翻訳と辞書 Words near each other ・ Interswitch ・ InterSwitch Trunk ・ Intersymbol interference ・ Intersystem crossing ・ InterSystems ・ InterSystems Caché ・ InterTAN ・ Intertarsal articulations ・ Intertec Superbrain ・ Intertec Systems ・ Intertech ・ Intertek ・ Intertek Consumer Goods and Retail ・ Intertel ・ Intertemporal budget constraint ・ Intertemporal CAPM ・ Intertemporal choice ・ Intertemporal consumption ・ Intertemporal equilibrium ・ Intertemporal law ・ Intertemporal portfolio choice ・ Intertestamental period ・ Intertex ・ Intertextuality ・ Interthalamic adhesion ・ Intertheoretic reduction ・ Intertidal ecology ・ Intertidal spider ・ Intertidal wetland ・ Intertidal zone Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Intertemporal CAPM ： ウィキペディア英語版 Intertemporal CAPM The Intertemporal Capital Asset Pricing Model, or ICAPM, was an alternative to the CAPM provided by Robert Merton. It is a linear factor model with wealth and state variable that forecast changes in the distribution of future returns or income. In the ICAPM investors are solving lifetime consumption decisions when faced with more than one uncertainty. The main difference between ICAPM and standard CAPM is the additional state variables that acknowledge the fact that investors hedge against shortfalls in consumption or against changes in the future investment opportunity set. ==Continuous time version== Merton considers a continuous time market in equilibrium. The state variable (X) follows a brownian motion: :$dX\; =\; \backslash mu\; dt\; +\; s\; dZ$ The investor maximizes his Von Neumann–Morgenstern utility: :$E\_o\; \backslash left\backslash$ whereT is the time horizon and B() the utility from wealth (W). The investor has the following constraint on wealth (W). Let $w\_i$ be the weight invested in the asset i. Then: :$W(t+dt)\; =\; (-C(t)\; dt)\backslash sum\_^n\; w\_i(r\_i(t+\; dt))$ where $r\_i$ is the return on asset i. The change in wealth is: :$dW=-C(t)dt\; +()\backslash sum\; w\_i(t)r\_i(t+dt)$ We can use dynamic programming to solve the problem. For instance, if we consider a series of discrete time problems: :$\backslash max\; E\_o\; \backslash left\backslash \backslash int\_t^\; U()ds\; +\; B()\; \backslash right\backslash \}$ Then, a Taylor expansion gives: : where $t^$ * is a value between t and t+dt. Assuming that returns follow a brownian motion: :$r\_i(t+dt)\; =\; \backslash alpha\_i\; dt\; +\; \backslash sigma\_i\; dz\_i$ with: :$E(r\_i)\; =\; \backslash alpha\_i\; dt\; \backslash quad\; ;\backslash quad\; E(r\_i^2)=var(r\_i)=\backslash sigma\_i^2dt\; \backslash quad\; ;\backslash quad\; cov(r\_i,r\_j)\; =\; \backslash sigma\_dt$ Then canceling out terms of second and higher order: :$dW\; \backslash approx\; (\backslash sum\; w\_i\; \backslash alpha\_i\; -\; C(t))dt+W(t)\; \backslash sum\; w\_i\; \backslash sigma\_i\; dz\_i$ Using Bellman equation, we can restate the problem: :$J(W,X,t)\; =\; max\; \backslash ;\; E\_t\backslash left\backslash$ subject to the wealth constraint previously stated. Using Ito's lemma we can rewrite: :$dJ\; =\; J()-J()=\; J\_t\; dt\; +\; J\_W\; dW\; +\; J\_X\; dX\; +\; \backslash fracJ\_\; dX^2\; +\; \backslash fracJ\_\; dW^2\; +\; J\_\; dX\; dW$ and the expected value: :$E\_t\; J()=J()+J\_t\; dt\; +\; J\_W\; E()+\; J\_X\; E(dX)\; +\; \backslash frac\; J\_\; var(dX)+\backslash frac\; J\_\; var()\; +\; J\_\; cov(dX,dW)$ After some algebra〔:$E(dW)=-C(t)dt\; +\; W(t)\; \backslash sum\; w\_i(t)\; \backslash alpha\_i\; dt$ :$var(dW)\; =\; ()^2\; var(\backslash sum\; w\_i(t)r\_i(t+dt))=\; W(t)^2\; \backslash sum\_\; \backslash sum\_\; w\_i\; w\_j\; \backslash sigma\_\; dt$ :$\backslash sum\_^n\; w\_i(t)\; \backslash alpha\_i\; =\; \backslash sum\_^n\; w\_i(t)(-\; r\_f)\; +\; r\_f$〕 , we have the following objective function: :$max\; \backslash left\backslash ^n">w\_i(\backslash alpha\_i-r\_f)+r\_f\; )\; -\; J\_WC\; +\; \backslash frac\; J\_\backslash sum\_^n\backslash sum\_^n\; w\_i\; w\_j\; \backslash sigma\_\; +\; J\_X\; \backslash mu\; +\; \backslash fracJ\_\; s^2\; +\; J\_\; W\; \backslash sum\_^n\; w\_i\; \backslash sigma\_\; \backslash right\backslash \}$ where $r\_f$ is the risk-free return. First order conditions are: :$J\_W(\backslash alpha\_i-r\_f)+J\_W\; \backslash sum\_^n\; w^$ *_j \sigma_ + J_ \sigma_=0 \quad i=1,2,\ldots,n In matrix form, we have: :$(\backslash alpha\; -\; r\_f\; )\; =\; \backslash frac\; \backslash Omega\; w^$ * W + \frac cov_ where $\backslash alpha$ is the vector of expected returns, $\backslash Omega$ the covariance matrix of returns, $$ a unity vector $cov\_$ the covariance between returns and the state variable. The optimal weights are: :$=\; \backslash frac\backslash Omega^(\backslash alpha\; -\; r\_f\; )\; -\; \backslash fracW\}\backslash Omega^\; cov\_$ Notice that the intertemporal model provides the same weights of the CAPM. Expected returns can be expressed as follows: :$\backslash alpha\_i\; =\; r\_f\; +\; \backslash beta\_\; (\backslash alpha\_m\; -\; r\_f)\; +\; \backslash beta\_(\backslash alpha\_h\; -\; r\_f)$ where m is the market portfolio and h a portfolio to hedge the state variable. 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「Intertemporal CAPM」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.