Modified Duration Definition, Formula, Calculate

This helps investors make smart investment decisions and manage what is modified duration investment risk. In addition, modified duration is also important for managing risk in a portfolio. By diversifying your investments across bonds with different modified durations, you can mitigate the risk of a significant drop in value due to changes in interest rates.

1. While both measures are used to assess how a bond’s price will react to changes in interest rates, they are not interchangeable.
2. With the inequalities being strict unless it has a single cash flow.
3. It gives the dollar variation in a bond’s value per unit change in the yield.
4. This measure is meant to simplify the understanding of the impact to a bond’s yield for a 1/32nd (or a “tick”) move in the price of the bond.

Modified duration illustrates the concept that bond prices and interest rates move in opposite directions – higher interest rates lower bond prices, and lower interest rates raise bond prices. To summarize, the bond has a face value of $1,000, a maturity period of 4 years, and an annual coupon rate of 6%. It follows the concept that bond prices and interest rates move inversely to each other.

Modified Duration vs: Macaulay Duration: Key Differences

Therefore, if interest rates rise 1% overnight, the price of the bond is expected to drop 2.71%. The calculation of Modified and Macaulay Durations assumes that interest rates change by a small amount, leading to a linear relationship between bond prices and yields. However, large interest rate changes can result in a non-linear relationship, causing discrepancies in predicted bond price changes. Keep in mind that modified duration assumes a linear relationship between changes in interest rates and changes in bond prices. In reality, this relationship may not be perfectly linear, especially for bonds with longer maturities or lower credit ratings.

When it comes to fixed-income securities, modified duration and Macaulay duration are two of the most commonly used measures of a bond’s sensitivity to changes in interest rates. Although both of these measures are used to assess the price change in response to changes in interest rates, there are some key differences between them. Investors should be aware of these differences to better understand which measure is best suited for their investment needs. While modified duration and Macaulay duration may seem similar at first glance, they take different approaches to measuring a bond’s price sensitivity to changes in interest rates. By understanding the differences between these measures, investors can make more informed decisions about their bond portfolios and better manage their exposure to interest rate risk. Modified duration is important to individual bond investors because it helps them evaluate the impact of interest rate changes on their investments.

Bond formulas

A bond with positive convexity will not have any call features – i.e. the issuer must redeem the bond at maturity – which means that as rates fall, both its duration and price will rise. Recall that modified duration illustrates the effect of a 100-basis point (1%) change in interest rates on the price of a bond. Zero-coupon bonds trade at a discount (below face value) and are redeemed at face value. The return of the bond is the difference between the face value and the discount value. This result shows that it takes 2.753 years to recoup the true cost of the bond. With this number, it is now possible to calculate the modified duration.

Macaulay Duration and Bond Immunization

We will also have some examples so that we can further understand the calculation of modified duration. Investors need to be savvy regarding the valuation of bonds as they are more sensitive to changes in interest rates compared to stocks. The face value is the principal amount that you’ll receive at the maturity of the bonds. However, duration only reveals one side of a fixed income security. A full analysis of the fixed income asset must be done using all available characteristics.

1. Modified duration and Macaulay duration are two measures commonly used to calculate a bond’s duration and provide different insights into the bond’s price sensitivity to interest rate changes.
2. Duration is a function of the bond’s first partial derivative with respect to yield.
3. Macaulay duration, on the other hand, takes into account the timing of a bond’s cash flows.
4. Particularly, determining the value of a bond requires fairly complex calculations.
5. The higher the modified duration, the greater the bond’s price sensitivity to interest rate changes.
6. Modified duration is important because it provides critical valuation insight to bond investors.

Relative to the Macaulay duration, the modified duration metric is a slightly more precise measure of price sensitivity. That is, a component that is linear in the interest rate changes plus an error term which is at least quadratic. This formula can be used to calculate the VaR of the portfolio by ignoring higher order terms. Quadratic terms, when included, can be expressed in terms of (multi-variate) bond convexity.

It is the most commonly used tool in the bond markets as an assessment of the interest rate sensitivity of a fixed income security. This example shows how knowing the modified duration allows us to make a simple calculation to determine the (approximate) price of the bond. Of course, we could recalculate the price of the bond by accounting for the yield changes, but that is more complicated then the above approach. Modified duration is a formula that measures the sensitivity of the valuation change of a security to changes in interest rates. Modified duration could be extended to calculate the number of years it would take an interest rate swap to repay the price paid for the swap.

Director, Relationship Management

The traditional bond structure includes a series of cash flows, such as coupon payments that occur before the bond matures, culminating with a maturity where the principal is fully repaid. Effective duration is a useful measure of the duration for bonds with embedded options (e.g., callable bonds). A bond with an embedded option tends to behave differently from an option-free bond when yields move as the bond may be either called or put if the embedded option is in-the-money. This means that the price change for a given change in yield is not constant. For those who work on Wall Street trading desks though, the concept of modified duration was still not direct enough.

Therefore, for a given interest rate increase, it can be expected that the bond with the longer term to maturity will have a larger interest rate risk than a shorter bond with the same coupon. To price such bonds, one must use option pricing to determine the value of the bond, and then one can compute its delta (and hence its lambda), which is the duration. The effective duration is a discrete approximation to this latter, and will require an option pricing model. If interest rates increase by 1%, the price of our hypothetical three-year bond will decrease by 2.67%. Conversely, if interest rates decrease by 1%, the price of the bond will increase by 2.67%.

Modified duration is a rate of change, the percent change in price per change in yield. Therefore, looking for Macaulay duration, in this case, does not make sense. However, Modified duration can still be calculated since it only takes into account the effect of changing yield, regardless of the structure of cash flows, whether they are fixed or not.