- 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?
Answer: It reduces interest rate risk by setting a price floor below which the bond's value is unlikely to fall.
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.
- 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?
Answer: Both bond prices will fall, but Bond B's price will fall by a greater percentage.
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).
- 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?
Answer: Bond P, because a lower initial yield results in higher price sensitivity.
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.
- An investor wants to minimize price volatility in a rising interest rate environment but still wishes to invest in corporate debt. Which of the following securities is the most suitable choice?
Answer: A 5-year, floating-rate note (FRN).
Floating-rate notes (FRNs) have coupon payments that periodically reset based on a benchmark interest rate (e.g., SOFR). Because their coupon payments adjust to changes in market rates, their prices are relatively stable and exhibit very low interest rate risk. In a rising rate environment, an FRN's coupon will increase, protecting its value. All the other options are fixed-rate bonds that would experience significant price depreciation as rates rise, with the long-term and low-coupon bonds being the most vulnerable.
- 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?
Answer: A zero-coupon bond with a maturity of 12 years.
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.
- For a non-callable bond, duration is a better measure of interest rate sensitivity than maturity primarily because duration:
Answer: accounts for the timing and magnitude of all of the bond's cash flows.
Maturity only considers the timing of the final principal payment. Duration, specifically Macaulay duration, is the weighted-average time until the bond's cash flows are received, where the weights are the present values of each cash flow. Modified duration uses this concept to provide a more accurate, comprehensive measure of a bond's price sensitivity to interest rate changes because it incorporates the size and timing of all coupon payments as well as the principal repayment. The other options are incorrect: while duration is in years (A), that's not why it's better; duration is not constant (C); and while duration is most accurate for parallel shifts, this is a limitation, not the reason it's superior to maturity (D).
- Which of the following statements regarding the price-yield relationship and interest rate risk is LEAST accurate?
Answer: A bond's price sensitivity to a 1% change in yield is constant across all levels of yield.
Statement D is the least accurate. A bond's price sensitivity to yield changes is not constant; it changes as the level of yield changes. Specifically, price sensitivity (duration) is higher at lower yield levels and lower at higher yield levels. This is a direct consequence of the convex shape of the price-yield curve. Statements A, B, and C are all accurate descriptions of key principles of interest rate risk and bond convexity.
- 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?
Answer: The value will likely increase, as the price gain on the 20-year bond will exceed the price loss on the 2-year note.
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.
- 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?
Answer: The callable bond's price sensitivity will be dampened as the likelihood of the issuer calling the bond increases.
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.
- Which of the following bonds would be expected to exhibit the greatest degree of positive convexity, assuming all have the same yield-to-maturity?
Answer: A 20-year, 2% coupon bond.
Positive convexity is a measure of the curvature of the price-yield relationship. Generally, convexity increases with maturity and decreases with the coupon rate. Therefore, the bond with the longest maturity and the lowest coupon rate will have the greatest convexity. Comparing the options, the 20-year, 2% coupon bond has the longest maturity and lowest coupon, and thus would exhibit the most convexity.
- The fundamental economic reason for the inverse relationship between bond prices and market interest rates is that:
Answer: the present value of a bond's fixed future cash flows decreases as the discount rate increases.
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.
- 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?
Answer: Reinvestment risk has become the more prominent concern for future cash flows.
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.
- 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?
Answer: A movement down along the existing price-yield curve, resulting in a lower price.
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.
- 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?
Answer: Bond B, because its more dispersed cash flows result in higher convexity.
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.
- The graph shows four possible price-yield relationships for a bond. Which curve best represents a 20-year callable bond?
Answer: Curve D
A callable bond behaves like a standard option-free bond when interest rates (yields) are high, exhibiting positive convexity (like Curve A). However, as yields fall, the price of the bond approaches the call price, and the probability of it being called increases. This caps the potential price appreciation, causing the price-yield curve to flatten and become concave. This feature is known as negative convexity. Curve D correctly illustrates this pattern: it is convex at high yields but becomes concave and flattens as yields decrease.
- A bond is currently trading at par value. If its yield to maturity (YTM) remains constant but its perceived credit risk increases, what is the most likely impact on the bond's price?
Answer: The price will fall as investors demand a higher yield to compensate for the increased risk.
This question tests understanding of how yield is composed. Yield to maturity (YTM) reflects the total return, including compensation for the risk-free rate, inflation, and credit risk. If credit risk increases, investors will demand a higher yield spread over the risk-free rate. This increases the overall required market yield for the bond. According to the inverse price-yield relationship, an increase in the required yield will cause the bond's price to fall below par.
- 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?
Answer: The price of Bond X will increase by a greater percentage than the price of Bond Y.
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.
- 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?
Answer: A decrease of less than 5.25%
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%.
- Given the investor's goal described in the passage, which of the following risks is the primary concern they are trying to mitigate?
Answer: Interest rate risk, representing the uncertainty in the terminal value of the investment due to the offsetting effects of price and reinvestment risk.
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.
- 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?
Answer: Bond prices are more sensitive to a decrease in yield than to an equivalent increase in yield.
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.
