Understanding Fixed Income Interest Rate Risk: A Comprehensive Guide

Fixed income interest rate risk is the risk of a fixed income assetFixed Income RisksFixed income risks occur based on the volatility of the bond market environment. Risks impact the market value of the security when it is sold, cash flow from the security while it is held, and additional income made by reinvesting cash flows. losing value due to a change in interest rates. Since bonds and interest rates have an inverse relationship, as interest rates rise, the value/price of bondsBondsBonds are fixed-income securities that are issued by corporations and governments to raise capital. The bond issuer borrows capital from the bondholder and makes fixed payments to them at a fixed (or variable) interest rate for a specified period. falls. Interest rate risk can be measured by the full valuation approach or the duration/convexity approach. This article will focus on the convexity approach.

What affects interest rate risk?

Interest rateInterest RateAn interest rate refers to the amount charged by a lender to a borrower for any form of debt given, generally expressed as a percentage of the principal. risk affects bonds differently based on the features that the bonds possess. Some of these features include maturity date, coupon rate, and embedded options

Maturity

Bonds with a longer maturity rate are more susceptible to changing interest rates. If a 20-year bond has a yield of 4%, it would lose value if the interest rate rises to 5%. This is because investors have more incentive to buy the 5% bond. Thus, the 4% yield bond will need to have a lower price to give investors a reason to buy it. The price has to decrease by a large amount, as it accounts for 20 years of lower coupon ratesCoupon RateA coupon rate is the amount of annual interest income paid to a bondholder, based on the face value of the bond.. However, if the bond matures in two years, the price will stay relatively the same. This is because the price decrease only accounts for two years of interest payments with a lower coupon rate.

Coupon rate

The next feature of a bond that determines the impact of interest rates is the coupon rate. The yield to maturity – YTMYield to Maturity (YTM)Yield to Maturity (YTM) – otherwise referred to as redemption or book yield – is the speculative rate of return or interest rate of a fixed-rate security. – of the old bond must be the same as the YTM of the newer bond offering a higher interest rate. Imagine one bond with a 2% coupon rate and one with a 4% coupon rate. The face value of the 2% bond will have to drop to match up appropriately with the 4% bond.

Embedded options

Lastly, embedded options react to interest rates differently depending on the optionOptions: Calls and PutsAn option is a derivative contract that gives the holder the right, but not the obligation, to buy or sell an asset by a certain date at a specified price..  For example, when the interest rate increases, the price for a callable bondCallable BondA callable bond (redeemable bond) is a type of bond that provides the issuer of the bond with the right, but not the obligation, to redeem the bond before its maturity date. The callable bond is a bond with an embedded call option. These bonds generally come with certain restrictions on the call option. and option-free bond will both decrease. However, the price of the callable bond will not fall as much, by comparison.

The equation for the price of a callable bond is:

Price of callable bond = price of option-free bond – the price of an embedded call option

• option-free bond:  $50
• embedded call option: $20
• Price of callable bond: $30

If the interest rate rises, then the price of the option-free bond will drop. But the drop is offset by the drop in the embedded call option.

• option-free bond: $50-$10= $40
• embedded call option: $20-$5 = $15
• price of callable bond: $25

As shown by the example above, the price of the option-free bond dropped by $10. However, the embedded call option only dropped by $5. This is because the $5 decrease in the call option offset the change. The value of the callable bond is not as exposed to interest rate risk.

Measuring interest rate risk

Interest rate risk can be measured by durationDurationDuration is one of the fundamental characteristics of a fixed-income security (e.g., a bond) alongside maturity, yield, coupon, and call features. and convexity. Duration measures the approximate sensitivity of the value of the bond to the change in interest rate. Convexity is another measure of the change in price. An important note is that this measure is not the same as the convex shape of the price/yield relationship.

Convexity

As the price/yield relationshipYield CurveThe Yield Curve is a graphical representation of the interest rates on debt for a range of maturities. It shows the yield an investor is expecting to earn if he lends his money for a given period of time.  The graph displays a bond's yield on the vertical axis and the time to maturity across the horizontal axis. is curved, the duration measure is not accurate. Duration only measures the linear relationship between the price and the yield of the bond, and does not consider the curved shape. Simply put, as the yield on a bond changes, so does the duration. Thus, measuring the impact of convexity is important for understanding interest rate risk. For bonds with a more convex price/yield curve, the interest rate increase has less effect on the price. On the other hand, as the interest rate decreases, the bond price increases more for bonds with a more convex shape.

The formula for the convexity measure is:

• Convexity measure = (V₊ + V_– – 2V₀) / (2V₀(Δy)²)

Where:

• V₀ = initial price
• V₊ = price if yields increase by Δy
• V_– = price if yields decrease by Δy
• Δy = change in yield

The convexity measure produces a number that is not simple to interpret. Thus, the convexity adjustment is used to estimate the percentage of price change.

The formula for the convexity adjustment is:

• Convexity adjustment = convexity measure x (Δy)² x 100

The convexity adjustment is a percentage that remains the same regardless of whether the change in yield is an increase or decrease. To get the estimated percentage price change, add the convexity adjustment to the estimated change using duration. If the number is 31%, then that means the price will increase by approximately 31%.

Why it matters

By understanding the impact of interest rates, investors can make more knowledgable decisions on the purchase of fixed income securities. This gives investors a better idea as to what type of bonds they would like in their portfolio. An investor with a greater risk tolerance can purchase a bond with a high estimated percentage price change while a risk-averse investor can choose one with lower duration and convexity.

Additional Resources

Thank you for reading CFI’s article on fixed income interest rate risk. To keep learning and advancing your career, we recommend these additional CFI resources:

• Fixed Income RiskFixed Income RisksFixed income risks occur based on the volatility of the bond market environment. Risks impact the market value of the security when it is sold, cash flow from the security while it is held, and additional income made by reinvesting cash flows.
• Floating Rate NoteFloating Rate NoteA floating rate note (FRN) is a debt instrument whose coupon rate is tied to a benchmark rate such as LIBOR or the US Treasury Bill rate. Thus, the coupon rate on a floating rate note is variable. It is typically composed of a variable benchmark rate + a fixed spread.
• Fixed Income Bond TermsFixed Income Bond TermsDefinitions for the most common bond and fixed income terms. Annuity, perpetuity, coupon rate, covariance, current yield, par value, yield to maturity. etc.
• Fixed Income TradingFixed Income TradingFixed income trading involves investing in bonds or other debt security instruments. Fixed income securities have several unique attributes and factors that