# Why Are Warrant Markets Sustained in Taiwan but Not in China?

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Data and Methodology

#### 3.1. Data

#### 3.2. Methodology

#### 3.2.1. Mean-Variance (MV) Criteria

_{j}as the set of utility functions such that:

^{(i)}is the ith derivative of the utility function U.

_{y}and µ

_{z}and standard deviations σ

_{y}and σ

_{z}, respectively, the MV rule (Markowitz [50]; Bai, et al. [51]; Leung, et al. [52]) is such that Y is said to dominate Z if µ

_{y}≥ µ

_{z}and σ

_{y}≤ σ

_{z}, and if the inequality holds in at least one of the two conditions. Wong [53] and Guo and Wong [54] show that if Y dominates Z by the MV rule, denoted by $Y{\succ}_{MV}Z$, then risk averters with u

^{(}

^{1)}> 0 and u

^{(}

^{2)}< 0 will attain higher expected utility by holding Y than Z under certain conditions. The theory can be extended to non-differentiable utilities (see Wong and Ma, [55]).

#### 3.2.2. Stochastic Dominance (SD) Approach

_{1}, x

_{2}, … x

_{k}, the jth-order SD test statistic, ${T}_{j}\left(x\right)$ (j = 1, 2, and 3), is defined as:

**Hypothesis**

**1 (H1).**

**Hypothesis**

**2 (H2).**

**Hypothesis**

**3 (H3).**

**Hypothesis**

**4 (H4).**

## 4. Empirical Results

#### 4.1. Moments Analysis

#### 4.2. CAPM Analysis

#### 4.3. SD Analysis

#### 4.4. Volume Analysis

## 5. Concluding Remarks

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Ascending DD statistics distribution for C23-T33. Note: ${T}_{j}$ is the test statistic defined in (3) for j = 1, 2 and 3. F and G are the CDFs of the excess warrant returns for C23 and T33, respectively.

**Table 1.**Summary statistics and CAPM using daily excess returns for selected Chinese and Taiwanese warrants.

Warrant Code | Mean | Std. Dev. | Skewness | Kurtosis | JB | Sharpe | Beta | Treynor | Jensen |
---|---|---|---|---|---|---|---|---|---|

C06 | −0.0201 | 0.0781 | −3.7196 | 33.9411 | 10084.75 | −0.2579 | 0.0150 | −1.3384 | −0.0186 |

C12 | −0.0186 | 0.1440 | −13.0898 | 242.2479 | 1160912.00 | −0.1294 | −0.0009 | 20.5741 | −0.0183 |

C14 | −0.0638 | 0.2956 | −8.3235 | 80.9023 | 30407.42 | −0.2157 | −0.0059 | 10.8959 | −0.0624 |

C23 | 0.0011 | 0.0555 | 0.4351 | 5.1238 | 52.02 | 0.0204 | 0.0175 | 0.0647 | −0.0056 |

C44 | −0.0057 | 0.0300 | 2.7879 | 24.6026 | 6885.69 | −0.1527 | 0.0115 | −0.4943 | −0.0058 |

C47 | −0.0365 | 0.3155 | −13.5417 | 197.7772 | 377048.90 | −0.1158 | −0.0174 | 2.0965 | −0.0298 |

C52 | −0.0270 | 0.2297 | −13.2963 | 195.6075 | 373322.80 | −0.1175 | 0.0397 | −0.6796 | −0.0405 |

C55 | −0.0189 | 0.1171 | −2.2507 | 29.5247 | 7117.58 | −0.1615 | 0.0003 | −60.9548 | −0.0190 |

T1 | −0.0511 | 0.2409 | −0.4242 | 12.6574 | 454.26 | −0.2121 | 0.0814 | −0.6280 | −0.0565 |

T12 | −0.0341 | 0.4486 | −0.0494 | 20.9576 | 1679.60 | −0.0760 | 0.0289 | −1.1812 | −0.0307 |

T13 | −0.0573 | 0.2730 | 1.3731 | 15.5192 | 800.82 | −0.2100 | 0.0232 | −2.4702 | −0.0560 |

T15 | −0.0374 | 0.1388 | −2.2828 | 22.0487 | 2925.68 | −0.2693 | 0.0225 | −1.6632 | −0.0343 |

T17 | 0.0053 | 0.0588 | 1.9440 | 11.7270 | 475.41 | 0.0892 | 0.0056 | 0.9310 | 0.0037 |

T25 | −0.0434 | 0.1742 | 0.2863 | 11.0227 | 336.94 | −0.2491 | 0.0103 | −4.2091 | −0.0441 |

T26 | −0.0032 | 0.2247 | 0.9245 | 5.1186 | 41.19 | −0.0144 | 0.1324 | −0.0245 | −0.0109 |

T33 | 0.0128 | 0.1545 | −1.0409 | 10.6930 | 320.22 | 0.0829 | 0.0523 | 0.2451 | 0.0094 |

Pairwise Comparison | t Test | F Test | MV Dominance |
---|---|---|---|

C14-T13 | µ_{C} < µ_{T}−0.1474 | σ_{C} > σ_{T}1.1529 | No |

C23-T33 | µ_{C} < µ_{T}−1.041 | σ_{C} < σ_{T}7.7611 *** | C23 ${\succ}_{MV}$ T33 |

C44-T17 | µ_{C} < µ_{T}−2.6106 *** | σ_{C} < σ_{T}3.8564 *** | No |

C47-T12 | µ_{C} < µ_{T}−0.0597 | σ_{C} < σ_{T}2.0222 *** | C47 ${\succ}_{MV}$ T12 |

C06-T15 | µ_{C} > µ_{T}1.6191 | σ_{C} < σ_{T}3.1598 *** | C06 ${\succ}_{MV}$ T15 |

C23-T17 | µ_{C} < µ_{T}−0.6578 | σ_{C} < σ_{T}1.1249 | No |

C47-T17 | µ_{C} < µ_{T}−1.4663 | σ_{C} > σ_{T}28.7523 *** | C47 ${\succ}_{MV}$ T17 |

C52-T26 | µ_{C} < µ_{T}−0.9425 | σ_{C} > σ_{T}1.0449 | No |

C55-T25 | µ_{C} < µ_{T}1.5869 | σ_{C} < σ_{T}2.2131 *** | C55 ${\succ}_{MV}$ T25 |

C12-T17 | µ_{C} < µ_{T}−1.8125 * | σ_{C} > σ_{T}5.9872 *** | T17 ${\succ}_{MV}$ C12 |

C23-T01 | µ_{C} > µ_{T}3.1743 *** | σ_{C} < σ_{T}18.8615 *** | C23 ${\succ}_{MV}$ T01 |

C14-T33 | µ_{C} < µ_{T}−2.4578 ** | σ_{C} > σ_{T}3.5309 *** | T33 ${\succ}_{MV}$ C14 |

Pairwise Comparison | Ascending SD |
---|---|

C14-T13 | No SD |

C23-T33 | $\mathrm{C}{\succ}_{2,3}\mathrm{T}$ |

C44-T17 | $\mathrm{C}{\succ}_{2,3}\mathrm{T}$ |

C47-T12 | $\mathrm{C}{\succ}_{2,3}\mathrm{T}$ |

C06-T15 | $\mathrm{C}{\succ}_{2,3}\mathrm{T}$ |

C23-T17 | $\mathrm{C}{\succ}_{2,3}\mathrm{T}$ |

C47-T17 | No SD |

C52-T26 | $\mathrm{C}{\succ}_{2,3}\mathrm{T}$ |

C55-T25 | $\mathrm{C}{\succ}_{2,3}\mathrm{T}$ |

C12-T17 | $\mathrm{C}{\succ}_{2,3}\mathrm{T}$ |

C23-T01 | $\mathrm{C}{\succ}_{2,3}\mathrm{T}$ |

C14-T33 | No SD |

Warrant Code | Mean | Std. Dev. | Skewness | Kurtosis | JB |
---|---|---|---|---|---|

C06 | 96,150.9500 | 73,283.1200 | 2.1843 | 10.0706 | 690.7704 |

C12 | 173,603.0000 | 324,388.6000 | 3.4949 | 17.0166 | 4926.9010 |

C14 | 46,306.6400 | 44,987.5000 | 1.8837 | 7.1179 | 150.5576 |

C23 | 55,458.4900 | 46,573.7300 | 1.9508 | 8.4068 | 440.8489 |

C44 | 214,101.4000 | 178,940.0000 | 1.9563 | 7.5217 | 718.0678 |

C47 | 40,012.9900 | 40,078.6000 | 2.3406 | 10.4683 | 760.7066 |

C52 | 59,475.6700 | 51,874.5500 | 2.4878 | 10.7968 | 848.3305 |

C55 | 48,996.5800 | 60,061.5300 | 3.2302 | 16.5166 | 2216.2940 |

T1 | 15.3537 | 103.6143 | 10.5616 | 113.3553 | 61,544.3700 |

T12 | 18.4588 | 72.0669 | 9.8558 | 105.4079 | 57,098.5700 |

T13 | 25.7770 | 127.7570 | 10.4158 | 111.5797 | 60,098.8800 |

T15 | 11.4235 | 75.4091 | 13.2409 | 178.1744 | 240,636.5000 |

T17 | 0.1405 | 0.4666 | 4.8718 | 29.5315 | 4194.0060 |

T25 | 37.7894 | 74.4648 | 2.3908 | 8.2631 | 265.4654 |

T26 | 79.8744 | 149.2158 | 7.2949 | 69.3507 | 24,230.2100 |

T33 | 107.3186 | 117.9072 | 2.8163 | 14.5546 | 839.9515 |

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**MDPI and ACS Style**

Wong, W.-K.; Lean, H.H.; McAleer, M.; Tsai, F.-T.
Why Are Warrant Markets Sustained in Taiwan but Not in China? *Sustainability* **2018**, *10*, 3748.
https://doi.org/10.3390/su10103748

**AMA Style**

Wong W-K, Lean HH, McAleer M, Tsai F-T.
Why Are Warrant Markets Sustained in Taiwan but Not in China? *Sustainability*. 2018; 10(10):3748.
https://doi.org/10.3390/su10103748

**Chicago/Turabian Style**

Wong, Wing-Keung, Hooi Hooi Lean, Michael McAleer, and Feng-Tse Tsai.
2018. "Why Are Warrant Markets Sustained in Taiwan but Not in China?" *Sustainability* 10, no. 10: 3748.
https://doi.org/10.3390/su10103748