基于分形市场理论的基金投资风格漂移及其风险测度研究
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摘要
经过2008年美国次贷危机的巨大冲击,全球金融业发展面临着严峻挑战,美国金融全球霸主地位开始动摇,以亚洲为中心的新兴资本市场迅速崛起。2010年,我国作为亚洲最大的新兴资本市场发生了深刻变化,股指期货、融资融券等做空机制的推出增加了市场深度,基金产品的不断大量创新发行为我国基金业发展打开了空间,基金产品的开发有望成为我国基金业发展中的一道亮丽风景线。在金融危机与分形市场的现实背景下,我国基金业发展该如何去迎接挑战,寻找新的发展机遇——对基金产品进行定位、把握产品创新设计的灵魂?美国基金市场的发展经历了从无序到有序,从有序到有效的过程。在基金产品设计定位方面,经历了从提供理财服务转向提供产品与提供理财服务相结合的过程;在理财目标方面,基金投资者经历了从追求超额收益转向追求满意收益,再到追求风险收益的过程;在理财策略方面,经历了从依赖基金经理个人能力转向依赖投资风格理念,再到依赖投资风格理论的过程。在当今欧美资本市场中,基金投资风格与风格投资等理念已经完全被接受,逐步深入人心。未来我国基金业的发展又该如何从量变到质变,在产品设计与投资风格理念上走向世界的前列?
国外对基金投资风格漂移研究始于20世纪90年代初,至今仍是个热点问题,在理论上已取得了丰硕成果,在实践上也得到了广泛应用。但与美国基金市场相比,我国基金发展初具规模,在基金产品设计灵魂上没有表现出显著的差异性,在投资运作过程中,基金投资风格趋同导致发生风格漂移现象。新兴市场的分形特征为基金发生投资风格漂移提供了现实可行性,基金经理宁愿违背宣称时的投资风格而发生所谓的风格漂移,意味着其背后折射出有获得短期超额收益的机遇,但机遇与风险并存,其中可能带来的漂移风险的可控性也就成了风格漂移能否成功的关键。本文基于此,引入分形理论来探索研究我国开放式基金投资风格漂移现象,对投资风格漂移收益的非线性特征及其风险测度进行系统研究,构建出科学的投资风格识别方法与漂移风险测度模型,以期为监管部门、基金公司、基金经理和投资者对投资风格漂移收益分形特征与所带来的漂移风险进行量化及控制提供方法基础,同时为我国未来基金业的繁荣发展提供理论指导。
本文研究主要得出以下4点结论:
1、通过引入非线性科学中的分形理论构建了分形市场现实背景下的基金投资风格理论分析框架,实证检验了我国股市风格资产存在长记忆性、标度不变性等分形特征;
2、在我国资本市场呈分形特征的基础上,运用基于盒子分形维的基金投资风格识别方法与基于弹性分形维的基金投资风格漂移分析法对我国基金投资风格漂移进行了系统研究,一致得出我国基金普遍存在漂移现象,该结论也符合分形市场的现实背景;
3、运用滑动窗口MF-DFA方法对我国开放式基金投资风格漂移收益进行了多重分形分析,得出基金投资风格漂移收益具有多重分形特征,进一步得出我国基金市场是非完全有效的,呈一定的分形特征,这为基金发生投资风格漂移提供了现实可行性;
4、基金投资风格漂移是把双刃剑,在获取短期超额收益的同时,其背后也折射出巨大的风格漂移风险。通过构建多重分形波动率MF-VaR测度模型对基金投资风格漂移风险进行了测度,结果得出我国开放式基金普遍存在较大的风格漂移风险,这为监管部门进一步控制较严重的风格漂移现象,规范基金产品发行与投资行为提供理论支持。
国内外学者已在基金投资风格识别、投资风格漂移的影响因素及其对基金业绩的影响等方面做了大量研究,但都是基于有效市场理论线性研究范式下开展的,在分形市场理论非线性研究范式下的基金投资风格漂移及其风险测度研究至今仍是空白。比较已有的相关研究成果,本文主要创新之处与贡献点如下:
1、通过引入分形理论对基金投资风格理论体系做修正探索研究,构建了基金投资风格的分形分析框架,实证检验了股市风格资产的长记忆性、标度不变性等分形特征;
2、在比较两种主流投资风格识别方法的基础上,结合我国资本市场的分形特征,提出了盒子分形维的投资风格识别方法FDSR与投资风格漂移程度的量化指标CIS,该方法相比传统识别方法能够避免风格资产多重共线性、缺乏T统计量显著检验等缺陷;
3、提出了基于弹性分形维的基金投资风格漂移分析方法,推导出弹性分形维的计算公式,通过挖掘出其经济含义给出了投资风格漂移的阀值,为研究基金投资风格漂移提供了一种新范式,这可能成为测度与控制基金投资风格漂移风险的新工具;
4、对基金投资风格漂移进行了量化,得到了投资风格漂移收益的计算公式。对传统MF-DFA方法进行了改进,提出了滑动窗口MF-DFA多重分形分析方法,该方法能在数据丢失与序列顺序倒置等方面得到改进,减少了分析结果的误差。并运用改进后的方法对我国开放式基金投资风格漂移收益的多重分形特征及其谱参数进行了研究;
5、根据多重分形谱参数与奇异指数提炼出多重分形波动率测度,构建了投资风格漂移风险MF-VaR测度模型,并运用该模型对我国79只开放式基金投资风格漂移风险进行了测度,相比最新GARCH族高级计量模型,具有更高的测度精度与稳健性。
After the huge strike of U.S. subprime crisis in 2008, global financial industry faced serious challenges. While the role of the United States as a global hegemony in finance began to shake, Asia-centered emerging capital markets rapidly rose. As the largest emerging capital market in Asia,China underwent profound changes in 2010, when stock index futures, margin trading and other short mechanisms increased the depth of the market. The constant issuing innovation of fund-products widened the road for the funds development, which might be expected to become a beautiful landscape in fund industry. In the background of fractal market and financial crisis, how can Chinese fund industry meet the challenge and find new development opportunities-positioning fund products and grasping the soul of product innovation? The development of the U.S. fund market has gone through disorder to order, and then to effective process. At the aspect of product design and position, fund industry has experienced a shift from the product provision to a combination of financial services and product provision; at the aspect of financial goal, the fund investors’pursuit has changed from excess returns to satisfactory returns,and then to risk returns; at the aspect of financial strategy, there has been a conversion from relying on the ability of managers to dependend on investment style philosophy, and then to investment style theory. In today's capital market in Europe and America, philosophy such as investment style and style investment has been fully accepted, and gradually popular. How can the fund-industry development in China transform from quantity to quality? How can the concept of product design and investment style be on the forefront of the world?
Foreign research on fund investment style drift began in the early 1990s, which is still a hot issue so far. The research in this field has achieved fruitful results in theory, it also has been widely used in practice. Compared with U.S. fund market, China's fund development just begins to take shape. The funds do not show significant difference in the soul of product design in China. What’s more, the investment-style convergence results in style drift in the course of investment operation. It is the fractal characteristic of emerging markets that provides a realistic possibility for fund investment style drift. Contrary to the claimed investment style, fund managers might prefer to the so-called style drift, reflecting an underlying opportunity of short-term excess returns. However, opportunities coexist with risk, and the controllability of the drift risk will become the key factor to the success of style drift. Based on this, this paper use fractal theory to explore investment style drift of the open-end funds.Besides,this paper does a systematic study on the nonlinear characteristic of investment style drift return, and constructs a scientific model to measure the investment style drift risk. The study is expected to offer methods of quantifying the fractal characteristics of investment style drift return and drift risk for regulators, fund companies, fund managers and investors, as well as to provide theoretical guidance for the prosperous development of the fund industry in the future.
The main conclusions of this paper are as follows:
1.By introducing fractal theory in non-linear science, this paper constructs a theoretical framework of fund investment style in the reality of fractal market, and empirical test finds that: the style asset of China's stock market has a fractal feature of both long memory and invariant scaling and so on;
2.Considering fractal characteristics of Chinese capital market, this paper systematically studies the fund investment style drift by recognizing fund investment style based on the box-fractal dimension and analyze fund investment style drift based on elastic-fractal dimension. They draw the same conclusion that the investment style drift is a common phenomenon, which is also consistent with the real fractal market;
3.Using sliding window MF-DFA method, this paper carries out multi-fractal analysis on investment style drift return of open-end funds. It is concluded that the investment style drift return shows multifractal characteristics, and found fund market is non-fully effective in China, presenting fractal characteristic to some extent, which provides a realistic feasibility for fund investment style drift;
4.The fund investment style drift is a double-edged sword. Along with obtaining short-term excess return, it also reflects the huge style drift risk. This paper measures the investment style drift risk by constructing multifractal volatility MF-VaR model. The result indicates that drift risk is generally high in the open-end funds, which provides theoretical support for regulators to control the serious style drift, as well as to regulate fund products issue and investment behavior.
Scholars home and abroad have studied a lot on the fund investment style identification, investment style drift factors and its impact on the fund's performance, but they are all carried out under the linear paradigm based on efficient market theory. Comparatively, research on fund investment style drift and risk measurement under non-linear paradigm based on fractal market theory is still blank.Comparison of the existing research results, innovation and contribution of this paper are as follows:
1.This paper introduces fractal theory to revise exploratory research on the field of fund investment style, constructs a fractal analytical framework of fund investment style, and proves that the Chinese stock style asset has a fractal feature of long memory and invariant scaling;
2.After comparing the two traditional investment style identification methods, this paper recognizes fund investment style based on the box-fractal dimension(FDSR) and analyzes fund investment style drift based on the elastic-fractal dimension CIS, according to the fractal characteristic of capital market. Compared to the previous identification method, this method is able to avoid style assets having multi-collinearity or lacking T-statistic significant test and other defects;
3.This paper proposes analysis the fund investment style drift method based on elastic- fractal dimension, and deduces the computing formula of elastic-fractal dimension.In addition, this paper gives the threshold of investment style drift by mining its economic implications, which provides a new kind of research on fund investment style drift and may become a new tool to measure and control the fund investment style drift risk;
4.This paper quantifies fund investment style drift and derives investment style drift return formula. It modifies the traditional MF-DFA and put forword the multi-fractal analysis method of sliding window MF-DFA. The method makes an improvement in data loss and sequence inversion and reduces analysis result error. And use the modified method to analyze the multi-fractal characteristic and spectrum parameter of investment style drift return;
5.This paper extracts the multifractal volatility measurement according to multifractal spectrum parameter and singularity exponent, and constructs a MF-VaR model to measure investment style drift risk. This paper uses the MF-VaR model to measure investment style drift risk of 79 open-end funds, whose measurement results are more precise and robust than the latest GARCH family high-level econometric models.
国外对基金投资风格漂移研究始于20世纪90年代初,至今仍是个热点问题,在理论上已取得了丰硕成果,在实践上也得到了广泛应用。但与美国基金市场相比,我国基金发展初具规模,在基金产品设计灵魂上没有表现出显著的差异性,在投资运作过程中,基金投资风格趋同导致发生风格漂移现象。新兴市场的分形特征为基金发生投资风格漂移提供了现实可行性,基金经理宁愿违背宣称时的投资风格而发生所谓的风格漂移,意味着其背后折射出有获得短期超额收益的机遇,但机遇与风险并存,其中可能带来的漂移风险的可控性也就成了风格漂移能否成功的关键。本文基于此,引入分形理论来探索研究我国开放式基金投资风格漂移现象,对投资风格漂移收益的非线性特征及其风险测度进行系统研究,构建出科学的投资风格识别方法与漂移风险测度模型,以期为监管部门、基金公司、基金经理和投资者对投资风格漂移收益分形特征与所带来的漂移风险进行量化及控制提供方法基础,同时为我国未来基金业的繁荣发展提供理论指导。
本文研究主要得出以下4点结论:
1、通过引入非线性科学中的分形理论构建了分形市场现实背景下的基金投资风格理论分析框架,实证检验了我国股市风格资产存在长记忆性、标度不变性等分形特征;
2、在我国资本市场呈分形特征的基础上,运用基于盒子分形维的基金投资风格识别方法与基于弹性分形维的基金投资风格漂移分析法对我国基金投资风格漂移进行了系统研究,一致得出我国基金普遍存在漂移现象,该结论也符合分形市场的现实背景;
3、运用滑动窗口MF-DFA方法对我国开放式基金投资风格漂移收益进行了多重分形分析,得出基金投资风格漂移收益具有多重分形特征,进一步得出我国基金市场是非完全有效的,呈一定的分形特征,这为基金发生投资风格漂移提供了现实可行性;
4、基金投资风格漂移是把双刃剑,在获取短期超额收益的同时,其背后也折射出巨大的风格漂移风险。通过构建多重分形波动率MF-VaR测度模型对基金投资风格漂移风险进行了测度,结果得出我国开放式基金普遍存在较大的风格漂移风险,这为监管部门进一步控制较严重的风格漂移现象,规范基金产品发行与投资行为提供理论支持。
国内外学者已在基金投资风格识别、投资风格漂移的影响因素及其对基金业绩的影响等方面做了大量研究,但都是基于有效市场理论线性研究范式下开展的,在分形市场理论非线性研究范式下的基金投资风格漂移及其风险测度研究至今仍是空白。比较已有的相关研究成果,本文主要创新之处与贡献点如下:
1、通过引入分形理论对基金投资风格理论体系做修正探索研究,构建了基金投资风格的分形分析框架,实证检验了股市风格资产的长记忆性、标度不变性等分形特征;
2、在比较两种主流投资风格识别方法的基础上,结合我国资本市场的分形特征,提出了盒子分形维的投资风格识别方法FDSR与投资风格漂移程度的量化指标CIS,该方法相比传统识别方法能够避免风格资产多重共线性、缺乏T统计量显著检验等缺陷;
3、提出了基于弹性分形维的基金投资风格漂移分析方法,推导出弹性分形维的计算公式,通过挖掘出其经济含义给出了投资风格漂移的阀值,为研究基金投资风格漂移提供了一种新范式,这可能成为测度与控制基金投资风格漂移风险的新工具;
4、对基金投资风格漂移进行了量化,得到了投资风格漂移收益的计算公式。对传统MF-DFA方法进行了改进,提出了滑动窗口MF-DFA多重分形分析方法,该方法能在数据丢失与序列顺序倒置等方面得到改进,减少了分析结果的误差。并运用改进后的方法对我国开放式基金投资风格漂移收益的多重分形特征及其谱参数进行了研究;
5、根据多重分形谱参数与奇异指数提炼出多重分形波动率测度,构建了投资风格漂移风险MF-VaR测度模型,并运用该模型对我国79只开放式基金投资风格漂移风险进行了测度,相比最新GARCH族高级计量模型,具有更高的测度精度与稳健性。
After the huge strike of U.S. subprime crisis in 2008, global financial industry faced serious challenges. While the role of the United States as a global hegemony in finance began to shake, Asia-centered emerging capital markets rapidly rose. As the largest emerging capital market in Asia,China underwent profound changes in 2010, when stock index futures, margin trading and other short mechanisms increased the depth of the market. The constant issuing innovation of fund-products widened the road for the funds development, which might be expected to become a beautiful landscape in fund industry. In the background of fractal market and financial crisis, how can Chinese fund industry meet the challenge and find new development opportunities-positioning fund products and grasping the soul of product innovation? The development of the U.S. fund market has gone through disorder to order, and then to effective process. At the aspect of product design and position, fund industry has experienced a shift from the product provision to a combination of financial services and product provision; at the aspect of financial goal, the fund investors’pursuit has changed from excess returns to satisfactory returns,and then to risk returns; at the aspect of financial strategy, there has been a conversion from relying on the ability of managers to dependend on investment style philosophy, and then to investment style theory. In today's capital market in Europe and America, philosophy such as investment style and style investment has been fully accepted, and gradually popular. How can the fund-industry development in China transform from quantity to quality? How can the concept of product design and investment style be on the forefront of the world?
Foreign research on fund investment style drift began in the early 1990s, which is still a hot issue so far. The research in this field has achieved fruitful results in theory, it also has been widely used in practice. Compared with U.S. fund market, China's fund development just begins to take shape. The funds do not show significant difference in the soul of product design in China. What’s more, the investment-style convergence results in style drift in the course of investment operation. It is the fractal characteristic of emerging markets that provides a realistic possibility for fund investment style drift. Contrary to the claimed investment style, fund managers might prefer to the so-called style drift, reflecting an underlying opportunity of short-term excess returns. However, opportunities coexist with risk, and the controllability of the drift risk will become the key factor to the success of style drift. Based on this, this paper use fractal theory to explore investment style drift of the open-end funds.Besides,this paper does a systematic study on the nonlinear characteristic of investment style drift return, and constructs a scientific model to measure the investment style drift risk. The study is expected to offer methods of quantifying the fractal characteristics of investment style drift return and drift risk for regulators, fund companies, fund managers and investors, as well as to provide theoretical guidance for the prosperous development of the fund industry in the future.
The main conclusions of this paper are as follows:
1.By introducing fractal theory in non-linear science, this paper constructs a theoretical framework of fund investment style in the reality of fractal market, and empirical test finds that: the style asset of China's stock market has a fractal feature of both long memory and invariant scaling and so on;
2.Considering fractal characteristics of Chinese capital market, this paper systematically studies the fund investment style drift by recognizing fund investment style based on the box-fractal dimension and analyze fund investment style drift based on elastic-fractal dimension. They draw the same conclusion that the investment style drift is a common phenomenon, which is also consistent with the real fractal market;
3.Using sliding window MF-DFA method, this paper carries out multi-fractal analysis on investment style drift return of open-end funds. It is concluded that the investment style drift return shows multifractal characteristics, and found fund market is non-fully effective in China, presenting fractal characteristic to some extent, which provides a realistic feasibility for fund investment style drift;
4.The fund investment style drift is a double-edged sword. Along with obtaining short-term excess return, it also reflects the huge style drift risk. This paper measures the investment style drift risk by constructing multifractal volatility MF-VaR model. The result indicates that drift risk is generally high in the open-end funds, which provides theoretical support for regulators to control the serious style drift, as well as to regulate fund products issue and investment behavior.
Scholars home and abroad have studied a lot on the fund investment style identification, investment style drift factors and its impact on the fund's performance, but they are all carried out under the linear paradigm based on efficient market theory. Comparatively, research on fund investment style drift and risk measurement under non-linear paradigm based on fractal market theory is still blank.Comparison of the existing research results, innovation and contribution of this paper are as follows:
1.This paper introduces fractal theory to revise exploratory research on the field of fund investment style, constructs a fractal analytical framework of fund investment style, and proves that the Chinese stock style asset has a fractal feature of long memory and invariant scaling;
2.After comparing the two traditional investment style identification methods, this paper recognizes fund investment style based on the box-fractal dimension(FDSR) and analyzes fund investment style drift based on the elastic-fractal dimension CIS, according to the fractal characteristic of capital market. Compared to the previous identification method, this method is able to avoid style assets having multi-collinearity or lacking T-statistic significant test and other defects;
3.This paper proposes analysis the fund investment style drift method based on elastic- fractal dimension, and deduces the computing formula of elastic-fractal dimension.In addition, this paper gives the threshold of investment style drift by mining its economic implications, which provides a new kind of research on fund investment style drift and may become a new tool to measure and control the fund investment style drift risk;
4.This paper quantifies fund investment style drift and derives investment style drift return formula. It modifies the traditional MF-DFA and put forword the multi-fractal analysis method of sliding window MF-DFA. The method makes an improvement in data loss and sequence inversion and reduces analysis result error. And use the modified method to analyze the multi-fractal characteristic and spectrum parameter of investment style drift return;
5.This paper extracts the multifractal volatility measurement according to multifractal spectrum parameter and singularity exponent, and constructs a MF-VaR model to measure investment style drift risk. This paper uses the MF-VaR model to measure investment style drift risk of 79 open-end funds, whose measurement results are more precise and robust than the latest GARCH family high-level econometric models.
引文
注7国内学者最早进行实证研究的见熊鹏,刘煜辉.近四成投资基金“言行不一”[J].新财富,2003,(11):40-42.
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