## Measuring yield curve risk, Financial Management

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Rate duration can be defined as the sensitivity of the change in value to a particular change in spot rate. Every point in a spot rate curve has a rate duration. Therefore, instead of one rate duration, we will have a vector of durations representing each maturity on the spot rate curve. If all rates change by the same number of basis points then the total change in value would give us the duration of a security or portfolio to a parallel shift in rates.

Donald Chamber and Willard Carleton suggested this approach for the first time in 1988. They called it "Duration Vectors". After that, Robert Reitano came with "partial Durations," which is similar to the duration vectors approach. In 1992, Thomas Ho came up with a new version of this approach which gained much popularity. This approach concentrates on 11 key maturities of spot rate curve. These rate durations are called key rate durations. Key rate duration is measured for 3 month, 1-year, 2-year, 3-year, 5-year, 7-year, 10-year, 15-year, 20-year, 25-year, and 30-year maturities on the spot rate curve. The changes between any two rates are calculated using a linear approximation.

We can measure the impact of any type of yield curve by using key rate durations. A level shift can be measured by changing all key rates by same basis points. The impact of steepening of the yield curve can be found by decreasing the key rates at the short end of the yield curve and determining the positive changes in the portfolio value using the corresponding key rate durations and increasing the key rates at the long end of the yield curve, and determining the negative changes in the portfolio value using the corresponding key rate durations.

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