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Understanding the Closed-end Fun

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					   Understanding the Closed-end Fund Puzzle from the
                                  Chinese Experience

                                                                                  ¤
                      Gongmeng Chen, Oliver Rui, and Yexiao Xu

                                   This version: April 2004



                                              Abstract

           Although many characteristics of Chinese closed-end funds resemble those of the
        U.S. funds, investors and environment are different. For example, institutions such
        as insurance companies hold a substantial amount in closed-end funds, there are no
        capital gains taxes, and there is no private investment by the funds. These differences
        allow us find that the discounts are negatively related to liquidity, percentage of stock
        holdings, and past risk-adjusted performance. Discounts are also positively influenced
        by the R2 from a market model applied to the underlying asset returns, managerial
        ownership, and the size of the fund. We further show that “investor overconfidence”
        and liquidity are major factors that affect the dynamics of discounts.



  ∗
      Chen is at the Department of Accountancy, The Hong Kong Polytechnic University, Rui is with the
Faculty of Business Administration of The Chinese University of Hong Kong, and Xu is at the School
of Management, The University of Texas at Dallas. We are grateful to Burton G. Malkiel, Jeff Pontiff,
Ravi Ravichandran, Z. Jay Wang, and to the seminar participants in the 2002 European Financial Man-
agement Association Conference, the 2002 Financial Management Association Conference, the tenth Asia
Pacific Finance Association Annual Conference, and the 2002 APFA/PACAP/FMA Finance Conference
for their helpful comments. The work described in this paper was fully supported by a grant from the
Hong Kong Polytechnic University (Project No. A-PC 27). The address of the corresponding author is:
Yexiao Xu, School of Management; The University of Texas at Dallas; Richardson, TX 75083. Email:
yexiaoxu@apache.utdallas.edu


                                                   1
Understanding the Closed-end Fund Puzzle from the
               Chinese Experience




                                       Abstract

    Although many characteristics of Chinese closed-end funds resemble those of the
 U.S. funds, investors and environment are different. For example, institutions such
 as insurance companies hold a substantial amount in closed-end funds, there are no
 capital gains taxes, and there is no private investment by the funds. These differences
 allow us find that the discounts are negatively related to liquidity, percentage of stock
 holdings, and past risk-adjusted performance. Discounts are also positively influenced
 by the R2 from a market model applied to the underlying asset returns, managerial
 ownership, and the size of the fund. We further show that “investor overconfidence”
 and liquidity are major factors that affect the dynamics of discounts.




                                            2
Introduction

An enduring puzzle in finance is the so called “closed-end fund puzzle.” We often observe that
shares of closed-end funds sell at prices below the net asset value (NAV) of the underlying
portfolio of securities.

   Although the first closed-end fund, the New York Stock Trust, was offered to the public
in 1889, this pricing discrepancy was not formally documented until Pratt (1966). Since
then, we have learned from empirical study that the useful factors explaining discounts on
closed-end funds include: unrealized capital gains (Pratt, 1966; Vives, 1975; Malkiel, 1977;
and Mendelson, 1978), portfolio turnover (Pratt, 1966; and Boudreaux, 1973), distribution
policy (Malkiel, 1977; Mendelson, 1978; and Thompson, 1978), private investment by closed-
end funds (Malkiel, 1977; and Anderson and Born, 1987), and investor sentiment or market
conditions (Zweig, 1973; Malkiel, 1977; De Long, Shleifer, Summers, and Waldmann, 1990;
and Brauer, 1993). Other factors derived from theoretical models include the open-ending
option proposed by Brauer (1988), the tax-timing option of Brickley, Manaster, and Schall-
heim (1991) and Kim (1994), and the stochastic turnover risk that was modeled by Xu
(2000).

   The dynamics of closed-end fund discounts are also interesting. Various empirical studies
(for example, Thompson, 1978; Hardouvlis, La Porta, and Wizman, 1993; and Pontiff, 1995)
show that funds with positive premiums provide negative abnormal future returns, but funds
with discounts earn positive abnormal future returns.

   These studies suggest that no single explanation accounts for all of the discounts. Many
factors matter. In fact, currently, we can at best explain only fifty percent of the discounts
on closed-end funds using “rational factors” (see Malkiel, 1995), so it is possible that other,
unknown, factors are contributing to the discount issue. In other words, we are still unable
to conclude whether the remaining unexplained discounts are due to market inefficiency.

   Most research into closed-end funds has concentrated on funds traded in mature capital
markets, such as the U.S. and U.K., including country funds that hold international stocks.
Given the divergent conclusions of studies in this field, we might obtain further insights
through investigating an alternative set of financial markets, in particular a set of emerging
markets.


                                              1
   Emerging capital markets present an unique investment environment with special insti-
tutional details and different groups of investors with distinctive social and culture back-
grounds. Such markets have low correlations with more developed markets. Hence, any
possible data-snooping biases resulting from focusing only on developed markets are less-
ened. Although the majority of closed-end funds in the U.S. and U.K. are country funds,
studies focused on these funds may not offer the same premise as those actually traded in
emerging markets. There are two reasons. First, Cooper and Kaplanis (1994) provide ev-
idence of home bias in investor portfolios, suggesting that the discounts could be due to
market segmentation. Second, the majority of investors in these funds are from the U.S. or
U.K., and the funds are operated under the same regulatory environment.

   The Chinese closed-end fund market is both ideal and unique in terms of institutional
structure and investors’ behavior. As an emerging capital market, the Chinese stock mar-
kets are much less efficient than those in mature markets. If the majority of investors are
individual investors, and if a factor such as investor sentiment is important, then this factor
should influence the level of discounts for Chinese closed-end funds more than would be the
case for the U.S. funds. Over 95% of closed-end fund investors in the U.S. and U.K. are
individual investors. Individual investors were also the majority in China until February 25,
2000, when the authorities began to allow insurance companies and pension management
companies to hold closed-end funds. Now, the majority of investors in the Chinese closed-end
fund markets are institutional investors. This structural change may shift the importance of
the sentiment risk for the Chinese closed-end funds.

   There are also significant differences in the tax environment in China. Currently, the
Chinese government does not levy capital gains taxes. Thus, factors found in U.S. data that
are related to capital gains taxes and the way in which the gains are realized and distributed
are inapplicable in the Chinese case. Moreover, all of the closed-end funds in China are
invested in the publicly traded domestic securities. Since these securities are actively traded
in China, the valuation of the underlying holdings is not an issue. These unique differences
suggest the usefulness and the importance of examining the Chinese closed-end funds.

   The first closed-end fund in China was sold to the public in April 1998. Since then, the
industry has grown steadily. Using the unique data set on the Chinese closed-end funds, we
document some of the stylized facts about Chinese closed-end funds. We note that these
funds share many characteristics with those in the U.S. market. For example: there are


                                              2
substantial and persistent discounts for majority funds; most closed-end funds enjoy high
premiums at their IPO stage, which disappear after six months; and discounts can predict
future fund returns. However, there are some critical differences in Chinese institutional
structure, investors’ behavior, and investment environment. At the same time, there are
factors that are more universal, for example, the investor sentiment risk, the imperfect
arbitrage opportunity, the stochastic turnover risk, and the information asymmetric. By
comparing the characteristics found in the Chinese closed-end fund market with those of the
mature capital markets, we may better understand the behavior of closed-end funds.

   Our empirical results suggest that the closed-end fund discounts are negatively related to
fund’s liquidity, percentage of stock holdings, and past risk-adjusted performance. Discounts
are positively influenced by the R2 from a market model applied to the underlying asset
returns, managerial ownership, and size of the fund. We also show that discounts fluctuate
with the trading volume and the returns of a small-size portfolio over time. Due to the
unique features of the Chinese market, we believe that investor overconfidence (not investor
sentiment) and liquidity are major factors that affect the dynamics of premiums or discounts
in the Chinese closed-end fund market. However, with the increasing presence of institutional
investors in the Chinese closed-end fund market, the overconfidence effect is disappearing.

   Section 1 presents a brief history of Chinese investment companies. In Section 2 we
discuss our unique data set and the hypotheses that we test. In Section 3 we establish some
of the stylized facts about Chinese closed-end funds. Section 4 presents our empirical tests
of various hypotheses. Section 5 studies the time series behavior of discounts and the issue
of predictability. Section 6 concludes the paper.




                                              3
1     The Development of Chinese Investment Companies

The first investment fund in China, the Nanshan Venture Capital Fund, was established in
November 1991. This marked the beginning of the fund industry in mainland China. At the
beginning, most of the funds were established with the approval of the local government or the
People’s Bank of China. Because the funds were intended to attract capital, their investment
covered a wide spectrum, from private equities to real estate, and from government bonds
to traded stocks. They were named “old funds” as opposed to the relatively standardized
investment funds.

    These old funds expanded rapidly. By the end of 1997, there were 75 old funds with more
than 5.8 billion RMB in book value and 10 billion RMB in market value. However, many
aspects of these old funds were not standardized, including fund initiation, fund operations,
information disclosure, supervision, and regulation. Because there were so many problems
in their daily operation, there has been a virtual halt in the offering of new funds since 1994.

    On November 14, 1997, the Securities Committee of the State Council (which was later
merged into the China Securities Regulatory Commission, CSRC) issued its “Interim Regula-
tions on Securities Investment Funds” (IRSIF). The CSRC later promulgated detailed rules,
elaborating on fund initiation, capital raising and trading, fund trustees and managers, the
rights and obligations of fund holders, fund investment operations, and supervision and man-
agement. As stipulated by the IRSIF, the percentage of bond and equity investments made
by a fund cannot fall below 80 percent of the fund’s total asset value; the total stock value
of one listed company cannot exceed 10 percent of the fund’s NAV; and the percentage of
investments in national bonds cannot fall below 20 percent of the fund’s NAV. Within three
months after the approval of a new fund, the fund must raise 200 million RMB, an amount
that must exceed 80 percent of the target size of the fund. These rules have had a major
impact on the investment behavior of the investment companies.

    In March 1998, two new funds founded in line with the IRSIF Fund Kai Yuan and
Fund Jintai, were issued nationwide, and publicly listed in April (see Table 1). Since the
new funds were only allowed to invest in publicly traded stocks and bonds in the Chinese
security markets, they were called “securities investment funds” (hereafter referred to as the
closed-end funds). From the regulatory perspective, such funds are established for two main
purposes. One is to exploit the advantages of expert management and to provide individual

                                              4
investors with a good investment tool. The other is to nurture institutional investors and to
promote the steady, healthy development of the security markets.


                             Insert Table 1 Approximately Here


   To support the healthy development of those closed-end funds, the Chinese government
has issued a series of preferential policies. On October 11, 1998, the CSRC promulgated the
“Notice on the Distribution of New Issues to the Securities Investment Funds.” The Notice
gave the funds preferential rights in the distribution of new issues. Under the original rules,
shares of the new issues distributed to a fund could not be traded until two months after the
IPO. However, this rule was modified on November 11, 1999, allowing a fund to trade half
of the allocation on the day of the IPO, while holding the rest for six months.

   In May 2000, the CSRC abolished this preferential policy. Every fund can now set up
its stock accounts just like any other investor. Funds can participate in issuing new shares,
new share distributions, and in booking new share distributions. There is no limit on how
many shares can be allocated to each investment fund.

   After years of development, the number of funds was growing and the old funds were
gradually being standardized and transformed into new funds. The restructuring of the old
funds began in the latter half of 1999, and nearly all the new funds that went public in the
first half of 2000 were conversions of the old funds. The motivation behind the restructuring
of the old funds was to increase the capital and to revive the operations of the funds by
clarifying the assets of several old funds. These restructured funds are operated under the
same methods as the newly issued funds.

   By the year 2001, there were 48 publicly traded closed-end funds in China under the
management of 14 fund management companies, with a total 68.67 billion fund units and
69.12 billion RMB in net asset value. Among them, 27 were formed by reconstructing old
funds. There were three open-end funds with 11.75 billion fund units and 11.81 billion in
net asset value. In total, there were 51 funds in China, with 80.42 billion fund units and
80.92 billion RMB in net asset value. These funds have become a very important force in
the Chinese security markets.




                                              5
2     Data and Stylized Facts

The discount phenomenon on most closed-end funds is the predominant issue in the closed-
end fund literature. As a first step in studying Chinese closed-end funds, we document some
of the stylized facts here. We begin with a discussion of our data source.



2.1    Data

We obtain data on Chinese closed-end funds from the only two stock exchanges in China,
the Shanghai Stock Exchange and the Shenzhen Stock Exchange. This is a quality data set,
since it was directly provided by the two stock exchanges.

    The data set starts from the inception of the first two closed-end funds in April 1998
and continues to the end of 2001. It is a weekly data set of all the funds that have ever
existed in China. Out of a total of 48 funds, we excluded 12 funds that offered their IPOs
after September 2001 because of insufficient data. Although these funds are traded daily,
information on their net asset value (NAV) is available only weekly.

    As in the U.S., the NAVs are published on either the Wednesday or Friday edition of
major Chinese financial newspapers, such as Shenzhen Securities Times, China Securities,
and other such publications. The information includes weekly closing prices, the NAVs of
fund portfolios, total weekly returns including dividends, weekly trading volume in terms of
number of shares traded in a week, percentage of holdings by the funds’ initiators, and the
total market capitalization of each fund. Table 2 reports the summary statistics for those
variables over each quarter.

    Since we know little about the validity of the CAPM in Chinese stock markets, we use
a market model to decompose security returns into their market-related and idiosyncratic
parts. Although the results are similar when we use the CAPM, the market model is con-
ceptually far more robust. As a proxy for the market portfolio we use a value-weighted
composite index portfolio of all the stocks traded on both Shanghai and Shenzhen stock
exchanges. This index is available from the 2001 version of the China Stock Market & Ac-
counting Research (CSMAR) database, which is the most reliable and widely used security




                                             6
database in China1 . We compound the weekly index returns from the daily index returns.


                                Insert Table 2 Approximately Here


      The number of funds gradually increases from two to 36 over the four-year sample period.
Although relatively small, the total market capitalization of Chinese closed-end funds grew
rapidly from 7.61 billion RMB (about $0.89 billion U.S. dollars) to 58.25 billion RMB (about
$6.8 billion U.S. dollars) over the four-year period. There are many ways to define trading
volume. We use the ratio between the total number of shares traded in a week and the total
number of shares outstanding. We find that the average weekly trading volumes fluctuate
between 0.7% and 3%, excluding the starting quarter of the data set. These numbers are
close to the trading volume for common stocks in the Chinese equity markets. Therefore,
closed-end funds are actively traded securities in China. In contrast to U.S. closed-end funds,
the percentage held by the initiators of the fund is relatively small (about 2%). The average
share price is around 1.2 RMB, which is comparable to the IPO price of 1RMB.



2.2      Establishing Stylized Facts about Chinese Closed-end Funds

To study the characteristics of Chinese closed-end funds, in Figure 1 we plot the average
weekly closed-end fund premiums across funds. Because few funds existed in 1998 and most
of those were in the IPO stage, we begin our plot in 1999. To alleviate the extreme premiums
in the beginning, we exclude the first four weeks of data after the IPO. In the first half of
1999, the premiums are mostly positive. The premiums disappear and turn into discounts
in the second half of 1999. The downward trend continues into the first quarter of 2000, at
which point the trend reverses itself.


                               Insert Figure 1 Approximately Here


      Although premiums or discounts tend to fluctuate over time, this apparent change in the
trend indicates the policy change that allowed insurance companies and pension companies
  1
      The construction of this index is similar to the composite index of NYSE/AMEX/NASDAQ found in
the CRSP tape.



                                                  7
to invest in closed-end funds. Therefore, the majority of investors before and after February
25, 2000 were different. In the second half of 2001, we see moderate premiums instead.

       We also note from Table 2 that in most of the quarters in our sample period, the aggregate
returns from the NAV underperform the market index returns when the average premiums
are negative. This finding indicates that investors lose interest in the closed-end funds when
they perform poorly relative to the market. On average, Figure 1 shows that the same
discount phenomenon exists in the Chinese closed-end fund market.

       Lee, Shleifer, and Thaler (1991), using U.S. data, show that in the initial public offerings,
closed-end funds are issued at premiums of nearly 10%, but the premiums quickly turn into
discounts within four months. If the same results are true for the Chinese capital markets,
showing aggregate premiums (discounts) over time could be biased towards premiums when
the number of newly issued funds increases over time. Therefore, we study the discount issue
from the “life cycle” perspective, especially for newly established markets.

       Given the uniqueness of our data set, which includes both the IPO and post-IPO periods
for each fund, we can also investigate the discount issue using the event study approach.
In Figure 2 we plot the average weekly premiums across individual funds after their IPOs.2
The pattern is surprisingly similar to that of the U.S. closed-end funds documented by Lee,
Shleifer, and Thaler (1991). A 35% premium at the IPO for a typical fund disappears in
30 weeks. Therefore, we define the first 30 weeks as the IPO period. In the U.S., there
might be a price supporting period during a fund’s IPO by underwriters, which is similar to
the IPO of a public firm. There is no such price support for the Chinese closed-end funds.
Therefore, the IPO period we define here is purely mechanical. In the post IPO stage, we
observe substantial discounts. It takes about a year and a half for the average discount to
stabilize at around 10%. This process seems to be longer than it is in the U.S. Consistent
with the huge premium at the IPO, aggregate fund returns are abnormally high in the first
two weeks.3 The returns rapidly retreat to around zero.


                                  Insert Figure 2 Approximately Here
   2
       As a convention, Figure 2 shows premiums instead of discounts. Although we have 185 weeks of data,
the last 40 weeks of data are not shown in the graph since we have fewer than five funds.
   3
     This is also consistent with findings in Chen, Firth, and Kim (2000) who studied 277 IPOs in China.
They find that the mean market-adjusted initial return for the A-share IPOs is extremely high. The average
across the two exchanges is 350%.


                                                     8
       To investigate the dynamics of closed-end fund returns and discounts, we first compute
the autocorrelation for an equally weighted index of premiums across all funds starting in
1999. In Figure 3 the first line suggests that premiums (discounts) are persistent, as they
are in Figure 1, with an autocorrelation of 98.8% at the first lag. The correlation only drops
to 95% at the sixth lag. Such persistence is much higher than that found in other studies.

       Perhaps the most interesting time series property is the negative (positive) correlation
between premiums (discounts) and future returns. Using the equally weighted index of fund
returns and the index of premiums, in Figure 3 we also plot such cross-correlations between
current fund premiums δt and future returns Rt+i as a function of future date i. The cross-
correlations are substantial, with a magnitude of 17% at the first lag and 9% at the sixth lag.
In contrast, fund return autocorrelations are relatively small, and fluctuate at around zero at
different lags. We note that the autocorrelation is 11% at the first lag. The cross-correlation
that we observe for Chinese closed-end funds cannot be explained by the popular dividend
taxation effect proposed by Pontiff (1995), because there are no capital gains taxes in China.


                                  Insert Figure 3 Approximately Here


       The qualitative characteristics of Chinese closed-end funds resemble those of the U.S.
and UK closed-end fund markets. We examine the summary statistics at the individual fund
level. Because Figure 2 suggests that there are substantial differences in a fund’s premiums
during the IPO period compared to the post-IPO period, in Table 3 we study each subsample
period separately.4

       Since we are dealing with very skewed random variables, we prefer to use median statistics
rather than mean statistics. The reported distribution suggests that the majority of funds
are sold at a premium in the IPO period, with an average premium of 10%. These premiums
become discounts in the post-IPO stage, with a magnitude of 8%.

       In contrast to a positively skewed distribution for premiums, the negative premiums in
the post-IPO stage have a negatively skewed distribution. That is, we are likely to observe a
large premium in the IPO stage and a large discount in the post-IPO stage. At the same time,
   4
       For stationary purposes, we ignore the first four weeks of data in computing the summary statistics.
Moreover, the reported average discount in the post-IPO period should not be the same as shown in Figure
2, since the number of weeks with available data is different across funds.


                                                     9
discounts in the IPO stage are more persistent (about 97% compared to 91%). Although
the persistence of discounts seems to vary much less across funds in the post-IPO stage than
in the IPO stage, the volatilities of the discounts over time are about the same in both the
IPO and post-IPO stage (about 7.5%). Therefore, we observe large, stable discounts more
often in the post-IPO period.


                             Insert Table 3 Approximately Here

   The average weekly fund return is negative (about ¡0.235%) in the IPO period and
slightly positive (about 0.04%) in the post-IPO period. The average weekly returns from the
NAVs of underlying assets during the IPO and the post-IPO periods are just the opposite
(about 0.424% compared to ¡0.032%). This pattern seems to be inconsistent with the
premium (discount) pattern over the two different periods, since we might expect to see a
higher return for a closed-end fund than the return from its NAVs when the fund is traded at
a premium. Our calculations suggest that the pattern indicates nothing more than a decline
in premiums in the IPO period and a shrinking of discounts in the post-IPO period. We also
note that in the IPO period, the underlying assets of closed-end funds perform well, with an
average return of 0.424% relative to that in the post-IPO period.

   Since new funds come into the markets fairly evenly throughout our sample period (see
Table 2), the average returns in the two sample periods are comparable. The difference in
returns could not be due to different market conditions. Perhaps a high return in the IPO
stage merely reflects the level of risk exposure. Therefore, we also estimate the average beta
measure by fitting the market model in Table 3. These average betas show no significant
change during the two different periods. Moreover, the risk-adjusted alpha measure also
points to the same direction, with 0.22% and 0.09% in the IPO and post-IPO periods, re-
spectively. If performance reflects effort, this performance difference suggests that managers
work harder in the early stage of a fund. It could also partly due to the fact that prior to
May 2000, many of the funds receive preferential treatment in obtaining IPO stocks. In any
case, the difference in alphas is a preliminary indication that the performance of a fund may
be an important cause of the discounts in the post-IPO stage.

   A puzzling observation that appears in Table 3 is that a fund itself is exposed to less
market risk than are its underlying assets, regardless of whether it is in the IPO stage or in
the post-IPO period. For example, the average betas are 0.55 for the fund returns and 0.60

                                             10
for the underlying asset returns over the post-IPO period. This phenomenon can only happen
when there are systematic factors unique to closed-end funds that are partially negatively
correlated with the market factor. However, the differences are statistically insignificant, as
Table 4 shows. In other words, the market risks are similar for both the underlying assets
and for the fund as a whole.

   The average R2 s from fitting the market model are over 67% and 41% for the NAV
returns and the fund returns, respectively. Since a fund must be exposed to at least the
same amount of market risk as its underlying assets in general, the differences in R2 s suggest
that the Chinese closed-end funds are subject to other risks in an important way.

                             Insert Table 4 Approximately Here


   Although returns from the underlying assets vary substantially (about 2.46%) in the IPO
stage, the fund returns fluctuate much more (about 3.26%). If we interpret the net asset
value as the fundamental value of the closed-end fund, such a discrepancy in the volatilities is
consistent with the so-called “excess volatility” phenomenon found in stock returns by Shiller
(1989) and later confirmed by Pontiff (1995) for closed-end funds. Although both returns
fluctuate less in the post-IPO period, Table 4 shows that the excess volatility phenomenon
is much more severe than in the IPO period. Given similar market risks in both the fund
return and its NAV as discussed above, the difference in total volatilities must mean that
the idiosyncratic volatility relative to the market factor for a fund return is larger than
for its underlying asset returns. Table 4 confirms this observation. Therefore, although
persistent discounts can only be attributed to systematic risk factors, many idiosyncratic
factors influence fund returns. In fact, some of the idiosyncratic volatilities could be due to
unknown systematic factors other than the market factor. We also observe that on average,
betas are well below one, since Chinese closed-end funds hold between one-quarter to one-
third of their assets in government bonds.

   Table 3 shows that cross-correlations between current premium and future returns are
mostly negative and substantial (about ¡26%) in the post-IPO period. However, the cross-
correlation varies substantially across funds and is much smaller (about 16%) during the
IPO stage. Such a correlation is unlikely from a correlation between current premiums and
future returns of the NAVs. The reason is that, given a large and persistent discount in
the post-IPO stage, we expect to see a positive cross-correlation between current premium

                                              11
and future returns from the NAVs. On the contrary, Table 3 shows that the correlation is
negative in the post-IPO period.

   Despite the structural and institutional differences between the U.S. and Chinese capital
markets, the qualitative characteristics of closed-end funds are similar, but with greater
magnitude. Although inefficiency may play a vital role in causing the discounts on most
Chinese closed-end funds, many important rational factors such as tax-related effects, the
distributional policy on gains, and the liquidity of the underlying assets are irrelevant to
understanding the discounts on Chinese funds. Therefore, studying the Chinese closed-end
funds not only serves as a robust check for the known rational factors, but also provides
opportunities in exploring other factors that may have existed in a different environment.
To gain additional insights, we focus on the issue of post-IPO discounts, the issue explored
in many other studies.




                                            12
3     Hypotheses

Since most funds are traded at the negative premium, we use the term “discount” instead
of “premium” in the rest of the paper.

    The discount phenomenon is not unique to mature capital markets. In fact, the aggregate
behavior of the closed-end funds that are traded in emerging markets, such as the Chinese
markets, is similar to that of U.S. closed-end funds. Because we far from fully understand
the cause of discounts using the U.S. and U.K. data, we examine the same issue from a
different perspective, such as a different capital market with a unique structure and different
investors. By doing so, we avoid the issue of data snooping, and we can reevaluate the known
factors and consider additional factors.

    Attributing anything that we do not fully understand to irrationality is an easy resolution
to the closed-end fund puzzle. It may be that irrationality is partly responsible for the
discounts we observe. The important question is how important irrationality actually is. If
rational factors can explain a greater portion of discounts in Chinese closed-end funds than
in U.S. funds, irrationality or market inefficiency may not be a dominant factor in discounts,
because mature capital markets tend to be more efficient. Using variance-ratio tests, Chen,
Lee, and Rui (2001) reject the hypothesis that stock returns follow a random walk process
in China. Therefore, should market inefficiency be an important factor, we would expect to
need fewer explanations for the level of discounts or premiums for the Chinese closed-end
funds relative to the U.S. closed-end funds.

    Many important known determinants of discounts offer few or no insights into discounts
on Chinese closed-end funds, since the structure of the Chinese capital markets is so different
from that of the U.S. For example, one of the most important factors influencing discounts is
unrealized capital gains. Since unrealized capital gains impose tax liabilities on current fund
holders even when they are not entitled to such capital gains, closed-end funds should sell
at discounts relative to their net asset value when there are large unrealized capital gains.
As noted, the Chinese government does not currently levy capital gains taxes. Any factors
that are related to capital gains or to the way a fund distributes the gains does not apply to
Chinese closed-end funds.

    In addition, the liquidity of the underlying assets should also have little impact on dis-


                                               13
counts. Unlike the U.S. or U.K. closed-end funds that are heavily invested in foreign securities
and private assets, there are no foreign investments or restricted securities in the portfolios
of Chinese closed-end funds. If its investments are not held in cash, each fund is required
to invest in either traded government bonds or traded equities. At the same time, since the
majority of Chinese investors can only invest in Chinese securities, home bias is not an issue.

       One reason for investors to hold an actively managed fund is to have access to manage-
ment skills and/or private information. Therefore, if the premium is the price that investors
pay to gain access to the unique abilities and private information of managers and the dis-
count compensates investors for poor management, then the premium or discount should
be related to performance. Despite the fact that all the major assumptions underlying the
CAPM model are unlikely to apply in China, we must still adjust for risk when measuring
performance.

       Similar to computing the Jensen’s alpha, we use the intercept (α) from a market model as
a measure of the risk-adjusted performance of a fund.5 If a fund manager possesses superior
management skills, the returns from the net asset value should have a large alpha. Naturally,
these funds will experience high demands, which will drive up prices due to the fixed supply
and opaque portfolio holdings of these funds. In other words,


Hypothesis 1 the discounts (premiums) are negatively (positively) related to a fund’s risk-
adjusted performance of the net asset value.


We note that an important assumption supporting this line of argument is that no fund
portfolios can be perfectly replicated at all times, which is reasonable even in the U.S.
Further, in addition to management skills, superior performance can also be tied to unique
information.

       When the portfolio held by a fund is easy to arbitrage, the discount will be relatively
small. We use a more powerful measure, R2 from the same regression for the market model
using returns from the NAVs. We can consider the R2 measure as a relative measure of
Pontiff’s (1996) replication risk6 . The higher the R2 , the easier it is to use a market portfolio
   5
       Alternatively, one can also subtract the riskfree rate from such an intercept. However, since the weekly
interest rate is very stable and small, we do not consider it here.
   6
     He measures the risk using residual variance. As Malkiel and Xu (1997) have found that residual variance
and firm size are negatively correlated, such a measure could be subject to the size effect.


                                                       14
to replicate a fund portfolio. Therefore, discounts should be low. However, in the Chinese
markets, the arbitrage opportunities are hard to realize in practice when there is a discount
due to the lack of a short selling mechanism.

      At the same time, there is a second effect. When a fund portfolio is very close to a market
portfolio, investors will lose interest, because the fund portfolio is unlikely to offer much in
the way of unique investment opportunities and management skills. Therefore, there will
be selling pressure, which will increase discounts. This selling pressure is sustainable, since
short sales are not allowed in China and there is no option market.

      This argument also relies on an implicit assumption of being able to hold fully diversified
portfolios. Although individual investors might not have enough funds and there is no
index fund during our sample period, we can mimic the market performance by holding 20
randomly selected stocks, as shown by Xu (2003). Institutional investors such as pension
funds might be interested in funds with large R2 s, since such investors are not allowed
to directly participate in stock markets. We control for this effect by using the portfolio
composition variable. Given this effect, institutional investors, just like individual investors,
again will prefer funds with unique investment opportunities7 .

      A caveat is that high fund R2 s could also be due to the possible holdings of stocks
with large R2 s. Morck, Yeung, and Yu (2000) suggest that high R2 s for individual stocks
in the emerging markets might be related to the degree of transparency or the quality
of corporate governance. Investors are certainly interested in firms with good corporate
governance, which usually have low R2 s. This effect is difficult to separate from investment
opportunities without examining the floating ratio of the underlying stocks (see Wang and
Xu, 2003), for which we do not have information. In any case, since imperfect arbitrage is
unlikely to materialize, we believe that the second effect is more important. Therefore, the
R2 s for the underlying asset returns should be positively correlated with the discounts of the
funds.

      A more direct way to test this investment opportunity hypothesis is as proposed by Xu
(2000), who examines the composition of the fund portfolio. A Chinese closed-end fund
holds only domestic equities and government bonds. The more government bonds it holds,
  7
      If they prefer, pension funds can hold a portfolio of all the closed-end funds to achieve the market
performance.



                                                    15
the less investment expertise it will offer to investors. This factor has become especially
important since February 25, 2000, when insurance companies and pension companies were
first given the permission to invest in closed-end funds. Before this date, these institutions
were only allowed to hold government bonds. Since these institutional investors are still
not allowed to invest directly in the equity market, they are probably low on stock holdings
relative to the optimal portfolios between stocks and bonds. Therefore, a fund with smaller
stock holdings is less preferable to complete their optimal portfolios. As we note earlier, the
portfolio composition variable can also serve as a control variable for the R2 measure. Thus,
we have the following joint hypothesis:


Hypothesis 2 A closed-end fund discount is positively correlated with the R2 s of a fund’s
underlying asset returns with respect to a market model and the relative size of government
bond holdings


       “Investor sentiment” is a frequently tested factor in the literature. This factor may
have played a large role in an immature capital market due to the speculative nature of
that market and the short investment horizon of investors. Lee, Shleifer, and Thaler (1991)
suggest that investor sentiment will likely affect small stocks and closed-end funds at the
same time. If this is the case, there should be a negative relation between the returns from a
small stock portfolio and changes in the discounts of closed-end funds. During periods when
investors hold positive views or sentiments toward investment, especially when investors
favor closed-end funds, discounts should narrow8 .

       At the same time, anecdotal evidence suggests that Chinese investors are aggressive
and more enthusiastic about individual stocks when the markets are high. During stock
market slumps, individual investors try to seek professional help by investing in closed-end
funds. Thus, “investor overconfidence” might be more important in affecting the discounts
of Chinese closed-end funds, since closed-end funds are held solely by domestic investors and
there were no open-end mutual funds in China for our sample period. The overconfidence
hypothesis predicts an opposite relationship between a size-portfolio’s returns and changes
in the discounts of funds.9
   8
       Bodurtha, Kim and Lee (1995) tested the investor sentiment hypothesis using closed-end country funds
(CECFs). They found that changes in the average discount on CECFs are negatively related to returns on
the U.S. stock market, controlling for the returns on the foreign market and exchange rate movements.
   9
     It may be more accurate to use an overall stock market index instead. However, only relatively large

                                                     16
Hypothesis 3 The correlation between returns of a small size-portfolio and changes in the
closed-end fund’s discounts should be positive if the overconfidence effect dominates and neg-
ative if the sentiment risk is important.


There are differences between sentiment and overconfidence. Investor sentiment refers to the
phenomenon of noisy investors holding more (or less) risky assets than do their counterparts.
Investor overconfidence results in an investor holding more stocks when market-wide returns
are high, since investors incorrectly attribute the gains to their talents or to private infor-
mation. Overconfidence has been discussed extensively in recent years including by Gervais
and Odean (2001) and Kyle and Wang (1997). However, we associate overconfidence with
investors’ beliefs in the value of their private information and investment talents compared
to the private information and skills of professionals during different market conditions.

    Perhaps the most significant difference between U.S. and Chinese closed-end funds is in
the type of investors. Over 95% of the investors in closed-end fund in the U.S. are retail-
oriented individual investors. By contrast, more than 50% of Chinese closed-end funds are
now held by institutional investors, including insurance companies and pension management
companies. If an institutional investor is more sophisticated than a typical individual, neither
the sentiment risk nor the overconfidence effect should matter nowadays. This study provides
a unique venue to exam the issue using different sample periods.

    Another variable that may affect the discounts on closed-end funds is the liquidity of the
fund itself. A liquid asset can be traded rapidly and at a low bid/ask cost. Therefore, if
there is a liquidity premium, a more liquid fund will enjoy a higher premium than will an
illiquid fund. This liquidity effect suggests the following hypothesis:


Hypothesis 4 The trading volume should be negatively related to the closed-end fund dis-
counts.


Most current studies of U.S. markets emphasize the liquidity effect of the underlying assets
of a closed-end fund. This perspective is irrelevant for Chinese closed-end funds, since these
funds are only allowed to hold shares in publicly traded domestic companies. Trading volume
and well-established companies are allowed to go public in China. Therefore, we use the same proxy to test
both hypotheses since potential differences are small.



                                                    17
may also be highly correlated with fund size. Similar to large stocks, large funds are more
actively traded than small funds. Therefore, we also control for the size effect.

   For several reasons the size variable itself offers explanatory power for the cross-sectional
differences in fund discounts. First, large funds tend to hold more shares in large companies.
Since there is a size effect for Chinese stocks as shown by Wang and Xu (2003), smaller
stocks may offer better investment opportunities. Apart from the size effect, the majority
of shares in a publicly traded company are owned by the state, which affects corporate
governance. Size may also serve as a proxy for the efficient management of a company,
since state ownership is highly correlated with the size variable. It is also possible that the
performance of a large fund might be similar to a market portfolio. Thus, such a fund is less
likely to offer unique investment opportunities. In any case, we should observe:


Hypothesis 5 There is a positive relation between the discount of a closed-end fund and its
market capitalization (size).


   The first hypothesis (performance hypothesis) has been rejected in most empirical studies,
except for the study by Chay and Trzcinka (1999), who found that discounts are negatively
related to the future alpha of underlying assets. The second hypothesis (investment oppor-
tunity hypothesis) is new to this study. Most recent studies on closed-end funds have focused
on the investor sentiment risk. Instead, in hypothesis 3 we suggest that investor overconfi-
dence might also play a role. However, both effects depend on the types of investors, which
we test in this study. The liquidity hypothesis (hypothesis 4) has been studied extensively
by Datar (2001). Here, we reexamine the issue from the Chinese market perspective. The
last hypothesis (size effect) is new and may offer additional insight into the discount issue.
In addition, we study the informational content of trading volumes and prices in predicting
future discounts. We test these five hypotheses by using both a time series analysis and
cross-sectional regressions. Although any empirical findings may also be consistent with
other theories, the related evidences by themselves are important.




                                              18
4     Understanding Discounts—A Cross-sectional Perspec-
      tive

Due to the unique features of the Chinese capital market, many useful factors, including
unrealized capital gains, income distribution policies, and illiquid assets cannot be applied.
We face both challenges and opportunities to investigating new factors as formulated in the
above five hypotheses.

    Similar to most empirical studies on U.S. and U.K. closed-end funds, we also focus on the
post-IPO period by adding a fund to our sample 30 weeks after its IPO. Further, we require
that at least 12 funds be available in the cross-sectional regression at any given point in time.
Therefore, our sample actually starts on February 25, 2000, which coincides with the event
of allowing institutional investors to invest in closed-end funds. To test the five hypotheses
discussed in the previous section, we apply Fama and MacBeth’s (1973) regression technique
for each regression equation. The dependent variable is the current week’s discount. The
independent variables are the previous week’s fund turnover (ηt−1 ) computed by dividing the
week (t¡1)’s trading volume by the fund’s total outstanding shares, the previous week’s stock
to bond holding ratio (Compositiont−1 ), the percentage of the fund initiator’s ownership
(OSt−1 ), the log of a fund’s net asset value (ln(Sizet−1 )), and the intercept (αN AV,t−1 ) and
                                 2
the coefficient of determination (RN AV,t−1 ) from the market model fitted to the previous 23
weeks of the NAV returns. Table 5 reports these cross-sectional regression results.


                             Insert Table 5 Approximately Here


    Fund managers may possess unique information or management skills in choosing the
underlying securities of their portfolios. Since the composition of the portfolio cannot be
perfectly replicated, a low demand for under performed funds creates discounts if perfor-
mance persists. Past returns do not seem to explain the cross-sectional difference in the U.S.
closed-end fund discounts.

    Perhaps what is more relevant is the risk-adjusted measure (α) for the underlying asset
returns noted in Hypothesis 1. Equation (5) in Table 5 shows that the relation is negative
and statistically significant at the 1% level. Since we estimate those alphas at any given
week by using the NAV return data for the previous 23 weeks, excluding the current week’s

                                               19
data, the regression is predictive. Chinese investors do seem to rely on past performance to
pick a fund, as measured by alpha. However, such a relation does not necessarily imply that
funds with successful past performance will continue to outperform in the long run.

       It is also useful to separate the imperfect arbitrage argument of Pontiff (1996) from the
investment opportunity effect of Xu (2000). The imperfect arbitrage argument predicts a
positive relation between discounts and residual variance. The investment opportunity ar-
gument predicts an opposite sign or a positive relation by using a more powerful measure
 2
RN AV,t−1 , as stated in Hypothesis 2. Equation (6) in Table 5 suggests that discounts are pos-
                        2
itively related to the RN AV,t−1 variable, which inclines us toward the investment opportunity
argument. The relation is significant at the 1% level, with an average explanatory power
of 14% for a typical individual cross-sectional regression at a given time10 . Such a positive
relation continues to be strong after controlling for the size effect, as shown in equation (9).
                                                                         2
Moreover, the past-performance effect seems to disappear when we use the RN AV,t−1 variable
in equation (10). This evidence suggests that investment opportunity plays a more important
role than perceived performance in explaining the cross-sectional difference in discounts.

       In equation (2) of Table 5 we use the Compositiont−1 measure to test the investment
                                                                               2
opportunity effect. The relation is negative and significant at a 1% level. The RN AV,t−1 mea-
sure does not seem to be a substitute for the Compositiont−1 variable, as shown in equation
(11). Both variables are now statistically very significant, with an average explanatory power
of 18%.

       We tried to control for the potential size effect in equation (12). All variables continue to
be very significant and have the correct signs. In general, investors prefer funds with a greater
unique investment opportunity and a large stock position. This conclusion is especially true
for institutional investors with large bond positions. Therefore, investment opportunities do
seem to have an effect on cross-sectional differences in discounts.

       Although the liquidity issue for the underlying assets is much less important for Chinese
closed-end funds than for U.S. or U.K. funds, the liquidity in the trading of a fund itself
could affect the fund’s discounts, as discussed in Hypothesis 4. To capture this effect, we
use the relative weekly trading volume η, which is a ratio between weekly trading volume
  10
       We are aware of the problem of interpreting this average cross-sectional R2 as summary statistics. This
measure is only intended to provide an idea of the tightness of the relation.



                                                       20
and total share outstanding, as a proxy for liquidity in equation (1) of Table 5. Less liquid
funds seem to command large discounts. Although the relation is statistically significant at
the 1% level, the effect disappears once we add the size variable to equation (7). Despite the
low power in explaining the cross-sectional difference in discounts, the liquidity effect may
still be important for capturing the time variation of closed-end fund discounts.

       Since our data set also includes the initiators’ holding, we wish to see if it helps to explain
cross-sectional differences of closed-end funds’ discounts. We do so in regression equation (3)
of Table 5. The coefficient is not only positive, but also significant at the 1% level. Before
reaching a conclusion, we must control for the potential size effect, since holdings may be
proportional to a fund’s market capitalization. As shown in equation (8), it is not due to
the size effect. To understand this result, we study the ownership structure.

       After its IPO the initiators of a fund that includes brokerage companies, investment
management companies, and trust and investment companies continue to hold around 3% of
the fund. The largest holders are usually trust and investment companies that are owned by
the state. Agency theory suggests that the larger the proportion owned by the management
company, the smaller the discount on a fund, since managers will likely work hard. Since
the results suggest that this is not the case and the percentage of ownership is not very high
in absolute terms, we must further examine the institutional details.

       In China, the percentage of the initiators’ holdings and any later changes are not volun-
tarily determined by managers. Rather, they are decided by the China Securities Regulatory
Commission. Therefore, the percentage might signal to the public the nature of a fund’s rela-
tionship with the CSRC. Because the majority of funds are sold at discounts, most initiators
have the incentive to hold as little as possible of their own funds. The fact that the CSRC
would allow a particular fund’s initiators to invest only a small amount suggests a good
relationship with the CSRC. It is now accepted that a good relationship with the govern-
ment will result in preferential treatment (or expected benefits), which might enhance the
performance of a fund. If it is the public’s perception about the management of a fund mat-
ters, and if this perception is correlated with the managers’ ability to establish a connection
with government and acquire private information on policy changes, the percentage of the
holdings might approximate the managerial externality.11 In other words, the low ownership
  11
       We emphasize that it is not the actual relationship with the government that we are trying to capture.
Rather, the size of an initiator’s ownership is a better proxy for managerial externality.


                                                      21
signals potential large managerial externality, which leads to a smaller discount. Like the
investment opportunity hypothesis, this story is both unique to China and consistent with
our findings.

   Another interesting result we observe is the significance of the size effect, suggested
in Hypothesis 5, in explaining the cross-sectional differences of closed-end fund discounts.
Equation (4) in Table 5 suggests that the natural logarithm of a fund size alone can explain
over 40% of the differences in discounts. Large funds tend to have large discounts. This
result may be due to the fact that large funds are likely to hold more poorly managed firms.
It could also mean nothing more than that large funds are more difficult to manage and less
likely to deliver superior performance.

   In the last equation of Table 5 we jointly test Hypotheses 1, 2, 4, and 5 with the ownership
variable. Overall, the six-variable regression equation explains more than 62% of the cross-
sectional difference in discounts. All of the variables have the correct signs, as predicted,
except for the alpha variable. Although this variable is statistically significant at the 1%
level, the sign is wrong. Since there may be mutilcollinearity problems, as shown in equation
(10), we should not overlook this result. The liquidity variable continues to be insignifi-
cant in the multivariate regression. The significant variables in the multivariate regression
should provide convincing evidence. Therefore, we conclude that investment opportunity,
managerial externality, and portfolio size are useful factors in understanding the post-IPO
discounts of Chinese closed-end funds. Some of the factors discussed here might also explain
the discounts observed in the U.S. or U.K. data.

   We also investigate the determinants of the cross-correlations between current discounts
and future fund returns. In the absence of capital gains taxes in China, such cross-correlations
cannot be explained by the dividend taxation effect proposed by Pontiff (1995). When a
fund suffers a large discount, its current price will be low. All else equal, future returns
will be high for the same amount of income distribution. That is, the factors that affect
closed-end fund discounts will likely influence the cross-correlations. For this reason, we
run a similar cross-sectional regression of cross-correlations on the four significant factors
discussed above. With the exception of the ownership variable, the other variables explain
much of the differences in the cross-correlations.




                                              22
   In the following equation, we report only the three-variable cross-sectional regression.

    Corr(δ, RC ) =                                             2
                       1.221 + .026Comp. ¡ .044ln(Size) ¡ .123RN AV ,      R2 = 33.2%. (1)
                       (4.37) (3.10)        (¡3.38)         (¡3.93)

As described above, all of the variables should have signs the opposite of those in Table 5.
They are indeed the case. When a fund’s stock holdings increase, or the size decreases, or
     2
its RN AV for the underlying asset returns decreases, the discount is likely to be low. This
result means that future returns are likely to be low, which will induce a positive relation
between the current discount and future returns. Therefore, both the investment opportunity
argument and the size effect are important in explaining the cross-correlations.




                                             23
5      A Time Series Perspective on Discounts

We now investigate what explains fluctuations in premiums or discounts over time. The
investor sentiment argument has been extensively discussed in the recent literature. Re-
searchers have used variables related to small stock portfolio returns as proxies for sentiment
risk (see Lee, Shleifer, and Thaler, 1991; and Brauer, 1993). However, given the speculative
nature of the Chinese capital markets, it is possible that changes in investors’ overconfidence
in their investment talents and their private information on different market conditions are
more important in affecting discounts over time.

     Although we use the same proxy, the effect will be different. We construct a size portfolio
as a proxy for sentiment risk. We sort all of the A-share stocks traded on either the Shanghai
or Shenzhen stock exchanges into five groups according to their market capitalization at the
beginning of each year. We compute the size portfolio return Rsz by subtracting the largest
equally weighted portfolio returns from the smallest portfolio returns. Although the liquidity
variable does not seem to have a strong influence on the level of the discounts, it might affect
the dynamics of discounts. Therefore, we test the implications discussed in Hypotheses 3 and
4.

     In our sample, new funds are introduced over time. To accommodate this structure, we
first study the time series behavior of discounts by using aggregate data across funds with
value weights. To balance the extremely high premium at the beginning of the IPO period,
we ignore the first four weeks of data in aggregation. Unlike a cross-sectional study, we
require only at least five funds at any given time to compute the aggregate data. Therefore,
we can study two separate sample periods from January 8, 1998 to February 24, 2000, and
from February 25, 2000 to December 29, 2001. The natural break point corresponds to the
date on which institutions were allowed to hold closed-end funds. As mentioned before, the
aggregate discount variable is very persistent.

     We begin by performing unit root tests on the aggregate discount δt in each subsample
period. The results are reported in equation (1) of Table 6. The numbers in parentheses
are standard deviations. Clearly, we cannot reject the unit root hypothesis. Therefore, we
use the first difference in the aggregate discount ∆δt throughout this section for stationary
purposes.



                                              24
                             Insert Table 6 Approximately Here


   To test Hypothesis 3, we regress differences in discounts on contemporaneous returns
from a size portfolio proxy Rsz,t . The sentiment hypothesis predicts that investors will be
optimistic about closed-end funds when small stocks do well. Equation (2) of Table 6 shows
that changes in discounts covary positively with the size proxy in the first sample period. This
result contradicts the investor sentiment hypothesis. On the contrary, the result indicates
most investors seem to flee from professionally managed funds and pick stocks themselves
when the markets are doing well. Thus, it is the investor overconfidence that drives changes
in the discounts.

   Different from the first subsample period, during which all of the investors are retail-
oriented individual investors, a large number of investors in the second subsample period
are institutional investors. Both sentiment risk and overconfidence risks are less likely to
play a major role. This is exactly the case, as shown in equation (2) for the second sample
period. To further verify the difference in the two subsample periods, we can run a similar
regression over the whole sample period using a time dummy variable Dt , which equals one
for the second subsample period. The results are shown in the following equation,

                ∆δt = 0.245 + 0.317Rsz,t ¡ 0.479Rsz,t ¤ Dt ,        R2 = 5.7%.               (2)
                          (1.55) (2.86)       (¡2.63)

The differential effect, which is indicated in the last term in equation (2), is indeed significant
at a 1% level. Therefore, our results not only suggest that investor overconfidence is an
important factor driving the fluctuations in discounts over time, but also indicate that such
a risk is most likely to occur when the majority of investors are individual investors.

   Despite the fact that trading volume is less effective when we use it with other variables to
explain differences in cross-sectional discounts, we reexamine the last hypothesis from a time
series perspective. Because many empirical studies show that trading volume is persistent,
our estimates will be biased if we do not appropriately control for this persistence. Therefore,
we include a lagged trading volume, but do not report it in Table 6 to save space.

   Equation (3) in Table 6 suggests that the relative trading volume variable ηt is statistically
significant at the 1% level. Moreover, it explains over 9% and 12% of the variations in the
discount over the first and second subsample periods, respectively. The negative sign on the

                                              25
estimate is thus consistent with the liquidity premium hypothesis.

   We are also interested to see if there is any difference in the liquidity effect over the
two subsample periods. We continue to use the same dummy variable Dt in the following
regression equation:

     ∆δt = 0.713 ¡ 0.250ηt + 0.067ηt−1 ¡ (0.250ηt + 0.004ηt−1 ) ¤ Dt ,        R2 = 10.2%. (3)
               (3.19) (¡2.61)      (0.70)       (¡1.43)     (0.02)

Clearly, there are no significant changes in the magnitude of the liquidity effect over time.
This result suggests that both institutional and individual investors prefer funds with large
liquidity.

   Apparently, variables Rsz,t and ηt are highly correlated in the first subsample period.
When we use both variables in equation (4) of Table 6, due to a mutilcollinearity problem
none of the variables is statistically significant. Therefore, innovations in trading volume (liq-
uidity) rather than the volume levels are important factors in understanding time variations
in the discounts of Chinese closed-end funds.

   We study the predictability issue of closed-end fund returns, because discounts can serve
as important predictors due to the cross-correlations. Thompson (1978) suggests using some
kind of abnormal return measure, but we use the first difference in return instead. Due to the
persistent nature of discounts, we continue to use the first difference of discount. In equation
(5) of Table 6, we regress changes in aggregate fund returns on the lagged innovation in
discounts. The regression coefficients are significant at the 1% level in both sample periods,
and have the correct signs. The R2 is twice as high in the first subsample period (39%) as
in the second sample period (18%).

   We are also interested to see that changes in the closed-end fund returns are strongly
related to changes in trading volume in the same direction, as shown in equation (6) of
Table 6. The R2 s are as high as 46.7% and 22% for the first and the second subsample
periods, respectively. This evidence suggests that investors prefer funds with high liquidity,
which is consistent with our evidence on discounts. When we use both the lagged discount
variable and the volume variable to predict changes in fund returns, both variables continue
to be significant, with R2 s over 65% and 32% for the first and second samples, respectively.
Therefore, the cross-correlations between current discounts and future fund returns are not
only highly significant, but also very robust.

                                                26
   When we use the same specification for returns from the NAVs of underlying assets,
 N
Rt AV , we find that the results on the relation between discounts and future returns from
the NAVs (not reported in the table) are not robust to different sample periods. This result
suggests that the predictability of discounts is not due to the persistence of the underlying
asset returns.




                                             27
6     Concluding comments

Our research offers additional insights into the issue of discounts in closed-end funds by
exploring a less mature capital market, the Chinese closed-end fund market, which has
different investment environments. Because our data set is unique, we are also able to study
the issue of discounts for different types of investors.

    As a first study of Chinese closed-end funds, we document some stylized facts. In general,
Chinese closed-end funds are sold at a substantial premium of 10% in the IPO period, which
lasts for about 30 weeks. After the IPO stage, the majority of funds trade at 8% below
their net asset value. Current discounts are also highly correlated with future fund returns.
Qualitatively, these phenomena are similar to those found in the U.S. Quantitatively, they
are much stronger and more persistent.

    While market inefficiency may be a direct cause for the discounts in the Chinese closed-
end fund markets, many important factors, such as those related to capital gains taxes and
to the liquidity of the underlying assets, are irrelevant to understanding Chinese closed-end
funds. Instead, we use the risk adjusted performance of the underlying assets, trading volume
of a fund, the market capitalization of a fund, the R2 from a market model applied to the
underlying asset returns, portfolio holdings, and ownership as proxies for other factors such as
risk-adjusted performance, liquidity premium, investor sentiment/overconfidence, investment
opportunity, and managerial externality. Among these factors, investment opportunity, the
managerial externality, and the size effect seem to be most important in explaining the
cross-sectional difference in discounts.

    At the same time, changes in investor overconfidence and liquidity are crucial in de-
termining the time variations in discounts when the majority of investors are individuals.
When there is a large presence of institutional investors, such as insurance companies and
pension management companies, only the liquidity factor seems to capture changes in fund
discounts.




                                              28
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                                            29
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                                             30
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[25] Shiller, Robert J. (1981), ‘Do Stock Prices Move Too Much to Be Justified by Subsequent
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                                            31
     Table 1: Fund Information (including old funds listed after restructuring)


No.    Name        Date of    Listing    Date of         Size     Magt         Trustee
                   Setup      Place      Listing        (100 m)   Company
1      Kaiyuna     03/27/98   Shenzhen   04/07/98         20      Nanfang      Industrial & Commercial Bank
2      Jintai      03/27/98   Shanghai   04/07/98         20      Guotai       Industrial & Commercial Bank
3      Xinghua     04/28/98   Shanghai   05/08/98         20      Huaxia       Bank of Construction
4      Anxin       06/22/98   Shanghai   06/26/98         20      Hua’an       Industrial & Commercial Bank
5      Yuyang      07/25/98   Shanghai   07/30/98         20      Boshi        Agricultural Bank
6      Puhui       01/06/99   Shenzhen   01/27/99         20      Penhua       Agricultural Bank
7      Jingbo      09/22/99   Shenzhen   10/22/99         10      Daheng       Agricultural Bank
8      Jingyang    09/17/99   Shanghai   10/22/99         10      Dacheng      Agricultural Bank
9      Yuyuan      09/21/98   Shanghai   10/28/98         15      Boshi        Industrial & Commercial Bank
10     Tongsheng   11/01/99   Shenzhen   11/26/99         30      Changsheng   Bank of China
11     Jinxing     10/21/99   Shanghai   11/26/99         30      Guotai       Bank of Construction
12     Taihe       04/08/99   Shanghai   04/20/99         20      Jiashi       Bank of Construction
13     Tongyi      04/08/99   Shenzhen   04/21/99         20      Changsheng   Industrial & Commercial Bank
14     Jinghong    05/05/99   Shenzhen   05/18/99         20      Dacheng      Bank of China
15     Hansheng    05/10/99   Shanghai   05/18/99         20      Fuguo        Agricultural Bank
16     Anshun      06/15/99   Shanghai   06/22/99         30      Hua’an       Bank of Communications
17     Yulong      06/15/99   Shenzhen   06/24/99         30      Boshi        Agricultural Bank
18     Xinghe      07/14/99   Shanghai   07/30/99         30      Huaxia       Bank of Construction
19     Pufeng      07/14/99   Shenzhen   07/30/99         30      Penghua      Industrial & Commercial Bank
20     Tianyuan    08/27/99   Shenzhen   09/20/99         30      Nanfang      Industrial & Commercial Bank
21     Jingfu      12/30/99   Shenzhen   01/10/00         30      Dacheng      Agricultural Bank
22     Hanxing     12/30/99   Shanghai   01/10/00         30      Fuguo        Bank of Communications
23     Hanbo       07/12/00   Shanghai   10/17/00         5       Fuguo        Bank of Construction
24     Longyuan    07/24/00   Shenzhen   10/18/00         5       Nanfang      Industrial & Commercial Bank
25     Yuhua       11/10/99   Shenzhen   04/24/00         5       Boshi        Bank of Communications
26     Tongzhi     03/08/00   Shenzhen   05/15/00         5       Changsheng   Bank of China
27     Yuze        03/27/00   Shenzhen   05/17/00         5       Boshi        Industrial & Commercial Bank
28     Jinsheng    04/26/00   Shenzhen   06/30/00         5       Guotai       Bank of Construction
29     Jinyuan     03/28/00   Shanghai   07/11/00         5       Nanfang      Industrial & Commercial Bank
30     Xingke      04/08/00   Shenzhen   07/18/00         5       Huaxia       Bank of Communications
31     Handing     06/30/00   Shanghai   08/17/00         5       Fuguo        Industrial & Commercial Bank
32     Jinding     05/16/00   Shanghai   08/04/00         5       Guotai       Bank of Construction
33     Xing’an     07/20/00   Shenzhen   09/20/00         5       Huaxia       Bank of China
34     Hongfei     05/18/01   Shenzhen   11/28/01         5       Boying       Bank of Construction
35     Tianhua     07/21/00   Shenzhen   08/08/01         25      Yinhua       Agricultural Bank


                                                   32
                                      Table 1. (Continued)
No.   Name       Date of    Listing     Date of         Size     Magt         Trustee
                 Setup      Place       Listing        (100 m)   Company
36    Anjiu      07/04/00   Shenzhen    08/31/01         2       Huaan        Bank of Communications
37    Puhua      11/06/00   Shenzhen    08/28/01         5       Penghua      Industrial & Commercial Bank
38    Kehui      04/20/01   Shenzhen    06/20/01         8       Yifangda     Bank of Communications
39    Kexiang    04/20/01   Shenzhen    06/20/01         8       Yifangda     Industrial & Commercial Bank
40    Hongyang   12/10/01   Shenzhen    12/18/01         20      Boying       Agricultural Bank
41    Tongbao    05/25/01   Shenzhen    09/06/01         5       Rongtong     Bank of Construction
42    Anrui      07/18/00   Shanghai    08/30/01         5       Huaan        Industrial & Commercial Bank
43    Jinye      08/15/00   Shanghai    12/19/01        3.73     Dacheng      Agricultural Bank
44    Purun      08/08/00   Shanghai    09/04/01         5       Penghua      Industrial & Commercial Bank
45    Xingye     08/18/00   Shanghai    07/27/01         5       Huaxia       Agricultural Bank
46    Kexun      04/20/01   Shanghai    06/20/01         8       Yifangda     Bank of Communications
47    Tongqian   08/29/01   Shanghai    09/21/01         20      Rongtong     Bank of Construction
48    Tongde     10/20/00   Shanghai    08/01/01         5       Changsheng   Agricultural Bank




                                                  33
         Table 2: Summary Statistics for Chinese Closed-end Equity Funds
In this table, we report the number of funds “#,” the average index return RIdx (%), the average fund
return RC (%), the average return from a fund’s NAV RNAV (%), average trading volume “Vol.” (%), the
average fund ownership “OS” (%), and the total market capitalization, “Cap,” in millions of RMB.

               Quarter     #      RIdx       RC    RN AV      Vol.      OS         Cap
               98.II        2    0.699     4.586    0.347 6.930 3.000          7613.33
               98.III       4 -0.751 -1.730 -0.040 1.232 3.000 11221.42
               98.IV        5 -0.552 -0.809         0.150 0.951 3.000 12544.61
               99.I         5    0.137 -0.153       0.500 0.687 3.000 11752.00
               99.II        6    2.438     1.684    2.513 3.053 2.365 13592.30
               99.III      12 -0.139 -0.258         0.096 2.304 2.295 34311.42
               99.IV       15 -1.105 -0.562 -0.492 0.695 2.014 41215.38
               00.I        20    2.923     1.245    2.284 2.915 2.088 53821.81
               00.II       22    0.549 -0.267       0.520 0.979 1.777 56219.58
               00.III      26 -0.080       0.203    0.031 1.798 1.788 61766.92
               00.IV       31    0.608     0.539    0.564 1.955 1.682 65762.91
               01.I        33    0.011     0.378 -0.179 1.624 1.685 71117.72
               01.II       33    0.264     0.874    0.208 2.681 1.685 64395.41
               01.III      36 -1.760 -0.690 -0.890 1.625 1.616 64752.00
               01.IV       36 -0.671 -0.785 -0.379 1.004 1.616 58246.58
               Average 20        0.164     0.273    0.344 2.029 2.174 41888.89




                                                   34
               Table 3: Characteristics of Chinese Closed-end Equity Funds
This table summarizes the statistics for Chinese equity closed-end funds. The results are based on weekly
                                          ¯
data from February 1999 to December 2001. δ, ρδ , and σδ are the average, the persistent coefficient (AR(1)
coefficient), and the volatility of premiums over time, respectively. Rc , ρRc , and σRc denote the time series
average, the autocorrelation, and the volatility of the returns from a closed-end fund, respectively, while
RNAV , σRN AV , and σRN AV are the average, the autocorrelation, and the volatility of returns from net asset
                                     2                                                          c
values, respectively. αx , βx , and Rx are from fitting return x to the market model. Corr(δt , Rt+1 ) and
           N AV
Corr(δt , Rt+1 ) are the cross-correlations between current discounts and future fund returns and future
NAV returns, respectively. “10%,” “50%,” and “90%” are the tenth, fiftieth, and ninetieth percentiles across
funds. All of the numbers in the table are in percentage form.

                                     IPO Period                            post-IPO Period
                            10%       50%      90%        Mean      10%       50%       90%      Mean
               ¯
               δ          -7.269     9.751 47.19          13.23 -15.108 -7.989         13.44 -3.747
               σδ          4.452     7.783 15.36          10.30   3.7000     7.484     11.70     7.868
               ρδ          69.12     90.79 97.45          85.52   76.362     96.94     98.45     91.13
             Rc           -0.802 -0.234 0.413 -0.235 -0.3815                 0.199     0.403     0.041
            σRc            1.583     3.258 5.768          3.457   1.8406     2.486     3.776     2.744
            ρR c          -30.91 -7.529 22.49 -4.951 -7.8588                 3.647     14.79     3.809
            αRc           -0.857 -0.249 0.320 -0.211              0.0943     0.227     0.385     0.292
            β Rc           0.174     0.504 0.813          0.498   0.4187     0.527     0.672     0.550
             2
            RR c           2.052     37.94 69.35          36.77   26.193     43.96     53.64     41.01
            N AV
           R              -0.135     0.447 1.103          0.424 -0.3350 -0.053         0.380 -0.032
          σRN AV           1.164     2.460 3.438          2.489   1.5592     1.898     2.852     2.069
           ρRN AV         -15.97     0.671 28.66          3.908 -4.0914      13.31     22.23     9.536
           αN AV          -0.040     0.227 0.474          0.216 -0.0550      0.085     0.229     0.090
           βN AV           0.225     0.594 0.760          0.544   0.4559     0.610     0.700     0.595
            2
           RN AV           0.175     0.577 0.784          0.527   0.6115     0.682     0.804     0.672
                 c
     Corr(δt , Rt+1 )     -44.64 -14.66 7.275 -16.27 -42.891 -22.49 -16.15 -26.47
                N AV
     Corr(δt , Rt+1 )     -26.06     12.17 31.33          6.354 -26.406 -14.93 -0.262 -14.69




                                                     35
Table 4: The Returns on Closed-end Funds versus the Returns from the Funds’
NAVs
This table provides test statistics for the hypothesis of no difference between the various characteristics of the
returns on Chinese equity closed-end funds and returns from their NAVs. The results are based on weekly
data from February 1999 to December 2001. Rc and σRc denote the time series return and the volatility of
the returns from a closed-end fund, respectively, while RN AV and σRN AV are the return and the volatility
                                                                      2
of returns from net asset values, respectively. αx , βx , σI,x , and Rx are from fitting return x to the market
                                                                                        p
model. The t statistics for the cross-sectional average of variable x is computed as n mean(x) , where n is
                                                                                             Std(x)

the number of funds.

                                   IPO Period                     post-IPO Period
                    µ      µRc ¡ µRN AV     tµRc −µRN AV     µRc ¡ µRN AV      tµRc −µRN AV
                    α        -0.4280           -5.1771          0.2025            2.9025
                    β        -0.0463           -0.6823          -0.0453          -1.6341
                    σ         0.9681           3.1299           0.6751            3.2886
                    σI        0.9002           4.3991           0.6854            5.5934
                       2
                   R         -16.011           -2.9483          -26.260          -9.9567




                                                       36
Table 5: Explaining Discounts of Closed-end Funds from Cross-sectional Regres-
sions
This table shows the significance of determinants for cross-sectional differences in closed-end fund discounts.
The Fama and MacBeth (1973) regression technique is used for each cross-sectional regression, with the
discount as the dependent variable. The weekly samples from 2.25.2000 to 12.31.2001 are used in the
regression. The numbers in the parentheses denote the t ratios. η, “Composition,” “OS,” and ln(Size)
denote the last period’s turnover, the last period’s stock to bond ratio, ownership, and the last period’s
                                        2
log fund size, respectively. αN AV and RNAV are the intercept and coefficient of determination from the
market model fitted to the previous 23 weeks of the NAV returns. R2 is the average of the coefficient of
determinations of each cross-sectional regression.


                                                                                              2
 Equation    Constant      ηt−1     Compositiont−1     OSt−1      ln(Sizet−1 )   αN AV,t−1   RN AV,t−1    R2
     1         11.47      -1.337                                                                         10.14
              (10.02)    (-3.521)
     2         11.66                     -1.017                                                          4.67
              (10.56)                   (-3.441)
     3         8.024                                      1.617                                          7.18
              (5.167)                                  (6.014)
     4         -144.8                                                7.282                               41.47
              (-9.639)                                              (10.99)
     5         10.67                                                              -1.676                 3.90
              (9.081)                                                            (-2.361)
     6         -0.048                                                                          15.70     13.99
              (-0.032)                                                                        (13.23)
     7         -144.0     -0.106                                     7.234                               45.76
              (-9.131)   (-0.348)                                   (10.42)
     8         -140.4                                     0.428      7.048                               45.48
              (-8.244)                                 (3.046)      (9.391)
     9         -153.6                                                7.448                     7.824     51.01
              (-11.37)                                              (12.26)                   (6.208)
    10         -0.666                                                             -1.239       16.43     17.29
              (-0.429)                                                           (-1.506)     (12.38)
    11         1.391                     -1.359                                                16.34     17.92
              (0.965)                   (-4.438)                                              (13.58)
    12         -162.1                    -1.229                      7.898                     8.242     53.75
              (-13.74)                  (-4.634)                    (14.69)                   (6.705)
    13         -162.8     -0.184         -1.458           0.492      7.914         4.203       8.273     62.34
              (-10.59)   (-0.622)       (-5.535)       (2.970)      (11.28)       (4.612)     (5.780)



                                                     37
Table 6: Explaining Discounts of Closed-end Funds from a Time Series Perspec-
tive
This table shows the results that explain time variations of discounts using time series regressions. δt denotes
the value-weighted average of discounts at time t across individual funds. ηt is also the value-weighted average
of the relative weekly trading volume at time t. In the following regression, we use ηt−1 as a control variable,
                                                                                     c
but is not reported in the table to save space. Rsz,t is the size portfolio return. Rt is the aggregated closed
fund return. “*” means that a coefficient is significant at the 5% level and “**” represents significance at
the 1% level.


 Eq    Dep.                       Prior 2000.2.25                                          Post 2000.2.25
                                                                     2
 #     var.     Const.   δt−1     ∆δt−1     Rsz,t      ηt        R       Const.   δt−1     ∆δt−1    Rsz,t      ηt      R2
  1    ∆δt      -.623    -.042     -.306                         12.0     .132    -.004     -.233                      6.5
                (.343)   (.028)    (.123)                                (.257)   (.018)   (.110)
                    ∗                           ∗
  2    ∆δt      .628                        .317                 6.8     -.089                      -.087              0.8
                (.297)                      (.142)                       (.145)                     (.100)
  3    ∆δt      1.13∗∗                               -.292∗∗     9.2      .080                               -.358∗∗   12.2
                (.374)                               (.127)              (.230)                              (.108)
  4    ∆δt       1.02                       .156      -.210      10.2     .090                      -.070    -.350∗∗   12.7
                (.395)                      (.179)   (.158)              (.231)                     (.096)   (.109)
         c                             ∗∗                                                      ∗∗
  5    ∆Rt      -.778             1.17                           39.2     .073             .722                        17.6
                (.462)             (.178)                                (.219)            (.168)
         c                                                  ∗∗
  6    ∆Rt       .310                                1.10        46.7     .332                               .633∗∗    22.0
                (.534)                               (.181)              (.390)                              (.183)
         c
  7    ∆Rt      -.537             .854∗∗             .928∗∗      65.0     .148             .577∗∗            .565∗     32.4
                (.460)             (.147)            (.151)              (.328)            (.160)            (.165)




                                                       38
                                          Figure 1. Weekly Closed-End Fund Premia (1999.01-2001.12)


          20



          15



          10



           5



           0
Premium




           -5



          -10



          -15



          -20



          -25
            99.0199.0299.0499.0599.0699.0799.0899.0999.1099.1200.0100.0200.0300.0500.0600.0700.0800.0900.1100.1201.0101.0301.0401.0501.0601.0801.0901.1001.1101.12

                                                                                    Date
                                                    Figure 2. Close-End Fund Premia and Returns after IPO


             50




             40


                                                                                        Aggregate Premium

             30                                                                         Aggregate Return



             20
Percentage




             10




              0
                   1   5   10   15   20   25   30    35   40   45   50   55   60   65   70   75   80   85   90   95 100 105 110 115 120 125 130 135 140



             -10




             -20
                                                                                        Week
                                                      Figure 3. AutoCorrelations and Cross-Correlations for Returns and Premia


                                 50.00%                                                                                                                        100.00%
                                           98.78%    98.17%     97.28%    96.40%    95.69%   94.75%   93.69%   92.52%    91.34%
                                                                                                                                   89.75%   88.31%
                                                                                                                                                      86.34%
                                 40.00%                                                                                                                        80.00%




                                 30.00%                                                                                                                        60.00%
                                                                   AutoCorrelations of Returns
Scale for the First Two Series




                                                                                                                                                                         Scale for the Last Series
                                                                   Cross-Correlations
                                                                   AutoCorrelations of Premia
                                 20.00%                                                                                                                        40.00%


                                           10.61%
                                                                                    9.37%
                                 10.00%                                   7.66%
                                                                                                                                    6.99%                      20.00%
                                                                 5.14%
                                                                                                                                                      3.69%

                                                       -0.98%
                                  0.00%                                                                                                                        0.00%
                                             1         2          3         4         5        6        7        8         9        10       11        12
                                                                                                                         -5.91%              -3.20%
                                                                                               -8.54% -9.05%   -12.69%
                                                                                                                                    -5.73% -5.99%     -5.54%
                                 -10.00%                                            -7.48%                                -7.88%                               -20.00%
                                                                          -10.86%              -10.20%-9.77%
                                                                -12.20%                                         -8.39%
                                                     -14.59%
                                           -16.62%
                                 -20.00%                                                                                                                       -40.00%
                                                                                             Number of Lags

				
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