The Description of Sample Data

To make the MMMR threshold calculation precise and simultaneously include all the volatility of previous price range of Taiwan stocks, the data of this study were retrieved 企om the daily return data of the listed companies in the archive of TEJ after ex-rights and ex-dividend. The research period was 企om

January 4, 1980⁹ to December 31, 2010, totally 30 years. In the TWSE, there is not any limit of price range for new stocks within the first five days after being listed, so ifthe GARCH-jump model is applied to the estimation ofparameters, it is easy to cause estimation errors, so they are excluded. Meanwhile, according to the Standards Goveming Margin Purchase and Short Sale of Securities, the TWSE will announce that a common stock is allowed having margin purchase and short sale transactions after a common stock is listed for six months, there is not any abnormal phenomenon, such as drastic stock price volatility, excessive

concen仕ation of shareholding, or abnormal trading volume, the book value per share is more than the face value, and the number of units are more than sixty-mil1ion units. Therefore, newly listed companies can not obtain the qualification in the beginning. For the convenience of calculation, the samples and stocks which were listed for less than six months and whose capital was tess than NT$600 millions were eliminated. Finally, the research days were 8,515 days in total, including 2,536 days with the price range of 5%, during which the price range was reduced to 3% for 297 days, unnecessarily continuous, and 5,604 days

9 This was the earliest data in the archive ofTEJ.

28 Adjus的zg Minimal Maintenance Margin Requirement W有enPrice Limits Widening

with the price range of 7%, during which the price range was reduced to 3.5% for 78 days, unnecessarily continuous. To discover if futures maintenance margin requirements and securities 扎晶晶1R result in different guaranties for futures brokers or credit institutions, products linked to the spots market of Taiwan stocks, such as the Large TAIEX, the Small TAIEX, the Taiwan 50 futures, the electronic

h仙res， and the fmancial futures, were selected, and the day return data of the recent month were regarded as the calculation basis. The data were also retrieved

企omthe archive of TEJ, and the data of futures maintenance margin requirements were manually sorted and retrieved 企omthe official documents on the website of the Taiwan Futures Exchange about the adjustment of futures maintenance margin requirements. The data were compared by respectively two people in order to avoid mistakes.

4.2 The Estimation Result of the GARCH-jump Parameters

Before the variance-covariance approach was used to calculate VaR, a model with the feature of jumps was applied to the parameter estimation of the historical data of all the listed stocks. Table 1 displays the estimation result of the Taiwan stocks weighted index by means of the ARJI(1, 1) and GARJI(1, 1) models ^{10. In} terms of optimal model test, it was found in the Schwarz Criterion and the Likelihood ratio test that the GARJI model was better than the ARJI family model, and it was also shown in the LR test that the GARJI model was better than the ARJI family model. Furthermore, when the Q test statistic ofLjung-Box, indicating whether or not autocorrelation sti1l existed among the residuals of the estimated models, was behind 15 periods, none reached any statistical significance except the ARJI -constant model. p and

r

^{were both} si伊ificantly different from 0 in the ARJI family model and the GARJI mode^l. p is

“

persistence parameter,"

indicating that the arrival of jump events is considerably high. A greater p also represents that the effect of changes over time is significant.

r

represents the inf1uence of the residuals of jump intensity in early days. A greater value indicates

10 The number of maximum jumps within a unit time was set as ²⁰ times in this study. Please refer to Chan and Maheu (2002).

Chiao Da Management Review Vo/. 34 No.l, 2014 29

Table 1

The Estimation Values of the ARJI and GARJI Parameters

Parameter Constant ARJI _ARJI-Rt~1 ARJI -ht GARJI

μ 0.0985 0.1017 0.1069 0.2393 0.0072

Note : The number inside the parentheses are the standard e訂ors;LGL means Likelihood ratio test;

SC indicates Schwarz Criterion; Q2 is the modified Q statistic.

30 A哼usting Minimal Maintenance M呵in

Requirement When Price Limits ^Widening

th剖 jumps cluster together. The estimation results were similar to Maheu and

Mccurd)句 (2004) and Chen and Sun's (2010) studies. The unconditional jurnp intensity was 0.166 according to [E[Â._t IφJ= 扎 /(1 -p汀， which was very close to the post-jump expectation, namely (Â.₁ =0.164), indicating th剖 the jump expectations estimated by the GARJI model were not biased. The pre-jump variance accounted for

0.356 血 the

total return variance¹¹, namely 35% of the conditional variance could be regarded as the jurnp element. The result of American stocks was between 20% and 90% (Maheu and Mccurdy, 2004).

Meanwhile, it indicates that the variation factors representing the GARCH model could only catch stable daily volatility, but the GARJI model could catch the volatility caused by sudden news in the market, which is in favor of an accurate estimation of the M1-血，fRthreshold when drastic changes occur in the market and further results and critical for guaranteeing accurate results. Overall, the GARJI model is better than the ARJI family model and the GARCH model in terms of the volatility estimation of Taiwan stocks. Therefore, GARJI(I,I) was employed to estimate the conditional variance of each stock to further calculate the VaR in this study.

4.3 Estimating Thresholds by VaR

In this study, the GARJI( 1,1) model was first used to estimate the conditional variance parameters of individual stocks, and the VaR under the confidence of 99%, 95%, and 90% was respectively calculated and converted into the MMMR thresholds by means ofFormulas (12) and (13). The estimation result is listed in Table 2. As expected, the higher the confidence is, the higher the MMMR threshold is. That is, the threshold of the 99% confidence was higher than the threshold of the 95% confidence while the threshold of the 95% confidence

was 凶gherthan the threshold of the 90% confidence. In normal price range, (5%

and 7%), the thresholds of different levels of confidence within the 7% price range were all higher than the thresholds with the 5% price range due to greater

11 The formula: [Var(ε2.1 Iφ I_l)/Var(~ Iφ1-1) ] 。

Chiao Da Management Review Vol. 34 No.1, 2014 31

Table 2

The Descriptive Statistics of the Return Thresholds of the Listed Securities in theTWSE

Price Limits Confidence

Mean S.D. ^Min M缸

Level

99% 113.32% 5.29% 100.18% 143.76%

All Samples 95% 109.12% 3.51% 100.13% 128.36%

90% 106.98% 2.65% 100.10% 121.14%

99% 111.84% 2.21% 100.18% 125.33%

3.0% 95% 108.16% 1.49% 100.13% 116.99%

90% 106.27% 1.13% 100.10% 112.89%

99% 116.87% 4.98% 101.25% 136.95%

3.5% 95% 111.48% 3.28% 100.88% 124.25%

90% 108.77% 2.46% 100.68% 118.18%

99% 109.91% 4.78% 100.18% 128.08%

5.0% 95% 106.83% 3.23% 100.13% 118.74%

90% 105.25% 2.46% 100.10% 114.17%

99% 113.53% 5.25% 100.18% 143.76%

7.0% 95% 109.26% 3.48% 100.13% 128.36%

90% 107.09% 2.62% 100.10% 121.14%

conditional variance. On the other hand, when the price range declined, the

M}.必1R t尬的holds were all higher than the thresholds within the normal price range under different levels of confidence. For example, when the price range decreased from 7% to 3.5% (or from 5% to 3%)

,

the M1心1R thresholds within the decreased price range were all higher than the thresholds within the original price range. The reason should be related to the time-space environment in which the price range decreased. When special political or economic events occur, the competent authorities tend to take tempora可 measures to prevent investors 台om

overreacting, which may cause stock prices to decline rapidly. When the stock market stabilizes, the authorities will a再just the range back to the original one, so the volatility of stock prices will be greater within the decreased price range. This is consistent with the hypotheses ofHuang et al. (2001) and Cho et al. (2003) that investors tend to accelerate stock prices when they are close to price limits and resu1t in overreaction. Kim and Rhee (1997) and Chen (1998) addressed that when stock prices reaches the upper price limit (lower price limit), the trends of

32 A哼usting Minimal Maintenance Margin Requirement W有enPrice Limits Widening

the stock prices will continue on the next day likely since the information transfer hypothesis in which investors respond to the content of information causes great volatility in stock prices within a short time. When price range is widened in the

futu呵， impact caused by potential political and economic events are still inevitable. Hence

,

it is necessaη， to consider the maximum loss in abnormal times instead of depending on the 1品，也1R estimated by means of the thresholds in normal times. Fortunately, the data for abnormal times were incIuded in this study, which increased the reliability of this study.

4.4

The

MMMR

Thresholds of the

10

⁰

10

Price Range Analogized by Different Levels of Price Range

According the ~瓜，f.MRthresholds of the price range of respectively 5% and 7% in normal times in Table 2, the upper bound percentage approach was used to estimate the thresholds of the maintenance margin requirements of the 10% price range. Table 3 displays the MMMR thresholds of the 10% price range under the confidence level of respectively 99%, 95%, and 90% by means of the upper bound percentage approach. It was found that although the ~ threshold was 119.37 when the confidence was 99%

,

the threshold was still lower than the current rv心心1R of 120%, indicating the current :t\.晶晶1Rof 120% can still ensure the claims safety of credit institutions. Figure 1 shows the non-linear relationship between M:t\.必1R thresholds and price limits. It was found that the lower the confidence is, the lower the percentage of the ~ threshold is in the upper bound. For instance, when the price limit was 5%, the percentages of the thresholds of the confidence levels of 99%, 95%, and 90% in the upper bounds were respectively 99.91 %, 96.41 %, and 94.99%. More importantly, it was found that under the same confidence, the percentages of the thresholds in the upper bounds tended to decIine. For example, when the confidence was 99%, the threshold of the 5% price limit accounted for 99.91% of the upper bound, but when the price limit became 7%, the threshold accounted for 98.19% ofthe upper bound. SimilarIy, the thresholds descended in the confidence of respectively 95%

and 90%. Therefore, the descending trend of the percentages that the thresholds of the 5% and 7% price limits accounted for in the upper bounds were based, and a

Chiao Da Management Review Vol. 34 No.1^, 2014 33

Table 3

The Thresholds ofNew Price Range in Normal Times by the Upper Bound Percentage Approach

Tbe non-linear relationship between MMMR thresholds and price limits

100.00

34 Adjusting Minimal Maintenance Margin Requirement W有enPrice Limits Widening

linear approach was used to calculate the descending 仕endof the percentages. The hypothesis was linear in this approach, but each 1晶晶1R threshold was standardized into a percentage by the upper bound, so a non-linear relationship might exist between the finally obtained MM11R thresholds and price limits.

Similarly, based on the MMMR t尬的holds in normal times, the percentage approach was used to estimate the thresholds of the maintenance margin requirements in abnormal times. Table 4 shows the ~晶晶1Rthresholds of the 4%

price range in abnormal times under the confidence of respectively 99%, 95%, and 90% by means of the normal-time threshold percentage approach. It was found that the MMMR t趾eshold in abnormal times was 124.3 only when the confidence was 99%, which is higher than the current MMMR, namely 120, indicating that the current 120% ~晶晶1R is only slightly insufficient in abnormal times. Moreover, if price range dec1ined in abnormal times, under the price limits of 3%, 3.5%, and 4%, the upper bounds of the thresholds of the ~也1R were respectively 106.28, 107.39, and 108.51, which were all10wer than the current

120% 斟酌且在R. Consequently, when price range dec1ines in abnormal times, the

120% 弘也1MR is sti11 sufficient to ensure the c1aims of securities and financial compames.

4.5 Robustness Test

4.5.1 The MMMRs Simulated by Portfolios

The aforementioned calculation of the MMMR thresholds was based on individual stock returns, but the calcu1ation of the current maintenance margin requirement is based on each account, so the situation that an investor engages in the credit transactions of multiple stocks was simulated in this study in order to discover the thresholds of the account maintenance margin requirement. It was assumed that investors form nine portfolios, such as 1 margin purchase and 1 short sale, 1 margin purchase and 20 short sales, 1 margin purchase and 50 short sales, 20 margin purchases and 1 short sale, 20 margin purchases and 20 short sales, 20 margin purchases and 50 short sales, 50 margin purchases and 1 short sale, 50 margin purchases and 20 short sales, and 50 margin purchases and 50 short sales. The p凹pose of analyzing the nine portfolios is to simulate the

Chiao Da Management Review Vol. 34 No.l, 2014 35

volatility con仕onted by the portfolios of an account in different situations. For instance, when margin purchases and short sales are extremely unbalanced, the volatility con企onted by the portfolios of an account will be different, so the threshold of the account maintenance margin requirement wil1 also be different.

The previously ca1culated individual stock parameters were used to establish the collateral value and claims value of each portfolio. Similarly, the expected volatility of two continuous days under different levels of price range and the 99%

confidence were applied to the calculation of the portfolios in order to obtain the thresholds of account maintenance margin requirements and further analogize the

t尬的hold of the M:tv心1R of each portfolio under the 10% price range for understanding the M::M1咀支 ofeach possible portfolio.

According to di宜erent levels of price range, the nine portfolios were respectively sampled for 100 times, and the statistics were then compiled 12. The result is displayed in Table 5. The formulas for ca1culating the thresholds of margin purchases and short sales are different, such as Formulas (12) and (13).

Hence, it was impossible to combine the portfolios and then compile the statistics of the thresholds. In addition, investors may only have Ïnvestment in either margin purchase or short sale. Therefore, it is better to ca1culate them separately, so they are listed in two separate colurnns. Theoretical旬， the more constituent stocks there are in a portfolio, the better the non-systematic risk is dispersed, that

芯， the less constituent stocks there are, the higher the risk is. Meanwhile, the risk of possessing either margin purchases or short sales is higher than the risk of simultaneously possessing both margin purchases and short sales.

Panel A in Table 5 shows the statistic result of combining different levels of price range. It was found that in terms of margin purchase, when there was only one stock, the threshold tended to be high. For example, the Max threshold of Portfolio (1,50) was 116.61%, which was the highest, and the standard deviation (SD) ofthe t尬的holdwas higher. Furthermore, in terms of short sale, when there

12 According to the number of the stocks in the portfolios, they were randornly selected. The statistic volume of each random constituent stock was first calculated, and the statistic volume of 100 times was then calculated.

36

Table 4

Adjusting Minimal Maintenance Margin Requirement When Price Limits Widening

The Thresholds of New Price Range in Abnormal Times by the Normal-Time Threshold Percentage Approach

Price Limits

3% Price Limits 3.5% Price Limits Estimation ofthe 4% Price Limits Confidence

Level % ofthe

Threshold of % ofthe

Threshold of ^{%of 也e} Threshold of Abnormal-time

Abnormal-time Abnormal-time

Abnormal-time Abnormal-time

Abnormal-time

Threshold in the Threshold the Threshold in the

Normal-time MMMR

Normal-time ^MMìI在R Normal-time ^MM1位主

Threshold Threshold Threshold

Upper Bound

106.28 107.39 108.51

100% C.

Level

99%C. 101.76% 111.84 102.94% 116.87 104.13% 124.30

Level

95%C. 101.24% 108.16 102.03% 111.48 102.82% 116.31

Level

90%C. 100.97% 106.27 101.57% 108.77 102.17% 112.35

Level

Chiao Da Management Review Vol. 34 No.l^, 2014 37

Table 5

The Thresholds of Different PO此folios

Panel A: All Samples

Margin Purchase Short Sale

Portfolios

Mean Min Max S.D. Mean Min Max S.D.

(1,1) 11^1.81 % 109^.41% 114.92% 2.02% 110.81 % 110.36% 111.06% 0^.27%

(1,20) 112.21% 109.10% 112.55% ^1.09% 11^1.40% 11 0.95% 11^1.70% 0.25%

(1,50) 111.69% 107.44% 116.61% 2.86% 111.48% 111.19% 111.68% 0.17%

(20,1) 113^.42% 112.60% 114^.49% 0.60% 112^.41% 11^1.02% 114.00% 0.73%

(20,20) 112.57% 111.79% 113^.32% 0.61% 11^1.79% 11^1.43% 112.21% 0.29%

(20,50) 113.12% 112.43% 114.23% 0.53% 111.57% 111.30% 111.97% 0.23%

(50,1) 113.39% 112.64% 113.76% 0^.30% 111.57% 110.11% 114.00% 1.39%

(50,20) 113.23% 112.78% 113.70% 0^.35% 111.54% 11^1.07% 11^1.83% 0.24%

(50,50) 113.47% 113.13% 113.79% 0.22% 111.46% 111.25% 111.67% 0.13%

Note: The numbers inside the parentheses of the portfolios indicate the numbers of the margin purchase and short sa1e stocks.

Panel B: The Samples of the 5% Price Range

Margin Purchase Short Sale

Portfolios

Mean ^扎1in Max S.D. ^扎1ean Min 孔1ax S.D.

(1,1) 111.43% 109.41% 115.97% 1.91% 110.82% 106.00% 116.61% 3^.38%

(1,20) 109.38% 105.72% 115.86% 2.59% 108.83% 108.34% 109.31% 0.35%

(1,50) 109.37% 107.96% 113.23% ^1.71% 108.88% 108.68% 109.20% 0.16%

(20,1) 11 0.03% 108.11% 11^1.28% 0.83% 110.76% 102.87% 115.29% 5.09%

(20,20) 109.82% 109.26% 110.49% 0.44% 108.63% 108.09% 109^.21% 0^.37%

(20,50) 109.97% 109.51% 110.72% 0.39% 108.92% 108.54% 109.16% 0.18%

(50,1) 109.91% 109.66% 110.17% 0.18% 104.91 % 102.87% 109^.21% 2^.41%

(50,20) 109.87% 109.54% 110.22% 0.21% 108.88% 108.15% 109^.42% 0^.41%

(50,50) 109.99% 109.53% 110.84% 0.44% 108.82% 108.27% 109.16% 0^.32%

Note: The numbers inside the parentheses of the portfolios indicate the numbers of the margin purchase and short sale stocks.

38 Adjusti略 Minimal Maintenance Margin Requirement W有enPrice Limits Widening

Panel C: The Samples ofthe 7% Price Range

The Thresholds ofPortfolios within the 10% Price Range by the Upper Bound Percentage Approach Thresho1d in the _扎晶晶t1R Thresho1d in the _h心血tIR

UpperBound UpperBound

Chiao Da Management Review Vol. 34 No.1, 2014 39

was only one stock, the threshold also tended to be high. For instance, the Max thresholds ofPortfolios (20,1) and (50,1) were 114.0%, which was the highest, and the SDs were also higher than the SDs of the portfolios with 20 or 50 short-sale constituent stocks. It indicates that the threshold of the single-stock portfolio tends to be high, and the volatility tends to be great. Secondly, Panel B displays the statistic result of the 5% price range. The threshold of the single-stock portfolio was higher than the thresholds of other portfolios in terms of margin purchase and short sale. The margin-purchase and short-sale Max thresholds of Portfolio (1,1) were respectively 115.97% and 116.61, which were both the highest. Panel C shows the statistic result of the 7% price range.

Similarly, the threshold of the single-stock portfolio was higher than the thresholds of other portfolios in terms of margin purchase and short sale. The margin-purchase Max threshold of Portfolio (1,50) was 116.61%, which was the highest while the short-sale Max thresholds of Portfolios(20,1) and (50,1) were both 113.93%, which was the highest. According to the results, the current 120%

孔心1MR is still su伍cient for the risk of credit institutions. The conclusion is similar to the conclusions of Chiu et al. (2004), Chou and Chen (2004), and Hung et al. (2005) that the 120% MMMR is sufficient for the risk of credit institutions within the 7% price range.

Sirnilarly, it was assumed that price range was widened to 10%, and the upper bound percentage approach was used to estimate the thresholds of the maintenance margin requirements of different portfolios. Table 6 displays the thresholds of different portfolios under the 10% price range, which were estimated by the upper bound percentage approach. It was found that in terms of short sale, the threshold ofthe maintenance margin requirement ofPortfolio (50,1) was 122.41%, higher than the current 120% MMMR. None of the thresholds of other portfolios exceeded the current 120% MMMR. It indicates that when the price range is widened to 10%, the 120% maintenance margin requirement only results in slight risk for the safety of credit institutions.

40 Adjusting Minimal Maintenance Margin Requirement When Price Limits Wìdening

Table 7

The Descriptive Statistics ßased on the Threshold Groups of Maintenance Margin Requirements

Price Range Risk Group N 扎1ean S.D. Min Max

L 7,517 109.73% 2.05% 100.16% 111.76%

3.0% M 10,021 111.90% 0.47% 105.71% 113.31%

H 7,516 113.88% 1.74% 106.30% 124.00%

L 9,689 111.18% 2.29% 101.25% 114.95%

3.5% ^扎4 12,917 116.70% 1.68% 106.79% 121.60%

H 9,688 122.79% 2.48% 115.11% 137.04%

L 51,811 104.92% 2.03% 100.16% 107.61%

5.0% M 69,080 109.27% 1.33% 104.43% 112.53%

H 51,810 115.79% 2.97% 105.80% 129.41%

L 722,620 108.09% 1.54% 100.16% 111.93%

7.0% M 963,493 112.77% 1.65% 104.98% 119.78%

H 722,619 119.98% 3.77% 107.56% 133.43%

Note: Risk Group L indicates low risk (30%); M indicates medium risk (40%); H indicates high risk (30%)

4.5.2 The MMMRs of Stock Groups under Different Risks

In practice, investors may inc1ude highly risky constituent stocks in their portfolios and cause the con仕act-default risk to increase individually. Therefore, Anderson, Bollerslev, Diebold and Ebens 's (2001) realized volatility was

In practice, investors may inc1ude highly risky constituent stocks in their portfolios and cause the con仕act-default risk to increase individually. Therefore, Anderson, Bollerslev, Diebold and Ebens 's (2001) realized volatility was

在文檔中 Adjusting Minimal Maintenance Margin Requirement When Price Limits Widening (頁 27-43)