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Finance, Economics, and Mathematics by Robert C. Merton, Oldrich A. Vasicek

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Part FiveMarkets, Portfolios, and Securities

Let

equation

be the value at time zero of a bond portfolio with payments c05-math-001 due at times c05-math-002 and let

equation

be the Macaulay duration of the portfolio. Here

equation

and c05-math-003 are the forward rates. Let c05-math-004 be the future value of the portfolio at time c05-math-005,

equation

Put

equation

Suppose the forward rates change instantaneously to new values c05-math-006. If K is an upper bound for the change in the slope of the forward ...

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