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Unformatted text preview: Asset Markets Professor John Diamond ECON 370: Microeconomic Theory Lecture 9 Assets: Introduction Physical asset commodity providing a flow of returns in the form of services over time House Car Computer Financial asset security providing a flow of financial returns over time Stocks Bonds Indexed bonds (Treasury TIPS) Assets: Uncertainty Certainty of returns Typically asset returns are uncertain Initially, assume certain returns Later, add uncertainty of returns Value of assets calculated as PV of future cash flows (initially, known with certainty) Selling An Asset: Introduction Decision rules for selling an asset Example Suppose value of asset over time is V(t) = 1000 + 1000t 10t 2 Can calculate maximum value of asset Selling An Asset: Graph 10 20 30 40 50 601000 4000 9000 14000 19000 24000 Value Years V(t) = 1000 + 1000t 10t 2 Selling An Asset: Calculating Maximums V(t) = 1000 + 1000t 10t 2 To find maximum, set V(t)= dV(t)/dt=0, or V(t) = 1000 20t = 0 t = 50 Selling An Asset: Graph Max. value of $24,000 in year 50 10 20 30 40 50 601000 4000 9000 14000 19000 24000 Value Years Selling An Asset: Rates of Return But maximum value NOT optimal time to sell Decision rule depends on relative rate of return Rateof return R in year t = earnings in t/value Must compare R to relevant interest rate r Hold asset until R=r, then sell and invest at r Selling An Asset: Example The rateofreturn of the asset at time t is V(t) V(t) In the example V(t) = 1000 + 1000t 10t 2 V(t)=dV/dt = 1000 20t V(t) = ____1000 20t____ V(t) 1000 + 1000t 10t 2 Selling An Asset: Example The asset should be sold when r=i, or V(t) = ____1000 20t____ = 0.1 V(t) 1000 + 1000t 10t 2 t = 10 Note: Use quadratic formula to solve for t Selling An Asset: Graph 10 20 30 40 50 601000 4000 9000 14000 19000 24000 Value Years Selling An Asset: Graph Sell at 10 years even though asset value only $8,000 (not max of $24,000) 10 20 30 40 50 601000 4000 9000 14000 19000 24000 Value Years Selling An Asset Gain from optimal sale of asset (not at max) Compare to FV=$24,000 in year 50 Sell in year 10 for $8,000 Invest $8,000 at i=0.1 for years $8, ( ) $362, $24, 000 1 0 1 074 000 40 Arbitrage: Introduction Arbitrage Taking advantage of differences in rates of return across assets Making an easy profit Basic principle: w/o uncertainty, all profit opportunities will be found Tax system offers opportunities for arbitrage, but limited by special rules Arbitrage: Prices Over Time Implications for prices over time?...
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 Spring '08
 DIAMOND
 Microeconomics

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