均值方差均衡下的证券价格: CAPM 再认识 (Security Prices in Mean-Variance Equilibrium: A Further Study on CAPM)

Chinese Abstract: CAPM 所在的资本市场是非完全的,并且是 一 个 Hilbert 空间,我们找出了该市场中 SDF 模仿支付的显式表达式。纯风险证券的局部均衡中,CAPM 公式成立,CAPM 等价于市场组合恰好为切点组合,并且证券价格的通解在一维空间中。给定投资者的禀赋和均值方差偏好,结合 CAPM 的价格通解,资本市场的均衡条件转化为单变量的方程,从而求得均值方差均衡价格的解析解。证券价格是内生的,全体风险证券是作为 一 个整体被定价的,貌似真实的风险决定收益是局部均衡的产物,其错误在于把市场收益率当成外生的。我们还通过数值例子,分析均值方差决策与无套利的关系,化解不可能前沿的危机,展示贝塔定价导致欧式看涨期权负价格,以及不可以使用贝塔估计权益资本成本。CAPM 实证方面,我们区分了均衡收益率与时序收益率,讨论被忽视的 DGP 和平稳性等问题,并结合均衡解析解给出针对预测型因子模型的建议。 English Abstract: The capital market for CAPM is incomplete and is a Hilbert space, we find out the analytic expression for the SDF mimicking payoff in this market. CAPM is equivalent to the condition that the market portfolio is the tangent portfolio. CAPM holds under the partial equilibrium of pure risky assets, and the general solution to asset prices has only one dimension. Given investor’s endowment and mean-variance preference, applying the general solution from CAPM, the condition of market equilibrium turns out to be an equation of only one variable, from which we work out the closed form solutions. By the mistake that the return of market portfolio is assumed to be exogenous, the risk-return characteristics is a concept from the partial equilibrium of pure risky assets, thus it is illusory, for the assets are priced as a whole and the prices are endogenous. By way of numerical examples, we explore the relationship between mean-variance equilibrium and free of arbitrage, defuse the crisis of impossible frontier, present the negative price of European call option pricing by beta, and point out the incorrect practice of the estimation of cost of equity by beta. On the empirical study of CAPM, we emphasize the difference between rate of return in mean- variance equilibrium and the one computed by price time series. We discuss the unnoticed issues such as DGP, stationarity and others. For the predictive factor models, we provide suggestions based on the closed form solution of mean-variance equilibrium.