Bond duration Wikipedia

For example, if the Fund Manager is anticipating an increase in Interest Rates, he/she might decide to reduce the Modified Duration of the portfolio by investing in short-maturity Debt Instruments. This will help reduce the adverse impact of the Interest Rate increase on the Debt Fund. On the other hand, when the Fund Manager anticipates a decrease in Interest Rates, he/she might decide to maintain a high Modified Duration in the portfolio by investing in long-maturity Bonds. This will help the Debt Fund generate high returns when Bond Prices increase due to the decrease in Interest Rates.

Shorter duration bonds will be relatively price stable; they will pay out most of their promised cash flow in the near future. Longer duration bonds are less stable; long duration bonds have all the risk of taking longer to pay out their funds, including a shift in the market’s demanded yield. For a one percent increase in interest rates, the bond’s market price will decrease by the percentage shown by the modified duration. For a one percentage point decrease in interest rates, the bond price will increase by the percentage shown by the modified duration.

To better understand the potential impact of an Interest Rate change on the performance of a Debt Fund, another key parameter of your Debt Fund that you need to look at closely is the Macaulay Duration. Our writing and editorial staff are a team of experts holding advanced financial designations and have written for most major financial media publications. Our work has been directly cited by organizations including Entrepreneur, Business Insider, Investopedia, Forbes, CNBC, and many others. Finance Strategists is a leading financial education organization that connects people with financial professionals, priding itself on providing accurate and reliable financial information to millions of readers each year. Our team of reviewers are established professionals with decades of experience in areas of personal finance and hold many advanced degrees and certifications. By that, it means that the duration of individual securities in a portfolio can be combined into a duration for that entire portfolio.

The Macaulay Duration of a bond is directly related to the bond’s price sensitivity to changes in interest rates. A bond with a longer Macaulay Duration will have a greater price change for a given change in interest rates than a bond with a shorter Macaulay Duration. Consequently, this approach respects the diverse values and durations of individual bonds within a comprehensive portfolio, providing a more accurate duration measure for the entire portfolio. Investment professionals frequently use Macaulay Duration to manage interest rate risk and align bond portfolio durations with investment horizons. As a rule of thumb, the longer the Macaulay Duration, the higher the interest rate risk for a bond.

  1. No matter how high interest rates become, the price of the bond will never go below $1,000 (ignoring counterparty risk).
  2. The modified duration is an adjusted version of the Macaulay duration, which accounts for changing yield to maturities.
  3. In our example above, using our analogy, you may be able to see that the bond on the bottom with the higher coupon rate will have a shorter duration as more of the weight sits on the left hand side of the see-saw.
  4. As a matter of fact, for coupon-paying bonds, the duration of that bond will always be shorter than the term to maturity of that bond.
  5. This formula shows that each cash flow is weighted by the time at which it is received, reflecting the time value of money.

It is a crucial tool for investors and portfolio managers who need to manage the interest rate risk of their bond investments effectively. In plain-terms – think of it as an approximation of how long it will take to recoup your initial investment in the bond. In our example above, using our analogy, you may be able to see that the bond on the bottom with the higher coupon rate will have a shorter duration as more of the weight sits on the left hand side of the see-saw. Comparing this with the bond on the top with smaller coupon payments, you will see that the fulcrum is further out to the right hand side, meaning a longer duration. 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. From the series, you can see that a zero coupon bond has a duration equal to it’s time to maturity – it only pays out at maturity.

Relationship Between Macaulay Duration and Bond Prices

Not surprisingly, a bond with a longer remaining term to maturity will have a longer duration. This makes intuitive sense using our see-saw as a longer bond would require moving the fulcrum further to the right, increasing the Macaulay duration. Duration helps you understand, at a glance, how sensitive your bond portfolio is to interest rate changes. Mortgage-backed securities (pass-through mortgage principal prepayments) with US-style 15- or 30-year fixed-rate mortgages as collateral are examples of callable bonds.

Portfolio immunization is a strategy used by investors to shield their portfolios from interest rate risk. By balancing the duration of assets and liabilities, investors can protect their portfolios from significant losses when interest rates change. This formula shows that each cash flow is weighted by the time at which it is received, reflecting the time value of money.

Modified duration equals Macaulay duration divided by 1 + required yield per period. It gives us the estimated change in the price of a bond in response to a 1% change in yield. Macaulay Duration serves as a link between bond prices and interest rates, measuring how sensitive a bond’s price is to changes in interest rates. It’s based on the principle that bond prices and interest rates move in opposite directions. Macaulay Duration can change with market conditions, especially for bonds with embedded options. If interest rates change significantly, the issuer or bondholders may choose to exercise their options, changing the bond’s cash flows and thus its Macaulay Duration.

The effective duration is a discrete approximation to this latter, and will require an option pricing model. Well, the key parameters of Average Maturity, Macaulay Duration, and Modified Duration can give valuable insight into how a scheme’s performance will be impacted macaulay duration and modified duration by future changes in Interest Rates. One of the reasons why returns of Debt Funds can be volatile in the short run is the change in Interest Rates. The impact of Interest Rate changes is not uniform across Debt Fund categories or even funds within a category.

Formula and Calculation of Modified Duration

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. Therefore, market participants came up with a more practical duration measure, called modified duration. Relative to the Macaulay duration, the modified duration metric is a slightly more precise measure of price sensitivity.

Risk – duration as interest rate sensitivity

It will compute the mean bond duration measured in years (the Macaulay duration), and the bond’s price sensitivity to interest rate changes (the modified duration). The modified Duration of a bond is a measure of how much the price of a Bond changes because of a change in its Yield To Maturity (YTM) or interest rate. In the simplest terms, if the Modified Duration of a Bond is 5 years and the market Interest Rate decreases by 1%, then the Bond’s price will increase by 5%.

The Macaulay duration is calculated by multiplying the time period by the periodic coupon payment and dividing the resulting value by 1 plus the periodic yield raised to the time to maturity. Then, the resulting value is added to the total number of periods multiplied by the par value, divided by 1, plus the periodic yield raised to the total number of periods. The yield-price relationship is inverse, and the modified duration provides a very useful measure of the price sensitivity to yields. For large yield changes, convexity can be added to provide a quadratic or second-order approximation.

Interpreting the Modified Duration

Macaulay Duration plays a pivotal role in ALM, as institutions often seek to match the durations of their assets and liabilities to minimize interest rate risk. While the first approach is the more theoretically correct approach, it is harder to implement in practice. Therefore, the second approach below is the more commonly method used by fixed income portfolio managers. By adding up the present values of each of the three years, we get to a sum of $102.78, which is the bond’s price.

A bond with a higher Macaulay duration will be more sensitive to changes in interest rates. In contrast, the modified duration identifies how much the duration changes for each percentage change in the yield while measuring how much a change in the interest rates impact the price of a bond. Thus, the modified duration can provide a risk measure to bond investors by approximating how much the price of a bond could decline with an increase in interest rates. It’s important to note that bond prices and interest rates have an inverse relationship with each other. The term duration is mathematically defined as the sum of the weighted average time of each of the cash flows that make up a bond. In other words, “pure” duration (denoted in years) is how long it will take for an investor to receive the bond’s present value based on the expected future cash flows of the bonds.