Duration

# Duration - minimize the variance of a portfolio of bonds...

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Duration Duration is a measure of the average life of a debt instrument on a PV basis. A zero coupon bond that matures in n years has a duration of n. A coupon bond has duration < n because payments are made before maturity. Financial institutions often try to match the duration of their assets to the duration of their liabilities. Duration is also useful for hedging. 1

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Duration Matching This involves hedging against interest rate risk by matching the durations of assets and liabilities It provides protection against small parallel shifts in the zero curve 2
Duration of a bond that provides cash flow ci at time ti is where B is its price and y is its yield (continuously compounded). Duration 3 - = B e c t i yt i n i i 1

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The % change in the price of a bond in response to a % change in yield is proportional to the duration. This can be used to find the optimal number of contracts to

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Unformatted text preview: minimize the variance of a portfolio of bonds and futures. • We want to set the duration of the hedged portfolio equal to zero. Duration and hedging 4 y D B B ∆-= ∆ Duration-Based Hedge Ratio (N*) VF Contract Price for Interest Rate Futures DF Duration of Asset Underlying Futures at Maturity P Value of portfolio being Hedged DP Duration of Portfolio at Hedge Maturity 5 F F P D V PD Example: Text Problem 6.17 • Two month hedge is required for a \$10 million portfolio. Duration of the portfolio in 2 months will be 7.1 years. • 2-month T-bond futures price is 91-12 so that contract price is \$91.375.99. • Duration of cheapest to deliver bond in 2 months is 8.8 years. • The manager should short 88 contracts. 6 30 . 88 8 . 8 00 . 375 , 91 1 . 7 000 , 000 , 10 = × ×...
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Duration - minimize the variance of a portfolio of bonds...

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