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Corporate finance tri vi dang columbia university

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Unformatted text preview: h E[r]=x% Which portfolio with E[r]=x% has minimal variance. Minimization problem: min V subject to (1 ,.., N ) N i E[ri ] x i 1 i 1 N i 1 N N i 1 i 1 min L V 1 ( i E[ri ] x) 1 ( i E[ri ] 1) (1 ,.., N ) Corporate Finance, Tri Vi Dang, Columbia University, Fall 2013 31 FOC dL 0 d 1 dL 0 d 2 dL 0 d N Solution to the equation system with N equations and N unknowns is the optimal portfolio. Remark: See Exercise 3. Corporate Finance, Tri Vi Dang, Columbia University, Fall 2013 32 I.1.O. CAPM Corporate Finance, Tri Vi Dang, Columbia University, Fall 2013 33 Assumptions All agents (only) care about mean and variance (or have quadratic utility) Or all assets are normally distributed. There exists a riskless asset with the risk free rate rf . Implications All agents will hold the market portfolio and the risk free asset. The contribution of risk of asset i to the variance of the market portfolio is given by the covariance between asset i and the market portfolio and PF α i ² σ i ² 2α i α M σ iM α M ² σ M ² Corporate Finance, Tri Vi Dang, Columbia University, Fall 2013 34 Theorem (CAPM) Given the assumption above, the equilibrium expected return of asset i is given by: i rf ( M rf ) β i where cov(x j , m) βi σM ² . Corporate Finance, Tri Vi Dang, Columbia University, Fall 2013 35 Remark Now we have a theory of the interest rate and we can use it to discount expected payoff of a project...
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This document was uploaded on 02/16/2014 for the course ECON w4280 at Columbia.

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