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摘要上世纪50年代，Markkowitz基于收益率和风险关系建立了资产组合模型，随后Sharp，Lintner和Mossin相继发现了资本资产定价模型（CAPM）。CAPM以其简单的建立条件为投资组合风险评估分析提供了原始的基础。但是，在其建立的假设条件中，CAPM假定无风险资产的借贷都是同一利率，然而事实上，精明的投资者面对存在利差的情况下，作出的投资方案是有很大区别的，投资组合的收益率不仅跟系统风险有关系，还会因其他因素改变。因此，探讨不同借贷利率情况下资产组合的有效边界是很有意义的。4503
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本文引入了不同的无风险资产借贷利率对CAPM模型进行修正，简要地对传统的CAPM模型进行推导，在理论方面分析加入不同借贷利率CAPM模型假设条件的变化，随后引入借贷利率不同的条件再次推导出新的CAPM模型。最后，选取上证基金通筛选后的7只基金2014年2月1日到2014年12月31日数据贷入模型，运用Eviews7.2软件进行实证分析研究，并比较传统模型与引入利差的模型的结果的前后差异。得出如下结论:（1）不同借贷利率条件下的CAPM的有效前沿不再是一条线段，而变成了两条线段之间夹一小段曲线，也就是说新模型变成了分段函数。（2）在不同借贷利率条件下同时有可能使得投资者的投资效用变小。（3）由实证得出，中国股市市场更适合存在不同借贷利率的CAPM模型。
[关键词]：CAPM模型；有效边界；不同借贷利率
Abstract
In the 50's of last century, based on the relationship between yield and risk, Markkowitz established the asset portfolio model. Followed by Sharp, Lintner and Mossin have improved the capital asset pricing model (CAPM). The simple establishment condition of CAPM provides the original foundation for the analysis of portfolio risk. But in the assumptions of the establishment of the CAPM assumes no risk asset of borrowing and lending is the same interest rate. However in fact, savvy investors face interest rate difference and make the investment plan is very different, portfolio yields not only with the system risk relationship, but also due to other factors change. Therefore, it is significant to explore the effective boundary of asset portfolio under different loan interest rates.
This paper introduces the different risk free asset lending rates by modifying the CAPM model, the traditional CAPM model are briefly deduced, analysis changes with different lending rates CAPM model assumptions in theory, then introduce different interest rates conditions again derived from the new CAPM model. Finally, select the Shanghai fund after screening 7 funds from February 1, 2014 to December 31, 2014 data is credited to model, analyze and research the use of Eviews7.2 software, and compared the difference between before and after the traditional model and the results of the model spreads. Draw the following conclusions: (1) the effective frontier under different loan interest rates of the CAPM is no longer a segment, and between the two lines into a short clip curve, that is to say the new model into a piecewise function. (2) in different conditions at the same time, lending rates may make investors less utility. (3) by the empirical analysis, China stock market CAPM model is more suitable for different loan interest rates.
[Key Words]：CAPM；Effective boundary; different interest rates
目 录
摘 要I AbstractII
1、绪论1
1.1问题的提出1
1.2有关不同借贷利率下CAPM模型的文献综述1
1.3研究方法与结构2
2、资本资产定价模型（CAPM）2
2.1资本资产定价模型产生的背景3
2.2资本资产定价模型的假设条件 4
3、不同借贷利率的新资本资产定价模型（CAPM）4
3.1引入不同借贷利率的CAPM模型的假设条件5
3.2不同借贷利率的CAPM模型的的推导10