Lecture 4 - F10 Lecture 4 Interest Rates Interest Rate...

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Lecture 4 Interest Rates • Interest Rate Mechanics 6 • Real vs. Nominal Rates • Loanable Funds Model • Debtor-Creditor Redistribution –M&
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Present Value (PV) $PV now invested for m years at interest rate i has Future Value (FV): FV = PV (1 + i ) m Future payment of $FV to be paid in m yrs has PV: E.g., FV = $100, i = 5% (.05), m = 1 yr: PV = $100 / (1.05) = $95.24. or, if m = 20 yr, PV = $100 / (1.05) 20 = $100 / 2.6533 = $37.69. Need x y or ^ key on calculator to compute! Note: nominal interest rate i is “ R m i ) 1 ( FV PV + =
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implies that holding FV constant, i ↑→ PV , i ↓→ PV • Also, effect of Δ i on PV grows stronger with m : Δ PV/PV - Δ i · m Examples: m = 1 yr, i rises from 5% to 6%, Δ i = +1%, FV = 100: - Δ i · m = - (+1%)(1yr) = -1% (Actual Δ PV/PV = (94.34 – 95.24)/95.24 = - .0094 = - 0.94%) m = 10 yrs, i rises from 5% to 6%: - Δ i · m = - (+1%)(10YR) = -10% (Actual Δ PV/PV = (55.84 – 61.39)/61.39 = - .090 = - 9.0%) Leads to Interest Rate Risk when banks or thrifts lend long, borrow short. m i ) 1 ( FV PV + =
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i from FV / PV: PV = FV / (1+ i ) m (1+ i ) m = FV / PV, 1+ i = (FV / PV) 1/m , so i = (FV / PV) 1/m –1 E.g., FV = $100, PV = $50, m = 10 yrs., i = (100 / 50) 1/10 –1 = 2 0.1 – 1 = 1.0718 – 1 = 0.0718 = 7.18%. Note: 0.01% = one “Basis Point”.
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Bonds Face Value $F to be paid at maturity m Coupons $C paid each year for m years. (Assume annual for simplicity) Bond Present Value (PV B ) i ↑→ PV B , i ↓→ PV B m i i i ) 1 ( F C ) 1 ( C ) 1 ( C PV 2 B + + + + + + + = K
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Bond Duration Effect of Δ i on PV B again stronger, the longer its m. However, now, Δ PV B /PV B ≈Δ i · D, where the bond’s Duration D equals the present- value-weighted average maturity of its payments: Generally, D = m if C = 0, D < m if C > 0, D increases with m B 2 PV / ) 1 ( F) (m)(C ) 1 ( (2)C ) 1 ( (1)C + + + + + + + = m i i i D K
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Yield to Maturity (YTM)
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This note was uploaded on 11/08/2010 for the course ECON 520 taught by Professor Ogaki during the Fall '07 term at Ohio State.

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Lecture 4 - F10 Lecture 4 Interest Rates Interest Rate...

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