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Modified duration is the name given to the price sensitivity. It is (-1) times the rate of change in the price of a bond as a function of the change in its yield. [4] Both measures are termed "duration" and have the same (or close to the same) numerical value, but it is important to keep in mind the conceptual distinctions between them. [5]
The more curved the price function of the bond is, the more inaccurate duration is as a measure of the interest rate sensitivity. [2] Convexity is a measure of the curvature or 2nd derivative of how the price of a bond varies with interest rate, i.e. how the duration of a bond changes as the interest rate changes. [3]
Duration is a linear measure of how the price of a bond changes in response to interest rate changes. It is approximately equal to the percentage change in price for a given change in yield, and may be thought of as the elasticity of the bond's price with respect to discount rates. For example, for small interest rate changes, the duration is ...
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This is equal to the Macaulay duration times the discount rate, or the modified duration times the interest rate. If the elasticity is below -1, or above 1 if the absolute value is used, the product of the two measures, value times yield or the interest income for the period will go down when the yield goes up.
The price you pay for a bond may be different from its face value, and will change over the life of the bond, depending on factors like the bond’s time to maturity and the interest rate ...
For instance, a bond paying a 10% annual coupon will always pay 10% of its face value to the owner each year, even if there is no change in market conditions. However, the effective yield on the bond may well be different, since the market price of the bond is usually different from the face value. Yield return is calculated from
The price sensitivity of a stock versus duration, often called modified duration, is the percentage change in price in response to a 1% change in the long-term return that the stock is priced to deliver. The modified duration is duration divided by (1 + growth rate).