Question: Duration of a security is defined as a weighted average of the maturity of its cashflows, where the weights are proportional to the present value

Duration of a security is defined as a weighted average of

Duration of a security is defined as a weighted average of the maturity of its cashflows, where the weights are proportional to the present value of the cashflows. For example, if a security provides a cashflow of CF1 to CFT, then its duration is D=t=1Twtt where wt=t=1TPV(CFt)PV(CFt) (a) Suppose the interest rate is r per period. What is the duration of a perpetuity? Hint: set up the following equation D=r11[(1+r)11+(1+r)212+(1+r)313+]. 2 Note that the term 1/r in the denominator is the present value of the perpetuity with a payment of $1 per period. Multiply the above equation by (1+r) and get a second equation. Manipulate these two equations to solve for D. (b) Suppose the interest rate is r per period. What is the duration of a growing perpetuity with a growth rate of g per period, where g

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