Overview. This chapter discusses a market value-based model for assessing and managing interest rate risk: Duration Computation of duration Economic interpretation Immunization using duration * Problems in applying duration. Price Sensitivity and Maturity.
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D = SNt=1[CFt• t/(1+R)t]/ SNt=1 [CFt/(1+R)t]
D = duration
t = number of periods in the future
CFt = cash flow to be delivered in t periods
R = yield to maturity.
D = SNt=1[t (Present Value of CFt/P)]
duration < maturity
[ΔP/P] [ΔR/(1+R)] = -D
ΔP/P = -D[ΔR/(1+R)] = -MD × ΔR
where MD is modified duration.
ΔP = -D[ΔR/(1+R)]P = -(MD) × (ΔR) × (P)
(ΔP/P)/(ΔR/R) = -D[ΔR/(1+(R/2)]
= -[5 - 3(90/100)]100[.01/1.1] = - $2.09.
CX = Scaling factor × [capital loss from 1bp rise in yield + capital gain from 1bp fall in yield]
CX = 108[DP-/P + DP+/P]
= 108[(999.53785-1,000)/1,000 + (1,000.46243-1,000)/1,000)]
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