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A Stochastic discount factor (SDF) is a concept in financial economics and mathematical finance. If there are n assets with initial prices at the beginning of a period and payoffs at the end of the period (all x's are random variables), then SDF is any random variable satisfying : This definition is of fundamental importance in asset pricing. The name "stochastic discount factor" reflects the fact that the price of an asset can be computed by "discounting" the future cash flow by the stochastic factor and then taking the expectation. == Properties == If each is positive, by using to denote the return, we can rewrite the definition as : and this implies : Also, if there is a portfolio made up of the assets, then the SDF satisfies : Notice the definition of covariance, it can also be written as : Suppose there is a risk-free asset. Then implies . Substituting this into the last expression and rearranging gives the following formula for the risk premium of any asset or portfolio with return : : This shows that risk premiums are determined by covariances with any SDF. The existence of an SDF is equivalent to the law of one price. The existence of a strictly positive SDF is equivalent to the absence of arbitrage opportunities. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「stochastic discount factor」の詳細全文を読む スポンサード リンク
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