Finance Quiz: Bond Price Yield Relationship

20 questions · exam conditions

0:00

Bond Price Yield RelationshipQuestion 1 of 20

An investor has a specific financial liability of $100,000 due in exactly 7 years. The investor wishes to purchase a single bond to fund this liability and is most concerned with minimizing the risk that the portfolio's value will not match the liability's value at the 7-year mark.

Given the investor's goal described in the passage, which of the following risks is the primary concern they are trying to mitigate?

Credit risk, because a default would result in a failure to meet the liability.

Reinvestment risk, because lower rates on coupon payments would reduce the final accumulated value.

Price risk, as rising interest rates could decrease the bond's sale price before the liability is due.

Interest rate risk, representing the uncertainty in the terminal value of the investment due to the offsetting effects of price and reinvestment risk.

← Back to quizzes

Finance Quiz

Finance Quiz: Bond Price Yield Relationship

Practice Bond Price Yield Relationship in Finance with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Bond Price Yield Relationship, giving you a quick way to practice the rules, question types, and explanations that matter most for Finance.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

Given the investor's goal described in the passage, which of the following risks is the primary concern they are trying to mitigate?

Credit risk, because a default would result in a failure to meet the liability.
Reinvestment risk, because lower rates on coupon payments would reduce the final accumulated value.
Price risk, as rising interest rates could decrease the bond's sale price before the liability is due.
Interest rate risk, representing the uncertainty in the terminal value of the investment due to the offsetting effects of price and reinvestment risk. (correct answer)

Explanation: The investor is concerned with having a specific amount of money at a specific future date. This is a classic immunization problem. The primary risk is interest rate risk, which has two components: price risk (the value of the bond at the end of the horizon) and reinvestment risk (the return from reinvesting coupons). An investor with a 7-year horizon holding a bond is exposed to both. Holding a 7-year zero-coupon bond would eliminate reinvestment risk but not price risk if sold before maturity. Holding a longer-term bond creates a mismatch. The overall goal is to manage the net effect of these two components of interest rate risk to ensure the terminal value meets the liability.

Question 2

An analyst is comparing two bonds. Bond A is a 15-year, 5% coupon bond. Bond B is a 15-year zero-coupon bond. If the yields on both bonds increase by 75 basis points, what is the expected impact on their prices?

Both bond prices will fall, but Bond A's price will fall by a greater percentage.
Both bond prices will fall, but Bond B's price will fall by a greater percentage. (correct answer)
Both bond prices will fall by the same percentage because their maturities are identical.
Both bond prices will rise, with Bond B's price rising by a greater percentage.

Explanation: For a given maturity, a zero-coupon bond has the highest possible interest rate sensitivity (duration). This is because its only cash flow is the principal repayment at maturity, making its weighted-average time to receive cash flows equal to its maturity. A coupon bond has intermediate cash flows, which lowers its duration relative to a zero-coupon bond of the same maturity. Therefore, when yields rise, the price of the zero-coupon bond (Bond B) will fall by a greater percentage than the price of the coupon bond (Bond A).

Question 3

A portfolio consists of a 2-year Treasury note and a 20-year Treasury bond. An economist predicts that the Federal Reserve will raise short-term rates while long-term inflation expectations fall, leading to a flattening of the yield curve. What is the most likely impact on the value of this portfolio?

The value will likely increase, as the price gain on the 20-year bond will exceed the price loss on the 2-year note. (correct answer)
The value will likely decrease, as the price loss on the 2-year note will exceed the price gain on the 20-year bond.
The value will likely decrease, as both the 2-year note and the 20-year bond will fall in price.
The value will likely increase, as both the 2-year note and the 20-year bond will rise in price.

Explanation: A flattening yield curve in this scenario means short-term rates rise (decreasing the price of the 2-year note) and long-term rates fall (increasing the price of the 20-year bond). Long-term bonds are significantly more sensitive to interest rate changes than short-term bonds. Therefore, the percentage price increase on the 20-year bond from a drop in long-term rates will almost certainly be much larger in magnitude than the percentage price decrease on the 2-year note from a rise in short-term rates. This will lead to a net increase in the portfolio's value.

Question 4

An analyst observes that a particular 10-year, option-free corporate bond's price increased by 5.25% when its yield to maturity fell by 50 basis points. Based on the principle of bond convexity, what is the most likely price change if the bond's yield to maturity were to increase by 50 basis points from its original level?

A decrease of exactly 5.25%
A decrease of more than 5.25%
A decrease of less than 5.25% (correct answer)
An increase of less than 5.25%

Explanation: The price-yield relationship for an option-free bond is convex. This means the magnitude of the price increase for a given decrease in yield is greater than the magnitude of the price decrease for an equivalent increase in yield. Since the price increased by 5.25% for a 50 bps yield decrease, the price decrease for a 50 bps yield increase must be less than 5.25%.

Question 5

An insurance company needs to immunize a single liability due in 12 years. The company's analyst is considering four different option-free bond portfolios. Which portfolio would be the most effective at minimizing the interest rate risk associated with this liability?

A portfolio of bonds with an average maturity of 12 years.
A zero-coupon bond with a maturity of 12 years. (correct answer)
A portfolio of bonds with a Macaulay duration of 15 years.
A portfolio of floating-rate notes with an average maturity of 12 years.

Explanation: To immunize a single liability, the ideal asset is one that provides a certain cash flow at the exact time the liability is due. A zero-coupon bond with a maturity of 12 years provides a single, known cash flow in 12 years, perfectly matching the liability. This strategy eliminates both price risk (as the bond is held to maturity) and reinvestment risk (as there are no coupons to reinvest). Matching Macaulay duration works for small, parallel yield curve shifts but is not as perfect as a zero-coupon bond. Matching maturity is less precise than matching duration, and floating-rate notes are unsuitable for locking in a value for a future liability.

Question 6

A puttable bond gives the bondholder the right to sell the bond back to the issuer at a predetermined price prior to maturity. How does this feature affect the bond's interest rate risk from the perspective of the bondholder?

It increases interest rate risk because the put option adds complexity and uncertainty to the bond's cash flows.
It has no effect on interest rate risk, as the bond's coupon and maturity remain unchanged.
It reduces interest rate risk by setting a price floor below which the bond's value is unlikely to fall. (correct answer)
It transforms interest rate risk into credit risk, as the value of the put depends on the issuer's financial health.

Explanation: The embedded put option provides downside protection for the bondholder. If market interest rates rise significantly, the price of a standard bond would fall. With a puttable bond, the holder can sell the bond back to the issuer at the put price, which acts as a price floor. This feature reduces the bond's price sensitivity to interest rate increases, thereby lowering the bondholder's interest rate risk.

Question 7

Assume the price of a 10-year, 4% coupon bond is $922.05 at a market yield of 5%. If the market yield suddenly drops to 4%, the bond's price will rise to $1,000. If instead the market yield had risen to 6%, the bond's price would have fallen to $851.23. This example provides the strongest support for which of the following bond principles?

Bonds with lower coupons have lower interest rate risk.
The price-yield relationship is approximately linear for small changes in yield.
Bond price changes are symmetric for equal increases and decreases in yield.
Bond prices are more sensitive to a decrease in yield than to an equivalent increase in yield. (correct answer)

Explanation: This question requires analyzing the price changes. The price increase from a 1% yield drop (5% to 4%) is $1000 - $922.05 = $77.95. The price decrease from a 1% yield rise (5% to 6%) is $922.05 - $851.23 = $70.82. Since the price increase ($77.95) is larger in magnitude than the price decrease ($70.82) for an equal-sized change in yield, this demonstrates the principle of positive convexity. This principle states that bond prices are more sensitive to yield decreases than to equivalent yield increases.

Question 8

An analyst is comparing two option-free bonds with identical coupons and maturities. Bond P is trading at a premium (YTM < Coupon Rate) and Bond D is trading at a discount (YTM > Coupon Rate). Which bond will experience a larger percentage price change if the market-wide yield for both bonds changes by 25 basis points?

Bond P, because a lower initial yield results in higher price sensitivity. (correct answer)
Bond D, because a higher initial yield results in higher price sensitivity.
Both will experience the same percentage price change because their coupons and maturities are identical.
It cannot be determined without knowing the exact yield-to-maturity for each bond.

Explanation: A bond's price sensitivity to yield changes (its duration) is inversely related to its yield-to-maturity. A bond trading at a premium has a lower YTM than a similar bond trading at a discount. Because Bond P has a lower initial yield, its price will be more sensitive to a given change in market rates. Therefore, Bond P will experience a larger percentage price change.

Question 9

A portfolio manager holds a long-term, option-free bond. Immediately after purchase, prevailing market interest rates fall sharply and are expected to remain low. Which of the following best describes the change in the primary interest rate risk faced by the manager for this specific bond?

Price risk has increased because the bond is now trading at a significant premium.
Reinvestment risk has become the more prominent concern for future cash flows. (correct answer)
Both price risk and reinvestment risk have decreased due to the lower interest rates.
Neither risk has changed, as the bond's coupon and maturity are fixed.

Explanation: The sharp fall in interest rates leads to an increase in the bond's price, so the immediate price risk has worked in the investor's favor. However, the manager now faces a greater reinvestment risk, which is the risk that the periodic coupon payments will have to be reinvested at the new, lower rates, resulting in a lower total return over the bond's life than originally anticipated. Therefore, reinvestment risk becomes the more prominent concern.

Question 10

Consider a 20-year, 6% coupon callable bond that is currently trading at a premium. If market interest rates decline significantly, how will the bond's price sensitivity to further rate decreases be affected compared to an otherwise identical non-callable bond?

The callable bond will become more price-sensitive as the value of the embedded call option increases.
The callable bond's price sensitivity will be dampened as the likelihood of the issuer calling the bond increases. (correct answer)
The callable bond's price sensitivity will be identical to the non-callable bond's, as the coupon and maturity are the same.
The callable bond will exhibit greater positive convexity, leading to accelerated price appreciation.

Explanation: As interest rates fall, the price of the callable bond rises, but its price appreciation is limited by the call price. This is because the probability of the issuer calling the bond increases, effectively putting a ceiling on its price. This phenomenon is known as negative convexity or price compression. Therefore, the callable bond's price sensitivity to further rate decreases is dampened compared to a similar non-callable bond.

Question 11

A portfolio manager is choosing between two option-free bonds that have the same duration, maturity, and yield-to-maturity. Bond A is a standard coupon bond. Bond B is a 'barbell' portfolio consisting of a short-term zero-coupon bond and a long-term zero-coupon bond, structured to have the same duration as Bond A. If the manager expects high interest rate volatility without a clear view on direction, which investment is preferable?

Bond A, because its cash flows are more evenly distributed, reducing overall risk.
Bond B, because its more dispersed cash flows result in higher convexity. (correct answer)
Neither, as they will perform identically because their durations are the same.
It cannot be determined without knowing the coupon rate of Bond A.

Explanation: For a given duration, a portfolio with more dispersed cash flows will have greater convexity. The barbell portfolio (Bond B) concentrates its cash flows at two distant points in time, while the standard coupon bond (Bond A) has cash flows spread out. Greater convexity is advantageous in a volatile rate environment because the portfolio gains more when rates fall than it loses when rates rise by an equal amount. Therefore, Bond B is preferable.

Question 12

An investor is evaluating two option-free bonds from the same issuer with identical credit quality.

Bond X: 10-year maturity, 2% coupon rate
Bond Y: 10-year maturity, 8% coupon rate

If the market yield for both bonds decreases by 100 basis points, which of the following statements is most accurate regarding the percentage price change of the bonds?

The price of Bond X will increase by a greater percentage than the price of Bond Y. (correct answer)
The price of Bond Y will increase by a greater percentage than the price of Bond X.
The prices of both bonds will increase by approximately the same percentage because their maturities are identical.
The prices of both bonds will decrease, with Bond X decreasing by a greater percentage than Bond Y.

Explanation: For bonds with the same maturity, the one with the lower coupon rate will have a higher duration and thus exhibit greater price sensitivity to changes in interest rates. Therefore, a decrease in market yield will cause the price of the lower-coupon Bond X to increase by a larger percentage than the price of the higher-coupon Bond Y. This is because a larger portion of Bond X's total return is dependent on the principal repayment at maturity, making its present value more sensitive to discount rate changes.

Question 13

The fundamental economic reason for the inverse relationship between bond prices and market interest rates is that:

issuers adjust the coupon rates of existing bonds downward when market rates fall.
the credit quality of bond issuers tends to improve when interest rates fall.
the present value of a bond's fixed future cash flows decreases as the discount rate increases. (correct answer)
the Federal Reserve mandates that bond prices be adjusted to reflect current market yields.

Explanation: A bond's price is the present value of its future stream of cash flows (coupon payments and principal repayment). The market interest rate serves as the discount rate in this calculation. If the market interest rate (discount rate) increases, the present value of these fixed cash flows must decrease. Conversely, if the discount rate decreases, the present value of the cash flows increases. This mathematical relationship is the fundamental reason for the inverse price-yield relationship.

Question 14

A decrease of exactly 5.25%
A decrease of more than 5.25%
A decrease of less than 5.25% (correct answer)
An increase of less than 5.25%

Question 15

Price risk has increased because the bond is now trading at a significant premium.
Reinvestment risk has become the more prominent concern for future cash flows. (correct answer)
Both price risk and reinvestment risk have decreased due to the lower interest rates.
Neither risk has changed, as the bond's coupon and maturity are fixed.

Question 16

Both bond prices will fall, but Bond A's price will fall by a greater percentage.
Both bond prices will fall, but Bond B's price will fall by a greater percentage. (correct answer)
Both bond prices will fall by the same percentage because their maturities are identical.
Both bond prices will rise, with Bond B's price rising by a greater percentage.

Question 17

It increases interest rate risk because the put option adds complexity and uncertainty to the bond's cash flows.
It has no effect on interest rate risk, as the bond's coupon and maturity remain unchanged.
It reduces interest rate risk by setting a price floor below which the bond's value is unlikely to fall. (correct answer)
It transforms interest rate risk into credit risk, as the value of the put depends on the issuer's financial health.

Question 18

An economic report is released showing unexpectedly high inflation. What is the most likely immediate effect on the price-yield relationship for existing long-term, fixed-rate government bonds?

A movement down along the existing price-yield curve, resulting in a lower price. (correct answer)
A movement up along the existing price-yield curve, resulting in a higher price.
A shift of the entire price-yield curve upward, as all prices increase for any given yield.
No change, as the price-yield curve only reflects credit risk, not inflation.

Explanation: Higher-than-expected inflation typically leads investors to demand higher nominal interest rates to compensate for the loss of purchasing power. This increase in required market rates (yields) causes a movement along the existing price-yield curve. Since the relationship is inverse, an increase in yields corresponds to a decrease in bond prices. Therefore, the immediate effect is a movement down along the curve to a new equilibrium point with a higher yield and a lower price.

Question 19

Bond A, because its cash flows are more evenly distributed, reducing overall risk.
Bond B, because its more dispersed cash flows result in higher convexity. (correct answer)
Neither, as they will perform identically because their durations are the same.
It cannot be determined without knowing the coupon rate of Bond A.

Question 20

A portfolio of bonds with an average maturity of 12 years.
A zero-coupon bond with a maturity of 12 years. (correct answer)
A portfolio of bonds with a Macaulay duration of 15 years.
A portfolio of floating-rate notes with an average maturity of 12 years.