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09_tels

Course: ECON 157, Spring 2008
School: Duke
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157 Economics Tauchen Notes on Telser's Criterion Fall 1999 Telser's criterion is to maximize subject to p = Erp ; Prrp rL ; where rp is the portfolio return, is a small number, e.g., = 0:05 and rL is some predetermined lower limit. If returns are normally distributed then Prrp rL = Pr rp , rL p , p = rL , p : p p p If = 0:05; then to ensure the constraint Prrp rL = 0:05 is satis ed, we must have rL ,...

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157 Economics Tauchen Notes on Telser's Criterion Fall 1999 Telser's criterion is to maximize subject to p = Erp ; Prrp rL ; where rp is the portfolio return, is a small number, e.g., = 0:05 and rL is some predetermined lower limit. If returns are normally distributed then Prrp rL = Pr rp , rL p , p = rL , p : p p p If = 0:05; then to ensure the constraint Prrp rL = 0:05 is satis ed, we must have rL , p p ,1:65: 1 Another way to write the constraint 1 is p ...

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Duke - ECON - 157
Economics 157 TauchenFall 1999Suppose the returns generating process isriFirst Look at APT= i + biF +rpi;i= 1; 2; : : : ; Ni;2where EF = 0; VarF = is whereF;2E i = 0; Var i =CovF; i = 0: The portfolio returnPN p=i=1 w
Duke - ECON - 157
Economics 157 TauchenFall 1999The APTThe Returns Process:For simplicity, we use a J = 2 factor model for the returns generating process: ri = i + bi1 F1 + bi2 F2 + i ; i = 1; 2; : : : ; N 1 where F1 and F2 are two common random risk factors s
Duke - ECON - 157
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Duke - ECON - 157
Economics 157 Tauchen The recent history of U.S. data is shown below:20 15 10 5 0 1960 20 15 10 5 0 1960 20 15 10 5 0 1960 1965 1970 1975 1980 1985 1990 1965 1970 1975 1980 1985 US 10Year Rate 1990 1965 1970 1975 1980 1985 US 1Year Rate 1990Fall 1
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Economics 157 TauchenFall 1999Fixed Income and DurationT T TValuationTConsider a portfolio of bonds with cash ows G1; G2; : : : :; G ; in periods j = 1; 2; : : : ; J: The value of the portfolio is X G V0 =J JLet denote the price of a pu
Duke - ECON - 157
Economics 157 TauchenFall 1999We want to derive the relationship between asset prices and payouts. Let Y denote the random payout of an asset with mean EY and variance Var Y. Think of Y as the total pro t one period hence of a particular investm
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Duke - ECON - 157
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Duke - ECON - 157
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Duke - ECON - 157
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Duke - ECON - 157
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Duke - ECON - 157
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Duke - ECON - 157
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Economics 157 TauchenSpring 1999The gure below shows below shows the Standard and Poor's Composite Price Index The market" from January 1, 1971 April 8, 1999.Levels Series 1200Standard and Poor's Composite Index10008006004002000 19
Duke - ECON - 157
Economics 157 Tauchen The recent history of U.S. data is shown below:20 15 10 5 0 1960 20 15 10 5 0 1960 20 15 10 5 0 1960 1965 1970 1975 1980 1985 1990 1965 1970 1975 1980 1985 US 10Year Rate 1990 1965 1970 1975 1980 1985 US 1Year Rate 1990Spring
Duke - ECON - 157
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Duke - ECON - 157
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Duke - ECON - 157
Economics 157 TauchenSpring 1999Valuation FormulasThe Constant Growth ModelWe assume, for now, that g k else the sum is in nite, which is totally unrealistic. Recall the formula for a geometric series 1 1 ; 2 ai = 1 , a i=0 which gives the va