Hi David, I notice that you have a different way of calculating the DV01 in your notes. Indeed, Tuckman defines it as follows: (1/)*(dP/dy). There are two items that must be clarified with respect to your question: Are you assuming an interest rate swap (IRS) at mid-market, i.e. at-the-money (ATM) or. In finance, the duration of a financial asset that consists of fixed cash flows, for example a bond, The formula can also be used to calculate the DV01 of the portfolio (cf. below) and it can be generalized to include risk factors beyond interest.

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Check date values in: Note that convexity can be positive or negative. Alternatively, and often more usefully, convexity can be used to measure how the modified duration changes as yields change. For every-day use, the equality or near-equality of the values for Macaulay calculztion modified duration can be a useful aid to intuition.

The modified duration, measured as percentage change in price per one percentage point change in yield, is:.

Convexity also gives an idea of the spread of future cashflows. Why Take the Exam?

### Bond duration – Wikipedia

Attack68 calculagion, 2 The yield-price relationship is inverse, and the modified duration provides a very useful measure of the price sensitivity to yields. Measures of Interest Rate Risks”. However, to use this, we end up negating ev01 e. Since PV has already factored in discount factors when arriving at the PV there is no need to reassert them again.

Modified duration is the name given to the price sensitivity and is the percentage change in price for a unit change in yield. The present value of these cash flows is:.

## DV01 Computation

Modified duration measures the size of the interest rate sensitivity. Transactions of the Society of Actuaries. Hi David, I notice that you have a different way of calculating the DV01 in your notes.

Dollar duration or DV01 is xv01 change in price in dollars, not in percentage. The total PV will be:.

Modified duration can be extended to instruments with non-fixed cash flows, while Macaulay duration applies only to fixed cash flow instruments.

When the price of an asset is considered as a function of yieldduration also measures the price sensitivity to yield, the rate of change of price with respect to yield caclulation the percentage change in price for a parallel shift in yields.

This is because the issuer can redeem the old bond at a high coupon and re-issue a new bond at a lower rate, thus providing the issuer with valuable optionality.

Modified duration is used more often than Macaulay duration in modern finance.

## Bond duration

And even beyond an exam view, DV01 inherits from duration a ‘second-class’ status anyhow as “merely” a linear approximation. With the use of computers, both forms may be calculated but expression 3assuming a constant yield, is more widely used because of the application to modified duration.

Retrieved 22 January Similarities in both values and definitions of Macaulay Duration versus Weighted Average Life can lead to confusing the purpose and calculation of the two. There are two items that must calculatoon clarified with respect to your question: This gives the well-known relation between Macaulay duration and modified duration quoted above.

Consider a bond with an embedded put option. In contrast to Macaulay duration, modified duration calculatiln abbreviated MD is calculatioon price sensitivity measure, defined as the percentage derivative of price with respect to yield the logarithmic derivative of bond price with respect to yield.

Similar risk measures first and second order used in the options markets are the delta and gamma. Macaulay duration is a weighted average time until repayment measured in units of time such as years while modified duration is a price sensitivity measure when the price is treated as a function of yield, the percentage change in price with cslculation to yield.

### DV01 Computation | Bionic Turtle

Just as the duration gives the discounted mean term, so convexity can be used to calculate the discounted standard deviation, say, of return. For a standard bond the Macaulay duration will be between 0 and the maturity of the bond.

In terms of standard bonds for which cash flows are fixed and positivethis means the Macaulay duration will equal the bond maturity only for a zero-coupon bond. Forwards Options Spot market Swaps.

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