Self-consistent asset pricing models

We discuss the foundations of factor or regression models in the light of the self-consistency condition that the market portfolio (and more generally the risk factors) is (are) constituted of the assets whose returns it is (they are) supposed to explain. As already reported in several articles, self-consistency implies correlations between the return disturbances. As a consequence, the alphas and betas of the factor model are unobservable. Self-consistency leads to renormalized betas with zero effective alphas, which are observable with standard OLS regressions. When the conditions derived from internal consistency are not met, the model is necessarily incomplete, which means that some sources of risk cannot be replicated (or hedged) by a portfolio of stocks traded on the market, even for infinite economies. Analytical derivations and numerical simulations show that, for arbitrary choices of the proxy which are different from the true market portfolio, a modified linear regression holds with a non-zero value α_i at the origin between an asset i's return and the proxy's return. Self-consistency also introduces “orthogonality” and “normality” conditions linking the betas, alphas (as well as the residuals) and the weights of the proxy portfolio. Two diagnostics based on these orthogonality and normality conditions are implemented on a basket of 323 assets which have been components of the S&P500 in the period from January 1990 to February 2005. These two diagnostics show interesting departures from dynamical self-consistency starting about 2 years before the end of the Internet bubble. Assuming that the CAPM holds with the self-consistency condition, the OLS method automatically obeys the resulting orthogonality and normality conditions and therefore provides a simple way to self-consistently assess the parameters of the model by using proxy portfolios made only of the assets which are used in the CAPM regressions. Finally, the factor decomposition with the self-consistency condition derives a risk-factor decomposition in the multi-factor case which is identical to the principal component analysis (PCA), thus providing a direct link between model-driven and data-driven constructions of risk factors. This correspondence shows that PCA will therefore suffer from the same limitations as the CAPM and its multi-factor generalization, namely lack of out-of-sample explanatory power and predictability. In the multi-period context, the self-consistency conditions force the betas to be time-dependent with specific constraints.     

组合投资与资本资产定价模型

根据效用理论 ,投资者在期望效用最大化准则下选择组合投资方案 ,通过改进均值 -方差模型假定 ,在完全市场 ( perfect markets)条件下由组合投资模型推导出广义的资本资产定价模型 .并证明了在投资者具有二次效用 ,或者收益率服从联合正态分布的情形下 ,它与夏普 -林特纳的资本资产定价模型 ( CA PM)一致     

对资本资产定价模型(CAPM)的检验

本文先将 CAPM模型由事前模型转换为可以使用历史数据的事后模型 ,然后用沪市的 17只股票对 CAPM模型进行检验 ,检验结果表明对沪市股票而言基本可以接受 CAPM模型     

Term structure of discount rates for firms in the insurance industry

There is strong evidence in the literature for the hypothesis that interest rates and the market risk premium are not constant during the business cycle. The beta risk of firms in the insurance industry is also time-varying. The major implication of these results is that discount rates for risky cash flows are time varying and must obey a term structure similar to the term structure of interest rates. The purpose of this paper is to estimate discount rates for cash flows with different time horizons for the U.S. insurance industry and for different insurance sectors. We find that the term structure cost of capital takes on different shapes depending on the business cycle. It is therefore meaningful for insurers to evaluate risky projects by selecting a discount rate most appropriate for the nature and the time horizon of each project.     

多重时间标度鞅半方差与加权鞅半方差β系数研究

本文根据投资者持有资产周期的不同,提出了基于小波多分辨率分析的多重时间标度CAPM模型,得到多重时间标度β系数。由于投资者在进行投资时更关注下行风险,本文进一步提出了基于鞅半方差与加权鞅半方差的下行β系数计算方法,并通过实证检验证明了用鞅半方差β系数与加权鞅半方差β系数来衡量系统风险较其他方法更具合理性及优越性。最后,本文将小波多分辨率分析与鞅半方差β系数及加权鞅半方差β系数结合,得到多重时间标度下的鞅半方差β系数及加权鞅半方差β系数计算方法。     

两类资产组合有效前沿边界的相切关系的严格证明

讨论了资本资产定价模型(CAPM)中两类资产组合有效前沿边界的相切关系,介绍了一些著作和教科书中对它的处理方式,事实上他们均未给出严格意义上的证明.本文对两类资产组合有效前沿边界的相切关系给出了三种较严格的证明.     

A note on a mean-lower partial moment CAPM without risk-free asset

The standard capital asset pricing model (CAPM) is invalid if the risk-free asset ceases to exist or if the risk-free lending and borrowing rates are different. In the mean–variance (MV) framework, we have an alternative model known as zero-beta CAPM. However, in the case of mean-lower partial moment (MLPM) framework, there is no such alternative. This article addresses this issue and develops an equivalent MLPM model, which is valid for situations described above. The MV zero-beta CAPM can be seen as a special case of this model.