wind8868 发表于 2012-2-6 03:18 
alpha 是回归方程式中的常数项. 现实点说, 指一个投资组合和指数大盘不相关的收益. 如果这个收益是正而beta ...
LS
的解答。我找了一些关于alpha
的资料,本来以为资料中的alpha
和LS
说的不一样,后来终于发现原来是一回事。
Definition: Alpha, or Jensen's alpha, is a measurement used to determine how well an asset or portfolio performed relative to its expected return predicted by an equilibrium model like the capital asset pricing model (CAPM). In efficient markets alpha is assumed to be zero, but if an asset over- or under-performs its expected return relative to risk, it could receive a positive or negative alpha respectively.
I've found two types of expression of alpha, which prove to be identical.
The first is known as the Jensen's alpha, calculated as follows by substituting the CAPM formula for E(Ri) and when βi is publicly available:
αi=Ri-E(Ri)=Ri-[Rf+βi(E(RM)-Rf)]         (1.1)
where Ri is the realized return on the portfolio,
E(Ri) is the expected return on the portfolio,
E(RM) is the expected market return,
Rf is the risk-free rate of return,
βi is the beta coefficient of the portfolio.
The second is the original definition of alpha, known as the intercept of the SCL (security characteristic line), a regression line plotting performance of a particular security or portfolio against that of the market portfolio at every point in time:
Ri,t-Rf=αi+βi(RM,t-Rf)+εi,t               (1.2)
where αi is called the portfolio’s alpha, meaning the abnormal rate of return.
When βi is unavailable, both coefficients αi and βi can be obtained through a simple regression of the SCL, hereinto
αi=avg(Ri,t-Rf)-βiavg(RM,t-Rf)= Ri-[Rf+βi(E(RM)-Rf)]
which is identical to equation (1.1).