Assets Pricing 资产定价（一）

Assets Pricing 资产定价（一）

文章目录

• • Lec 2 Equilibrium Pricing 均衡定价理论
  • • Consumption, Investment and Pricing in Capital Market: Certainty Case
    • Decision Making under Uncertainty: The Expected Utility Hypothesis 预期效用假设
    • • Expected Utility in Investment 期望效用
      • Risk preference and Utility function

Lec 2 Equilibrium Pricing 均衡定价理论

equilibrium 市场均衡

在CAPM中意味着same Sharpe Ratio

在APT中意味着no arbitrage

Consumption, Investment and Pricing in Capital Market: Certainty Case

Generalization of the Decision Process two steps:

• First choose the optimal production decision by taking on projects until the marginal rate of return on investment equals the market rate (市场利率).
• Choose the optimal consumption pattern by borrowing or lending along the market line to equate your subjective time preference ( r i r_i ri​) with the market rate of return (市场利率).

The Separation of Investment and Consumption in making decision is known as Fisher Separation Theorem (费雪定理)：

• Given perfect and complete capital markets, the production decision is governed by an objective market criterion (represented by attained wealth) without regard to the individuals’ subjective preferences which enter into their consumption decisions.

  完全竞争市场

  生产决策只受客观的市场标准决定而不考虑个人偏好

  在此之后才会进入基于个人偏好的消费决策

  费雪分离定理说明，投资决策和消费决策是分离的。

Decision Making under Uncertainty: The Expected Utility Hypothesis 预期效用假设

Expected Utility in Investment 期望效用

U ( x ~ ) = E ( u ( x ) ) = ∫ − ∞ ∞ u ( x ) f ( x ) d x = ∫ − ∞ ∞ u ( x ) d F ( x ) U(tilde x)=E(u(x))=int_{-infty}^{infty}u(x)f(x)dx=int_{-infty}^{infty}u(x)dF(x) U(x~)=E(u(x))=∫−∞∞​u(x)f(x)dx=∫−∞∞​u(x)dF(x)

f ( x ) f(x) f(x) is the probability density function (p.d.f) of random variable X X X.

F ( x ) F(x) F(x) is the distribution function (c.d.f) of random variable X X X.

U ( ⋅ ) U(·) U(⋅) is called VNM utility function.

Risk preference and Utility function

Jensen’s Inequality Theorem: Suppose u ′ ′ ( ⋅ ) ≤ 0 u''(·)leq 0 u′′(⋅)≤0, X X X is a random variable, then E [ u ( X ) ] ≤ u ( E [ X ] ) E[u(X)]leq u(E[X]) E[u(X)]≤u(E[X]).

f ( ⋅ ) f(·) f(⋅) is concave, i.e. f ′ ′ ( ⋅ ) < 0 f''(·)<0