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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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）和特殊风险（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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