Interest Rate Risk

Interest rate risk is the risk that a change in market interest rates will reduce the value of an investment or the income it produces. It matters most for fixed income securities: when rates rise, the prices of existing bonds fall, because new bonds offer more. The effect is larger for bonds with a longer maturity and a lower coupon rate.

Interest rate risk is a form of market risk and is separate from credit risk, the chance that the borrower fails to pay. Even debt with no meaningful credit risk, such as US Treasury securities, carries interest rate risk. Banks face it on their whole balance sheet, because they fund long-term loans with short-term deposits, and supervisors such as the Basel Committee set standards for measuring it.

Suppose you lend money for ten years at 4% a year, and next month new lenders start getting 5% for the same deal. Nobody wants to buy your 4% loan from you at the full price; to sell it, you would have to offer a discount large enough to make up for the lower interest. That discount is interest rate risk showing up in the price.

The longer your loan has left to run, the more years you are stuck with the lower rate, so the bigger the discount. If rates fall instead, your 4% loan becomes more attractive and its price rises. Holding to the end avoids the loss in money terms, but you still miss out on the higher rate available elsewhere.

A bond's price is the present value of its future payments, discounted at the current market yield. A higher discount rate makes each future payment worth less today, so the price drops. This is the inverse relationship at the heart of bond investing, and it is why the market's yield to maturity and a bond's price always move in opposite directions.

Rates move for many reasons: changes in inflation expectations, central bank decisions on the federal funds rate and asset purchases such as quantitative easing, and shifts in the supply of government debt. Short and long rates do not always move together, so a change in the shape of the yield curve is a source of risk as well.

The standard measure is duration. Macaulay duration is the weighted average time, in years, until a bond's cash flows are received. Modified duration converts that into price sensitivity:

• $\Delta P / P$ is the percentage change in the bond's price.
• $D_{\text{mod}}$ is modified duration, equal to Macaulay duration divided by $1 + y$ for a bond paying once a year.
• $\Delta y$ is the change in yield, written as a decimal.

Worked example: a 10-year bond with a $1,000 face value pays a 4% annual coupon and yields 4%, so it is priced at $1,000. Its Macaulay duration is about 8.4 years and its modified duration about 8.1. If market yields rise by one percentage point ($\Delta y = 0.01$), the formula predicts a price change of $-8.1 \times 0.01 = -8.1\%$, to about $919. Pricing the bond exactly at a 5% yield gives about $923. The small gap comes from convexity: the price curve bends, so duration slightly overstates losses when rates rise and understates gains when they fall.

The 2022 rate-rising cycle showed the scale of the risk. As central banks raised rates quickly to fight inflation, long-dated government bonds lost a large share of their market value, and many bond funds had their worst year in decades. In March 2023 Silicon Valley Bank failed after it sold securities at a loss and depositors rushed to withdraw, a bank run driven partly by large unrealized losses on long-dated bonds bought when rates were near zero.

Interest rate risk also affects other assets. Borrowers with floating-rate loans or a variable-rate mortgage face higher payments when rates rise, and equity valuations tend to fall because future profits are discounted more heavily.

Investors and institutions manage the risk in several ways:

• Shortening duration. Holding shorter maturities or floating-rate notes reduces price swings; money market funds are limited by a cap on their weighted average maturity for this reason.
• Laddering. Spreading money across bonds that mature in different years means some cash is always coming back to reinvest at current rates.
• Hedging. Banks and companies use an interest rate swap or futures to swap fixed rates for floating, or the reverse.
• Matching. Pension funds and insurers match the duration of their assets to their liabilities, so rate moves affect both sides roughly equally.

• Investor.gov (SEC): Bonds – FAQs