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7Lecture8interestrateriskIV

# Modified duration md md d 1r interest rate risk model

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Unformatted text preview: >0 21 Interest Rate Risk Model %Δr vs Dollar ΔPrice ΔB = - D * B* Δr Bigger D ► Higher the interest rate risk ΔB/B = -D * Δr %Δr vs %ΔPrice 22 B. Modified Duration~ MD • MD = D (1+r) Interest rate risk Model ΔB = - MD * B * Δr ΔB/B = - MD * Δr 23 Example ZCB, Par=100, Current YTM=7%, Maturity=7 years Q : ∆B if ∆r = 1% using D ? MD? ΔB = ΔB = or ΔB/ = 24 Example Using Modified Duration ΔB = ΔB = or ΔB/B = 25 Duration can be summed across portfolios of securities B/S (MV) W1 (= A1/(A1+A2)) D1◄ A1 W2 (= A2/(A1+A2)) D2◄ A2 DA L1 ►D1 *W1 (= L1/(L1+L2)) L2 ►D2 *W2(= L2/(L1+L2)) DL 26 Duration of Assets and Liabilities D Assets = ΣA WA DA Market D Liabilities = Σ L WL DL Value Weights 27 Interest Rate Risk of the B/S? Δ A = - {D A /(1+r)} * A * Δ r Δ L = - {D L /(1+r)} * L * Δ r Typically DA > DL if r ΔE? A >L E Borrow Lend 28 Interest Rate Risk of the B/S? A=L+ E E=A-L If Δr ► ΔE = ΔA - ΔL ΔE = [-DA*A *Δr/(1+r)] - [-DL*L *Δr/(1+r)] Assume equal ΔE = - [DA - DL * (L/A)] *A...
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