半均衡定价 : CAPM 公式 (Semi-Equilibrium Pricing: The CAPM Formula)

Chinese abstract: 我们发现了半均衡定价方法，它先求解投资者的最优组合，这一步与均衡定价方法一致，但半均衡定价的第二步只使用市场出清条件的一部分而不是全体约束。据此，我们揭示了 CAPM 公式不是均衡定价公式，而是半均衡定价公式：CAPM 公式成立时不能确保市场出清，只有给定风险证券总市值，CAPM 公式才能完全确定出基本证券的价格。此外，我们指出，SDF 定价公式是投资者实施组合优化的结果，它以线性定价函数的形式呈现，可以作为创建定价函数的基础模板。English abstract: We discover a new pricing method, the semi-equilibrium pricing method, which first solves the optimal portfolios of investors. This step is consistent with the equilibrium pricing method, but the second step of semi-equilibrium pricing method uses only a part of the market clearing conditions rather than the whole. Based on this, we show that the CAPM (Capital Asset Pricing Model) formula is not an equilibrium pricing formula, but a semi-equilibrium pricing formula: When the CAPM formula is valid, the market may not be cleared. Only when the total market value of risky securities is given, can the CAPM formula completely determine the price vector of the risky securities. In addition, we point out that the SDF (Stochastic Discount Factor) pricing formula is the result of investor's portfolio optimization and is presented in the form of a linear pricing function, can be used as a foundation template to establish pricing functions