Capital Asset Pricing Model[资本资产计价模型]
(CAPM[资本资产计价模型])

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总结

资本资产计价模型(Capital Asset Pricing Model,CAPM是结合风险与预期回报,对股票、债券、金融衍生品以及其他资产进行估价的一个经济工具。 CAPM的基本思想是——如果投资者必须接受额外风险,他们必然期望得到额外回报(即风险溢价)。


什么是CAPM 释义。

CAPM理论由Treynor(1961)、Sharpe(1964)和Lintner(1965)三位学者先后提出, CAPM通过引入系统性风险(Systemactic Risk特殊风险(Specific Rish概念,扩展了投资组合理论。 1990年,William Sharpe荣获诺贝尔经济学奖, 其获奖原因是“对金融资产价格构成理论——CAPM的发展做出了杰出贡献”。


CAPM认为, 投资者的预期回报等于无风险证券的回报率+风险溢价(Risk Premium)。 如果预期回报不等于,或者说超越要求回报,投资者则应该拒绝投资。

CAPM将投资组合风险分解为系统性风险(Systemactic Risk)和特殊风险(Specific Rish)。 系统性风险是指影响整个投资组合即多种资产的风险, 当市场变化运动时,每一项资产都随之增减。 每一项资产在一定程度上都在做这种市场增减变化,所以它们普遍承受着系统性风险。 特殊风险,则是指影响个别资产的风险, 它说明这项资产的回报与市场运动并无关联。

根据CAPM,市场只对系统性风险进行补偿, 因为特殊风险变化不定,而不予补偿。 任何投资组合中的每一单项资产都承受着特殊风险, 但是,由于投资多样化,投资者在市场上净暴露(Net Exposure)出的只有投资组合的系统性风险。


CAPM的公式

公式:

证券的预期收益 = 无风险证券的回报率 + 证券的贝塔系数 X 预期市场风险溢价

或:
r = Rf + beta x (RM - Rf)
 

{      亦或: r - Rf = beta x (RM - Rf)       }


其中,
- r            是证券的预期回报率;
- Rf          是无风险投资回报率,比如现金;
- RM        是预期市场回报。
 

贝塔系数(Beta)是指总体市场投资风险,如纽约证券交易所面对的市场风险。 贝塔系数的准确值被定义为1,00000。

此外,每个公司分别有一个自己的贝塔系数。 公司贝塔系数值是公司面对的风险与总体市场风险的比值。 例如,公司贝塔系数值为3.0,即说明公司所面的风险是总体市场风险的3倍。 贝塔系数揭示了证券相对于资产类别的挥发性。


单种证券投资

CAPM理论最终说明,投资单种证券是没有意义的,因为别人可以通过适当的资产类别、相同的资金组合,轻易地复制你的投资回报以及风险特征, 这也就是为什么CAPM理论的铁杆追随者们尽量避免投资有价证券,而在低价基金上建立投资组合。


CAPM的假设

请注意! CAPM是一个假设其他条件不变的模型, 只有在一定前提下,它才有效。 这些假设是:

  • 投资者反感风险,只对期末财富的最大化感兴趣。 暗含: CAPM有时间性,以一段时间为框架。
  • 投资者们对于资产回报有着相同的期望(信心)。 暗含: 所有投资者对市场机会有着同样的感知, 这就是说每个投资者在相同时间内获取相同信息。
  • 市场回报通过正态分布来分配。
  • 市场上存在一种无风险资产,投资者能够无限量借贷这种资产,并按照恒定不变的利率, 即无风险率。
  • 所有资产都有一个明确的数值,且在一定时期内保持固定不变。
  • 所有资产都可以完全分割,并在充分竞争的市场环境下进行定价。 暗含: 人力资本是不存在的,因为它不可分割,不能作为资产被拥有。
  • 资产市场没有摩擦,所以信息同时面向每一个投资者,且无偿使用。 暗含: 借款利率等于贷款利率。
  • 没有所谓的市场不完善,诸如税收、行规、限制或短缺,等等。

正常情况下,以上假设既不正确,也不现实。 然而, CAPM[资本资产计价模型]无论如何保持确定风险和返回的其中一个最常用投资模型。


参考书: William F. Sharpe - Portfolio Theory and Capital Markets [中译本《投资组合理论与资本市场》,机械工业出版社,2001]

参考书: Harry M. Markowitz - Mean-Variance Analysis in Portfolio Choice and Capital Markets

参考书: Mary Jackson - Advanced modelling in finance using Excel and VBA [中译本《基于Excel和VBA的高级金融建模》,中国人民大学出版社,2006]


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