Lecture_12

Lecture_12 - Fall 2010 Investment Management, Lecture 12...

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Investment Management, Lecture 12 Fall 2010 1 Professor Ruslan Goyenko Fixed-Income Securities
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Investment Management, Lecture 12 Fall 2010 2 § Time value of money § Future Value (FV), Present Value (PV), yield § Single payment security Example: zero coupon bond § Multiple payment security Annuities and perpetuities Outline
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Investment Management, Lecture 12 Fall 2010 3 Future Value, FV § Timeline § Investing for a single period FV = PV (1+r) § Investing for multiple periods Simple interest Compounding: Interest on interest FV = PV (1+r) t (1+r)t is the future value factor
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Investment Management, Lecture 12 Fall 2010 4 Present Value, PV § Single-period case: How much do you need to invest today, with an interest rate of r, to have $ FV next year? PV= FV  1/(1+r) § Multiple-period case: PV= FV  1/(1+r) t § Discount factor (= present value factor): 1/(1+r) t § Pricing of securities by arbitrage (Extremely important pricing principle!)
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Investment Management, Lecture 12 Fall 2010 5 PV, FV, r, t are tied together. If you know 3, you can find the last one § What is the yield, r ? Suppose you know the present value, and the (future) value at a given future time: What is the yield (or the return) ? § How many periods, t ? Suppose you have a given amount of money, you know the interest rate, and you know the future value that you need: How many periods does it take?
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Investment Management, Lecture 12 Fall 2010 6 Moving Along the Time Line Time 1 2 3 0 2 1 (1 ) t t r - + 2 t 1 t multiply by 2 1 (1 ) t t r - + divide by
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Investment Management, Lecture 12 Fall 2010 7 Multiple Payments § Timeline § Future value of stream of cash flows C (0),C(1),…,C(T) : § Present value : § Yield: Internal Rate of Return (discussed later) ) ( ... ) 1 )( 1 ( C ) 1 )( 0 ( C ) ( 1 T C r r T FV T T + + + + + = - T r T C r PV ) 1 ( 1 ) ( ... ) 1 ( 1 ) 1 ( C ) 0 ( C + + + + + =
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Investment Management, Lecture 12 Fall 2010 8 Annuities § Annuities: Definition: Pays a fixed cash flow, C , for T periods Pricing by arbitrage: PV = (C / r)  [ 1 – 1/(1+r) T ] § Example: Which car you afford? You have no large amount of cash. You can afford $632 per month. You can borrow at an interest rate of 1% per month. You want to have paid the loan in full in 48 month.
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Fall 2010 v Example of Present Value of an Ordinary Annuity ( PV ) Using Annual Interest: If A = $100, r = 0.09, and n = 8, then PV = ? PV
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Lecture_12 - Fall 2010 Investment Management, Lecture 12...

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