"Rule number one: never lose money. Rule number two: never forget rule number one." –Warren Buffett
This simple set of rules is likely one of the driving forces behind many investors' motivation to invest in bonds. But with interest rates hovering near historic lows, bond holders are acutely aware that a rise in interest rates puts them at risk of breaking rule number one. In an attempt to reduce sleepless nights for these investors, risk measurements like duration have been developed to help estimate how bond investments will react to interest-rate movements.
A Layman's Perspective
While the calculations for duration can be tricky, the information duration provides is a little more straightforward. Duration tells you how sensitive a bond or bond portfolio will likely be to changes in interest rates. The longer the duration, the more the bond price is expected to change in response to a change in interest rates. And, the shorter the duration, the less sensitive a bond price is likely to be to changes in rates.
Simply put, duration estimates a bond's expected percentage price change for every percentage point change in interest rates. For example, if interest rates move up 1%, a bond with a duration of six years would expect to see its price decline 6%.
1% (interest rate rise) x 6 years (duration) = 6% (price decline)
Duration combines a bond's coupon payments, principal repayment, yield to maturity and payment schedule into a single data point that lets you compare interest-rate sensitivity across a variety of bonds.
Additionally, because duration is typically quoted in years, there's often confusion between duration and maturity. A bond's maturity is when principal is repaid; duration reflects the weighted average number of years to receive the bond's future cash flows (interest payments and principal). The weighting of each flow is its present value relative to the bond price. Except in instances where no interest payments are made during the life of the bond (e.g. zero-coupon bond), duration will always be shorter than maturity.
Thinking about duration in terms of the bond's cash flow can help to make the various factors that influence duration more readily understood.
Flavors of Duration
Unfortunately, when someone says "duration," it takes a little more digging to make sure you're on the same page. While there's no official industry standard, here are some of the most common duration formulas used:
- Macaulay duration (developed by Frederick Macaulay in 1938) is the most basic duration formula and can be thought of as the weighted average number of years an investor must hold the bond to receive the present value of the bond's cash flows.
- Modified duration improves on Macaulay duration by accounting for the fact that market rates, and hence yields, change over the life of the bond.
- Effective duration or option-adjusted duration, which tends to be the most widely used, improves on modified duration by allowing for changes in the bond's cash flows that may occur due to provisions such as calls or floating rates.
Duration's Sweet Spot
Regardless of the formula used, duration works best for small changes in interest rates. The larger the change in interest rates, the more likely the results from a duration calculation will underestimate or overestimate the effect on a bond's price. That's because while duration calculates the price sensitivity of a bond, the results are linear. In reality, as yields rise, bond prices fall at a decreasing rate, and vice versa.
Convexity adjusts duration to account for the non-linear relationship between changes in yields and bond prices. To add to the complexity of convexity, the curve can be positive or negative. Positive convexity is typical for non-callable bonds. Callable bonds and mortgage-backed securities (MBS) may exhibit negative convexity at some price-yield points. This occurs because as yields fall, these bonds exhibit smaller price increases due to the fact that they are more likely to be called, or in the case of MBS, underlying mortgages are likely to be refinanced.
