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Ch08 - Chapter 8 Time Value of Money Road Map Part A...

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Chapter 8 Time Value of Money Road Map Part A Introduction to Finance. Part B Valuation of assets, given discount rates. Part C Determination of discount rates. Historical asset returns. Time value of money. Risk. Portfolio theory. Capital Asset Pricing Model (CAPM). Arbitrage Pricing Theory (APT). Part D Introduction to corporate. Main Issues Theroy of Real Interest Rates Nominal Interest Rates Term Structure Hypotheses
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8-2 Time Value of Money Chapter 8 Contents 1 Theory of Real Interest Rates . . . . . . . . . . . . . . . . . 8-3 2 Nominal Interest Rates . . . . . . . . . . . . . . . . . . . . . 8-7 3 Term Structure Hypotheses . . . . . . . . . . . . . . . . . . 8-8 3.1 Expectations Hypothesis . . . . . . . . . . . . . . . . . . . . . . 8-8 3.2 Liquidity Preference Hypothesis . . . . . . . . . . . . . . . . . . . 8-10 4 Homework . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-13 15.407 Lecture Notes Fall 2003 c Jiang Wang
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Chapter 8 Time Value of Money 8-3 1 Theory of Real Interest Rates Real interest rates are determined by supply and demand of funds in the economy. Three factors in determining real interest rates: 1. Aggregate endowments 2. Aggregate investment opportunities 3. Aggregate preferences for different consumption path. Dollars, date 0 Dollars, date 1 e 1 e 0 ( e 0 , e 1 ) payoff invest (1+ r ) u ( c 0 , c 1 ) u c Jiang Wang Fall 2003 15.407 Lecture Notes
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8-4 Time Value of Money Chapter 8 Consider a representative investor: has endowment of ( e 0 , e 1 ) faces a bond market with interest rate r . He maximizes his utility over his consumption now and later: max u ( c 0 ) + ρu ( c 1 ) s.t. c 0 = e 0 b c 1 = e 1 + (1 + r ) b where b is his bond holding, u > 0 and u < 0 . The optimality condition is u ( c 0 ) = (1 + r ) ρu ( c 1 ) or (for c 1 = c 0 + dc ) r = u ( c 0 ) ρu ( c 1 ) 1 1 ρ 1 1 ρ c 0 u ( c 0 ) u ( c 0 ) dc c 0 . 15.407 Lecture Notes Fall 2003 c Jiang Wang
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Chapter 8 Time Value of Money 8-5 Thus, the real interest rate is given by r = 1 ρ 1 + 1 ρ c 0 u ( c 0 ) u ( c 0 ) dc c 0 . The interest rate is determined by 1. Investors’ time-impatience coefficients ρ 2. Rate of consumption growth 3. Relative sensitivity of marginal utility to consumption.
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