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Calculate Bond Yield Relationships - Series 7

  1. A bond's yield to maturity decreased from 4.25% to 3.95%. This change represents a decrease of how many basis points?
    Answer: 30 basis points One basis point is equal to 1/100th of 1%, or 0.01%. The change in yield is 4.254.25% - 3.95% = 0.30%. To convert this to basis points, multiply by 100. Thus, 0.30∗100=300.30 * 100 = 30 basis points.
  2. A bond is priced at 97 with 5 years to maturity and 6% coupon. Compared with current yield, YTM is generally:
    Answer: Higher because discount is accreted to par This question tests Series 7 competency in calculating bond yields and understanding their price relationships and interest rate sensitivity. A bond's yield provides insight into its return, with current yield, yield to maturity, and yield to call being key metrics. This scenario involves a discount bond with years to maturity, which highlights how YTM incorporates the capital gain to par over time. The correct answer is choice B because it correctly applies the yield calculation or concept, as shown by the accretion of the discount adding to the yield beyond the current income. Choice A is incorrect due to a common error of assuming discounts lower YTM, which occurs when students ignore the gain component. Effective strategies include practicing yield calculations under different scenarios and understanding the impact of interest rate changes on bond pricing, along with recognizing common pitfalls like miscomparing current yield and YTM.
  3. An investor purchases a newly issued bond at its par value of $1,000 with a 4.5% coupon. One year later, similar new issue bonds are being offered with a 5.5% coupon. The original bond's current yield will now be:
    Answer: higher than 4.5%. Since new bonds are offering a higher coupon of 5.5%, market interest rates have risen. Due to the inverse relationship between interest rates and bond prices, the price of the original 4.5% bond must fall below par to be competitive. Current yield is annual interest divided by market price. Since the annual interest ($45) remains constant and the market price has decreased, the current yield must now be higher than the 4.5% nominal yield.
  4. If the Federal Reserve announces a significant increase in the federal funds rate, which of the following bonds would likely experience the largest percentage decrease in market value?
    Answer: A 2% coupon bond maturing in 20 years. Bond price sensitivity to interest rate changes (interest rate risk or duration) is greatest for bonds with longer maturities and lower coupons. The 2% coupon, 20-year bond has both the longest maturity and the lowest coupon among the choices, making it the most volatile and susceptible to the largest price decrease when rates rise.
  5. An investor purchases a 10-year, 6% bond for $900. The bond's yield to maturity is:
    Answer: greater than 6.67%. The bond was purchased at a discount ($900 price for a $1,000 par value). For a discount bond, the yield to maturity (YTM) is always higher than the current yield, which is higher than the nominal yield. The nominal yield is 6%. The current yield is $60/$900=6.67\$60 / \$900 = 6.67%. Therefore, the YTM must be greater than 6.67%.
  6. A bond's price has just moved from 97 to 101.5. This change means its current yield has:
    Answer: decreased, and its yield to maturity has decreased. An increase in a bond's market price causes a decrease in its yields. Both the current yield (Annual Interest / Market Price) and the yield to maturity will move inversely to the price. Since the price increased, both the current yield and the yield to maturity must have decreased.
  7. A 30-year callable bond and a 30-year non-callable bond are issued by the same corporation with identical coupon rates and credit ratings. If both bonds are trading at a premium, which statement is most likely true?
    Answer: The callable bond will trade at a lower price and have a higher yield. A call feature benefits the issuer and represents a risk (reinvestment risk) to the bondholder. To compensate for this additional risk, a callable bond must offer a higher yield to an investor compared to a similar non-callable bond. For the yield to be higher, the price must be lower. Therefore, the callable bond will trade at a lower price and have a higher yield.
  8. A 6% callable bond is priced at 104, callable at 102 next year. Which yield is most affected by call price?
    Answer: Yield to call This question tests Series 7 competency in calculating bond yields and understanding their price relationships and interest rate sensitivity. A bond's yield provides insight into its return, with current yield, yield to maturity, and yield to call being key metrics. This scenario involves a premium callable bond with a near-term call, which highlights how call price influences yield calculations. The correct answer is choice B because it correctly applies the yield calculation or concept, as shown by yield to call incorporating the call at 102, affecting the return if exercised. Choice A is incorrect due to a common error of prioritizing current yield over call-adjusted measures, which occurs when students ignore call provisions. Effective strategies include practicing yield calculations under different scenarios and understanding the impact of interest rate changes on bond pricing, along with recognizing common pitfalls like overlooking call price impacts.
  9. A 10-year Treasury note with 4% coupon is priced at 98. If market yields fall, what happens to its price?
    Answer: Price increases toward or above par This question tests Series 7 competency in calculating bond yields and understanding their price relationships and interest rate sensitivity. A bond's yield provides insight into its return, with current yield, yield to maturity, and yield to call being key metrics. This scenario involves a Treasury note trading at a discount with falling market yields, which highlights the inverse yield-price relationship. The correct answer is choice B because it correctly applies the yield calculation or concept, as shown by lower yields increasing the present value of future cash flows, pushing price toward or above par. Choice A is incorrect due to a common error of confusing yield direction with price movement, which occurs when students reverse the inverse relationship. Effective strategies include practicing yield calculations under different scenarios and understanding the impact of interest rate changes on bond pricing, along with recognizing common pitfalls like misinterpreting discount dynamics.
  10. A municipal bond yields 3.50%; an investor is in the 32% federal bracket. What is the taxable equivalent yield?
    Answer: 5.15% This question tests Series 7 competency in calculating bond yields and understanding their price relationships and interest rate sensitivity. A bond's yield provides insight into its return, with current yield, yield to maturity, and yield to call being key metrics. This scenario involves a municipal bond and tax bracket consideration, which highlights the calculation of taxable equivalent yield to compare with taxable bonds. The correct answer is choice C because it correctly applies the yield calculation or concept, as shown by 3.50% / (1 - 0.32) ≈ 5.15%. Choice B is incorrect due to a common error of using the muni yield without adjustment, which occurs when students forget the tax-equivalency formula. Effective strategies include practicing yield calculations under different scenarios and understanding the impact of interest rate changes on bond pricing, along with recognizing common pitfalls like overlooking tax effects.
  11. A bond's duration is 3. If yields fall 2%, estimated price change is closest to:
    Answer: Up about 6% This question tests Series 7 competency in calculating bond yields and understanding their price relationships and interest rate sensitivity. A bond's yield provides insight into its return, with current yield, yield to maturity, and yield to call being key metrics. This scenario involves estimating price impact from a yield decrease using duration, which highlights positive price sensitivity to falling rates. The correct answer is choice B because it correctly applies the yield calculation or concept, as shown by approximate change = -duration × yield change = -3 × (-2%) = +6%. Choice A is incorrect due to a common error of applying the wrong sign for yield decline, which occurs when students mishandle the formula. Effective strategies include practicing yield calculations under different scenarios and understanding the impact of interest rate changes on bond pricing, along with recognizing common pitfalls like sign errors in duration estimates.
  12. A 6% bond priced at 103 is callable at 100 in 2 years. Which yield measure is most relevant if rates fall?
    Answer: Yield to call This question tests Series 7 competency in calculating bond yields and understanding their price relationships and interest rate sensitivity. A bond's yield provides insight into its return, with current yield, yield to maturity, and yield to call being key metrics. This scenario involves a premium callable bond with falling rates, which highlights the relevance of yield to call when early redemption is likely. The correct answer is choice B because it correctly applies the yield calculation or concept, as shown by lower rates increasing call probability, making YTC the key metric for return estimation. Choice A is incorrect due to a common error of focusing on YTM despite call features, which occurs when students underestimate reinvestment risk. Effective strategies include practicing yield calculations under different scenarios and understanding the impact of interest rate changes on bond pricing, along with recognizing common pitfalls like misprioritizing yield types.
  13. A $1,000 par bond with a 4% coupon is priced at $1,020. Which statement about YTM versus coupon rate is correct?
    Answer: YTM is less than 4.00% because price is above par This question tests Series 7 competency in calculating bond yields and understanding their price relationships and interest rate sensitivity. A bond's yield provides insight into its return, with current yield, yield to maturity, and yield to call being key metrics. This scenario involves a bond priced above par, which highlights the inverse relationship between price and yield to maturity compared to the coupon rate. The correct answer is choice B because it correctly applies the yield calculation or concept, as shown by the premium price indicating YTM below the coupon rate to account for the price decline to par. Choice C is incorrect due to a common error of reversing the price-yield relationship, which occurs when students misremember that premiums imply lower yields. Effective strategies include practicing yield calculations under different scenarios and understanding the impact of interest rate changes on bond pricing, along with recognizing common pitfalls like confusing premium and discount effects.
  14. A 5% corporate bond is priced at $950; annual coupon is $50. What is the bond's current yield?
    Answer: 5.26% This question tests Series 7 competency in calculating bond yields and understanding their price relationships and interest rate sensitivity. A bond's yield provides insight into its return, with current yield, yield to maturity, and yield to call being key metrics. This scenario involves a corporate bond trading below par with a given annual coupon, which highlights how current yield is calculated using the market price rather than par value. The correct answer is choice C because it correctly applies the yield calculation or concept, as shown by dividing the annual coupon by the market price: $50 / $950 ≈ 5.26%. Choice B is incorrect due to a common error of using the nominal coupon rate directly, which occurs when students ignore the adjustment for market price. Effective strategies include practicing yield calculations under different scenarios and understanding the impact of interest rate changes on bond pricing, along with recognizing common pitfalls like confusing current yield with nominal yield.
  15. A 5% bond's price is $1,050. Using Current yield=annual couponmarket price\text{Current yield}=\frac{\text{annual coupon}}{\text{market price}}, what is current yield?
    Answer: 4.76% This question tests Series 7 competency in calculating bond yields and understanding their price relationships and interest rate sensitivity. A bond's yield provides insight into its return, with current yield, yield to maturity, and yield to call being key metrics. This scenario involves a bond trading above par, which highlights how current yield is lower than the nominal rate due to the premium price. The correct answer is choice A because it correctly applies the yield calculation or concept, as shown by $50 / $1,050 ≈ 4.76%. Choice B is incorrect due to a common error of using the coupon rate without adjustment, which occurs when students forget to divide by market price. Effective strategies include practicing yield calculations under different scenarios and understanding the impact of interest rate changes on bond pricing, along with recognizing common pitfalls like equating current yield to nominal yield.
  16. A 10-year, 5% bond is priced at $1,000. If market yields rise to 6%, what happens to the bond's price?
    Answer: Price falls below $1,000 This question tests Series 7 competency in calculating bond yields and understanding their price relationships and interest rate sensitivity. A bond's yield provides insight into its return, with current yield, yield to maturity, and yield to call being key metrics. This scenario involves a market yield increase above the coupon rate, which highlights the inverse relationship between yields and bond prices. The correct answer is choice B because it correctly applies the yield calculation or concept, as shown by higher market yields causing the bond to trade at a discount to make its effective return competitive. Choice A is incorrect due to a common error of misunderstanding the yield-price inverse, which occurs when students think rising yields increase prices. Effective strategies include practicing yield calculations under different scenarios and understanding the impact of interest rate changes on bond pricing, along with recognizing common pitfalls like ignoring market yield effects.
  17. A corporate bond is trading at 102. Which of the following statements must be true?
    Answer: The bond's nominal yield is higher than its yield to maturity. A bond trading at 102 is trading at a premium. For a premium bond, the yields are ranked from highest to lowest: Nominal Yield > Current Yield > Yield to Maturity > Yield to Call. Therefore, the nominal yield must be higher than the yield to maturity.
  18. A zero-coupon bond is purchased at a deep discount and matures at par. For this type of bond, which of the following statements is correct?
    Answer: The nominal yield and current yield are both effectively 0%. Zero-coupon bonds do not make periodic interest payments. Therefore, their nominal yield (coupon) is 0%, and their current yield (annual interest / market price) is also 0%. The investor's return comes from the accretion of the discounted purchase price to the par value at maturity, which is reflected in the yield to maturity.
  19. An investor buys a 7% JKL corporate bond at 98. The bond pays interest semiannually. What is the bond's current yield?
    Answer: 7.14% Current yield is calculated based on the annual interest, regardless of payment frequency. The annual interest is 7% of $1,000 par, which is $70. The market price is 98% of $1,000, which is $980. Current Yield = Annual Interest / Market Price = $70/$980=7.14\$70 / \$980 = 7.14%. The semiannual payment information is a distractor.
  20. A 9% bond's annual coupon is $90 and market price is $900. What is the current yield?
    Answer: 10.00% This question tests Series 7 competency in calculating bond yields and understanding their price relationships and interest rate sensitivity. A bond's yield provides insight into its return, with current yield, yield to maturity, and yield to call being key metrics. This scenario involves a bond trading below par with a given annual coupon, which highlights how current yield exceeds the nominal rate in discount situations. The correct answer is choice B because it correctly applies the yield calculation or concept, as shown by $90 / $900 = 10.00%. Choice A is incorrect due to a common error of using the nominal rate directly, which occurs when students ignore the market price impact. Effective strategies include practicing yield calculations under different scenarios and understanding the impact of interest rate changes on bond pricing, along with recognizing common pitfalls like confusing yield measures.

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