Price and yield move in opposite directions

Welcome to Smarti Exam Prep. Securities Industry Essentials Exam, Lesson Eight. Bond questions become manageable when you keep price, par value, coupon, current yield, and yield to maturity in separate boxes. This complete lesson follows the authoritative long Private source and preserves its worked examples. Multiple-choice drills remain in the rapid-fire video. Build one central map: the coupon cash flow is fixed by the bond contract, the market price can change, and the yield an investor earns changes in the opposite direction from price.

The bond contract separates par, coupon, and maturity

Start with the bond contract. Par value, usually one thousand dollars in an exam question unless another amount is stated, is the principal the issuer promises to repay at maturity. The coupon rate is applied to par value, not to the bond's changing market price. Maturity is the date when the issuer is scheduled to return principal. A five-percent coupon on one thousand dollars produces fifty dollars of annual interest even if the bond later trades for nine hundred fifty dollars or one thousand fifty dollars. Keep the promised cash flow separate from the market price.

A bond quote is a percentage of par

Corporate and municipal bond prices are commonly quoted as a percentage of par. A quote of one hundred means one hundred percent of one thousand dollars, or one thousand dollars. A quote of ninety-five means ninety-five percent of par, or nine hundred fifty dollars. A quote of one hundred two point five means one hundred two and one-half percent of par, or one thousand twenty-five dollars. Translate the quote before doing yield math. Below one hundred is a discount, exactly one hundred is par, and above one hundred is a premium.

Coupon yield uses annual interest divided by par

Coupon yield, also called the nominal yield in many exam materials, begins with the stated coupon rate. Multiply that rate by par to find annual interest. A four-and-one-half-percent coupon on a one-thousand-dollar bond pays forty-five dollars each year, usually in two equal semiannual payments. The coupon yield remains four-and-one-half percent because both the coupon dollars and par value come from the contract. It does not change merely because a later buyer pays a premium or discount. Market price matters when you calculate current yield and the broader return measures.

Current yield compares annual interest with market price

Current yield answers a different question: how much annual coupon income is produced relative to the price paid now? The formula is annual interest dollars divided by current market price. Do not put the coupon percentage directly over the price. First turn the coupon rate into dollars by multiplying it by par. Then divide those annual dollars by the market price. Current yield ignores the time remaining, the gain or loss when principal is repaid, and reinvestment assumptions. It is an income snapshot, not the bond's complete expected return.

A five-percent bond at 95 yields about 5.26 percent

Work the long source's core example. A five-percent bond with one thousand dollars par pays fifty dollars per year. A market quote of ninety-five means a price of nine hundred fifty dollars. Divide fifty by nine hundred fifty. The current yield is approximately five point two six percent. The result is higher than the five-percent coupon because the same fifty-dollar income stream was purchased for less than par. Before choosing an answer, perform a direction check: buying fixed income at a discount should make current yield greater than coupon yield.

Rearrange current yield when price is missing

The same formula can solve for market price. If annual coupon interest is sixty dollars and current yield is six point five percent, divide the annual interest by the yield written as a decimal. Sixty divided by zero point zero six five equals about nine hundred twenty-three dollars and eight cents. Because six point five percent current yield is greater than the six-percent coupon yield on one thousand dollars par, the answer must be below par. That direction check catches decimal errors and reversed formulas before they cost you an exam point.

Yield to maturity includes income and the path back to par

Yield to maturity is broader than current yield. It estimates the annualized return if the investor holds the bond to maturity, the issuer makes the promised payments, and the calculation's reinvestment assumptions are met. It includes coupon interest, the price paid, the time remaining, and the gain or loss as the bond moves toward par at maturity. A discount bond can add a gain when one thousand dollars is repaid. A premium bond can produce a loss of premium. That is why yield to maturity sits farther from coupon yield than current yield does.

Callable bonds add yield to call and yield to worst

A callable bond may be redeemed before maturity, so investors also evaluate yield to call. Yield to call uses the assumed call date and call price instead of the final maturity date and par repayment. Yield to worst compares the relevant return paths and identifies the lowest potential yield under the stated assumptions, without treating issuer default as the scenario. Current yield, yield to maturity, and yield to call answer different questions. When a problem says earliest call date or call price, do not automatically use the maturity calculation.

At a discount, yield to maturity is highest

For a bond selling below par, memorize the yield order and understand why it works. Coupon yield is based on par. Current yield is higher because the same interest is divided by a lower market price. Yield to maturity is higher still because it also includes the gain from buying below par and receiving par at maturity. The order from lowest to highest is coupon yield, current yield, then yield to maturity. Written from highest to lowest, it is yield to maturity, current yield, coupon yield. The direction comes from the discount's built-in gain.

At par, the principal yield measures are equal

When a standard fixed-rate bond trades exactly at par and no special feature changes the calculation, coupon yield, current yield, and yield to maturity align. The investor pays the same principal amount that will be repaid, so there is no discount gain or premium loss. A five-percent bond bought at one thousand dollars produces fifty dollars divided by one thousand dollars, or five percent current yield, and the maturity path does not add a price adjustment. This equality is a useful anchor between the discount and premium yield ladders.

At a premium, yield to maturity is lowest

For a bond selling above par, the order reverses. Coupon yield remains tied to par. Current yield becomes lower because the annual coupon dollars are divided by a price above par. Yield to maturity is lower still because it includes the loss of premium as the investor receives only par at maturity. From highest to lowest, the order is coupon yield, current yield, then yield to maturity. If a premium bond's proposed current yield is above its coupon rate, stop: the direction is wrong.

Market rates and existing bond prices move inversely

The defining relationship is inverse. When market interest rates rise, newly issued bonds can offer higher coupons or yields, so an older fixed coupon becomes less attractive. Its market price must fall until its return becomes competitive. When market rates fall, an older higher fixed coupon becomes more attractive, so investors may bid its price upward. The coupon dollars do not change; the price changes, which changes yield. Picture a seesaw with market rates and yields on one side and existing fixed-rate bond prices on the other.

A four-percent bond falls when new bonds yield five percent

Suppose an outstanding bond pays a four-percent coupon while comparable new bonds begin yielding five percent. Investors will not normally pay one thousand dollars for the older forty-dollar income stream when a new bond can provide fifty dollars at the same par amount and similar risk. The older bond must trade below par so its current and overall yield rise toward the market. The precise price depends on maturity and other features, but the direction is clear: market rates rose, so the fixed-rate bond's price falls to a discount.

A six-percent bond rises when new bonds yield five percent

Now reverse the numbers. An outstanding bond pays six percent while comparable new bonds yield five percent. The older bond's sixty-dollar annual income is more attractive than the fifty dollars available from a new one-thousand-dollar issue with similar risk. Buyers may pay more than par for that larger fixed cash flow. The price rises to a premium until the return becomes competitive with the market. Again, the coupon stays six percent of par; paying the premium reduces the buyer's current yield and yield to maturity.

Lower-coupon bonds are generally more rate sensitive

When two otherwise similar bonds have the same maturity and credit quality, the lower-coupon bond generally has greater interest-rate sensitivity. More of its value arrives later through principal repayment, while the higher-coupon bond returns more cash earlier. Distant cash flows are affected more by changes in the discount rate. This comparison assumes the other features are truly similar. Do not compare coupon alone when maturities, call features, credit risk, or embedded options differ. For the clean exam setup, lower coupon means greater price movement when rates change.

Longer maturities are generally more rate sensitive

Maturity also changes sensitivity. Between otherwise similar fixed-rate bonds, the longer-maturity bond generally moves more when market rates change. Its principal and more of its total cash flow remain exposed to the new rate environment for longer. A short-maturity bond is pulled toward par sooner because repayment is closer. The exam usually asks for a relative ranking, not an exact price change. Hold coupon and credit quality constant, then choose the longer maturity as the bond with greater interest-rate risk.

Combine coupon and maturity to rank interest-rate risk

Put the two sensitivity rules together. Long maturity increases interest-rate exposure, and low coupon increases it. Therefore, among plain fixed-rate bonds with comparable credit and features, the long-term low-coupon bond is usually the most price sensitive. The short-term high-coupon bond is usually the least. The remaining combinations sit between those endpoints. This matrix is more reliable than memorizing isolated slogans because it forces you to compare both dimensions. Always check for an embedded call, conversion feature, or unusual cash flow before applying the plain-bond ranking.

A zero-coupon bond concentrates value at maturity

A zero-coupon bond makes no periodic coupon payments. The investor buys it below par and receives par at maturity if the issuer pays as promised. Because the cash flow is concentrated at the end, a zero-coupon bond with a given maturity is generally more sensitive to interest-rate changes than a coupon bond with the same maturity and credit quality. Its current yield is zero because it pays no annual coupon interest, even though its yield to maturity can be positive through the discount accreting toward par.

Duration summarizes price sensitivity to rate changes

Duration is a sensitivity measure that combines the timing and present value of a bond's expected cash flows. A higher duration generally means a larger price response to a given change in yield. Duration is expressed in years, but it is not simply the bond's remaining maturity. Coupon level, time to maturity, yield, and embedded features can affect it. For an introductory exam question, use duration as the bridge from rate movement to approximate price movement: higher duration means more sensitivity, and lower duration means less.

Duration gives a first approximation of price movement

A common approximation says that a bond's percentage price change is roughly the negative of its duration multiplied by the change in yield, for a relatively small rate move. If duration is five and yield rises by one percentage point, the estimated price change is about negative five percent. If yield falls by one percentage point, the estimate is about positive five percent. The negative sign captures the inverse relationship. This is an approximation, not an exact promise, because bond-price curvature, changing cash flows, and embedded options can alter the result.

Current yield falls when the bond price rises

Hold the coupon dollars constant and change only the market price. A bond pays fifty dollars annually. At a price of nine hundred fifty dollars, current yield is about five point two six percent. If the price rises to one thousand fifty dollars, current yield becomes fifty divided by one thousand fifty, or about four point seven six percent. The numerator did not move, so the higher denominator pushed the yield lower. This simple arithmetic is the inverse price-yield relationship in miniature and gives you a fast direction check.

Use remaining maturity, not the bond's original term

A bond may have been issued as a thirty-year bond, but an investor who buys it with eight years left owns an eight-year remaining cash-flow stream. Yield to maturity and interest-rate sensitivity depend on the time remaining now, not the original label alone. The maturity date is fixed in the contract, while remaining maturity shrinks as time passes. On a question, subtract the current date from the maturity date when needed. Do not automatically treat every bond originally issued for thirty years as though thirty years remain.

Treasury credit strength does not remove market-price risk

U.S. Treasury securities are commonly used as the baseline for very low credit risk, but their market prices can still move sharply when interest rates change. A long-term Treasury bond can lose market value when yields rise even though investors expect the federal government to make the promised payments. If the investor holds to maturity, interim price movement may not change the stated principal payment, but selling early can realize a loss. Separate credit risk from interest-rate risk and from opportunity cost; they are different questions.

Apply the yield ladder before calculating

An investor buys a one-thousand-dollar par bond at a quote of one hundred four. The bond has a five-percent coupon and will mature at par. Without calculating an exact yield to maturity, rank coupon yield, current yield, and yield to maturity. The bond is at a premium. Current yield must be below the five-percent coupon because fifty dollars is divided by more than one thousand dollars. Yield to maturity is lower still because the investor also loses the premium by maturity. The correct order from highest to lowest is coupon yield, current yield, yield to maturity.

The complete Lesson Eight price-and-yield map

Bring the Lesson Eight map together. Par is the principal due at maturity, coupon interest is based on par, and price is what the market pays now. Current yield is annual interest divided by price. Yield to maturity adds time and the path back to par; callable bonds add yield to call and yield to worst. Discount bonds have yield to maturity above current yield above coupon yield, while premium bonds reverse that order. Rates and existing fixed-rate bond prices move inversely. Longer maturity, lower coupon, higher duration, and zero-coupon cash flows generally increase sensitivity. Continue at Smarti Exam Prep.

Continue learning

Continue to Lesson Nine for bond ratings, calls, conversion, and sale methods, or choose the Products and Risks rapid-fire practice.