资本预算中的确定当量法之澄清

A Clarification on the Certainty Equivalence Approach in Capital Budgeting

摘要:

与风险调整折现率法不同，主观确定当量法无法得到一个投资项目的客观估值结果。即使给定决策主体，主观确定当量本身也难以同时满足可加性和可乘性，因而不能保证投资项目评估结果的逻辑一致性。对二叉树模型的无套利分析揭示了确定当量法、风险调整折现率法和风险中性概率法这三种估值方法之间的联系，并发现确定当量这一概念本质上应当是风险中性期望。在资本资产定价模型成立的条件下，给出了客观确定当量的计算公式。

Abstract:

Unlike the risk adjusted discount rate (RADR) approach, the (subjective) certainty equivalence (CEQ) approach can not results in objective valuation results. Moreover, (subjective) CEQ derived from popular utility functions such as CARA and CRRA normally can not satisfy the requirements of additivity and multiplicativity simultaneously, hence this approach could lead to contradictions during capital budgeting, even under the viewpoints of a given decision maker. Analysis based on the non-arbitrage axiom in a binomial model reveals the relationship among RADR, CEQ, and risk neutral probability (RNP) approach, which implies that CEQ used in capital budgeting should be the risk-neutral expectation in nature. (Objective) CEQ formulated in beta and market risk premium with absolute prices in the CAPM framework restores its objective nature and facilitates its application.