A bond issued at par pays a five percent coupon, fifty dollars a year on one thousand dollars of face value. Comparable new bonds of the same quality now pay seventy dollars a year when bought at par. Why will no buyer now pay par for the older bond?

Its issuer must now raise the coupon to seven percent at the next payment date, and buyers prefer to wait for that higher payment

A new bond pays twenty dollars a year more for the same outlay at par, so the older bond is now worth less

Its face value repaid at maturity is cut in proportion to the lower coupon it carries relative to the new bonds of the same quality

Its credit quality is presumed to have declined, since the higher coupons on the new bonds signal that its issuer is now a weaker credit

An outstanding bond pays fifty dollars a year on one thousand dollars of face value. Market rates on comparable bonds then fall to three percent. An investor buys the bond at its new market price and holds it to maturity. What does that investor experience?

A price at par, with a total return of five percent because the coupon stays fixed at fifty dollars a year

A price above par, with a total return of five percent because the full coupon is still received every year

A price above par, with a total return near three percent once the premium lost at maturity is counted

A price below par, with a total return near three percent because the coupon now exceeds the market rate

Market interest rates rise sharply. Which of these holders of the same long-term fixed-rate bond is least exposed to a capital loss from the price risk component of interest rate risk?

A trust that bought the bond to hold it to its maturity date and has no foreseeable need to sell it

A dealer carrying the bond in its trading inventory in order to sell it on to customers over the coming weeks

A bank holding the bond in a liquidity reserve that it may have to sell at short notice if depositors withdraw funds

None of them, since the bond's market value falls by the same amount whichever of them happens to hold it

An investor must cut a bond portfolio's sensitivity to interest rate changes but is not allowed to shorten its maturities. Which switch, among bonds of the same maturity and credit quality, lowers that sensitivity?

Into lower-coupon bonds, which have less coupon income at stake whenever market interest rates move

Into higher-coupon bonds, which hand back more cash earlier and leave less in the distant par payment

Into zero coupon bonds, whose single payment at maturity is fixed and so cannot change with market rates

Into bonds bought further below par, whose lower price leaves fewer dollars at risk when rates change

A bond has a modified duration of five. The market yield on it rises by one and a half percentage points. Using duration alone, approximately how does its price change?

It rises by about seven and a half percent

It falls by about seven and a half percent

It falls by about three and a third percent

Why does holding a coupon bond for a period exactly equal to its Macaulay duration produce its yield to maturity whatever interest rates do during that period?

Over that period the bond's price is frozen at its purchase level, so a sale realises no gain and no loss

Over that period the coupon resets to the market rate, so the bond's income tracks whatever rates do

At that point the issuer must repurchase the bond at its yield to maturity price, whatever the market price

A rate change moves the bond's price and the income from reinvested coupons in opposite, offsetting directions

A bond has ten years remaining to maturity, and its Macaulay duration is calculated at exactly ten years. What does that show about the bond?

It makes no payment before maturity, so all of its cash flow arrives on the final date, as a zero coupon bond does

It pays its coupon only once a year, and infrequent coupons push a bond's weighted average time out to the final date

It trades exactly at par, and any coupon bond priced at par has a Macaulay duration equal to the time left to its maturity

Its yield is very low, and a very low yield lifts a coupon-paying bond's Macaulay duration all the way up to its maturity date

A standard non-callable bond has a modified duration of eight, so duration predicts an eight percent price fall for a one percentage point rise in yield. Given that the bond has positive convexity, what actually happens when its yield rises by one percentage point?

The price falls by somewhat more than eight percent, as the curvature deepens the loss

The price falls by somewhat less than eight percent, as the curvature cushions the loss

The price falls by exactly eight percent, as convexity alters only gains when yields fall

The price rises slightly, as positive convexity outweighs the whole of the duration loss

On what condition does a zero coupon bond carry no reinvestment risk for its holder?

It is sold within a year, so that the accreted interest is paid out before market rates can change

It is bought below par, so that the discount locks in the reinvestment rate for every year it is held

It is held to maturity, so that there are no periodic payments to reinvest before par is received

It is issued by the Treasury, so that the accreted interest is guaranteed to compound at the issue yield

Four bonds have the same credit quality and the same yield. Which one's price is most sensitive to a one percentage point change in market rates?

A five-year zero coupon bond, paying no coupon

A two-year bond paying a one percent coupon

A ten-year bond paying an eight percent coupon

A thirty-year bond paying a six percent coupon

An income investor expects interest rates to rise and plans to move from long-term bonds into a company's fixed-rate preferred stock, which has no maturity date, to escape the price falls. Will the move protect her?

No: its fixed dividend gives it interest rate risk like a perpetual bond, so its price also falls when rates rise

Yes: its dividend is reset upward whenever market rates rise, so the share's price stays close to its issue level

Yes: it ranks ahead of the common stock, and that priority shields its price from any change in market rates

Yes: the issuer may call it at a set price, and that call price puts a floor under the share whenever rates rise

A company's shares promise no fixed payment at all. Why does a rise in interest rates still tend to reduce the value of its equity, and which kind of company does it affect most?

A higher discount rate cuts the present value of future earnings, most for mature firms valued on near-term earnings

A higher discount rate cuts the present value of future earnings, most for high-growth firms valued on distant earnings

Higher rates raise the company's dividend obligations, most for firms that pay out the largest share of their earnings

Higher rates raise the tax on equity gains, most for firms whose returns come mainly from capital appreciation

A bond portfolio is laddered, with its maturities distributed across many successive years. What does that structure do about reinvestment risk?

It removes reinvestment risk, since each bond matures in turn and is held until its own maturity date

It concentrates reinvestment in the final year, so the portfolio's income stays fixed until that year

It spreads reinvestment across time, so no single date's rates decide the return on most of the portfolio

It shifts reinvestment risk to the issuers, who must refinance each maturing bond at prevailing rates

A barbell portfolio combines short and long duration bonds, while a bullet portfolio is concentrated at a single maturity. If both are built to the same target duration, in what respect do they differ?

Their coupon income, since a bullet concentrated at one maturity must pay a higher average coupon

Their credit quality, since the barbell must hold lower-rated long bonds to reach the same duration

Their reinvestment dates, since the bullet's bonds mature evenly each year and the barbell's at once

Their convexity characteristics, even though the target duration of the two portfolios is the same

Interest Rate Risk — Duration, Convexity, and Reinvestment

Interest Rate Risk

Interest rate risk is the risk that changes in prevailing market interest rates will adversely affect the value of a fixed income investment or the income it generates, manifesting through two distinct and partially offsetting mechanisms — price risk, which is the risk that rising rates will reduce the market value of outstanding bonds, and reinvestment risk, which is the risk that falling rates will reduce the return earned when coupon payments and principal are reinvested. It is the primary risk inherent in all fixed-rate debt securities and is the foundational concept in fixed income risk management tested throughout the Series 7 and Series 65 examination curricula.

The Inverse Relationship Between Bond Prices and Interest Rates

The most fundamental and most heavily tested fact in fixed income analysis is that bond prices and interest rates move in opposite directions. When market interest rates rise, the prices of outstanding fixed-rate bonds fall. When market interest rates fall, the prices of outstanding fixed-rate bonds rise. FINRA's investor education resource on bonds confirms this directly: a well-known maxim of bond investing is that when interest rates fall, bond prices rise, and vice versa.

The economic logic is straightforward. A bond issued at a five percent coupon rate pays fifty dollars annually per one-thousand-dollar face value for the life of the instrument regardless of what happens to market interest rates after issuance. If market rates subsequently rise to seven percent, new bonds of comparable quality offer seventy dollars annually. No rational investor will pay full par value for a bond paying fifty dollars when they could pay par for a bond paying seventy dollars.

The price of the existing five percent bond must fall to the level at which its fifty-dollar annual payment, combined with the gain from receiving one thousand dollars at maturity despite paying less than one thousand dollars now, produces a total return equivalent to the prevailing seven percent market rate. The bond trades at a discount.

The reverse applies when rates fall. If market rates decline to three percent, new bonds offer only thirty dollars annually. The existing five percent bond paying fifty dollars becomes extremely attractive — investors will bid up its price above par until the total return including the loss from paying above par and receiving only par at maturity equals the prevailing three percent rate. The bond trades at a premium.

Price Risk — The Market Value Dimension

Price risk is the component of interest rate risk that affects investors who may need to sell their bonds before maturity. A long-term investor who holds a bond to its stated maturity date receives the full face value regardless of what happened to interest rates and market prices during the holding period — the price fluctuations are irrelevant if the investor never sells. For an investor who might need to liquidate before maturity, however, every basis point of rate increase translates directly into capital loss.

The severity of price risk depends on three bond characteristics that determine how sensitive a bond's price is to interest rate changes: maturity, coupon rate, and yield level.

Longer maturity bonds are far more sensitive to interest rate changes than shorter maturity bonds, because a greater proportion of their cash flows occur far into the future and are therefore discounted more severely when rates rise. A thirty-year zero coupon bond will experience far greater price swings per unit of rate change than a two-year bond. For short maturity bonds, the price approaches par as the maturity date nears, limiting how far the price can move regardless of rate changes.

Lower coupon bonds are more sensitive to interest rate changes than higher coupon bonds of the same maturity. A bond paying a low coupon has a greater proportion of its total cash flows concentrated in the distant par payment at maturity — which is discounted more severely when rates rise — and less cash returned early through coupon payments. A zero coupon bond has all of its cash flow at maturity and therefore maximum sensitivity to interest rate changes of any bond at a given maturity. A higher coupon bond returns more cash earlier through coupon payments, reducing the average time investors must wait to receive their money and thereby reducing price sensitivity.

Higher yield levels reduce the absolute dollar price change from a given basis point move in rates, because at higher starting yields the same percentage price change produces fewer dollars of movement on a lower base price. This relationship is captured by the concept of convexity.

Duration — The Measure of Interest Rate Sensitivity

Duration is the primary quantitative measure of a bond's price sensitivity to interest rate changes. FINRA's investor education resource confirms that bond duration is a measure of the degree to which a bond investment is likely to change in value if interest rates were to rise or fall — the higher the number, the more sensitive the bond to changes in interest rates.

Modified duration — the most practically useful form for price sensitivity estimation — measures the approximate percentage change in a bond's price for a one percentage point change in yield. A bond with a modified duration of seven years will experience approximately a seven percent price change for each one percent change in yield. If rates rise by one percent, the bond loses approximately seven percent of its market value. If rates fall by one percent, the bond gains approximately seven percent.

Duration is not the same as maturity, though it is closely related. For a coupon-paying bond, duration is always less than maturity because some cash flows arrive before maturity in the form of coupon payments. For a zero coupon bond, duration equals maturity exactly — all cash flows arrive at the single maturity date.

The Macaulay duration, developed by Frederick Macaulay in 1938, is the weighted average time to receipt of all cash flows from a bond, where each cash flow is weighted by its present value as a proportion of the bond's total price. It is expressed in years and provides an intuitive measure of how long the investor must wait on average to receive the bond's cash flows. The CFA Institute's fixed income curriculum confirms that Macaulay duration has a specific portfolio management application — holding a bond for exactly its Macaulay duration balances reinvestment risk and price risk, producing the yield to maturity regardless of what happens to interest rates during the holding period.

Modified duration equals Macaulay duration divided by one plus the periodic yield. For practical examination purposes, candidates must know that duration rises with longer maturity, rises with lower coupon rates, and falls when yield levels are higher.

Convexity — The Curvature of the Price-Yield Relationship

Duration is a linear approximation of the actual price-yield relationship, which is curved rather than straight. Convexity measures the curvature — the degree to which the actual price change for a given yield move departs from the linear duration estimate.

For standard non-callable bonds, the price-yield relationship exhibits positive convexity — the actual price increase when rates fall is greater than the duration estimate predicts, and the actual price decrease when rates rise is less than the duration estimate predicts. Positive convexity works in the investor's favour: the bond gains more than expected when rates fall and loses less than expected when rates rise.

Callable bonds and mortgage-backed securities can exhibit negative convexity under certain conditions — when rates fall and the issuer is likely to call the bond or when mortgage borrowers prepay — because price appreciation is capped by the approaching call or prepayment even as rates continue falling. Negative convexity works against the investor.

Raymond James's fixed income education resource confirms that a bond with positive convexity will have larger price increases due to a decline in yields than price declines due to an increase in yields — precisely the asymmetric behaviour that makes positive convexity valuable.

Reinvestment Risk — The Income Dimension

Reinvestment risk is the second component of interest rate risk and operates in the opposite direction from price risk. It is the risk that the periodic cash flows received from a bond — coupon payments and returning principal — will be reinvested at lower rates than the original yield to maturity, reducing the investor's actual total return below the promised yield.

When an investor purchases a bond with a yield to maturity of six percent, that six percent yield is only actually earned if every coupon payment received during the life of the bond is reinvested at six percent. If interest rates decline after the bond is purchased and coupons must be reinvested at four percent, the investor's actual realised return will be less than six percent even though every coupon and principal payment was received on schedule.

The CFA Institute's fixed income curriculum identifies the precise offsetting relationship: reinvestment risk and price risk are types of interest rate risk with an inverse relationship. Rising interest rates create price losses on the existing bond but increase the return available on reinvested cash flows.

Falling interest rates create price gains on the existing bond but reduce the return available on reinvested cash flows. For a long-term buy-and-hold investor, reinvestment risk dominates — rising rates actually improve long-term total return by enabling reinvestment at higher rates even while creating temporary unrealised price losses. For a short-term investor who may need to sell, price risk dominates.

Zero coupon bonds have no reinvestment risk for an investor who holds to maturity, because they make no periodic coupon payments to reinvest — the entire return is delivered as the difference between the purchase price and the par value received at maturity. This makes zero coupon bonds the instrument of choice when an investor needs to guarantee a specific future value with certainty, regardless of what happens to interest rates in the interim.

Factors Determining a Bond's Interest Rate Risk

Four factors determine how much interest rate risk a specific bond carries, and examination candidates must be able to rank bonds by their relative interest rate sensitivity.

Maturity is the most powerful factor. Longer maturity means greater interest rate risk — more years over which the fixed coupon must compete with changing market rates, and a larger proportion of cash flows discounted over longer periods.

Coupon rate is the second factor. Lower coupon bonds have higher interest rate risk at a given maturity because more of their total value is concentrated in the distant par payment. Zero coupon bonds have maximum duration and maximum price sensitivity.

Yield level affects sensitivity — at lower yield levels, duration is higher and price sensitivity is greater than at higher yield levels for the same bond. This is the mathematical consequence of discounting cash flows at a lower rate.

Call and prepayment features reduce effective duration at low rate levels because the issuer's right to call or borrowers' ability to prepay caps the bond's price appreciation — negative convexity limits the price rise that would otherwise occur when rates fall.

Interest Rate Risk and Different Asset Classes

Interest rate risk extends beyond traditional bonds. Any financial instrument that generates fixed or quasi-fixed cash flows over time carries interest rate risk.

Preferred stock with a fixed dividend rate has interest rate risk analogous to a perpetual bond — when rates rise, the fixed dividend becomes less competitive and the price falls. Mortgage-backed securities carry complex interest rate risk involving both duration risk and convexity from prepayment behaviour. Fixed annuities carry interest rate risk during the accumulation phase. Even equity valuations are affected by interest rates because the discount rate used in discounted cash flow models incorporates interest rate levels — rising rates increase the discount rate applied to future earnings, reducing the present value of all equities and particularly affecting high-growth companies whose value is concentrated in distant future cash flows.

Managing Interest Rate Risk

Fixed income portfolio managers employ several strategies to manage interest rate risk consistent with their investment objectives and duration targets.

Duration matching sets the portfolio's duration equal to the investment horizon, balancing reinvestment and price risks to produce the target return regardless of rate movements — the immunisation strategy formalised by Frank Redington in 1952. Laddering distributes bond maturities across multiple years, reducing the concentration of reinvestment risk at any single point in time and ensuring that maturing bonds are available to reinvest at prevailing rates throughout the cycle.

Barbell portfolios combine short and long duration bonds to achieve a target duration with different convexity characteristics than a bullet portfolio concentrated at a single maturity. Interest rate swaps allow portfolio managers to modify their effective interest rate exposure without buying or selling physical bonds.

Examination Relevance and Key Takeaways

Interest rate risk is tested on the SIE, Series 7, and Series 65 examinations in the context of fixed income analysis, bond pricing, duration, convexity, and portfolio risk management.

The key points to retain are these.

Interest rate risk is the risk that changes in market interest rates will reduce bond values or reinvestment income, manifesting through price risk and reinvestment risk. Bond prices and interest rates move inversely — rising rates reduce prices, falling rates increase prices — because the fixed coupon must compete with prevailing market yields and price adjusts until total return equalises.

Duration measures price sensitivity — a bond with seven years of modified duration experiences approximately a seven percent price change for each one percent rate change — with duration rising as maturity increases, coupon rates decrease, or yield levels fall.

Convexity measures the curvature of the price-yield relationship — positive convexity for standard bonds means price gains on rate declines exceed price losses on equal rate increases, working in the investor's favour, while negative convexity for callable bonds caps price appreciation. Reinvestment risk offsets price risk — rising rates hurt current prices but improve reinvestment returns, and the two risks balance precisely at the bond's Macaulay duration making duration matching the foundation of immunisation strategies.

Zero coupon bonds have maximum duration and maximum price risk at a given maturity but zero reinvestment risk for investors holding to maturity. The four factors determining relative interest rate risk are maturity — longer means more risk — coupon rate — lower means more risk — yield level — lower means more risk — and call or prepayment features — which reduce effective duration and create negative convexity at low rate levels.