Lecture2_AssetPrices

Lecture2_AssetPrices - ECON 3024 Managerial Macroeconomics...

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ECON 3024 Managerial Macroeconomics Expectations and Asset Prices
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Financial Markets Markets that trade financial assets such as equities, bonds, currencies and derivatives Supplier: commercial banks and investment banks Demander: anyone who has wealth Prices: asset prices How to compute asset prices? 2
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The expected present discounted value of a sequence of future payments is: the value today of this expected sequence of payments. Expected Present Discounted Values 3 The word “present” comes from the fact that we are looking at the value of a payment next year in terms of dollars today . The word “discounted” comes from the fact that the value next year is discounted 1/(1 + i t ) is the discount factor . The 1-year nominal interest rate, i t , is the discount rate .
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(a) One dollar this year is worth 1+ i t dollars next year. (b) If you borrow 1/(1+i t ) dollars this year, you will repay 1 dollar next year. So the present discounted value of a dollar next year is equal to 1/(1+i t ) (c) One dollar is worth dollars two years from now. (d) The present discounted value of a dollar two years from today is equal to: Computing Expected Present Discounted Values Expected Present Discounted Values 4 ( ) ( ) 1 1 1 i i t t 1 1 1 1 ( ) ( ) i i t t
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The present discounted value of a sequence of payments, or value in today’s dollars equals: When future payments or interest rates are uncertain, then: Present discounted value, or present value are another way of saying “expected present discounted value.” Computing Expected Present Discounted Values The General Formula Expected Present Discounted Values 5 $ $ ( ) $ ( ) ( ) $ V z i z i i z t t t t t t t    1 1 1 1 1 1 1 2 $ $ ( ) $ ( ) ( ) $ V z i z i i z t t t e t t e t e t    1 1 1 1 1 1 1 2
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This formula has these implications: Present value depends positively on today’s actual payment and expected future payments. Present value depends negatively on current and expected future interest rates. Using Present Values: Examples Expected Present Discounted Values 6
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The terms in the expression in brackets represent a geometric series. Computing the sum of the series, we get: Using Present Values: Examples Constant Interest Rates and Payments Expected Present Discounted Values 7 Assume that interest rates are expected to be constant over time, i ; and when the sequence of payments is equal—called them $ z , the present value formula simplifies to: $ $ [ / ( ) ] [ / ( ) ] V z i i t n 1 1 1 1 1 1 $ $ ( ) ( ) V z i i t n     1 1 1 1 1 1
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Assuming that payments start next year and go on forever, Using the property of geometric sums, the present value is: Which simplifies to: Using Present Values: Examples Constant Interest Rates and Payments, Forever Expected Present Discounted Values 8 $ ( ) $ ( ) $ ( ) ( ) $ V i z i z i i z t        1 1 1 1 1 1 1 1 1 2 1 1 $ $ (1 )1 (1/(1 )) t V z i i $ $ V z i t
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