可转换债券定价及投资策略研究
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摘要
可转换债券是我国证券市场近年来推出的一种金融衍生产品，尤其是这几年发展十分迅速，已成为我国上市公司一种重要融资工具和二级市场上的主要投资品种之一。但是由于可转换债券定价理论没有被充分的挖掘和被市场参与者认识，出现了可转换债券的市场定价偏低，收益风险不匹配等问题。正确定价可转换债券对于投资者和发行人及可转换债券市场今后的健康发展都具有重大的意义。
本文首先介绍了可转换债券的一些基本概念和特征以及国内这些年的发展状况，对国内外关于可转换债券的理论进行了回顾，并详细研究和介绍了国外部分影响深远的可转换债券经典理论文章，认为研究前人的优秀成果对我国可转换债券定价具有重大的借鉴。主要有Ingersoll(1977)早期的单因素模型、Brennan和Schwartz(1977)的双因素模型以及Ho和Pfeffer(1996)近些年提出了的双因素分析模型，尤其是后两篇还具有重大的实践运用价值。
结合我国现实情况，文章将可转换债券视为写在股票价格上的衍生品种，先从国内转债条款设计出发定性的分析了转债的股性和债性，以及转债定价的一般原理。在实证中采用了可转换债券双因素定价模型：可转换债券价值=投资价值+期权的权证价值-赎回期权价值。使用Black—Scholes模型计算其中的期权价值，以转债同类的企业债券的收益率曲线的时点值为折现收益率，以万科转债上市交易的周收盘价格为样本进行实证研究，结果表明在转股期前可转换债券的理论值高于其市场价值，存在低估；在赎回通知期，转债市场价格更接近转换平价而高于理论价格，这两个时期的误差都比较大；中间的这段时期转债的理论价值基本可以作为市价的参考。究其原因可能有二：一是可转债市场还比较小，流动性比较差，市场价格发现功能受到制约；二是市场缺乏做空机制，可转换债券的套利策略难以实现。
本文进一步对我国市场上2002—2003年发行的可转换债券进行了价值构成的实证分析，结果表明大部分的可转换债券对股票价格的波动比较敏感，转股溢价率比较低，甚至有时为负，即转换平价高于转债市场价格，存在明显的套利空间。
针对实证结果和国内可转换债券的特点，文章提出了可转换债券的投资策略。从实证分析中可知国内转债市场定价存在严重的偏差，可以利用市场的无效性获得无风险的套利收益，而且这种套利交易在客观上可以推动市场价值向理论价值回归，减少市场的无效性，值得提倡。
本文也还存在很多不足之处，如没有考虑到转债转股的稀释效应：利率波动对股票价格和期权价格的影响；对赎回期权的定价执行价格采用了赎回条件的30％涨幅与实际有所出入等，需要在以后的研究中再深入探讨。
Convertible bonds has appeared in China security market a few years ago, with drastic progress in recent years, which has already ranked among the main financial instruments for listing companies and investment varieties at the second-market. For the pricing theory of convertible bonds has neither been fully studied, nor sensed by market-participants, there arise a series of problems such as the relatively low price of convertible bonds at market, and mismatch of revenue and risk, etc. Thus, the appropriate pricing of convertible bonds bear favorably on investors and issuers, as well as the healthy development of the convertible bonds market.
This paper stars with some basic concepts and features of convertible bonds, along with description of the recent development of domestic market. Tracing back to the theories at home and abroad concerned convertible bonds, the author gives an in-depth study on some theoretical articles of international fame on convertible bonds and holds that predecessors' great achievements of study will offer great insights to our pricing of convertible bonds, which include Ingersoll's single-factor model (1977) , Brennan and Schwartz's two-factor model(1977), and newly established two-factor model of Ho and Pfeffer (1996) , with the latter two of great practical value. Combined with situations in China in this paper, convertible bond value is regarded as the derivative of underlying stock price. The author begins with the domestic design of terms for convertible bonds, and then prescriptively analyzes the stock nature and the bond nature of convertible bonds, as well as principles of pricing of convertible bonds. While in
positive study, two-factor pricing model is adopted: Bond price=Investment value+Warrant -Call option value. On the basis of Black-Scholes model for the calculations of the option value, the spots on the revenue rate curve of similar corporate bonds are referred as discount yield rate, and weekly closed price of Wanke convertible bonds are taken as samples for positive study. It has been found that the theoretical value of convertible bonds is higher than their market value before conversion date, which constitutes underpricing; during the period of call notice , market price of convertible bonds is closer to parity value and higher than theoretical price, and thus arise dramatic errors in both periods; the theoretical price in the gap between the two periods can be basically counted as reference to market price. The reasons of the underpricing include: the low liquidity of convertible bonds, which restricts the price-founding function of the market, and the lack of short-sell, which can achieve free arbitr
age if the market prices departure the equilibrium prices.
This paper furthers its positive study on the value constitution of convertible bonds
issued from 2002 to 2003, whose findings shows that most convertible bonds are very
sensitive to the fluctuations of stock prices, and parity premium runs low, even negative, that is, parity is higher than market price of convertible bonds, capable of obvious arbitrage space.
In consideration of positive results and features of domestic convertible bonds, the author presents the investment strategies of convertible bonds. Namely, positive study informs us of the existent grave errors in the pricing at domestic convertible bonds market, and thus invalidity can be used to gain risk-free arbitrage revenue, the transactions of which are, objectively, able to prompt the return of the market value to the theoretical value and the deduction of the invalidity of market, and should invite favorable evaluation.
Of course, this paper is not perfect. It doesn't involve the dilution effect of the conversion from bonds to stocks, the effect on option price brought by fluctuations of interest rate, and the discrepancy between the execution of the option pricing adopting 30% increase of call terms and that of reality. Consequently, further discussion will be called for.
本文首先介绍了可转换债券的一些基本概念和特征以及国内这些年的发展状况，对国内外关于可转换债券的理论进行了回顾，并详细研究和介绍了国外部分影响深远的可转换债券经典理论文章，认为研究前人的优秀成果对我国可转换债券定价具有重大的借鉴。主要有Ingersoll(1977)早期的单因素模型、Brennan和Schwartz(1977)的双因素模型以及Ho和Pfeffer(1996)近些年提出了的双因素分析模型，尤其是后两篇还具有重大的实践运用价值。
结合我国现实情况，文章将可转换债券视为写在股票价格上的衍生品种，先从国内转债条款设计出发定性的分析了转债的股性和债性，以及转债定价的一般原理。在实证中采用了可转换债券双因素定价模型：可转换债券价值=投资价值+期权的权证价值-赎回期权价值。使用Black—Scholes模型计算其中的期权价值，以转债同类的企业债券的收益率曲线的时点值为折现收益率，以万科转债上市交易的周收盘价格为样本进行实证研究，结果表明在转股期前可转换债券的理论值高于其市场价值，存在低估；在赎回通知期，转债市场价格更接近转换平价而高于理论价格，这两个时期的误差都比较大；中间的这段时期转债的理论价值基本可以作为市价的参考。究其原因可能有二：一是可转债市场还比较小，流动性比较差，市场价格发现功能受到制约；二是市场缺乏做空机制，可转换债券的套利策略难以实现。
本文进一步对我国市场上2002—2003年发行的可转换债券进行了价值构成的实证分析，结果表明大部分的可转换债券对股票价格的波动比较敏感，转股溢价率比较低，甚至有时为负，即转换平价高于转债市场价格，存在明显的套利空间。
针对实证结果和国内可转换债券的特点，文章提出了可转换债券的投资策略。从实证分析中可知国内转债市场定价存在严重的偏差，可以利用市场的无效性获得无风险的套利收益，而且这种套利交易在客观上可以推动市场价值向理论价值回归，减少市场的无效性，值得提倡。
本文也还存在很多不足之处，如没有考虑到转债转股的稀释效应：利率波动对股票价格和期权价格的影响；对赎回期权的定价执行价格采用了赎回条件的30％涨幅与实际有所出入等，需要在以后的研究中再深入探讨。
Convertible bonds has appeared in China security market a few years ago, with drastic progress in recent years, which has already ranked among the main financial instruments for listing companies and investment varieties at the second-market. For the pricing theory of convertible bonds has neither been fully studied, nor sensed by market-participants, there arise a series of problems such as the relatively low price of convertible bonds at market, and mismatch of revenue and risk, etc. Thus, the appropriate pricing of convertible bonds bear favorably on investors and issuers, as well as the healthy development of the convertible bonds market.
This paper stars with some basic concepts and features of convertible bonds, along with description of the recent development of domestic market. Tracing back to the theories at home and abroad concerned convertible bonds, the author gives an in-depth study on some theoretical articles of international fame on convertible bonds and holds that predecessors' great achievements of study will offer great insights to our pricing of convertible bonds, which include Ingersoll's single-factor model (1977) , Brennan and Schwartz's two-factor model(1977), and newly established two-factor model of Ho and Pfeffer (1996) , with the latter two of great practical value. Combined with situations in China in this paper, convertible bond value is regarded as the derivative of underlying stock price. The author begins with the domestic design of terms for convertible bonds, and then prescriptively analyzes the stock nature and the bond nature of convertible bonds, as well as principles of pricing of convertible bonds. While in
positive study, two-factor pricing model is adopted: Bond price=Investment value+Warrant -Call option value. On the basis of Black-Scholes model for the calculations of the option value, the spots on the revenue rate curve of similar corporate bonds are referred as discount yield rate, and weekly closed price of Wanke convertible bonds are taken as samples for positive study. It has been found that the theoretical value of convertible bonds is higher than their market value before conversion date, which constitutes underpricing; during the period of call notice , market price of convertible bonds is closer to parity value and higher than theoretical price, and thus arise dramatic errors in both periods; the theoretical price in the gap between the two periods can be basically counted as reference to market price. The reasons of the underpricing include: the low liquidity of convertible bonds, which restricts the price-founding function of the market, and the lack of short-sell, which can achieve free arbitr
age if the market prices departure the equilibrium prices.
This paper furthers its positive study on the value constitution of convertible bonds
issued from 2002 to 2003, whose findings shows that most convertible bonds are very
sensitive to the fluctuations of stock prices, and parity premium runs low, even negative, that is, parity is higher than market price of convertible bonds, capable of obvious arbitrage space.
In consideration of positive results and features of domestic convertible bonds, the author presents the investment strategies of convertible bonds. Namely, positive study informs us of the existent grave errors in the pricing at domestic convertible bonds market, and thus invalidity can be used to gain risk-free arbitrage revenue, the transactions of which are, objectively, able to prompt the return of the market value to the theoretical value and the deduction of the invalidity of market, and should invite favorable evaluation.
Of course, this paper is not perfect. It doesn't involve the dilution effect of the conversion from bonds to stocks, the effect on option price brought by fluctuations of interest rate, and the discrepancy between the execution of the option pricing adopting 30% increase of call terms and that of reality. Consequently, further discussion will be called for.
引文
1、孔繁军，《欧美可转债市场及借鉴意义》，证券市场导报，2001年11月10日
2、刘立喜，《可转换公司债券》，上海财经大学出版社，1999年版
3、林义相等，《可转换债券投资分析和运作》上海远东出版社，1998年版
4、范辛亭：《用久期-凸度法预测企业可转换债券的利率风险》，《预测》，2000第2期
5、范辛亭，方兆本：《一种随机利率条件下企业可转换债券定价的离散时间方法》，《系统工程理论与实践》，2002年第8期
6、华夏证券研究所，《可转换债券定价理论分析》，中国证券报，1998年2月21日
7、黄建兵：《中国的可转换债券与市场价格有效性研究》，《系统工程理论方法应用》，2002年3月
8、齐演峰、黄福广译，埃兹·内尔肯编著：《混合金融工具手册》，机械工业出版社，2002年版
9、秦学志、吴冲锋，《可赎回的可转换债券的博弈定价方法》，《系统工程》2000年9月
10、宋逢明：《金融工程原理——无套利均衡分析》，清华大学出版社，2002年版
11、托马斯·E·科普兰著，宋宪中译：《财务理论与公司政策》，东北财经大学出版社，2003年版
12、吴圣涛、胡春霞：《可转换债券定价与投资策略》，《证券市场导报》，2003年8月
13、杨大楷、黄海等：《可转换债券定价的经典理论研究》，《投资与合作》，2000年第11期
14、杨如彦、卫钢、刘孝红、孟辉：《可转换债券及其绩效评价》，人民大学出版社，2002年版
15、约翰·赫尔，张陶伟译：《期权、期货与衍生证券》，北京华夏出版社，1997年版
16、王承炜、吴冲锋：《上市公司可转换债券价值分析》，《系统工程》，2001年7月
17、张德华、陶融：《布莱克-斯科尔斯期权定价模型在可转换债券定价中的应用》，《财经理论与实践》，1999年第11期
18、张鸣：《可转换债券定价理论与案例研究》，上海财经大学学报，2001年5期
19、郑小迎、陈金贤：《关于可转换债券定价模型的研究》，《预测》，1999年第3期
20、祝小兵：《期权定价理论及其在我国的应用》，《上海投资》2000年2月
21、证券之星网站http://www.stockstar.com
22、中国证监会网站http://www.csrc.gov.cn
23、Wind咨询数据系统
1、Black F, Scholes M: "the pricing of options and corporate liabilities" Journal of Political Economy, 1973(81), 637-659
2、Carayannopoulos, P: "Valuing convertible bonds under the assumption of stochastic interest rates: An empirical investigation" Quarterly Journal of Business and Economics, 1996, 35(3): 17-31.
3、King, P.: "Convertible Bond Valuation: an Empirical Test" Journal of Financial Research, 1986, 9(1): 53-69.
4、Ho T S Y, Lee S B: "Term structure movement and the pricing of interest rate contingent claims" Journal of Finance, May 1986(42), 1129-1142
5、Ho T S Y, Pfeffer D M: "Convertible bonds: Model, Value attribution and analytics" Financial Analysts Journal, 1996(Sep/Oct), 35-44
6、Ingersoll J. E: "A contingent-claims valuation of convertible securities" Journal of Financial Economics, 1977a, 4(2), 289-321
7、Ingersoll J. E: "An Examination of Corporate Call Policies on Convertible Securities", Journal of Finance, , 1977b(32), 463-478
8、James E. Walter, Agustin V. Que: "The Valuation of Convertible Bonds", Journal of Finance, June 1973(28), 713-731
9、Brennan, Michael J., Eduardo S. Schwartz: "Analyzing Convertible Bond", Journal of Financial and Quantitative Analysis, 1980(15), 907-929
10、Brennan Michael J., E.S. Schwarz: "Convertible Bond: Valuation and Optional Strategies for Call and Conversion." Journal of Finance, December 1977, 17(5), 1699-1715
11、Merton R. " Theory of rational option pricing" Journal of Financial and Management Science, 1973, 4(1), 141-184
12、McConnell, Schwartz, "LYON Taming", The Journal of Finance, 1986(3), 561-577
13、Trippi Robert: "A test of Option market efficiency using a random-walk valuation model", Journal of Economic and Bussiness, 1977(29), 93-98
2、刘立喜，《可转换公司债券》，上海财经大学出版社，1999年版
3、林义相等，《可转换债券投资分析和运作》上海远东出版社，1998年版
4、范辛亭：《用久期-凸度法预测企业可转换债券的利率风险》，《预测》，2000第2期
5、范辛亭，方兆本：《一种随机利率条件下企业可转换债券定价的离散时间方法》，《系统工程理论与实践》，2002年第8期
6、华夏证券研究所，《可转换债券定价理论分析》，中国证券报，1998年2月21日
7、黄建兵：《中国的可转换债券与市场价格有效性研究》，《系统工程理论方法应用》，2002年3月
8、齐演峰、黄福广译，埃兹·内尔肯编著：《混合金融工具手册》，机械工业出版社，2002年版
9、秦学志、吴冲锋，《可赎回的可转换债券的博弈定价方法》，《系统工程》2000年9月
10、宋逢明：《金融工程原理——无套利均衡分析》，清华大学出版社，2002年版
11、托马斯·E·科普兰著，宋宪中译：《财务理论与公司政策》，东北财经大学出版社，2003年版
12、吴圣涛、胡春霞：《可转换债券定价与投资策略》，《证券市场导报》，2003年8月
13、杨大楷、黄海等：《可转换债券定价的经典理论研究》，《投资与合作》，2000年第11期
14、杨如彦、卫钢、刘孝红、孟辉：《可转换债券及其绩效评价》，人民大学出版社，2002年版
15、约翰·赫尔，张陶伟译：《期权、期货与衍生证券》，北京华夏出版社，1997年版
16、王承炜、吴冲锋：《上市公司可转换债券价值分析》，《系统工程》，2001年7月
17、张德华、陶融：《布莱克-斯科尔斯期权定价模型在可转换债券定价中的应用》，《财经理论与实践》，1999年第11期
18、张鸣：《可转换债券定价理论与案例研究》，上海财经大学学报，2001年5期
19、郑小迎、陈金贤：《关于可转换债券定价模型的研究》，《预测》，1999年第3期
20、祝小兵：《期权定价理论及其在我国的应用》，《上海投资》2000年2月
21、证券之星网站http://www.stockstar.com
22、中国证监会网站http://www.csrc.gov.cn
23、Wind咨询数据系统
1、Black F, Scholes M: "the pricing of options and corporate liabilities" Journal of Political Economy, 1973(81), 637-659
2、Carayannopoulos, P: "Valuing convertible bonds under the assumption of stochastic interest rates: An empirical investigation" Quarterly Journal of Business and Economics, 1996, 35(3): 17-31.
3、King, P.: "Convertible Bond Valuation: an Empirical Test" Journal of Financial Research, 1986, 9(1): 53-69.
4、Ho T S Y, Lee S B: "Term structure movement and the pricing of interest rate contingent claims" Journal of Finance, May 1986(42), 1129-1142
5、Ho T S Y, Pfeffer D M: "Convertible bonds: Model, Value attribution and analytics" Financial Analysts Journal, 1996(Sep/Oct), 35-44
6、Ingersoll J. E: "A contingent-claims valuation of convertible securities" Journal of Financial Economics, 1977a, 4(2), 289-321
7、Ingersoll J. E: "An Examination of Corporate Call Policies on Convertible Securities", Journal of Finance, , 1977b(32), 463-478
8、James E. Walter, Agustin V. Que: "The Valuation of Convertible Bonds", Journal of Finance, June 1973(28), 713-731
9、Brennan, Michael J., Eduardo S. Schwartz: "Analyzing Convertible Bond", Journal of Financial and Quantitative Analysis, 1980(15), 907-929
10、Brennan Michael J., E.S. Schwarz: "Convertible Bond: Valuation and Optional Strategies for Call and Conversion." Journal of Finance, December 1977, 17(5), 1699-1715
11、Merton R. " Theory of rational option pricing" Journal of Financial and Management Science, 1973, 4(1), 141-184
12、McConnell, Schwartz, "LYON Taming", The Journal of Finance, 1986(3), 561-577
13、Trippi Robert: "A test of Option market efficiency using a random-walk valuation model", Journal of Economic and Bussiness, 1977(29), 93-98