Interest Rate Risk and How to Measure It

Posted By: Advisor Analyzer Team

Bond investors often face the risk of interest rate changes that will adversely impact the price of their bond. Interest rate risk can be further broken into price and reinvestment risk for the principal and coupon components of a bond. While there are many different ways to measure investment risk, bonds often use duration and convexity to gauge potentially adverse price impacts from interest. Below are the risks associated with interest rate changes and ways to measure the risk.

Price and Reinvestment Risk

A major risk associated with bonds and fixed income portfolios is interest rate risk. Interest rate risk is the risk associated with interest rate fluctuations, and their subsequent impact on bond prices. Interest rate risk is a combination of two components: reinvestment risk and price risk. Each risk has a different reaction to interest rate fluctuations.

 

Price risk is the risk associated with adverse bond price fluctuations that result from a change in interest rates. Since there is an inverse relation between prices and interest, the risk of prices moving adversely decrease as interest rates decrease, and vice versa. Therefore, price risk has a positive relationship to interest rates changes. This is usually the larger portion of the overall price fluctuation, and the degree of risk depends on a variety of factors, including the size of payments and time to maturity.

 

Reinvestment risk has an inverse relationship with interest rate movements. When rates rise, the cash flows received can be reinvested at the higher rates, which ultimately increase the returns of the bond. As rates fall the return attributable to the coupon payments are also reduced. Therefore, the risk of reinvesting the coupon payments at lower rates increases as rates decrease, and decrease when rates rise. Like price risk, reinvestment risk is determined by the coupon payments and term to maturity.

 

At first, the relation to interest rates may seem counterintuitive. However, it should be noted that there is a difference between price risk and prices. While prices move inversely to rates, the risk of adverse movements increases as prices decrease, and vice versa, hence moving positively with interest rates. Likewise, when reinvesting cash flows, investors would prefer to reinvest at higher rates, and the risk of being unable to do so increase as interest falls.

Duration and Convexity

While equity risk is most often measured with standard deviation and beta, bond risk is better gauged using duration. Duration is a means to measure the degree of bond price fluctuation due to interest rate changes. More specifically, a bond’s duration represents the impact on a bond’s price attributable to a 1% change in interest rates. For example, a duration measure of 3 signifies a 1% decrease in rates would mean bond prices appreciate 3%.

 

The primary reason duration is used in lieu of standard deviation is the lack of pricing data available in the bond markets. While as a whole, the bond markets are much larger than equities, the frequency by which each bond position trades is significantly less. Therefore, the prices reflected may be stale, or an inaccurate representation of the bond’s fluctuation in response to interest rate changes.

 

Convexity is directly related to duration, or more specifically, is the second derivative of duration. It measures the non linear relationship between price and yield, and is used in combination with duration to get a more accurate representation of price fluctuations.

 

Duration is a linear measure, meaning it assumes bond prices will move in a straight line with interest rates. So regardless of the size of interest rate moves, the bond’s price is expected to change by the proportional amount. However, bond prices do not move in a linear fashion, usually prices increase at an increasing rate as yields fall (positive convexity) and fall at a decreasing rate as yields rise (negative convexity). Therefore, a convexity adjust is used to reflect the rate at which prices fall and increase relative to interest rate changes.

Conclusion

Interest rates have a significant impact on bond prices, and attention must be paid when investing. While investing in bonds is generally safer than equity investing, it can still be exposed to significant price fluctuations and volatility. Therefore, it is important for investors to understand and measure not only equity risk, but the impact of interest rate risk on their fixed income positions as well.