# L3v - ECON 3107/ECON5106 Lecture 3 Valuation Opportunity Sets Valentyn Panchenko The Opportunity Set Denition A set of feasible future payos

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ECON 3107/ECON5106 Lecture 3 Valuation: Opportunity Sets Valentyn Panchenko

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The Opportunity Set Deﬁnition: A set of feasible future payoﬀs available with a wealth of one unit of present value. Example: The opportunities for future apples for a present apple invested: Q { states*securities } is the payment matrix of the two securities: Q ( 2 × 2 ) = ± 20 43 20 28 ² Bond Stock Good Weather Bad Weather p S { 1*securities } is a vector of security prices: p S ( 1 × 2 ) = ( 19.0 30.875 ) Bond Stock
Value Relative Deﬁnition: Value relative associated with a given state of nature is the future payment per unit invested, that will be received if that state occurs. In our example the matrix for the value relatives is: vr ( 2 × 2 ) = ± 20 / 19 43 / 30.875 20 / 19 28 / 30.875 ² Bond Stock Good Weather Bad Weather = ± 1. 052 6 1. 392 7 1. 052 6 0.906 9 ² Bond Stock Good Weather Bad Weather The following script will do the job in MATLAB’s command prompt: >> Q = [20 43; 20 28]; >> ps = [19 30.875]; >> vr = Q./[ps; ps];

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Derivative securities By combining existing securities (the bond and the stock), one can synthesize a security that does not exist (e.g. a state-contingent
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## This note was uploaded on 07/13/2011 for the course ECON 3107 at University of New South Wales.

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L3v - ECON 3107/ECON5106 Lecture 3 Valuation Opportunity Sets Valentyn Panchenko The Opportunity Set Denition A set of feasible future payos

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