAP, we replace it with one randomly selected from the PACAP database.14 This generates the initial portfolio. Then, on each day, we assume that every stock has an equal probability of being replaced by another stock in the same size portfolio. The probability of a stock being replaced is set equal to a fund’s daily turnover ratio. Using this algorithm, we simulate each fund’s holdings starting from 1991 through 2001. We generate 400 synthetic funds for each corresponding actual fund. While the synthetic fund’s holdings will differ from the holdings of the actual funds, the characteristics such as turnover ratio and types of stocks held will be largely similar. In Section 6, we also simulate daily fund holdings for four sets of hypothetical funds to investigate whether our empirical results hold up across funds with different turnover ratios, number of securities in portfolio, stock size, and book-to-market ratio characteristics. Hence, we construct hypothetical funds along these dimensions. To con12

Although the simulated synthetic funds will not have exactly the same daily holdings as the actual funds, the key characteristics of the funds (such as annual turnover and types of stocks held) will be similar. Furthermore, there is no reason to believe that the simulation will bias any method in favor of any other method. In the case of a mutual fund seeking to implement our fair-pricing methodology, the manager will have knowledge of the fund’s daily composition and can therefore test and implement our methodology exactly as it is intended without the need for simulation. 13 There are 16 pure Japanese funds (excluding index funds) in the US market as of March 2004, according to Morningstar. 14 We are able to identify 87% of the stocks, leaving 13% unidentifiable either due to the stocks not being traded on the exchanges covered by PACAP, or due to irreconcilable differences in naming conventions used by Morningstar and PACAP to identify companies.

2313

struct hypothetical funds with varying turnover ratios, we assume that each fund holds 69 securities, which is the median number of securities held by the 16 actual funds, and that these 69 stocks are randomly drawn from the universe of all Japanese stocks in PACAP. We allow the annual turnover ratio to vary from 10% to 1000%. To construct funds with different numbers of constituent stocks, we assume that each fund has an annual turnover ratio of 92.5%, the median turnover ratio of the 16 actual funds. Again, these stocks are randomly drawn from the PACAP universe. We then construct the synthetic funds with the number of constituent stocks ranging from 25 to 500. The synthetic large-, mid-, and small-cap (high-, mid-, low- book-to-market ratio) funds are constructed by assuming that each fund has an annual turnover ratio of 92.5% and holds 69 stocks in the portfolios; then the securities for each fund are randomly drawn from its corresponding size (book-to-market ratio) category. Except for the experiments on the book-to-market ratio characteristic, where we replace stocks with the ones having the same book-to-market ratio membership, we always replace stocks based on their size characteristics. Again, we conduct 400 simulations for each fund. 4.2. Performance measures In comparing the effectiveness of fair-pricing methods, we examine three performance measures: (1) the method’s out-of-sample forecast accuracy; (2) exploitability of the method by alternative methods; and (3) profitability of the method in exploiting other methods. Intuitively a better method should be one that yields a more accurate out-ofsample forecast, one whose stated price is more successful in preventing exploitation by other methods, and one that can exploit more profit from the stated price of an alternative estimation method than other feasible methods. To calculate the out-of-sample forecast accuracy, we compare the share price forecasted by each fair-pricing method with the actual price of the fund measured at the next-day Japan open.15 Recall that our purpose is to provide the best estimates of the unobserved stock prices (and hence fund price) at US close. Since the true prices of Japanese stocks (and hence fund prices) at US close are unobserved, we use the next-day Japan open prices (which are the earliest observable prices in the future) as the best proxies and measure the performance of each method by how accurately that method forecasts the prices at next-day Japan open. In an efficient market where one cannot use information available at US close to forecast asset prices at next-day Japan open, this performance criterion gives us the same rankings of estimation methods as the ideal but yet infeasible criterion which measures how accurately one method estimates the (unobserved) prices at US close. The out-of-sample prediction error is com15 The actual share price of a fund is computed as the value-weighted average of the dollar price of the fund’s constituent stocks.

2314

C.T. Chua et al. / Journal of Banking & Finance 32 (2008) 2307–2324

Table 2 Descriptive statistics of 16 US-based Japanese mutual funds Fund name

Commonwealth Japan

Fund size (1) 9.0

Credit Suisse Japan equity fund Dimensional apan Sm Co Dreyfus premier Japan

41.5 6.6

Fidelity advisor Japan

19.3

Fidelity Japan

86.2

670.3

Fidelity Japan smaller companies GAM Japan capital fund

1149.1

Goldman sachs Japanese

58.6

Japan S

1.8

468.4

Japan smaller companies

4.7

JPMorgan Fleming Japan fund Matthews Japan

15.6

Morgan Stanley Instl: Japanese value equity Scudder Japanese equity

16.4 32.5 26.7

T. Rowe price Japan

194.6

Mean Median Standard deviation

175.1 29.6 304.1

Style (2)

Medium value Large growth Small value Large blend Large value Large growth Medium growth Large blend Large growth Large growth Small growth Medium blend Medium growth Large blend Large growth Large growth

Number of stocks (3)

Book-to-market ratio (4)

Market capitalization (5)

Turnover ratio (6)

Stocks and cash holdings (7)

52

0.790

2,758

28

100

49

0.772

11,193

117

973 52

0.858 0.779

255 5,589

16 167

100 100

71

0.779

9,501

99

100

100

0.724

7,121

86

100

167

0.874

966

43

100

66

0.827

8,844

127

100

86

0.769

8,596

115

100

109

0.811

5,524

80

100

33

0.583

479

39

98.5

108

0.779

2,123

797

99.7

33

0.724

3,014

77

100

66

0.729

7,050

79

100

63

0.605

11,908

137

100

82

0.811

4,472

255

96.2

132 69 214

0.763 0.779 0.074

5,587 5,557 3,553

141 93 174

99.6 100.0 0.9

99.2

This table provides sample statistics of 16 US-based Japanese mutual funds. Columns 1–3 report the fund size, style, and number of stocks in a fund, respectively, where the fund size is denominated in million US dollars. Column 4 reports the equal-weighted average of the book-to-market ratio. Column 5 reports the geometric average market capitalization of the fund’s constituent stocks in million dollars. Columns 6–7 report the average annual turnover ratio and the proportion of the fund’s assets held in stocks and cash, respectively. All the statistics are obtained from the March 2004 Morningstar CD, except for the book-to-market ratio. The Morningstar data are based on the funds’ portfolio disclosure between December 31, 2002 and February 29, 2004. The book-to-market ratio is obtained from PACAP, and is averaged over the sample period, from January 2, 1991 to December 31, 2001.

puted daily and the root mean squared error (RMSE) is calculated over the sample period as follows: " #1=2 D2 1 X 2 e ð3Þ RMSE ¼ N t¼D1 Q;t where ^pQ;tðUS closeÞ  ptþ1ðJapan openÞ ptþ1ðJapan openÞ ^pQ;tðUS closeÞ  ptðUS closeÞ ptðUS closeÞ  ptþ1ðJapan openÞ ¼ þ ptþ1ðJapan openÞ ptþ1ðJapan openÞ

eQ;t ¼

 gQ;t þ nt

ð4Þ

In the above equations, pt is the actual value and p^Q;t is the predicted value of the fund, both in dollar terms, and eQ,t is the percentage prediction error for method Q on day t,

which can be viewed as comprising two components: (i) the error in estimating a fund’s price at US close, gQ,t; and (ii) the error in predicting the fund’s price changes from US close to next-day Japan open, nt. In an efficient market, nt should be unpredictable and uncorrelated with gQ,t. D1, D2, and N denote the starting, ending, and length of the forecasting period, respectively. To conduct a formal statistical test for the relative forecast accuracy of two competing methods, Q1 and Q2, we form the difference of squared forecast errors and construct the associated t-statistic as follows: ð5Þ d t ¼ e2Q1 ;t  e2Q2 ;t ld pffiffiffiffi ð6Þ td ¼ rd = N where ld and rd are the sample (time-series) mean and standard deviation of dt, respectively.

C.T. Chua et al. / Journal of Banking & Finance 32 (2008) 2307–2324

It is in general a stringent requirement in forecasting exercises to use statistical significance as a criterion to evaluate competing forecasting methods.16 This is even more relevant in our current context because the term td defined in Eq. (6) underestimates the true t-statistic for comparing the relative forecasting abilities of two competing methods. To see this, we decompose the difference of squared forecast errors as follows: d t ¼ e2Q1 ;t  e2Q2 ;t 2

¼ ðgQ1 ;t þ nt Þ  ðgQ2 ;t þ nt Þ

5. Empirical results from 16 synthetic Japanese mutual funds ð7Þ

Note that the first term on the right hand side of Eq. (7), d 1t  ðg2Q1 ;t  g2Q2 ;t Þ, is the difference in the estimation errors by the two competing methods. Therefore, the true t-statistic to compare the relative performance of the two competing methods should be ld 1 pffiffiffiffi ð8Þ td 1 ¼ rd 1 = N where ld 1 and rd 1 are the sample mean and standard deviation of d1t. This statistic is not computable because we do not directly observe nt. Since nt is uncorrelated with gQ1 ;t and gQ2 ;t , the second term on the right hand side of Eq. (7), d2t, has mean zero, is uncorrelated with the first term d1t, and its variance increases with the variance of nt. Therefore, we have E½ld  ¼ E½ld 1  and rd > rd 1 , which implies that E½jtd j < E½jtd 1 j:

daily and averaged over the sample period. A method is exploitable by an alternative method if the profit of this trading strategy is significantly greater than a benchmark strategy. If our method is indeed better than the competing methods, we expect that it will be difficult for the alternative methods to exploit the stated price of our method and that our method could exploit more profit from the stated prices of alternative estimation methods than other feasible alternatives. A standard t-test is employed to test whether a trading profit is statistically different from zero.

2

¼ ðg2Q1 ;t  g2Q2 ;t Þ þ 2nt ðgQ1 ;t  gQ2 ;t Þ  d 1t þ d 2t

2315

ð9Þ

The above argument demonstrates that the t-statistic td defined in Eq. (6) that we will compute understates the true statistical significance of one estimation method against another. Finally, we measure the exploitability of an estimation method by an alternative method by calculating the profit of a simple trading strategy: buy a fund’s share when the stated price by an alternative method is higher than the price stated by the method to be exploited, and avoid investing in the fund when the stated price by the alternative method is lower than or equal to the price stated by the method to be exploited. As short selling mutual funds is in general not allowed, we assume that in the latter case the position is held in the US three-month T-bill. For simplicity, we assume that there are no transaction costs and that the decision is made daily.17 The trading profit is calculated 16 See Pesaran and Timmermann (1995) for evidence on forecasting stock returns, Kilian and Taylor (2003) and Qi and Wu (2003) on forecasting exchange rates, Duffee (2002) on forecasting interest rates, and Fama and French (1987) and Hartzmark (1991) on forecasting commodity futures. 17 Although the assumption of zero transaction cost may not be realistic, it is an acceptable assumption in our study because we are comparing alternative pricing methods. Furthermore, there exist many fund families that allow costless switching among funds in the same family at the stated NAV. As long as the assumption is applied uniformly across all methods, it will not bias the study in favor of any method.

Our out-of-sample forecasting exercise starts on January 6, 1993 and ends on December 31, 2001 for the 16 synthetic Japanese mutual funds. To implement our methodology, for each constituent stock in a fund on each day, we run a stepwise regression of Eq. (1) using the information set introduced in Section 3. Once the optimal set of factors is selected from the stepwise regression, we use the estimated parameters to calculate the stock price. The regression is performed daily with an accumulative window as each new observation becomes available. The alternative estimation method adjusts asset prices at the fund level using Eq. (2) with market-wide information. We explore seven sets of market-wide explanatory variables in this case: (1) the S&P500 futures; (2) the Nikkei225 futures; (3) the S&P500 futures plus Nikkei225 futures; (4) the Japan ETF; (5) the equally-weighted average ADR index; (6) the S&P500 futures plus the Japan ETF; and (7) the S&P500 futures plus the equally-weighted average ADR index. Goetzmann et al. (2001) use information set (1) in their work. The Nikkei225, the Japan ETF and the equally-weighted average ADR index have been suggested in the literature to serve as proxies for the Japanese market portfolio. However, Panel A of Fig. 2 shows that the RMSE of predicting the next-day Japan open prices using the Nikkei225 index alone is always lower than that using either the Japan ETF or the ADR index, while Panel B demonstrates that the RMSE using the Nikkei225 plus the S&P500 is superior to that using either alternative index plus the S&P500. Since the Nikkei225 is clearly dominant, we use only this index to proxy for the Japanese market portfolio, and report results using information sets (1)–(3).18 To avoid data mining, we use an accumulative estimation window for our method, while allowing the competing methods to use their respective optimal windows. An optimal window is defined as the one which produces the lowest RMSE over the forecasting period averaged across the 16 funds. This approach is conservative in that it selects the 18

In Fig. 2, all methods adjust asset price at the portfolio level. In addition, because the ETF data have a shorter history (from March 19, 1996) than the other two indices, Fig. 2A and B are based on the sample period where all three indices have observations, i.e. from March 19, 1996 to December 31, 2001.

2316

C.T. Chua et al. / Journal of Banking & Finance 32 (2008) 2307–2324

Panel A. RMSE of Alternative Japanese Market Indices 0.90% NK225 ETF ADR

0.88% 0.86% 0.84% 0.82% 0.80% 30

60

120

240

360

480

cumulative

Panel B. RMSE of Alternative Japanese Market Indices Combined with the S&P500 Index 0.90% S&P + NK225 0.86%

S&P + ETF S&P + ADR

0.82% 0.78% 0.74% 0.70% 30

60

120

240

360

480

cumulative

Panel C. RMSE of Competing Methods 0.76%

S&P NK225

0.72%

S&P + NK225

0.68% 0.64% 0.60% 30

60

120

240

360

480

cumulative

Fig. 2. RMSE comparison of alternative market indices and regression window sizes. Panel A plots the out-of-sample RMSEs with respect to different regression window sizes for fair-pricing estimation using three alternative Japanese market indices alone: the Nikkei225 futures index, the Japan ETF, and the equally-weighted average ADR index. Panel B displays the RMSEs using the S&P500 index combined with each of the three alternative Japanese market indices. Panel C plots the RMSEs of competing fair-pricing estimation methods with respect to different regression window sizes. All methods adjust asset price at the portfolio level. Because the Japanese ETF only started trading in March 19, 1996, Panels A and B use data from March 19, 1996 to December 31, 2001. Panel C employs data for the period from January 2, 1991 to December 31, 2001. The RMSEs are averages over 400 simulations.

best RMSE for alternative methods. Panel C of Fig. 2 reports the RMSE and the window size for each of the three competing methods. The cumulative window produces the lowest RMSE for the methods using the S&P500 and the Nikkei225 indices alone, while the 360-day fixed moving window is the optimal window size for the method using both the S&P500 and Nikkei225 indices. Hence, these respective optimal window sizes are used in estimation. 5.1. Root mean squared errors Table 3 reports the RMSE of predicting fund prices at next-day Japan open based on information available at

US close (4 pm EST) using our estimation method and three competing methods for the 16 US-based Japanese mutual funds. For ease of comparison, the result from stale pricing is also reported, although no estimation is needed in this case. In summary, our method adjusts asset prices at the security level using stepwise regressions; alternative method 1 adjusts asset prices at the portfolio level using the S&P500 futures index alone; alternative method 2 adjusts asset prices at the portfolio level using the Nikkei225 futures index alone; alternative method 3 adjusts asset prices at the portfolio level using both the S&P500 and Nikkei225 futures indices; and alternative method 4 is stale pricing without adjustment.

C.T. Chua et al. / Journal of Banking & Finance 32 (2008) 2307–2324

We report the RMSE for each estimation method. The t-statistic testing whether our method produces a lower RMSE than the alternative methods is reported below the RMSE of each alternative method. If the t-statistic is smaller than 1.96, then our method is considered to have a significantly lower RMSE than the alternative method at the 5% level. On the other hand, if the t-statistic is larger than 1.96, our method is considered to be worse than the alternative method at the 5% significance level. From Eq. (4), nt is a noise term that is present for all methods, while gQ,t captures the specific genuine estimation error of method Q. Therefore, the presence of nt makes the percentage difference in RMSE across competing methods smaller than the true percentage reduction due to the genuine estimation error. Also, as shown in Eq. (9), the t-statistics underestimate the true statistical significance of the difference between our method and the competing methods. With this caveat, an insignificant t-statistic will not necessarily imply that our method does not perform better, but a significant t-statistic will clearly indicate the superiority of our method relative a competing method. Two main observations can be made from Table 3. First, across estimation approaches, stale pricing yields the highest RMSE in predicting fund prices at next-day Japan open. Alternative method 2 (the Nikkei225 futures index alone) produces the second highest RMSE, followed by alternative method 1 (the S&P500 futures index alone), and alternative method 3 (the S&P500 futures and Nikkei225 futures indices combined). Our approach with stock-specific predictive variables produces the lowest RMSE among all methods. This is true across all 16 funds. Averaging over the 16 funds, we find that the mean RMSE using stale pricing is 0.771%. This number reduces to 0.694% for alternative method 2, 0.677% for alternative method 1, 0.651% for alternative method 3, and 0.632% for our method. Second, across all 16 funds, our method produces a lower RMSE than stale pricing with the average t-statistic of 8.758. While this is a markedly high statistic, it is not surprising given that stale price is a poor predictor of nextday open price. Compared with other fair pricing estimation methods, our method beats alternative method 1 (the S&P500 futures index alone) at the 1% significance level for all 16 funds, with an average t-statistic of 5.106; and beats alternative method 2 (the Nikkei225 futures index alone) at the 1% level across 16 funds, with an average t-statistic of 6.227. While our method outperforms alternative method 3 (with the S&P500 and Nikkei225 indices combined) by a smaller margin, it does so at the 1% significance level for 13 funds and at the 5% significance level for 2 additional funds. The average t-statistic over all 16 funds is 2.829, which is significant at the 1% level. 5.2. Exploitability Given a calculated price by one estimation method, we investigate if an alternative estimation method can profit from this stated price. In principle, an ideal method should

2317

employ the most updated and most relevant information and should use the information most effectively to come up with accurate estimate of a stock price at US close. A perfect estimate should yield the true (but yet unobserved) stock price at US close such that no method can profit from the declared price in an efficient market. However, in reality since no estimation method is perfect, when a stated price from one method is different from the true price, an alternative method which uses information not fully incorporated in the stated price may be able to profit from the stated price even if this alternative method may not necessarily be a superior method in terms of forecast accuracy. Of course, the more accurate an alternative method is in estimating the true price, the more likely the method is to profit from a stated price. Therefore, we evaluate the various estimation methods based on two additional criteria: (1) a good method should be one whose stated price is successful in guarding against exploitation by other methods; and (2) a good method should be one that can exploit more profit from a stated price of an alternative estimation method than other feasible alternative methods. Table 4 reports the results using the benchmark of holding the US T-bill.19 Panel A displays the mean excess returns and the associated t-statistics that our method can be exploited by the other alternative methods. For an alternative method to profit significantly at the 5% level from our stated price, a positive t-statistic larger than 1.96 is required. As the t-statistics show, none of the alternative methods can significantly exploit our method for any of the 16 funds. Not surprisingly, across the four alternative methods, alternative method 4 (stale price) is the weakest method in exploiting our stated price with the average t-statistic of 0.324 over 16 funds, whereas alternative method 3 (the S&P500 plus Nikkei225 indices) is the strongest with the average t-statistic equal to 1.271. Alternative method 1 (the S&P500 index alone) performs somewhat better than alternative method 2 (the Nikkei225 index alone). These results, consistent with those on the comparison of out-of-sample RMSE’s, imply that the S&P500 index in general contains more (or better) information than the Nikkei225 index in pricing Japanese stocks. However, neither factor can entirely substitute for the other. Combining the two indices clearly improves estimation efficiency, but the improved estimate is insufficient to profitably exploit our method. Organized in the same manner, Panel B of Table 4 presents the excess profits and the associated t-statistics that alternative method 1 (S&P500 index alone) can be exploited by the other methods. The t-statistics indicate that our method exploits all alternative methods. Across 16 funds, the average daily profit of our method over alternative method 1 is 0.200% (annualized to approximately 25%, 19

We also consider an alternative benchmark: buying-and-holding the mutual fund under investigation. Using this benchmark, our method can significantly exploit all other methods with the daily profit averaged over 16 funds ranging from 13% to 40% per annum. For brevity, the results are not reported but are available upon request.

This table reports the out-of-sample forecasting performance of our method and four alternative fair-pricing estimation methods for 16 US-based Japanese mutual funds. Our method adjusts asset prices at the security level using stepwise regressions; alternative method 1 adjusts asset prices at the portfolio level using the S&P500 futures index alone; alternative method 2 adjusts asset prices at the portfolio level using the Nikkei225 futures index alone; alternative method 3 adjusts asset prices at the portfolio level using both the S&P500 and Nikkei225 futures indices; and alternative method 4 is stale pricing without adjustment. The RMSE (in percent) of predicting asset prices at next-day Japan open is reported for each method. The t-statistic that our method yields a lower RMSE than an alternative method is reported below the RMSE of each alternative method. A t-statistic lower than 1.96 (2.58) indicates that our method outperforms an alternative method at the 5 (1) percent significance level in terms of forecasting accuracy. Both RMSEs and t-statistics are averages over 400 simulations. The sample period is from January 2, 1991 to December 31, 2001.

0.677 5.106 0.694 6.227 0.651 2.829 0.771 8.758 0.648 5.378 0.662 6.354 0.621 2.901 0.740 8.985 0.678 4.943 0.698 6.203 0.655 2.969 0.773 8.743 0.663 5.192 0.686 6.336 0.639 3.171 0.764 8.905 0.701 4.798 0.719 5.947 0.677 2.681 0.793 8.451 0.650 5.620 0.655 6.270 0.620 2.749 0.734 9.133 0.810 4.200 0.814 5.039 0.781 1.618 0.883 7.543 0.651 5.314 0.673 6.517 0.626 3.172 0.752 9.054 0.658 5.313 0.677 6.384 0.632 3.151 0.756 8.976 0.659 5.230 0.679 6.370 0.635 3.113 0.756 8.946 0.687 5.272 0.699 6.229 0.656 2.595 0.780 8.848 0.687 4.976 0.709 6.239 0.664 2.979 0.784 8.684 0.669 5.139 0.689 6.342 0.645 3.072 0.766 8.903 0.663 5.162 0.681 6.281 0.638 2.956 0.757 8.859 0.631 5.672 0.638 6.976 0.592 2.565 0.726 9.056 0.680 5.000 0.701 6.224 0.657 3.009 0.775 8.732 RMSE t-ratio RMSE t-ratio RMSE t-ratio RMSE t-ratio Alternative method 1 Alternative method 2 Alternative method 3 Alternative method 4

0.699 4.483 0.725 5.916 0.677 2.562 0.797 8.313

0.602

16 15

0.635 0.617

14 13

0.658 0.602

12 11

0.770 0.605

10 9

0.611 0.614

8 7

0.639 0.644

6 5

0.623 0.618

4 3

0.576 0.636 0.659 Our method

2 1

RMSE Fund

Table 3 Forecasting accuracy of alternative fair-pricing estimation methods for 16 US-based Japanese mutual funds

0.632

C.T. Chua et al. / Journal of Banking & Finance 32 (2008) 2307–2324

Ave.

2318

since a trade occurs in approximately half the trading days) and the associated average t-statistic is 4.278. This means that for a $1000 nominal investment, the expected profit per trade is $2, and the expected profit per year for implementing this strategy is $250 – an extraordinary return given that the strategy is exposed to market risk on only half the trading days. The respective profits and t-stats for alternative method 2 (Nikkei225 alone) are 0.204% per day (or about 26% per annum) and 4.292. Therefore, our method and alternative method 2 appear to be roughly equally efficient, and both methods are more effective than alternative method 3 in exploiting alternative method 1. Panel C shows that alternative method 2 (Nikkei225 alone) can be exploited profitably at the 5% significance level for the 16 funds by all alternative methods except the stale price. Comparing Panels B and C, it is interesting to note that alternative methods 1 and 2 in general can exploit each other. This is possible because each method employs partial information that arrives at the market to estimate the true stock prices at US close. If one variable (say the S&P500 index) contains some information that is not contained by the other variable (say the Nikkei225 index), we can expect one method to be able to profit from the other and vice versa. Among the three competing methods to exploit alternative method 2, our method appears to be the best in that our t-statistics are the highest for each fund. For all 16 funds, the average daily profit that our method can exploit alternative method 2 is by 0.176% with an average t-statistic of 3.676. This profitability is annualized as about 22%. Panel D demonstrates that our method can profit from alternative method 3 (the S&P500 and Nikkei225 combined) at the 5% significance level for 10 out of 16 funds, and at the 10% for 4 additional funds. The average profit over the 16 funds is 0.092% which is annualized at 12%. However, none of the other competing methods can significantly profit from alternative method 3 for any fund. Comparing the results in Panel D with those in Panels B and C, we can see that alternative method 3 can significantly exploit alternative methods 1 and 2, but not the other way around. Therefore it is important to combine information contained in both the S&P500 and the Nikkei225 indices. Panel E of Table 4 shows that alternative method 4 (the stale price) is highly vulnerable to speculation by all four fair price estimates, and our method is clearly the best method in exploiting the stale price. The average daily profit that our method can exploit from stale pricing is 0.296% with an average t-statistic of 6.878. This daily return translates into a profit of 37% per year. Panel F of Table 4 summarizes the profit from exploitation across all methods. It also provides the annualized average profit for convenience. It is evident from this table that our method is most successful in exploiting all alternative methods, with annualized profits ranging from 12% to 37%. It is also the most immune to exploitation, giving up annualized profits ranging from 1% to 8%.

C.T. Chua et al. / Journal of Banking & Finance 32 (2008) 2307–2324

In summary, the results reported in this section accord well with intuition and suggest that our method is significantly better than the existing methods. This argument is based on two grounds. First, our method predicts the next-day opening security prices in Japan most accurately among all methods. Second, our method produces the best fair price at US close in that our stated price cannot be significantly exploited by other methods. Furthermore, for any stated price from an alternative method, our method in general can exploit the stated price significantly and it can do so more profitably than other competing methods. 6. Robustness of results In this section, we conduct a number of simulations to check for the robustness of our method’s advantage over competing methods in pricing different types of funds. First, we examine how the average stock size in a fund can affect the relative performance of all estimation methods. Second, we study the impact of the portfolio turnover ratio on the forecast accuracy of the competing methods. Third, we investigate how the number of stocks contained in a fund can affect the relative forecast accuracy. Finally, we explore the possible effects of fund style (as proxied by book-to-market ratio) on the relative performance of the estimation methods. 6.1. Stock size In general, small-cap stocks have higher idiosyncratic risk than large-cap stocks; thus it may be more difficult to predict future prices of small-cap stocks using market-wide information. As a result, we may expect that the fair price of a fund consisting primarily of small-cap stocks may be more difficult to estimate than that of a fund consisting mainly of large-cap stocks, all else being equal. However, this problem likely affects all estimation methods. We follow the procedure described in Section 4 to simulate three mutual funds, consisting, respectively, of largecap, medium-cap and small-cap stocks. For each fund, we estimate the fair prices of the constituent stocks using the five methods and compute the RMSE of predicting the next-day open prices of the stocks in the Japanese market. The sample period for the simulation is identical to that of the actual funds. We conduct 400 simulations for each fund and report the average statistics over the 400 replications. Our simulation results, organized in the similar manner to those in Table 3, are reported in Panel A of Table 5. As expected, the RMSE increases as the market-cap of stocks in a fund decreases, regardless of the estimation method used. Stock size affects the estimation accuracy similarly across estimation methods. As for the 16 actual funds, our method produces a significantly lower RMSE than all alternative methods for each of the size-sorted mutual funds. The t-statistics vary little across the simulated funds.

2319

6.2. Portfolio turnover ratio A higher portfolio turnover ratio of a mutual fund changes the stock composition in the fund more frequently and can change the factor loadings of the portfolio over time. How this affects the performance of each estimation method is another empirical question. We simulate hypothetical funds with annual turnover ratios ranging from 10% to 1000%. We carry out 400 simulations and report the average statistics over the 400 replications in Panel B of Table 5. Interestingly, we do not find a high sensitivity of the RMSE to the portfolio turnover ratio for each estimation method. For all estimation methods, the RMSEs are similar at different turnover ratios. The relative performance of our estimation method does not vary much for different portfolio turnover ratios, as evidenced by the stable t-statistics across funds sorted by turnover ratio. Our method consistently outperforms all alternative methods regardless of the portfolio turnover ratio. 6.3. Number of stocks in a fund Our third experiment examines the effect of the number of stocks in a fund on the relative forecast accuracy of fund prices for the various estimation methods. This exercise is warranted because when the number of stocks in a fund increases, the improvement in forecast accuracy may vary across different methods. In other words, some methods may be more suitable for funds with a small number of stocks, while other methods may be more suitable for funds with a larger number of stocks in its portfolio. Thus our approach of estimating individual stock prices may not always be better than alternative approaches which adjust prices at the fund level for funds with a given number of stocks. We simulate five funds with the number of stocks in each fund ranging from 25 up to 500 stocks. Estimation results are reported in Panel C of Table 5. The RMSE monotonically decreases as the number of stocks in a fund increases for all estimation methods. This is likely because a more diversified portfolio will be more accurately priced by any estimation method. Regardless of the number of stocks in a fund, our method produces a lower RMSE than all alternative methods at the 5% significance level. Interestingly, as the number of stocks in a fund increases, our method seems to benefit relatively more than other methods in terms of forecasting accuracy. The t-statistic (in absolute value) increases monotonically with the number of stocks in a fund. While each method has the inherent uncertainty in estimating regression parameters, our stepwise regression can create additional noise in process of choosing explanatory variables for each stock (albeit it has the benefit of using better signals when the right explanatory variables are chosen). When the number of stocks increases, the noise in choosing the explanatory variables may decrease relative to the

2320

Table 4 Average profitability exploitable by an alternative estimation method for 16 US-based Japanese mutual funds benchmark: holding US T-bill Fund Panel A. Vulnerability of our method Alternative method 1 Return t-ratio Alternative method 2 Return t-ratio Alternative Method 3 Return t-ratio Alternative method 4 return t-ratio

1

2

(security level adjustment 0.043 0.046 0.923 1.005 0.018 0.018 0.358 0.365 0.060 0.067 1.235 1.413 0.038 0.032 0.787 0.670

3

4

using stepwise 0.001 0.029 0.063 1.319 0.039 0.796 0.051 1.094

5

regression) to exploitation 0.041 0.041 0.920 0.911 0.014 0.014 0.292 0.287 0.064 0.062 1.369 1.310 0.025 0.025 0.534 0.527

6

7

8

9

10

11

12

13

14

15

16

Ave

0.020 0.424 0.013 0.280 0.055 1.150 0.006 0.144

0.044 0.985 0.017 0.347 0.063 1.351 0.028 0.606

0.039 0.876 0.014 0.280 0.063 1.362 0.023 0.497

0.039 0.882 0.010 0.206 0.059 1.274 0.023 0.487

0.012 0.226 0.012 0.234 0.048 0.910 0.023 0.464

0.026 0.597 0.005 0.114 0.063 1.377 0.002 0.058

0.041 0.892 0.011 0.222 0.065 1.358 0.026 0.530

0.045 0.995 0.016 0.314 0.061 1.305 0.029 0.606

0.047 1.037 0.020 0.397 0.065 1.371 0.033 0.701

0.035 0.786 0.004 0.082 0.062 1.353 0.013 0.290

0.035 0.777 0.006 0.113 0.060 1.271 0.015 0.324

Panel B. Vulnerability of alternative method 1 (S&P500 futures index adjustment) to exploitation Our method Return 0.182 0.197 0.216 0.198 0.197 t-ratio 3.869 4.202 4.618 4.289 4.249 Alternative method 2 Return 0.176 0.201 0.219 0.206 0.199 t-ratio 3.686 4.250 4.569 4.379 4.250 Alternative method 3 Return 0.153 0.167 0.194 0.171 0.166 t-ratio 3.141 3.470 4.103 3.595 3.473 Alternative method 4 Return 0.045 0.056 0.024 0.052 0.045 t-ratio 0.928 1.172 0.504 1.094 0.946

0.196 4.166 0.199 4.197 0.168 3.459 0.058 1.196

0.213 4.498 0.211 4.355 0.185 3.836 0.038 0.800

0.195 4.235 0.201 4.330 0.167 3.505 0.052 1.097

0.199 4.338 0.205 4.401 0.170 3.591 0.049 1.038

0.195 4.270 0.199 4.316 0.165 3.502 0.047 1.009

0.219 4.203 0.219 4.144 0.197 3.734 0.030 0.568

0.210 4.596 0.221 4.745 0.194 4.203 0.046 0.995

0.197 4.146 0.200 4.143 0.166 3.401 0.045 0.937

0.193 4.188 0.195 4.183 0.162 3.387 0.046 0.975

0.194 4.160 0.201 4.261 0.166 3.461 0.054 1.135

0.203 4.415 0.209 4.467 0.178 3.787 0.051 1.091

0.200 4.278 0.204 4.292 0.173 3.603 0.046 0.968

Panel C. Vulnerability of alternative method 2 (Nikkei225 futures index adjustment) to exploitation Our method Return 0.170 0.182 0.176 0.178 0.177 t-ratio 3.555 3.828 3.471 3.763 3.754 Alternative method 1 Return 0.130 0.131 0.114 0.127 0.124 t-ratio 2.754 2.808 2.392 2.766 2.673 Alternative method 3 Return 0.164 0.165 0.147 0.161 0.161 t-ratio 3.462 3.495 2.981 3.414 3.416 Alternative method 4 Return 0.019 0.040 0.028 0.041 0.031 t-ratio 0.397 0.808 0.555 0.851 0.631

0.181 3.803 0.132 2.808 0.164 3.460 0.039 0.797

0.178 3.601 0.127 2.684 0.151 3.091 0.037 0.746

0.178 3.801 0.125 2.720 0.164 3.515 0.034 0.695

0.177 3.766 0.124 2.693 0.161 3.441 0.034 0.710

0.179 3.823 0.124 2.701 0.162 3.490 0.032 0.663

0.160 2.975 0.118 2.284 0.136 2.545 0.033 0.609

0.170 3.594 0.119 2.639 0.146 3.139 0.043 0.889

0.177 3.670 0.127 2.685 0.158 3.295 0.036 0.726

0.179 3.829 0.124 2.683 0.164 3.517 0.024 0.499

0.180 3.795 0.127 2.722 0.163 3.461 0.036 0.737

0.179 3.791 0.127 2.799 0.156 3.325 0.043 0.896

0.176 3.676 0.125 2.676 0.158 3.315 0.034 0.700

0.082 1.658 0.017 0.366 0.011 0.217 0.013 0.270

0.101 2.132 0.033 0.742 0.003 0.055 0.027 0.569

0.095 2.019 0.030 0.681 0.002 0.036 0.025 0.530

0.097 2.072 0.029 0.669 0.000 0.006 0.025 0.526

0.081 1.501 0.008 0.154 0.019 0.360 0.003 0.052

0.085 1.799 0.019 0.439 0.007 0.138 0.014 0.301

0.096 1.969 0.031 0.678 0.003 0.060 0.023 0.481

0.102 2.152 0.033 0.745 0.003 0.054 0.025 0.532

0.104 2.178 0.032 0.728 0.006 0.128 0.027 0.571

0.092 1.941 0.027 0.622 0.001 0.014 0.022 0.478

1.920 0.025 0.564 0.003 0.069 0.020 0.416

0.292 0.295 6.690 7.005 0.193 0.199 4.597 4.899 0.285 0.283 6.378 6.536 0.279 0.278 6.383 6.579 in parentheses)

0.291 6.819 0.196 4.774 0.281 6.400 0.276 6.445

0.296 7.004 0.189 4.681 0.290 6.753 0.284 6.743

0.296 6.878 0.191 4.633 0.289 6.575 0.283 6.568

Panel D. Vulnerability of alternative method 3 (S&P500 and Nikkei225 futures Our method Return 0.092 0.102 0.048 t-ratio 1.913 2.140 0.985 Alternative method 1 Return 0.022 0.033 0.006 t-ratio 0.739 0.120 0.495 Alternative method 2 Return 0.006 0.006 0.048 t-ratio 0.131 0.121 0.952 Alternative method 4 Return 0.013 0.027 0.003 t-ratio 0.280 0.561 0.063

index adjustment) to exploitation 0.098 0.099 0.101 2.072 2.085 2.108 0.031 0.031 0.031 0.700 0.700 0.684 0.003 0.003 0.007 0.063 0.056 0.132 0.025 0.024 0.025 0.542 0.509 0.518

Panel E. vulnerability of alternative method 4 (stale pricing without adjustment) to exploitation Our method Return 0.276 0.292 0.318 0.293 0.295 t-ratio 6.389 6.832 7.318 6.912 6.938 Alternative method 1 Return 0.194 0.197 0.172 0.193 0.196 t-ratio 4.640 4.789 4.165 4.759 4.802 Alternative method 2 Return 0.271 0.282 0.314 0.285 0.285 t-ratio 6.083 6.418 7.163 6.575 6.555 Alternative method 3 Return 0.269 0.278 0.299 0.279 0.279 t-ratio 6.203 6.475 6.927 6.587 6.567

0.291 0.306 0.294 0.295 0.295 0.305 0.301 6.770 6.984 6.966 7.009 7.042 6.260 7.114 0.197 0.187 0.197 0.196 0.196 0.172 0.181 4.772 4.456 4.864 4.850 4.883 3.685 4.508 0.280 0.302 0.283 0.287 0.283 0.313 0.300 6.345 6.787 6.560 6.662 6.588 6.367 7.031 0.276 0.294 0.278 0.281 0.278 0.299 0.295 6.412 6.743 6.579 6.664 6.629 6.150 7.006 Vulnerability of this method to exploitation by other methods (annualized percentage profits Our method

Panel F. Summary of exploitation profitability across all methods Profitability of this method in exploiting other methods

Our method Alternative method Alternative method Alternative method Alternative method

1 2 3 4

0.035 0.006 0.060 0.015

(4) (1) (8) (2)

Alternative method 1

Alternative method 2

Alternative method 3

Alternative method 4

0.200 (25)

0.176 (22) 0.125 (16)

0.092 (12) 0.025 (3) 0.003 (0)

0.296 0.191 0.289 0.283

0.204 (26) 0.173 (22) 0.046 (6)

0.158 (20) 0.034 (4)

(37) (24) (36) (35)

0.020 (3)

In this table, Panels A–E report the extent to which one fair-pricing estimation method is exploitable by other competing methods for 16 US-based Japanese mutual funds. Our method adjusts asset prices at the security level using stepwise regressions; alternative method 1 adjusts asset prices at the portfolio level using the S&P500 futures index alone; alternative method 2 adjusts asset prices at the portfolio level using the Nikkei225 futures index alone; alternative method 3 adjusts asset prices at the portfolio level using both the S&P500 and Nikkei225 futures indices; and alternative method 4 is stale pricing without adjustment. The returns are daily averages (in percent) relative to the benchmark of holding US T-bill. A t-statistic larger than 1.96 (2.58) indicates that the estimation method can be exploited by an alternative method at the 5 (1) percent significance level. Both returns and t-statistics are averages over 400 simulations. Panel F summarizes the results of Panels A through E. For each pair of methods, we take the average exploitation profitability across all 16 funds. We report both the average daily profit as well as the annualized profit (in parentheses). In a typical year, there would be approximately 125 trades. The sample period is from January 2, 1991 to December 31, 2001.

C.T. Chua et al. / Journal of Banking & Finance 32 (2008) 2307–2324

0.046 1.003 0.019 0.374 0.067 1.395 0.034 0.710

C.T. Chua et al. / Journal of Banking & Finance 32 (2008) 2307–2324

2321

Table 5 Forecasting accuracy of alternative fair-pricing estimation methods: robustness tests Stock size

Large

Panel A. Synthetic funds with different stock sizes Our method RMSE Alternative method 1

RMSE t-ratio RMSE t-ratio RMSE t-ratio RMSE t-ratio

Alternative method 2 Alternative method 3 Alternative method 4

Turnover

10

25

Panel B. Synthetic funds with different turnover ratios Our method RMSE 0.610 Alternative method 1 Alternative method 2 Alternative method 3 Alternative method 4

RMSE t-ratio RMSE t-ratio RMSE t-ratio RMSE t-ratio

0.664 5.845 0.669 6.496 0.627 2.582 0.757 9.309

No. of stocks in fund

Alternative method 2 Alternative method 3 Alternative method 4

Alternative method 2 Alternative method 3 Alternative method 4

0.633 5.451 0.656 6.647 0.608 3.411 0.735 9.191

0.668 5.397 0.669 6.431 0.633 2.320 0.744 8.425

0.762 6.263 0.729 4.382 0.717 2.581 0.795 8.197

100

500

1000

0.606

0.614

0.612

0.663 5.881 0.666 6.340 0.625 2.581 0.752 9.190

0.663 5.863 0.664 6.221 0.626 2.547 0.747 9.018

0.658 5.867 0.658 6.101 0.622 2.567 0.739 9.024

0.656 5.828 0.654 6.111 0.622 2.627 0.734 9.074

0.663 5.731 0.660 5.971 0.629 2.515 0.738 8.953

0.662 5.718 0.658 5.947 0.628 2.549 0.735 8.956

50

100

250

500

0.640

0.582

0.548

0.534

0.689 5.475 0.689 5.901 0.655 2.336 0.767 8.757

0.636 6.086 0.636 6.400 0.598 2.694 0.720 9.241

0.605 6.503 0.605 6.773 0.566 2.964 0.693 9.635

0.593 6.638 0.594 6.909 0.552 3.054 0.683 9.760

High (value)

RMSE t-ratio RMSE t-ratio RMSE t-ratio RMSE t-ratio

250

0.606

Panel D. Synthetic funds with stocks of different book-to-market ratios Our Method RMSE 0.598 Alternative method 1

0.698

0.610

0.763 4.770 0.763 5.121 0.733 1.983 0.833 7.919

Book-to-market

0.619

0.608

25

RMSE t-ratio RMSE t-ratio RMSE t-ratio RMSE t-ratio

Small

0.586

50

Panel C. Synthetic funds with different numbers of stocks in the funds Our method RMSE 0.719 Alternative method 1

Medium

0.649 5.723 0.631 5.604 0.614 2.629 0.690 8.248

Medium (blend)

Low (growth)

0.579

0.639

0.628 5.556 0.622 6.038 0.592 2.151 0.696 8.752

0.699 6.243 0.713 6.537 0.660 3.031 0.813 9.342

Panel A of the table reports the out-of-sample forecasting performance of our method and four alternative fair-pricing estimation methods for three synthetic funds with stocks of different sizes. Panel B, C, and D conduct the same exercise for synthetic funds with different turnover ratios, with different numbers of stocks in the funds, and with stocks of different book-to-market ratios, respectively. Our method adjusts asset prices at the security level using stepwise regressions; alternative method 1 adjusts asset prices at the portfolio level using the S&P500 futures index alone; alternative method 2 adjusts asset prices at the portfolio level using the Nikkei225 futures index alone; alternative method 3 adjusts asset prices at the portfolio level using both the S&P500 and Nikkei225 futures indices; and alternative method 4 is stale pricing without adjustment. The RMSE (in percent) of predicting asset prices at next-day Japan open is reported for each method. The t-statistic that our method yields a lower RMSE than an alternative method is reported below the RMSE of each alternative method. A t-statistic lower than 1.96 (2.58) indicates that our method outperforms an alternative method at the 5 (1) percent significance level in terms of forecasting accuracy. Both RMSEs and t-statistics are averages over 400 simulations. The sample period is from January 2, 1991 to December 31, 2001.

signals captured in our stepwise regression at the portfolio level. We suspect that this is why our method per-

forms better than other methods for funds with more stocks.

2322

C.T. Chua et al. / Journal of Banking & Finance 32 (2008) 2307–2324

6.4. Book-to-market ratio Our last experiment examines the performance of our method relative to other methods with respect to fund style in another dimension – the book-to-market ratio. To this end, we simulate three mutual funds, consisting, respectively, of high (value), medium (blend), and low (growth) book-to-market ratio stocks. Panel D of Table 5 shows the results. All estimation methods predict blend funds better than both value and growth funds, based on the reported RMSEs. Our method outperforms alternative methods 1, 2 and 4 at the 1% significance level for all three types of funds, and alternative method 3 for two types of funds consisting of value and growth stocks. Our method beats alternative method 3 for the blend fund at the 5% significance level. Overall, we find that the superior performance of our method over other competing methods is not affected by fund style.

method appears to be most successful in preventing profitable strategic exploitation in that none of the competing methods can significantly profit from our stated prices. Fourth, simulation results show that our method is superior to existing methods regardless of the fund characteristics, including turnover ratio, stock size, number of stocks in a fund, and book-to-market ratio. The mutual fund industry currently has various policies in place, such as front-end loads, redemption fees, and transaction restrictions, to deal with the stale pricing problem.20 While these methods can reduce the opportunities for a market timer to trade daily, they do not prevent strategic timing of purchases and do not eliminate the dilution impact on the performance of the funds. Our method, which is the least vulnerable to exploitation and can be easily implemented, can thus provide a useful alternative approach to solving the stale pricing problem in practice.

7. Conclusion Recent research demonstrates that simple trading strategies using readily available information can significantly exploit pricing errors when international mutual funds use final transaction prices in a foreign market to compute daily share prices. To remove return predictability, the literature suggests estimating fair fund prices at the portfolio level using market-wide information. This paper proposes a new methodology to estimate fair prices of international funds by adjusting prices at the individual security level using a broad set of information that is publicly available. To utilize information efficiently, we employ a stepwise regression to endogenously determine the stock-specific optimal set of economically and empirically meaningful factors in estimating the fair price of each stock in a fund. We provide a comprehensive evaluation of our approach compared to existing methods using 16 synthetic funds whose characteristics are extracted from corresponding actual US-based Japanese mutual funds, and obtain several interesting results. First, for all 16 funds, our method produces the most accurate prediction of fund prices at next-day Japan open, which are the best proxies for the unobserved prices at US close. It outperforms all existing methods at the 5% significance level or better in terms of prediction root mean squared errors. Second, while all existing methods remove much of the daily return predictability resulting from stale pricing, all of them remain highly vulnerable to exploitation by market timers. In particular, our method can produce excessive returns compared to the methods that use either the S&P500 or the Nikkei225 index of 25% and 22% annually. Our method can profit from the best alternative method which uses both the S&P500 and Nikkei225 indices by an annualized return of 12%. Third, our

Acknowledgements The authors would like to thank an anonymous referee and the Managing Editor of the Journal of Banking and Finance for many helpful comments and suggestions. This paper was reviewed and accepted while Professor Giorgio Szego was the Managing Editor of the journal and by the past Editorial Board. In addition, the authors would like to thank Andrew Abel, Yacine Ait-Sahalia, Ann-Marie Anderson, Marshall Blume, Ivan Brick, Charles Cao, Kalok Chan, N.K. Chidambaran, Bhagwan Chowdhry, Cheol Eun, Bruce Grundy, Allaudeen Hameed, Simi Kedia, Richard Kish, Ming Liu, Craig McKinlay, David Musto, David Myers, Nandkumar Nayar, Darius Palia, Dilip Patro, Christo Pirinsky, Krishna Ramaswamy, Heibatollah Sami, Ben Sopranzetti, Avanidhar Subrahmanyam, Marti Subrahmanyam, Geraldo Vasconcellos, Wenlong Weng, Yihong Xia, Hua Zhang, Feng Zhao, the anonymous referee and seminar participants at the Wharton School, the Chinese University of Hong Kong, Lehigh University, the National University of Singapore, Rutgers University, the University of Utah as well as summer camp participants at Singapore Management University. Choong Tze Chua and Sandy Lai are grateful to the Office for Research of Singapore Management University for financial support. Yangru Wu would like to thank the Rutgers Business School and the Whitcomb Center for financial support. Part of this research was conducted while Yangru Wu visited the Chinese Academy of Finance and Development of the Central University of Finance and Economics. We are solely responsible for any remaining errors. 20

For a description on these alternative methods of lessening exploitation by market timers, see, e.g. Investment Company Institute (2002) and Zitzewitz (2003), among others.

C.T. Chua et al. / Journal of Banking & Finance 32 (2008) 2307–2324

2323

Appendix This appendix describes the 12 industries, their SIC codes, and the 34 Japanese American Depository Receipts traded in the US over the period from January 2, 1991 to December 31, 2001. The proportion of times (in percent) each industry factor and ADR is selected into our empirical regression model is also reported. Industry Panel A. Industry classification 1. Consumer nondurables – food, tobacco, textiles, apparel, leather, Toys 2. Consumer durables – cars, TV’s, furniture, household appliances 3. Manufacturing – machinery, trucks, planes, off furn, paper, com Printing 4.

Oil, gas, and coal extraction and products 5. Chemicals and allied products 6. Business equipment – computers, software, and electronic equipment 7. Telephone and television transmission 8. Utilities 9. Wholesale, retail, and some services (laundries, repair shops) 10. Healthcare, medical equipment, and drugs 11. Money finance 12. Everything else – mines, constr, bldMt, trans, hotels, bus serv, entertainment

NO. ADR

SIC code

Proportion

0100–0999, 2000–2399, 2700–2749, 2770–2799, 3100–3199, and 3940–3989. 2500–2519, 2590–2599, 3630–3659, 3710–3711, 3714–3714, 3716–3716, 3750–3751, 3792–3792, 3900–3939, and 3990–3999 2520–2589, 2600–2699, 2750–2769, 3000–3099, 3200–3569, 3580–3629, 3700–3709, 3712–3713, 3715–3715, 3717–3749, 3752–3791, 3793–3799, 3830–3839, and 3860–3899 1200–1399 and 2900–2999

2.27

2800–2829 and 2840–2899 1.72 3570–3579, 3660–3692, 3694–3699, 3810–3829, and 7370–7379 1.18 4800–4899 4900–4949 5000–5999, 7200–7299, and 7600–7699

1.84 3.85 2.70

2830–2839, 3693–3693, 3840–3859, and 8000–8099

1.08

6000–6999 Others

1.74 1.65

Proportion

0.05

13

6.22

25

ORIX CORP

2.20

4.38

26

PIONEER CORP

2.70

8.38

27

11.4

5.37

28

SANYO ELECTRIC CO LTD SAWAKO CORP

3.83

29

3.23

14

3.54

15

4

1.12

16

JAPAN AIRLINES SYS KIRIN BREWERY LTD KUBOTA CORP

0.38

17

6

CRAYFISH CO LTD CROSSWAVE COMMUN INC CSK CORP

10.52

18

7

DAIEI INC

4.31

19

8

FUJI PHOTO FILM HITACHI LTD

3.32

20

12.43

21

MATSUSHITA ELECTRIC MILLEA HOLDINGS INC MITSUI & CO LTD NEC CORP

HONDA MOTOR LTD

1.61

22

NIDEC CORP

10

1.91

Proportion NO. ADR

3.02

9

2.59

Proportion NO. ADR

Panel B. Japanese ADRs 1 ADVANTEST CORP 2 AMWAY JAPAN LTD 3 CANON INC

5

1.77

KYOCERA CORP MAKITA CORP

2.13 5.71

30

SHISEIDO CO LTD SONY CORP

5.85

31

TDK CORP

4.28

8.86

32

3.66

33

0.03

34

TOYOTA 3.58 MOTOR CORP TREND MICRO 2.57 INC WACOAL CORP 5.31 (Continued on next page)

9.58

2324

C.T. Chua et al. / Journal of Banking & Finance 32 (2008) 2307–2324

Appendix (continued) NO. ADR 11 12

Proportion NO. ADR

INTERNET 3.69 INITIATIVE JP ITO YOKADO CO LTD 3.40

23 24

Proportion NO. ADR Proportion

NIPPON TELEGRPH & TELE NISSAN MOTOR CO LTD

References Beckers, Stan, Connor, Gregory, Curds, Ross, 1996. National versus global influences on equity returns. Financial Analysts Journal 52, 31– 39. Bhargava, Rahul, Bose, Ann, Dubofsky, David A., 1998. Exploiting international stock market correlations with open-end international mutual funds. Journal of Business Finance and Accounting 25, 765– 773. Boudoukh, Jacob, Richardson, Matthew, Subrahmanyam, Marti, Whitelaw, Robert F., 2002. Stable prices and strategies for trading mutual funds. Financial Analysts Journal 58, 53–71. Burns, Patrick, Engle, Robert, Mezrich, Joseph, 1998. Correlations and volatilities of asynchronous data. Journal of Derivatives 5, 7–18. Campbell, John Y., Hamao, Yasushi, 1992. Predictable stock returns in the United States and Japan: a study of long-term capital market integration. Journal of Finance 47, 43–69. Chalmers, John M.R., Edelen, Roger M., Kadlec, Gregory B., 2001. On the perils of financial intermediaries setting security prices: the mutual fund wild card option. Journal of Finance 56, 2209–2236. Chan, Kalok, Hameed, Allaudeen, Lau, Sie Ting, 2003. What if trading location is different from business location? Evidence from the Jardine Group. Journal of Finance 58, 1221–1246. Craig, Alastair, Dravid, Ajay, Richardson, Matthew, 1995. Market efficiency around the clock: some supporting evidence using foreignbased derivatives. Journal of Financial Economics 39, 161–180. Draper, Norman R., Smith, Harry, 1998. Applied Regression Analysis. Wiley, New York. Duffee, Gregory R., 2002. Term premia and interest rate forecasts in affine models. Journal of Finance 57, 405–443. Dumas, Bernard, Solnik, Bruno, 1995. The world price of foreign exchange risk. Journal of Finance 50, 445–479. Errunza, Vihang, Losq, Etienne, 1985. International asset pricing under mild segmentation: theory and test. Journal of Finance 40, 105–124. Eun, Cheol S., Janakiramanan, Sundaram, 1986. A model of international asset pricing with a constraint on the foreign equity ownership. Journal of Finance 41, 897–914. Fama, Eugene, French, Kenneth R., 1987. Commodity futures prices: some evidence on forecast power, premiums, and the theory of storage. Journal of Business 60, 55–73.

2.24 3.61

Fama, Eugene, French, Kenneth R., 1996. Multifactor explanations of asset-pricing anomalies. Journal of Finance 51, 55–84. Fama, Eugene F., French, Kenneth R., 1997. Industry costs of equity. Journal of Financial Economics 43, 153–193. Fama, Eugene F., French, Kenneth R., 1998. Value versus growth: the international evidence. Journal of Finance 53, 1975–1999. Froot, Kenneth A., Dabora, Emil M., 1999. How are stock prices affected by the location of trade? Journal of Financial Economics 53, 189–216. Goetzmann, William N., Ivkovic, Zoran, Rouwenhorst, K. Geert, 2001. Day trading international mutual funds: evidence and policy solutions. Journal of Financial and Quantitative Analysis 36, 287–309. Greene, Jason T., Hodges, Charles W., 2002. The dilution impact of daily fund flows on open-end mutual funds. Journal of Financial Economics 65, 131–158. Hartzmark, Michael L., 1991. Luck versus forecast ability: determinants of trader performance in futures markets. Journal of Business 64, 49– 74. He, Jia, Ng, Lilian K., 1998. The foreign exchange exposure of Japanese multinational corporations. Journal of Finance 53, 733–753. Hou, Keiwei, Karolyi, Andrew, Kho, Bong Chan, 2006. What fundamental factors drive global stock returns? Working Paper, Ohio State University. Investment Company Institute, 2002. Valuation and liquidation issues for mutual funds: 2002 supplement. ICI White Paper. Jorion, Philippe, 1990. The exchange-rate exposure of US multinationals. Journal of Business 63, 331–345. Kilian, Lutz, Taylor, Mark P., 2003. Why is it so difficult to beat the random walk forecast of exchange rates? Journal of International Economics 60, 85–107. Pesaran, M. Hashem, Timmermann, Allan, 1995. Predictability of stock returns: robustness and economic significance. Journal of Finance 50, 1201–1228. Qi, Min, Wu, Yangru, 2003. Nonlinear prediction of exchange rates with monetary fundamentals. Journal of Empirical Finance 10, 623–640. Rouwenhorst, K. Geert, 1998. International momentum strategies. Journal of Finance 53, 267–284. Zitzewitz, Eric, 2003. Who cares about shareholders? Arbitrage-proofing mutual funds. Journal of Law, Economics, and Organization 19, 245– 280.