PERSONAL FINANCES FOR 2004: Bond Measurements
July 14, 2004
Bond values are impacted by interest rate movements, the extent to which is covered here. The two measurements that provide insight to bond price changes versus a change in rates are duration and convexity. Additionally, a bond with option features—those that are callable by the issuer or can be put by the investor—also impact price as rates change.
Duration
Duration is the approximate percentage change in value of a bond given a 100 basis point (0.01) change in rates. There are a few variations on duration measurements, with effective duration the most comprehensive and the one covered here. Let’s first look at a price yield curve, with price on the y-axis and yield on the x-axis. As yield increases price goes down, but not linearly.
Duration however is a linear estimate or approximation of price change, so it is not quite right in terms of accuracy. The next chart adds duration to the price versus yield curve to better explain the concept.
So if interest rates decline, the price of the bond will rise along the duration line. Assuming the current yield is right where the duration line is tangent to the curve and we have a very small change in rates, the estimated change in price for the bond will be fairly accurate. However, for greater changes in rates (a more likely scenario for longer maturity bonds), the price change estimation is less accurate. Move up and left along the duration line to get a better sense for this.
Why does duration matter? Since interest rates are not stagnant over the term of the bond, bond managers and investors need to understand how rate changes throughout the life of the bond will affect its price. However, since duration is not a highly accurate measurement for greater absolute changes in rates, an additional measurement must be considered.
Convexity
Convexity is the term used to describe the curvature of the bond price-yield curve. A flat curve suggests low convexity while a steep, rounded curve suggests high convexity. The greater the convexity the greater a change in interest rates will impact bond price.
A convexity adjustment is used to improve the effective duration estimate. This adjustment represents the distance form the curve itself to the duration line to improve the actual impact of interest rate changes to bond prices.
While it may seem this is the perfect solution to estimating bond price changes, the bottom line is that these are theoretical values that will not provide exact price guidance into the future. Bond prices are still impacted by supply and demand factors, as well the market’s ability to price in future interest changes. That said, these measurements are still useful tools for bond portfolio managers.
Impact of Option Features
When a bond has a call feature attached to it (is “callable”) it means the issuer owns a call option for the bond, and can essentially accelerate maturity. This feature has value to the issuer (long the call), not the investor (short the call), so the issuer must sweeten the bond issue by offering increased rates for callable bonds.
The other option that can be found with bonds are puts which are investor rights. A bond with a put attached represents a long put position for the investor and a short put position for the issuer. If yields increase and the bond price decreases, the investor can put the bond to the issuer. Since this adds value to the investor a bond with such a feature will be offered at lower yields.
These two features change the shape of the price yield picture, with a call option capping price on the upside and a put feature placing a downside floor on the price. Bond managers and investors need to recognize these caps and floors in prices when considering impact to a bond portfolio.
The reason effective duration is considered a more comprehensive measure is because it takes into consideration the change in cash flows that result for bonds with options. Yield changes sufficient enough to trigger an option to be called or put will ultimately affect cash flows—effective duration recognizes that.
To see the previous articles in this series, please click here.
Clare White
Contributing Writer and Options Strategist
Optionetics.com ~ Your Options Education Site
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