An Empirical Study on the Closed-End Funds Performance in China

An Empirical Study on the Closed-End Funds Performance in China
using Conditional Measures
Yang Kuan
College of Business Management, HuNan University, Changsha, P.R.China,410082
Abstract Most studies of fund performance use unconditional measures that are susceptible to bias caused
by common time variation in risks and risk premia. We evaluate the closed-end fund performance of China
using information variables that has produced new insight about empirical analysis of the fund performance
in China. The results indicate the trading volume from China stock exchange is better conditioning
information, the performance evaluation using information variables: trading volume, Jensen alpha as are
higher when estimated with the conditional model and the number of significant timing coefficients is
greatly reduced.
Keywords Mutual funds; Performance evaluation; Conditional CAPM
1. Introduction
Fund manager performance is typically measured relative to some ‘normal’ or ‘expected’ performance.
The predominant definition of ‘normal’ applied in performance studies is based on the traditional CAPM
which assumes that fund risk and expected returns are stable over time. If fund risks and risk premia change
over time, however, the traditional performance measures will confound time variation with abnormal
performance. Ferson and Schadt(1996)advocate using performance measures that are conditioned on public
information variables in order to avoid the bias induced by using historical average returns to estimate
expected performance[1]. Their results demonstrate that using conditioning information is both statistically
and economically significant. The average poor performance and perverse market timing ability that is
commonly indicated by unconditional performance measures is negated using the conditional model.
This paper examines the effect of trading volume as lagged information variables in the analysis of
investment performance using weekly data for China closed-end funds over the period 2000–2004. The
study provides corroborating results to those of Ferson and Schadtand, Ferson and Warther(1996) [2].
Estimating conditional Jensen alphas causes the distribution of alphas to shift to the right towards positive
values, making the sample of funds look better. The traditional Treynor and Mazuy(1966)measure of market
timing[3] produces evidence that an average fund takes on more market exposure when market returns are
low. We find here that the conditional market timing model reduces the number of significant negative
timing coefficients.
2. The conditional models
The standard performance measures that are applied extensively in evaluating managed fund
performance were proposed more than three decades ago. The traditional CAPM was widely used as the
benchmark model to measure risk-adjusted portfolio performance (e.g., see Jensen,1968)[4]. The
risk-adjusted performance of managed portfolios, α p , then was given by:
rp ,t +1 = α p + β p rm ,t +1 + ε p ,t +1 , t = 0,K , T − 1, p = 1,K , N
where rp ,t +1 is the excess return on portfolio p between t and t + 1 ,
β p is
(1)
the sensitivity of the excess
return on the fund to the the excess return on the market portfolio, rm ,t +1 is the excess return on the
618
benchmark portfolio between t and t + 1 ,
ε p ,t +1 is
the random error of fund p in weekly t + 1 . Manager
ability is measured by what has become known as the ‘Jensen alpha’. Superior or inferior managers would
have consistently positive or negative.
In specifically considering managers’ ability to predict market moves, Treynorand Mazuy(1966)add a
quadratic term in another model based on CAPM that has become a standard for measuring timing ability.
rp ,t +1 = α p + β p rm ,t +1 + γ p rm2,t +1 + u p ,t +1 , t = 0,K , T − 1, p = 1,K , N
where
(2)
α p is a measure of timing-adjusted selectivity, β p is the beta, γ p is the market timing coefficient.
Positive alpha and gamma values indicate that the Manager has superior selection and timing skills,
respectively.
Multi-index models employed for example by Elton et al.(1993)improve the accuracy performance
measurement by controlling for style choice[5]; however, both single- and multi-index models suffer from
another problem: time-variation in risks and expected returns that may be misinterpreted as superior
selectivity or timing skills. Performance measures that use unconditional expected returns calculate
abnormal performance as the difference between the average portfolio excess return and a beta-adjusted
average market index excess returns. If the market risk premium changes and the performance metric does
not control for this, time variation in the market risk premium will be reflected in the estimate of abnormal
performance and mistaken for manager under- or over-performance.
Ferson and Schadt(1996)argue that evidence of return predictability using predetermined variables
represents changing required returns. They propose a modification to the Jensen alpha and market timing
models to incorporate conditioning information that allows for the estimation of time-varying conditional
betas. When incorporating lagged information variables on dividend yields and interest rates, they find that
the conditional model improves measured performance. Unconditional alphas indicate average poor
performance, however the distribution of conditional alphas is consistent with neutral performance. They
also find that evidence of perverse timing is removed when using the conditional market-timing model.
Ferson and Schadt(1996)modify the traditional Jensen alpha model(Eq.(1))by adding a vector of lagged
public information variables to equation to estimate α p the conditional measure of performance:
u p ,t +1 = α p + δ1 p um ,t +1 + δ 2' p ( zt um ,t +1 ) + ε p ,t +1
(3)
where u p ,t +1 and um ,t +1 are the excess return on portfolio p and on the market index over the risk-free rate
δ1 p is the parameter estimating the conditional beta of portfolio p; zt is the vector of public
information variables at time t; δ 2 p is the vector of parameters that measure how the conditional beta varies
at time t+1;
with respect to the vector of market indicators.
The conditional measure of timing, γ tmc , is estimated modifying Eq.(2):
u pt +1 = a p + bp ρ umt +1 + C p ( zt umt +1 ) + γ tmc [um ,t +1 ]2 + v pt +1
(4)
The public information variables, zt , represent information available at time t for predicting returns at time
t+1. These interaction terms pick up movements of conditional betas as they relate to market indicators. The
coefficients, C p , estimate the response of conditional betas to lagged market indicators. By capturing
information available to managers at t, the vector
[ zt × umt +1 ] precludes strategies that can be replicated
using public information from being ascribed with superior selectivity or timing ability on the basis of this
information. The statistical reason for this is that the interaction terms measure the covariance between
619
conditional beta and the expected value of the market return using lagged instruments. The difference
between unconditional and conditional alpha is determined by the average values of the interaction terms.
Positive(negative)covariance will result in lower(higher) abnormal performance.
The purpose of this study is to examine the performance of closed-end funds in China using conditional
models. The tests performed here provide insight into the effect of using conditioning information in
measuring the performance of China closed-end funds. Anther purpose is to indicate the trading volume
from China stock exchange is better conditioning information variable.
3. Data and Sample
In China, only the first 20 listed funds can provide above five year data. We take the period of fund data
existed from January 1,2000 to December 30, 2004.The observational period covering the latest five years
and better reflect the reality and the regulation of the securities market and the fund industry in China. In
observational period, the securities market in China becomes much stronger and rational with the
increasingly rapid growth. As for the sample, we include all longer 20 closed-end equity funds.
Now listed funds are all closed-end funds. According to the net asset per share publicly published every
week, the rate of the log returns can be examined as
 NAVit 
log Rit = log 

 NAVit −1 
(5)
，
where log Rit is the log return on fund i during week t NAVit is the net asset of the i fund per share during
week t.
Confined to the governing regulation, the stock holding of the fund portfolio should be no more than 80
percent. And the bond and cash section should be no less than 20 percent. So in addition to directly use the
marked mentioned above, we construct a new benchmark is composed of 40 percent of returns on the
Shenzhen A-stock Component Index and the Shanghai A-stock Composite Index separately, and 20 percent
of the cash and bonds yield (it is called the mix market index here after). One-year deposit interest rate is
used as risk free rate. However, the central bank decreased the interest rate for the two times on 99.6 and
02.2 separately. Accordingly the weighted adjusted weekly risk free rate we employ in this is 0.00039
(interest tax-free). And we replace the cash and bonds yield with the adjusted weekly risk free rate. The
rationale for the equal weights of two market index in the new mix index is the highly correlation between
these two market, the correlation coefficient of the returns on Shenzhen and Shanghai stock market in our
sample is 0.9326. The data of the index consists of the closing price on each Friday during sample period.
As market indicators that previous studies identify as predictors of security risks and returns over time.
The variables employs (1) the lagged level of the one-month Treasury bill yield, (2) the lagged dividend
yield of the CRSP value-weighted New York Stock Exchange (NYSE)and American Stock
Exchange(AMEX) stock index, (3) a lagged measure of the slope of the term structure (4) a lagged quality
spread in the corporate bond market and (5) a dummy variable for the month of January. As we is in
developing country, these variables don’t fit to predict of security risks and returns over time. We use the
trading volume yield from China stock exchange at the end of the previous week files to predict the future
returns. This is based on ‘it takes volume to make prices move’.
，
，
620
rit +1 = α + βiTOTOt + ui ,t +1
(6)
Where TOt variable represents turnover. According to the Eq.(6), we can construct the regression, as
shown in table 1. Table 1 shows that the turnover variable and return on funds have significant relation, so
we believe the trading volume yield from China stock exchange can predict the future returns.
Table1 Regression estimate parameter
ad R
β
2
0.16
T -Statistic
0.018
6.1
P -value
**
0.00
*Significant at the 1% level.
**Significant at the 5% level.
4. Empirical Results and analysis
Data are used in an ordinary least-squares(OLS)regression to estimate the unconditional Jensen model
Eq.(1)and the conditional model Eq.(3). The conditional model results are reported in Table 2.
There is evidence that the conditioning variables are individually and jointly significant, supporting the
proposition that the trading volume variables are related to excess fund return. In the all-funds sample tests,
abnormal return of 18 funds are significant at the 1% level, while fund JINGHONG are not significant. The
results provide evidence of the marginal explanatory power of conditioning information in the performance
measure. The adjusted R-squares are slightly higher for the conditional model. These results are similar to
those of Ferson and Schadt(1996).
Table2
Fund
α
JINTAI
0.0018
TAIHE
0.0026
ANXIN
0.0021
HANSHENG
0.0018
YUYANG
0.0019
Conditional Jensen measure of performance of 20 Samples
t -Statistic
3.44
ANSHUN
0.0027
3.55
XINGHE
0.0027
KAIYUAN
0.0021
PUHUI
0.0019
TONGYI
0.0025
JINGHONG
0.001
YULONG
0.0021
**
2.16
0.0025
0.0023
5
**
0.0022
0.0028
0.48
**
2.47
XINGHUA
JINXIN
17
**
4.26
JINGYANG
YUYUAN
δ1
**
2.44
2.5
Rank
2.11
0.41
0.47
15
0.44
17
9.3
13
9.2
10
0.56
**
7
0.37
12
**
4
0.5
12
2.83
3.89
1.86
**
8
0.6
**
2
0.5
**
3
0.56
*
13
0.49
**
16
0.44
**
3.8
1.35
2.37
11
18
12
**
4.12
2.94
0.52
t -Statistic
**
6
0.44
20
0.49
12
0.51
621
7.9
15
8.6
14
5.1
10
14
13
13
**
**
δ2
-0.04
-0.06
**
-0.06
**
-0.06
**
-0.05
t -Statistic
-2.3
-3.4
-4
**
0.71
**
0.78
**
-3.2
-2.8
0.66
**
0.61
-0.05
**
-0.03
-1.7
-1.1
**
-0.08
-4.4
-0.03
**
-0.04
**
**
**
-0.07
*
-2
0.59
**
**
**
R2
**
0.67
0.46
0.7
**
0.84
*
0.62
-0.04
-1.7
-1.4
0.76
-0.04
-1.5
0.58
**
-0.05
**
-0.03
**
-0.04
-3.6
**
0.6
**
0.68
-3.2
-1.4
-1.7
*
0.67
0.66
PUFENG
0.002
JINGBO
0.0017
TIANYUAN
0.0029
TONGSHENG
0.0023
3.23
2.62
3.1
**
14
**
**
4.02
**
0.53
19
0.5
1
0.55
9
0.52
15
17
9.7
21
**
-0.04
-1.8
**
-0.04
**
-0.06
-3.3
**
-0.05
-3.7
-2.1
*
0.73
**
0.7
**
0.71
**
0.75
*Significant at the 1% level.
**Significant at the 5% level.
Table 3 provides evidence on whether the conditional alphas are significantly different from the
traditional alphas. The number of alphas produced by the traditional measure is all smaller than condition’s
alphas. On the other hand, the number of t-statistic produced by the traditional measure only 4 of 20 superior
to the conditional model t-statistic. This implies that when public information is incorporated into the
performance measure, the distribution of the alphas shifts to the right and consequently makes the sample of
funds look better. The results are consistent with Ferson and Schadt(1996)and Ferson and Warther(1996),
that the conditional alphas are higher than the traditional alphas.
Table3
Fund
Conditional
approach
Traditional
approach
Conditional
t -Statistic
Traditional
t -Statistic
Fund
Conditional
approach
Traditional
approach
Conditional
t -Statistic
Traditional
t -Statistic
JINTAI
Traditional and conditional abnormal performancesof 20 Sample
HAN
YU
JING
XING
AN
TAIHE ANXIN
SHENG YANG
YANG
HUA
SHUN
JINXIN
YU
YUAN
0.0018
0.0026
0.0021
0.0018
0.0019
0.0022
0.0025
0.0027
0.0023
0.0028
0.0015
0.0022
0.0017
0.0013
0.0015
0.0019
0.0023
0.0021
0.002
0.0025
2.44
4.26
2.47
2.5
2.16
2.11
3.44
3.55
4.12
2.83
2.468
3.85
2.454
1.848
2.086
2.347
2.791
3.112
3.756
3.174
XING
HE
KAI
YUAN
PUHUI
TONG
YI
JING
HONG
YU
LONG
PU
FENG
JING
BO
TIAN
YUAN
TONG
SHENG
0.0027
0.0021
0.0019
0.0025
0.001
0.0021
0.002
0.0017
0.0029
0.0023
0.0024
0.0018
0.0013
0.0021
0.0008
0.0018
0.0017
0.0014
0.0024
0.0019
3.89
1.86
2.94
3.8
1.35
2.37
3.23
2.62
3.1
4.02
3.812
2.14
1.839
3.375
1.177
2.409
2.563
2.063
3.406
3.066
Timing coefficients in the traditional and conditional Treynor–Mazuy models Eqs.(2)and (4)are
estimated using individual funds. Ten of the 20 individual funds’ timing coefficient estimates are negative,
don’t indicating perverse timing where the manager lowers exposure to the market when the market
performs well and increases exposure in poor markets. Of these 10 estimates, only 3 are significant at the
5% level. Under the conditional version, 5 of the 20 estimates of the conditional timing coefficients of the
individual funds are negative. Of these 5 estimates, none are significant at the 5% level. Consistent with
Ferson and Schadt(1996)and Ferson and Warther(1996), the evidence of perverse timing ability is removed
under the conditional model.
622
Table4 Unconditional Treynor-Mazuy measure of performance of 20 Samples
Fund
α
JINTAI
0.0016
2.23
TAIHE
0.0024
3.82
ANXIN
0.0017
t -Statistic
2.15
**
**
**
**
HANSHENG
0.0018
2.38
YUYANG
0.0014
1.72 *
JINGYANG
XINGHUA
ANSHUN
0.0013
0.0018
0.0024
1.42
2.01
3.18
JINXIN
0.0019
3.16
YUYUAN
0.0019
2.12
XINGHE
0.0023
KAIYUAN
0.0005
PUHUI
0.0022
TONGYI
JINGHONG
YULONG
0.0025
0.0008
0.0018
3.13
2.76
3.54
2.23
3.29
JINGBO
0.0019
2.53
TONGSHENG
0.0024
*Significant at the 1% level.
**Significant at the 5% level.
**
**
**
**
**
0.99
0.0024
0.0021
**
0.52
PUFENG
TIANYUAN
**
2.65
3.52
**
**
**
**
**
β
t -Statistic
0.4648
21.1
0.5054
25.4
0.383
15.8
0.4523
18.6
0.4208
16.5
0.533
0.3599
0.476
19
12.6
19.9
30.6
0.4809
17.4
23.8
0.4598
15.9
0.425
16.8
0.4269
0.4776
0.4939
19.6
19.5
19.1
0.518
22.7
0.4896
21
0.5213
0.51
**
**
**
**
**
0.5878
0.5388
**
**
**
**
**
**
**
**
**
**
**
**
**
20.6
23.8
**
**
γ
t -Statistic
R2
-0.034
-0.08
0.7
-0.304
-0.83
0.77
0.0203
0.045
0.57
-0.697
-1.56
0.64
0.1439
0.307
0.59
0.7698
1.49
0.66
0.4971
0.942
0.46
-0.405
-0.92
0.67
0.1402
0.397
0.83
0.7768
1.53
0.63
0.1984
0.476
0.75
**
1.6208
3.034
-1.088
-2.33
-0.482
-1.2
0.67
0.0185
0.041
0.67
-0.081
-0.17
0.66
**
**
0.59
0.59
-0.878
-2.09
0.73
-0.647
-1.5
0.7
0.3758
0.807
0.7
-0.661
-1.68
0.75
From table4 and 5, that provides evidence to examining whether the conditional timing coefficients are
significantly different from the traditional timing coefficients. The t-test indicates that for the entire sample,
conditional timing coefficients are significantly different from the traditional timing coefficients. It should
be noted that the number of significant negative timing coefficients are greatly reduced when the conditional
model is used. This is consistent with Ferson and Schadt(1996)and Ferson and Warther(1996).
623
Table5 Conditional Treynor-Mazuy measure of performance of 20 Samples
Fund
JINTAI
α
0.0015
TAIHE
0.0024
ANXIN
0.0016
HANSHENG
0.0018
t -Statistic
2.6
3.8
2.1
2.3
**
b
0.4797
**
0.5247
**
0.4077
**
0.4711
YUYANG
0.0013
1.7 *
0.4425
JINGYANG
0.0012
1.4
0.5582
XINGHUA
0.0018
**
0.3763
2
ANSHUN
0.0023
JINXIN
0.0019
3.1
YUYUAN
0.0018
2.1
3.2
18
0.0022
2.7
0.5572
21
24
0.4899
17
**
0.4418
17
**
0.4431
TONGYI
0.0024
JINGHONG
0.0007
3.5
0.9
YULONG
0.0018
2.2
PUFENG
0.0024
JINGBO
0.0019
3.5
13
30
PUHUI
2.6
19
0.5021
3.1
0.4
0.0024
17
**
0.0022
0.0021
19
0.6019
0.0004
TIANYUAN
17
0.5033
XINGHE
TONGSHENG
26
**
KAIYUAN
2.5
12
**
**
3.3
t -Statistic
20
0.4894
19
**
0.5095
19
**
0.5242
22
**
0.5002
21
**
0.5479
**
0.5243
21
24
**
C
-0.05
**
-0.065
**
-0.083
**
-0.063
t -Statistic
-2.5
-3.3
-3.5
-2.6
**
γ
t -Statistic R 2
0.486
0.63
0.71
**
0.372
0.91
0.79
**
0.8809
1.76 *
0.6
**
-0.042
-0.1
0.66
**
0.9002
1.7 *
**
-0.073
**
-0.085
-3.1
**
1.6503
2.83
**
0.68
**
-0.055
-1.9 *
1.0697
1.77 *
0.47
**
-0.091
**
0.5472
1.12
0.7
**
-0.047
-2.5
**
0.6322
1.57
0.84
**
-0.071
-2.6
**
1.5156
2.63
**
0.8399
1.78 *
0.76
**
2.672
**
0.62
**
-0.501
**
-2.5
-1.6
0.0819
0.18
0.68
0.428
0.83
0.67
**
0.4614
0.85
0.67
-0.659
-1.4
0.73
0.7
-2.9
-3.9
**
-0.062
**
-0.101
-3.6
**
-0.056
-2.2
**
-0.054
**
-0.039
**
-0.052
**
-0.021
-2
-0.9
**
-0.036
-1.5
**
-0.089
**
-0.048
-2.7
-3.6
-2.2
**
4.48
-0.9
-0.277
-0.6
**
1.3021
**
**
-0.163
2.5
-0.4
0.61
0.64
0.6
0.71
0.76
*Significant at the 1% level.
**Significant at the 5% level.
5. Conclusion
From the above empirical investigation, this paper researches the following conclusion.
This study examines the effect of trading volume information variables in the evaluation of investment
performance using China closed-end funds data, using of conditioning information in performance is
statistically significant. Furthermore, using conditioning information improves the performance of the funds,
causing the distribution of the alphas to shift to the right. We find that the number of significant negative
timing coefficients is greatly reduced after incorporating public information variables into the model.
Finally, the tests in this study employ conditional versions of only the single-index model. An
important application of the Ferson–Schadt framework is to alternative models of equilibrium such as that
used by Elton et al. (1993)which includes the excess returns on an equity index of non-S&P small stocks and
on a bond market index to represent the performance of assets typically held by fund managers but not
represented in the S&P index.
624
References
[1] Ferson, W.E., Schadt, R., Measuring fund strategy and performance in changing economic conditions.
Journal of Finance, 1996,51:425–462.
[2] Ferson, W.E., Warther, V.A., Evaluating fund performance in a dynamic market. Financial Analysts
Journal, 1996,52(6): 20–28.
[3] Treynor, J., Mazuy, K., Can mutual funds outguess the market? Harvard Business Review, 1966,
44:131–136.
[4] Jensen, M.C., The performance of mutual funds in the period 1945–1964. Journal of Finance,
1968,23:389–416.
[5] Elton, E.J., Gruber, M.J., Das, S., Hlvaka, M., Efficiency with costly information: a reinterpretation of
evidence from managed portfolios. Review of Financial Studies,1993, 6:1–22.
625