contents

Background ................................................................................................................................................................ 3

Definition ........................................................................................................................................................... 3

Literature ................................................................................................................................................................... 4

Interest rate Sensibility ...................................................................................................................................... 4

Definition of sensibility .............................................................................................................................. 4

Literature ................................................................................................................................................... 4

Calendar effects on money market fund market ............................................................................................... 5

Definition ................................................................................................................................................... 5

literature .................................................................................................................................................... 5

Empirical Analysis ...................................................................................................................................................... 6

Date selection .................................................................................................................................................... 6

Descriptive statistics .......................................................................................................................................... 7

Autocorrelation test ........................................................................................................................................... 9

Stationary test .................................................................................................................................................. 10

LM-ARCH effect test ......................................................................................................................................... 11

Modeling and regression ................................................................................................................................. 15

Results .............................................................................................................................................................. 16

Conclusion ............................................................................................................................................................... 18

Conclusion ....................................................................................................................................................... 18

Follow-up and short-comings .......................................................................................................................... 18

Reference ................................................................................................................................................................. 19

2

Abstract

This paper aims to examine "Yu E Bao" funds for short-term sensitivity to changes in interest

rates in controls of calendar effects. According to comprehensive research experience of domestic

and foreign scholars , both the stock market and bond fund that market have ,to some degrees,

interest rate sensitivity and calendar effects ,which means market interest rates affect the yields

for investment products, and excess returns exist at some special time points. By using Garch

(generalized autoregressive conditional heteroskedasticity model) based on fat tail phenomenon

funds market rate of return for the balance of the fund size and calendar effects treasure factors

and short-term interest rates to make a regression test.

Keywords: Garch regression model, calendar effects, interest rate sensitivity.

3

Background Recently Yu E Bao became a hot topic of public concern, with endless related news , reports,

expert analysis. Although only launched less than a year the Yu E Bao, the rapid momentum of its

expansion was far beyond the industry's expectations, as of January 15, 2014 , the balance scale

has more than 250 billion yuan , 15 days -scale growth of 35 %. If calculated at 1:6.10 exchange

rate, 250 billion yuan is equivalent of $ 40.984 billion . According to Bloomberg statistics, as of

January 14 the latest global fund size data , the scale of this kind of Fund may be ranked 14th in the

Global Currency Fund. The fund size has achieved such a degree in nearly a year , making us admit

the existence of some kind miracle behind it . But controversy will always come with the popularity.

The safety, the legality and the prospect of such new-born fund, Yu E Bao were casted doubts by

the media, analysts and governors. So we are here interested in studying the mystery of returns of

Yu E Bao, and some essential factors that might contribute to high-leveled returns of this fund.

Definition

Yu E Bao is a value-added service provided by the Alipay—Chinese Paypal, the user transfer

their money from Alipay account to the pool of Yu E Bao, which means they buy a kind of

MMF(money market fund) that named Yu E Bao. It’s also can be used for net-purchase directly,

which means it can also be regarded as an E-money.

Since Yu E Bao is an MMF, it has common characteristics of MMF.

1. Fixed net assets value of per units fund, usually 1 yuan.

2. Criteria of the quality of fund performance are yields.

3. Good liquidity, capital safety. The market of MMF is a low-risk, high- liquid market .

Meanwhile, investors may not be restricted by the maturity date to transfer investment

out.

4. Low risk. Maturity of money market instruments are usually very short , with an average

duration of the portfolio of money market funds generally 4 to 6 months, whose prices are

usually only affected by market interest rates.

5. Low investment costs. Money market funds usually do not charge redemption fees , and

their management costs are low.

Besides as a new-born product, Yu E Bao has some creations.

1. Facilitation of the purchase. Based on the Chinese largest third-party payment platform

Aliay, investors can get access to purchase by simple operation in Alipay account without

going through the general fund complex application procedures.

2. T+0 redemption. Investors can obtain redeemed money at the date of redemption, which

guarantee the liquidity of that fund at most.

4

3. Platform advantages. Based on third-party payment platform-Alipay, and a large P2P

platform-Taobao, Yu E Bao has a large number of potential investors, especially in the

technical support of immediate transfer of payment.

Literature

Interest rate Sensibility

Definition of sensibility

Interest rate sensitivity refers to the money market fund yields on money market funds

subject to the impact of changes in macroeconomic factors, interest rate. In theory, increases in

interest rates will cause a result that a rational Monetary Fund investor might re-evaluate the

benefits and risks and might put more money in the bank to obtain a stable risk-free gains, thereby

reducing investment in the Fund, then the returns of fund might be reduced correspondently. But

on the other hand, increases in interest rates could lead to gains in the short-term money market

fund investments such as bonds, resulting positive impact on its earnings.

Literature

Many scholars have studied relationships between macroeconomic factors and yields of

MMF, Zakri bello (2009) selected dates between April 1991 to March 2006 of the U.S. MMF

(money market funds) monthly yields and tested the impacts of the risk premium in interest rates

and other factors on funds’ future benefits, research shows that including funds incomes itself and

interest rate, five economic variables and funds’ future benefits have strong correlations. And

refers to the preference of investors’ behaviors , Koppenhaver and Sapp (2005) found Monetary

Fund investors will directly invest T-bill Fund and the T-bill when interest rates rises, which means

that there is possibility that increases in interest rate may have negative impact on fund yields.

Domain (1992) used the Granger causality analysis to examine the relationship between MMMF

(money market mutual funds) yields and 7-days T-bill yields. The results show that the latter

affects the former; Conversely, the result was not significant. But he did not consider the issues of

stationary time series, leading to inaccuracies in the results. Then Bahmani-Oskooee, M (1996)

5

reuse Domain’s data for Granger causality analysis with DF, ADF and CRDW test, the results show

that the impact of those two yields is bidirectional.

Calendar effects on money market fund market

Definition

Calendar effect is an effect that can be viewed in a phenomenon that investors can gain

excess returns when trading at some special time point, including weekdays effects and month end

effects. Monetary Fund calendar effects refer to the calendar effects in MMF market, which means

that money fund yields rise abnormally compared with ordinary trading day at the end of months,

quarters or years, and then fall at the beginning of the subsequent month, quarter, and year.

literature

Fred.C.Kelly(1930) first put forward the Calendar effects, he discovered the phenomenon of

ultra-low yields in New York Stock Exchange on Monday, and later Wachtel pointed out that

abnormal returns and trading volume exist in January in his "seasonal changes in stock price

determination". After the 1970s, Theobalc and Prince (1984), and Jaffe and Westfield (1985)

successively proved the weekdays effects in the UK, Japan and Canada and Australia.

Zweig (1997) selected 1550 Securities Fund data from 1985 to 1995 as samples to study the

year-end effect on the U.S. fund market, the results shows that almost all the funds on the last day

gain far more than the ordinary trading days do, some funds even get the most proportion of the

year’s proceeds.

MarkM.Carhart, RonKaniel, DavidK.Musto and AdamV.Reed (2002) and other scholars

selected data of U.S. equity funds from July 1992 to July 2000 as samples for studies of calendar

effects, the results indicate that the fund net value significantly increases on the quarter-end

especially the last trading day of the year, while on the last trading day of month it does not

significantly move up, at least not statistically significant.

Kotomin, V., Smith, SD, & Winters, DB (2014) selected share data on retail money market

funds and institutional money market funds from June 1983 to October 2006 to study calendar

effects using GARCH model, the paper also added tax-day effects analysis . The results show that

the prevalence of changes in the share on the week , quarter and year-end and tax-day, indicating

that money market funds have calendar effects.

In the study of the causes of the calendar effect, there are two motivations that are

universally accepted for fund managers to seek excess returns at special date. One is to overcome

6

market index, another is to improve fund performance in order to attract more investors to

purchase.

Zweig believes fund managers have motivations to pull fund yields in some special event to

attract more investors to purchase.

MarkM Carhart made empirical test on the funds that defeat market index on the quarter-end

and year-end, the results illustrate that motivation to overcome the market index has not been

well documented.

Ippolito (1992), Sirri (1998) pointed out that the growth of purchase is more sensitive to those

funds that have better performances, hence the more top-ranking fund, the greater its power to

pull the net value. Carhart, by comparing the abnormal returns of different income groups funds,

finds that the better the fund performance, the more obviously its net value is pulled, and he

believes the motivation to improve their performance in order to attract subscription is

established .

DelGuercio and Tkac (2000) conducted a comparative study on the relationship between

mutual funds and pension funds inflows and performance , they found that, for both two types of

fund investors, fund performance accounts for a large weight on consideration in determining their

investment choices, while with respect to the fact that the pension fund investors are more

concerned about whether the fund to overcome S & P500 index, mutual fund investors are not

statistically significantly sensitive to the results of this indicator.

Empirical Analysis We study Yu E Bao treasure fund yields sensitivity to market interest rate, as well as its

calendar effect in this part.

According to researches that scholars ever conducted on Securities Fund, we choose GARCH

model (generalized autoregressive conditional heteroskedasticity model) that contains interest rate

factors, the calendar effect dummy variables to regress, and test the significance of coefficients by

various factors to determine whether and how relationships exist. This part is followed by

descriptive statistics, autocorrelation test, stability test, LM-ARCH effect test, and regression

modeling

Date selection

We select Yu E Bao treasure fund’s 7-day annul yields data from May 30, 2013 to 15 April

2014, the data downloaded from the GTA fund database. As for market interest rates, because

there is no clear specification on this kind of issue as a benchmark in china, we consider the

availability and authority of data and chose SHIBOR (Shanghai interbank offered rate) as market

7

interest rates. Besides, we generate a series of dummy variables associated (dummy). Therefore, a

total of 211 sets of data。

Descriptive statistics

Table4.1 displays the fundamental indicators of Yu E Bao treasure fund’s 7-day annul yields

distribution.

Table 4.1

Yu E Bao treasure fund’s 7-day annul yields

percentile minimum

1% 2.772 2.093

5% 4.377 2.728 No. of samples 211

10% 4.509 2.772 mean 5.24572

25% 4.796 3.023 deviation 0.8144116

50% 5.123 variance 0.6632662

maximum skewness -.4238447

75% 5.835 6.738 kurtosis 4.188146

90% 6.398 6.753

95% 6.618 6.761

99% 6.753 6.763

We can draw conclusion from table 4.1 that：

1. Mean and percentile minimum are significantly greater than zero, indicating the yield is

significant positive in this period.

2. Skewness is not equal to zero, indicating that the yield distribution is not symmetrical.

3. Kurtosis is greater than 3, illustrating yield distribution is a significant fat tail distribution.

Table 4.2 displays the same indicators of SHIBOR, from which we can draw the similar

conclusion as table 4.1

Table 4.2

SHIBOR

percentile minimum

1% 2.358 2.211

5% 2.997 2.258 No. of samples 211

10% 3.469 2.358 mean 4.392805

25% 3.701 2.403 deviation 1.162388

8

variance 1.351145

50% 4.193 maximum skewness 1.898206

75% 4.763 8.075 kurtosis 9.297776

90% 5.535 8.543

95% 6.703 8.843

99% 8.543 11.004

Paragraph 4.1,4.2 are scatter distribution of Yu E Bao treasure fund’s 7-day annul yield and

SHIBOR respectively .

Paragraph 4.1

Paragraph 4.2

date

Yu E B

ao

treasure fu

nd

’s 7-d

ay

ann

ul yield

s

9

As can be seen, the means are stable in some intervals, but the trends are not smooth. They

are often significant fluctuations, and there are “volatility clusterings”. i.e. the changes of similar

amplitude fluctuations appear together.

Autocorrelation test

Autocorrelation means that there is correlation between the values observed in the time

series analysis, or panel data analysis, especially in time series analysis.

Supposing a regression equation𝑦𝑡 = 𝑥𝑡β + 휀𝑡

cov(휀𝑡1, 휀𝑡2) ≠ 0

The classic OLS (least squares estimation) method requires a sequence-independent.

Assuming the existence of autocorrelation sequence, using OLS regression does not affect the

unbiasedness, but it increases the variance of estimate coefficients thus affecting the validity of

the results, a direct result of a variety of test failure.

However, in time series analysis, particularly when economic and financial issues are the

studied objects, the autocorrelation is very common, because a number of factors such as GDP,

interest rates, exchange rates, employment, unemployment and others have interreactions, so that

the current market will produce a series of linkage effects on the next period.

date

SHIB

OR

10

Using AC, PAC test on both Yu E Bao treasure fund’s 7-day annul yields and SHIBOR, we can

conclude that both two have significant autocorrelation. Table 4.3 and table 4.4 are the results

respectively.

Table4.3

lag AC PAC Q P-value

1 0.9543 0.9543 194.9 0.00

2 0.9128 -0.4725 374.08 0.00

3 0.8626 -0.2614 534.86 0.00

4 0.8121 0.0636 678.05 0.00

5 0.7567 -0.0308 802.98 0.00

6 0.6948 -0.1935 908.82 0.00

7 0.632 -0.0173 996.82 0.00

8 0.5681 -0.1813 1068.3 0.00

9 0.52 0.0091 1128.4 0.00

10 0.4774 0.0519 1179.4 0.00

Table4.4

lag AC PAC Q P-value

1 0.8989 0.9017 172.92 0.00

2 0.7898 -0.0988 307.05 0.00

3 0.7075 0.0823 415.19 0.00

4 0.6055 -0.1677 494.79 0.00

5 0.51 0.0032 551.54 0.00

6 0.434 0.0018 592.83 0.00

7 0.3363 -0.1486 617.74 0.00

8 0.253 0.0147 631.91 0.00

9 0.1949 0.0188 640.37 0.00

10 0.1427 0.0044 644.92 0.00

Stationary test

1. Generally, stationary test is essential step of time series analysis. Supposing a time series 𝑥𝑡 , if

𝑥𝑡 met the following conditions, we say that this time series is stationary.

E(𝑥𝑡) = 𝑚, m is a constant。

Var(𝑥𝑡) = 𝜎2

11

∀ integer k，Cov(𝑥𝑡 , 𝑥𝑡+𝑘)=f(k)。

To make sure the time series is stationary is to guarantee the series has station variation

characteristics. If not, the regression might be a spurious regression, making the results worthless.

There are many methods to test stationary, such as ADF test(Augmented Dickey-Fuller),

Phillips&Perron test. We choose ADF test in condition that both two series are higher-order

autocorrelation.

ADF test

There are four assumptions about the autocorrelation model that series fits. Differences lie on

whether intercept 𝛼0 and trend 𝛿𝑡 exist in following model.

𝑦𝑡 = 𝛼0 + 𝛿𝑡 + ρ𝑦𝑡−1 + ∑ 𝜖𝑛∆𝑦𝑡−𝑛𝑝−1𝑛=1 +휀𝑡

Intercept mainly portrays whether the mean of time series is zero, and time trend portrays

whether time series has recursive trends over time (ascending or descending).

According to previous descriptive statistics for Yu E Bao treasure fund’s 7-day annul yields

and SHIBOR, we choose to join the intercept and the time trend.

No intercept and trend

P-value test 1% 5% 10%

Yu E Bao 0.00 -4.967 -3.473 -2.883 -2.573

SHIBOR 0.0171 -3.252 -4.003 -3.435 -3.135

With intercept and trend

P-value test 1% 5% 10%

Yu E Bao 0.0312 -3.584 -4.003 -3.435 -3.135

SHIBOR 0.0389 -3.505 -4.003 -3.435 -3.135

In the case of including intercept and time trend, both two series reject the null hypothesis at

95% confidence level, so that there is no unit root and they are stationary time series.

LM-ARCH effect test

Using the GARCH regression model, we have to test whether the data is in compliance with

the assumptions of ARCH model. Mandelbrot (1963) found that many financial variables

distribution has fat tails, reflecting in the descriptive statistical analysis before. And the variances

are not stable, accompanied by volatility clustering. These features are against the classic OLS that

requires iid. In order to solve this problem, Engle（1982）proposed ARCH model.

The residual 휀𝑡 of ARCH model fits:

휀𝑡 = 𝛾𝑡ℎ𝑡 𝛾𝑡iid~N(0,1)

12

ℎ𝑡 = 𝛼0 + ∑ 𝛼𝑖휀𝑡−𝑖2

𝑞

𝑖=1

This model reflects the volatility of the variance, which is to say that the current variance is

affected by early spot variance and similar amplitude fluctuations will appear together.

Garch model is extension of ARCH model, adding autoregressive conditional variance to

conditional variance term:

ℎ𝑡 = 𝛼0 + ∑ 𝛼𝑖휀𝑡−𝑖2𝑞

𝑖=1 +∑ 𝛽𝑗ℎ𝑡−𝑗2𝑝

𝑗=1

GARCH model is suitable for high-lag ARCH effects.

Therefore, in order to determine whether the data is applicable to GARCH model, we use

Lagrange multiplier method (LM-Arch test) to test the ARCH effect.

For the dummy setting，we examine Year-end effect, quarter-end effect, month-end effect,

and weekdays effect. So there are 16 dummies in 4 groups as follow ：

1. AY,1 Indicates that the observed value is the first observation of the year, 0 indicates not；

2. AY2,1 Indicates that the observed value is the second observation of the year, 0 indicates

not；

3. BY,1 Indicates that the observed value is the last observation of the year, 0 indicates not；

4. BY2,1 Indicates that the observed value is the second last observation of the year, 0

indicates not；

5. AQ,1 Indicates that the observed value is the first observation of the quarter, 0 indicates

not；

6. AQ2,1 Indicates that the observed value is the second observation of the quarter, 0

indicates not；

7. BQ,1 Indicates that the observed value is the last observation of the quarter, 0 indicates

not；

8. BQ2,1 Indicates that the observed value is the second last observation of the quarter, 0

indicates not；

9. AM,1 Indicates that the observed value is the first observation of the month, 0 indicates

not；

10. AM2,1 Indicates that the observed value is the second observation of the month, 0

indicates not；

11. BM,1 Indicates that the observed value is the last observation of the month, 0 indicates

not；

12. BM2,1 Indicates that the observed value is the second last observation of the month, 0

indicates not；

13

13. wd1，1 indicates Monday, 0 indicates not；

14. wd2，1 indicates Tuesday, 0 indicates not；

15. wd4，1 indicates Thursday, 0 indicates not；

16. wd5，1 indicates Friday, 0 indicates not；

the function to test year-end effect is:

Mmfr𝑡 = 𝐶 + 𝑖rate𝑡+𝛼1𝐴𝑌𝑡 + 𝛼2AY2𝑡 + 𝛽1𝐵𝑌𝑡 + 𝛽2𝐵𝑌2𝑡 + 휀𝑡

And the functions to test quarter-end, month-end and weekdays effects are respectively:

Mmfr𝑡 = 𝐶 + 𝑖rate𝑡+𝛼1𝐴𝑄𝑡 + 𝛼2AQ2𝑡 + 𝛽1𝐵𝑄𝑡 + 𝛽2𝐵𝑄2𝑡 + 휀𝑡

Mmfr𝑡 = 𝐶 + 𝑖rate𝑡+𝛼1𝐴𝑀𝑡 + 𝛼2AM2𝑡 + 𝛽1𝐵𝑀𝑡 + 𝛽2𝐵𝑀2𝑡 + 휀𝑡

Mmfr𝑡 = 𝐶 + 𝑖rate𝑡+𝛼1𝑤𝑑1𝑡 + 𝛼2wd2𝑡 + 𝛼4𝑤𝑑4𝑡 + 𝛼5𝑤𝑑5𝑡 + 휀𝑡

If the residual 휀𝑡~ARCH(q)，

휀𝑡 = 𝛾𝑡ℎ𝑡 𝛾𝑡iid~N(0,1) (1)

ℎ𝑡 = 𝛼0 + ∑ 𝛼𝑖휀𝑡−𝑖2

𝑞

𝑖=1

Then LM=n𝑅2~𝒳2(q) n is the number of the sample，𝑅2 is the goodness fit of OLS

estimate of equation(1).

If LM> 𝒳2(q), the data have ARCH effect, otherwise, doesn’t。the results of four tests are

displayed on table4.5~4.8.

Table 4.5，LM-ARCH effect test on year-end effect assumption

lag 𝒳2 f P-value

1 191.730 1 0.0000

2 192.829 2 0.0000

3 190.383 3 0.0000

4 186.940 4 0.0000

5 184.308 5 0.0000

6 179.998 6 0.0000

7 175.597 7 0.0000

8 174.324 8 0.0000

9 178.953 9 0.0000

10 178.245 10 0.0000

Table4.6, LM-ARCH effect test on quarter-end effect assumption

14

lag 𝒳2 f P-value

1 195.713 1 0.0000

2 196.669 2 0.0000

3 195.466 3 0.0000

4 192.914 4 0.0000

5 190.227 5 0.0000

6 188.041 6 0.0000

7 184.381 7 0.0000

8 183.985 8 0.0000

9 188.982 9 0.0000

10 188.619 10 0.0000

Table4.7, LM-ARCH effect test on month-end effect assumption

lag 𝒳2 f P-value

1 194.065 1 0.0000

2 196.133 2 0.0000

3 194.472 3 0.0000

4 191.808 4 0.0000

5 189.157 5 0.0000

6 186.643 6 0.0000

7 183.415 7 0.0000

8 183.747 8 0.0000

9 187.622 9 0.0000

10 186.799 10 0.0000

Table4.7, LM-ARCH effect test on weekdays effect assumption

lag 𝒳2 f P-value

1 196.647 1 0.0000

2 196.960 2 0.0000

3 195.928 3 0.0000

4 193.155 4 0.0000

5 191.080 5 0.0000

6 193.302 6 0.0000

7 190.901 7 0.0000

8 189.570 8 0.0000

9 193.249 9 0.0000

15

10 192.321 10 0.0000

So the data above have high-lag ARCH effects, then the GARCH model is applicable

Modeling and regression

From the previous test, the data have high-lag autocorrelation ARCH effect, have no unit root,

and are stationary sequences, so to be adopted GARCH (1,1) model for regression：

1. {Mmfr𝑡 = 𝐶 + 𝑖rate𝑡 + 𝛼1𝐴𝑌𝑡 + 𝛼2AY2𝑡 + 𝛽1𝐵𝑌𝑡 + 𝛽2𝐵𝑌2𝑡 + 휀𝑡

ℎ𝑡 = 𝛼0 + 𝛼1휀𝑡−12 + 𝛽1ℎ𝑡−1

2

2. {Mmfr𝑡 = 𝐶 + 𝑖rate𝑡 + 𝛼1𝐴𝑄𝑡 + 𝛼2AQ2𝑡 + 𝛽1𝐵𝑄𝑡 + 𝛽2𝐵𝑄2𝑡 + 휀𝑡

ℎ𝑡 = 𝛼0 + 𝛼1휀𝑡−12 + 𝛽1ℎ𝑡−1

2

3. {Mmfr𝑡 = 𝐶 + 𝑖rate𝑡 + 𝛼1𝐴𝑀𝑡 + 𝛼2AM2𝑡 + 𝛽1𝐵𝑀𝑡 + 𝛽2𝐵𝑀2𝑡 + 휀𝑡

ℎ𝑡 = 𝛼0 + 𝛼1휀𝑡−12 + 𝛽1ℎ𝑡−1

2

4. {Mmfr𝑡 = 𝐶 + 𝑖rate𝑡 + 𝛼1𝑤𝑑1𝑡 + 𝛼2wd2𝑡 + 𝛼4𝑤𝑑4𝑡 + 𝛼5𝑤𝑑5𝑡 + 휀𝑡

ℎ𝑡 = 𝛼0 + 𝛼1휀𝑡−12 + 𝛽1ℎ𝑡−1

2

As mentioned before, the residual of ARCH model 휀𝑡 = 𝛾𝑡ℎ𝑡 𝛾𝑡iid~N(0,1),however, in

practice, 𝛾𝑡 can follow t-distribution and GED-distribution, difference among them is different

assumption about residual’s distribution. Compared to others, GED-distribution portrays financial

data’s fat tail characteristics better, so we choose it in empirical test, its probability density

function is ：

휀𝑡 = 𝛾𝑡ℎ𝑡 𝛾𝑡iid~GED(μ, 𝜎𝑝, 𝑝) , 𝑎𝑛𝑑 𝑎𝑐𝑐𝑜𝑟𝑑𝑖𝑛𝑔 𝑡𝑜 𝐺𝐴𝑅𝐶𝐻 𝑚𝑜𝑑𝑒𝑙, we have

E(𝛾𝑡)=0,var(𝛾𝑡)=1

Then,

Since GARCH model mainly uses logarithmic regression maximum likelihood estimation

method, so the log-likelihood function of the regression equation 1 can be written as：

16

lnL(θ)=-𝑡

2ln {

Γ(1

𝑝)

3

Γ(3

𝑝)Γ(

𝑝

2)

2} −1

2∑ 𝑙𝑛ℎ𝑡

2𝑡1 −

∑ ln *Γ(

3

𝑝)(Mmfr𝑡−𝐶+𝑖rate𝑡+𝛼1𝐴𝑌𝑡+𝛼2AY2𝑡+𝛽1𝐵𝑌𝑡+𝛽2𝐵𝑌2𝑡)2

ℎ𝑡2Γ(

1

𝑝)

+𝑡1

Then to access Max( lnL (θ)),we just use iterative methods.

Results

We select stata 12 as tool to regress the GARCH model, and the results are displayed on table

4.9-4.12

Table 4.9

Assumption 1

Mmfr coefficient Z P-value

Irate .0137084 2.56 0.011

BY 1.356574 4.03 0.000

BY2 1.133089 4.81 0.000

AY 1.203214 3.46 0.001

AY2 .7685332 2.18 0.029

C 4.877122 133.85 0.000

ARCH

𝛼1 1.034246 12.25 0.000

𝛽1 -.1421142 -12.10 0.000

𝛼0 .0035514 4.36 0.000

Table4.10

Assumption 2

Mmfr coefficient Z P-value

Irate .0896549 6.39 0.135

BQ .2572503 4.03 0.000

BQ2 .3584564 4.81 0.000

AQ .2850781 3.46 0.001

AQ2 .112893 2.18 0.029

C 5.178628 133.85 0.000

ARCH

𝛼1 1.111194 4.52 0.000

𝛽1 -.0755865 -3.63 0.000

17

𝛼0 .0042119 1.38 0.166

Table4.11

Assumption 3

Mmfr coefficient Z P-value

Irate .0194546 2.12 0.034

BM -.0872436 -0.92 0.355

BM2 -.0891698 -0.81 0.417

AM -.0367953 3.46 0.001

AM2 -.0206959 -0.22 0.829

C 5.123953 119.12 0.000

ARCH

𝛼1 .8651356 5.20 0.000

𝛽1 .1596791 2.80 0.005

𝛼0 .0000866 0.82 0.412

Table4.12

Assumption 4

Mmfr coefficient Z P-value

Irate .091812 6.02 0.000

Wd1 -.0675509 -3.11 0.002

Wd2 -.0288761 -1.11 0.265

Wd4 -.0380412 -0.86 0.390

Wd5 -.0319836 -0.22 0.829

C 4.640561 67.28 0.000

ARCH

𝛼1 .9952073 4.07 0.000

𝛽1 -.0485648 -0.40 0.691

𝛼0 .0040152 2.38 0.017

In conclusion

1. SHIBOR rate coefficients were significant factors is not 0 (p value = 0.00) in these four

regressions , indicating that Yu E Bao is sensitive to interest rate changes, and the coefficient is

positive representing a positive correlation.

2. As for year-end effect, regression shows that at the end of the last two days there is a

significant increase in yield, and a fall on the first day of next year. Therefore, we believe there

is a significant annual effect。

18

3. As for quarter-end effect，we can see that on the last two days and first day of the quarter,

the yields are above the mean，and there is a significant ascending trend from the last dayof

the quarter to the first day of next quarter, so that we believe that quarter-effect exists.

4. As for month-end effect, the regression shows that all four days have negative trends on

yields, which are against the assumption, what’s more, the results are not statistically

significant, so that we cannot draw a conclusion whether month-end effect exists.

5. As for weekdays effect，we can find out that there is (10% significant) Monday effect，Monday

witnesses a descend on yields.

Conclusion

Conclusion

In this paper, we select Yu E Bao treasure fund’s 7-day annul yields and SHIBOR as samples to

study the interest rate sensitivity and calendar effects on yields , the results indicate that Yu E Bao

treasure fund’s 7-day annul yields shows a significant positive interest rate sensitivity, a significant

year-end effect (i.e. at the end of the last one to two trading days, yields rise sharply, while at the

beginning of the next year yields fall ), a significant quarter-end effect and a significant Monday

effect (i.e. a significant decline in yields on Monday), these results can maintain a certain degree of

consistency with scholars’ relevant findings of closed-end securities investment funds about the

stock market, but no significant evidences of month-end effect and Friday effect are proved.

Follow-up and short-comings

Based on the study, a follow-up can be further studied.

1. longer performance of Yu E Bao.

2. Interest-sensitive and calendar effects research on fund purchase rate and redemption

rates.

3. Relevant study on Chinese MMF market as a whole.

We refer to lots of researches，and choose GARCH model added calendar effect dummies and

SHIBOR variance to conduct an empirical analysis. However, due to limited capability, there are

some deficiencies:

1. Since Yu E Bao is operating for a short time, with the small sample size, there may be a

large bias in the time-series study.

2. Since no a recognized benchmark interest rate, we chose SHIBOR as market interest rates.

Because SHIBOR is relatively high , the regression results may therefore omit some issues.

3. lacking access to information, we are unable to explain the empirical results in detail.

19

Reference [1] Bahmani-Oskooee, M. (1996). Money market mutual fund maturity and interest rates: A note. International

review of economics & finance, 5(1), 101-108.

[2]Bello, Z. Y. (2009). On The Predictability Of Mutual Fund Returns. Journal of Business & Economic

Studies, 15(1).

[3]Carhart, M. M., Kaniel, R., Musto, D. K., & Reed, A. V. (2002). Leaning for the tape: Evidence of gaming

behavior in equity mutual funds. The Journal of Finance, 57(2), 661-693.

[4]Domian, D. L. (1992). Money market mutual fund maturity and interest rates.Journal of Money, Credit and

Banking, 519-527.

[5]Guercio, D. D., & Tkac, P. A. (2002). The determinants of the flow of funds of managed portfolios: Mutual

funds vs. pension funds. Journal of Financial and Quantitative Analysis, 37(04), 523-557.

[6]Ippolito, R. A. (1992). Consumer reaction to measures of poor quality: Evidence from the mutual fund

industry. JL & Econ., 35, 45.

[7]Koppenhaver G, Sapp T (2005) Money markets or funds? Valuing intermediary services. J Financ ServRes

27:51–76

[8]Kotomin, V., Smith, S. D., & Winters, D. B. (2014). Interest-rate and calendar-time effects in money market

fund and bank deposit cash flows.Journal of Economics and Finance, 1-12.

[9]Sirri, E. R., & Tufano, P. (1998). Costly search and mutual fund flows. The journal of finance, 53(5),

1589-1622.

[10]Zweig, J. (1997). Watch out for the year-end fund flimflam. Money Magazine,11, 130-133.