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(L03)Bonds(f)2

# (L03)Bonds(f)2 - Lecture 3 Fixed Income Securities Reading...

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Primbs/Investment Science 1 Lecture 3: Fixed Income Securities Reading: Luenberger Chapter 3, Sections 1- 4

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Primbs/Investment Science 2 Fixed Income Securities Fixed Income Securities Definitions Annuity Formulas Bond Price and Yield Bond Details
Primbs/Investment Science 3 Definitions Financial Instrument – a legal obligation or claim having monetary value. Ex: stocks, bonds, mortgages, futures, insurance, etc... Security – A tradable financial instrument satisfying legal and regulatory requirements. Fixed income security – Securities that promise a fixed income to the holder over some span of time. Ex: bonds, mortgages, annuities.

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Primbs/Investment Science 4 Fixed Income Securities Fixed Income Securities Definitions Annuity Formulas Bond Price and Yield Bond Details
Primbs/Investment Science 5 Annuity Formulas Annuity – A contract that pays the holder money periodically according to a fixed schedule. Perpetual Annuity (perpetuity) – Pays a fixed sum periodically, forever. At a per period interest rate of r, the present value is r A r A P k k = + = = 1 ) 1 ( 4 3 2 1 0 5 6 A

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Primbs/Investment Science 6 Example Consider a perpetual annuity of \$1000 each year at 10% interest/year. Then, its present value is 000 , 10 \$ 1 . 0 000 , 1 \$ = = = r A P
Primbs/Investment Science 7 Finite-Life Streams Consider a stream that pays A for n periods, starting at period 1. What is its present value? n-1 3 2 1 0 n n+1 A = + = n k k r A P 1 ) 1 ( where r is the interest rate per period. + - = n r r A ) 1 ( 1 1

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Primbs/Investment Science 8 Finite-Life Streams A finite life stream can be thought of as the difference between two perpetuities. n 2 1 0 n+1 n+2 n 2 1 0 n+1 n+2 n 2 1 0 n+1 n+2
Primbs/Investment Science 9 Finite-Life Streams A finite life stream can be thought of as the difference between two perpetuities. r A PV = n 2 1 0 n+1 n+2 A

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Primbs/Investment Science 10 Finite-Life Streams A finite life stream can be thought of as the difference between two perpetuities. r A PV n = + = n r r A PV ) 1 ( 1 n 2 1 0 n+1 n+2 A
Primbs/Investment Science 11 Finite-Life Streams A finite life stream can be thought of as the difference between two perpetuities. r A PV = + - n r r A ) 1 ( 1 n 2 1 0 n+1 n+2 A + - = n r r A ) 1 ( 1 1

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Primbs/Investment Science 12 Example: Loan Calculation Suppose you have borrowed \$1,000 at 12% interest compounded monthly, and you have agreed to repay this loan with equal monthly payments over 5 years. How much are the monthly payments?
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(L03)Bonds(f)2 - Lecture 3 Fixed Income Securities Reading...

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