With interest rates at historic lows, now is a good time for bond investors to pay particular attention to the roles that both maturity and duration play with regard to interest-rate sensitivity. While the two concepts are related, they also differ significantly. About the Author Giulio Rocca's background is in investment banking and management consulting, including advising Fortune 500 companies on mergers and acquisitions and corporate strategy. There is no guarantee that any forecasts made will come to pass. The Macaulay duration will equal the final maturity if and only if there is only a single payment at maturity. Investments in securities are subject to market and other risks. However, high yield bonds are implied to have greater insulation to changes in interest rates versus the 3-7 year Treasuries.
This refers to the annual interest payable as a percent of the original face or par value. If investing in a fixed-income mutual fund, interest payments are in the form of mutual fund dividends and may be paid monthly. Fisher—Weil duration calculates the present values of the relevant cashflows more strictly by using the zero coupon yield for each respective maturity. It is applied only to investments with fixed rate of returns Modified Duration Modified Duration is a tool that measures change in price percentage relative to a unit change in yield. The circles represent the present value of the payments, with the coupon payments getting smaller the further in the future they are, and the final large payment including both the coupon payment and the final principal repayment. Transactions of the Society of Actuaries. Macaulay Duration can only be extended on instruments with fixed cash flows.
The lower the duration value attached to a bond, the less price sensitive it will be to changes in interest rates. This bond, following the basic bond pricing formula would have a market price of: Here are some principles of duration to keep in mind. Because of this, you might think bonds carry no risk, but this is not the case. But it has a cash flows out to 10 years and thus will be sensitive to 10-year yields. Formally, modified duration is a , the percent change in price for a unit change in yield, rather than an , which is a percentage change in output for a percentage change in input. In symbols, if cash flows are, in order, t 1 ,. The value is then multiplied by 10,000.
Bond Basics A basic bond is issued with a face value, coupon and maturity. Keep in mind the image of a see-saw on a playground conveying the idea that when interest rates go up, bond prices go down and the opposite is true. Modified duration is also useful as a measure of the sensitivity of a bond's market price to finite i. The longer the bond's maturity, the greater its duration. We have gone to great lengths to make sure our content is easily accessible and approachable.
Macaulay Duration The calculation of Macaulay Duration is shown below: Graphically, Macaulay Duration is the point of balance in years for the cash flows from the bond see below. This duration takes years to measure. Maturity and Duration are simply two measures among many that investors explore when attempting to separate the parts that make up the bond market. The Quantitative Fair Value Estimate is calculated daily. Recall that the formula s for duration measured how long it took for the cash flows to repay the initial investment.
Third, as interest rates increase, duration decreases and the bond's sensitivity to further interest rate increases goes down. Occasionally, a simulated average life may be computed from multiple cash-flow scenarios, such as those from an model. The difference between the two modified durations is the modified duration of the interest rate swap. 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. The modified duration of the receiving leg of a swap is calculated as nine years and the modified duration of the paying leg is calculated as five years. And yield-to-maturity, by definition, implies a flat yield curve. Now, the bottom line of the bottom line.
For example, a 5-year fixed-rate interest only bond would have a Weighted Average Life of 5, and a Macaulay Duration that should be very close. The term originally meant a member of the laity, i. Sometimes we can be misled into thinking that it measures which part of the yield curve the instrument is sensitive to. For every-day use, the equality or near-equality of the values for Macaulay and modified duration can be a useful aid to intuition. Understanding the complexities of the bond market is important when evaluating the types of products and exposure a portfolio has within the asset classes of fixed income. Two bonds may have the same maturities, but their sensitivity to interest rate changes may be different. Most of the reads give the example for interest rate.
Normally, if the yield is compounded continuously, the values we arrive at using both durations is same. About the Author Currently a resident of Chicago, Neil J. Complexity increases in the details of various ways duration is calculated. Investments in securities are subject to market and other risks. Then, the resulting value is added to the total number of periods multiplied by the , divided by 1, plus the periodic yield raised to the total number of periods.