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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Stochastic discount factor ： ウィキペディア英語版 Stochastic discount factor A Stochastic discount factor (SDF) is a concept in financial economics and mathematical finance. If there are n assets with initial prices $p\_1,\; ...,\; p\_n$ at the beginning of a period and payoffs $\backslash tilde\_1,\; ...,\; \backslash tilde\_n$ at the end of the period (all x's are random variables), then SDF is any random variable $\backslash tilde$ satisfying :$E(\backslash tilde\backslash tilde\_i)\; =\; p\_i,\; \backslash quad\; \backslash forall\; i.$ 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 $\backslash tilde\_i$ by the stochastic factor $\backslash tilde$ and then taking the expectation. == Properties == If each $p\_i$ is positive, by using $R\_i\; =\; \backslash tilde\_i\; /\; p\_i$ to denote the return, we can rewrite the definition as :$E(\backslash tilde\backslash tilde\_i)\; =\; 1,\; \backslash quad\; \backslash forall\; i,$ and this implies :$E((\backslash tilde\_i\; -\; \backslash tilde\_j))\; =\; 0,\; \backslash quad\; \backslash forall\; i,j.$ Also, if there is a portfolio made up of the assets, then the SDF satisfies :$E(\backslash tilde\backslash tilde)\; =\; p,\; E(\backslash tilde\backslash tilde)\; =\; 1.$ Notice the definition of covariance, it can also be written as :$1\; =\; cov\; (\backslash tilde,\; \backslash tilde)\; +\; E(\backslash tilde)\; E(\backslash tilde).$ Suppose there is a risk-free asset. Then $\backslash tilde\; =\; R\_f$ implies $E(\backslash tilde)\; =\; 1/R\_f$. Substituting this into the last expression and rearranging gives the following formula for the risk premium of any asset or portfolio with return $\backslash tilde$: :$E(\backslash tilde)\; -\; R\_f\; =\; -R\_f\; cov\; (\backslash tilde,\; \backslash tilde).$ 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 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.