Calculate Bond Yield Relationships - Series 7

1. What is the relationship between a bond's coupon rate and its market price relative to par?

   Coupon $>$ market: premium; coupon $<$ market: discount; equal: par

2. Calculate current yield for a $5\%$ bond priced at $95$ (par $=\$1{,}000$).

   Current yield $= \frac{50}{950} \approx 5.26\%$

3. State the formula for current yield on a bond.

   Current yield $= \frac{\text{annual interest}}{\text{market price}}$

4. Estimate $\%\Delta P$ for duration $7$ if yields rise by $0.50\%$.

   $\%\Delta P \approx -7 \times 0.005 = -3.5\%$

5. Identify the annual interest for a $6\%$ bond with $\$1{,}000$ par value.

   $60 per year

6. State the duration-based approximation for percent price change.

   $\%\Delta P \approx -\text{duration} \times \Delta y$

7. For a bond priced at par, how do coupon rate, current yield, and YTM compare?

   All are equal

8. Which has greater interest rate risk: a longer-maturity bond or a shorter-maturity bond?

   Longer-maturity bond

9. Estimate $\%\Delta P$ for duration $4$ if yields fall by $1.00\%$.

   $\%\Delta P \approx -4 \times (-0.01) = +4\%$

10. What is reinvestment risk for a bond investor?

    Risk that coupons will be reinvested at lower rates, reducing total return

11. Identify whether a bond at $105$ is at a premium, discount, or par.

    Premium

12. What is the relationship between a bond's price and its yield to maturity?

    Inverse: price $\uparrow$ implies YTM $\downarrow$, and vice versa

13. Identify whether a bond at $97$ is at a premium, discount, or par.

    Discount

14. What happens to a bond's YTM if it is purchased at a premium and held to maturity?

    YTM is below coupon rate due to amortization to par

15. Calculate current yield for a $6\%$ bond priced at $102$ (par $=\$1{,}000$).

    Current yield $= \frac{60}{1020} \approx 5.88\%$

16. Which bond is more price-sensitive to rate changes: $30$-year $3\%$ or $10$-year $6\%$?

    $30$-year $3\%$ bond

17. What is the relationship among coupon rate, current yield, and YTM for a premium bond?

    Coupon rate $>$ current yield $>$ YTM

18. Which yield measure assumes reinvestment of coupon payments at the same rate?

    Yield to maturity (YTM)

19. What is the relationship among coupon rate, current yield, and YTM for a discount bond?

    Coupon rate $<$ current yield $<$ YTM

20. Which has greater interest rate risk: a lower-coupon bond or a higher-coupon bond?

    Lower-coupon bond

21. What is duration used to estimate in bond analysis?

    Approximate price sensitivity to yield changes (interest rate risk)

22. What does yield to maturity (YTM) represent for a bond held to maturity?

    Total annualized return from coupons plus gain or loss to par at maturity

23. What is the relationship between bond prices and market interest rates?

    Inverse: rates $\uparrow$ implies prices $\downarrow$, and vice versa

24. Calculate the dollar price for a bond quoted at $103.25$ with $\$1{,}000$ par value.

    $103.25\% \times 1000 = \$1{,}032.50$

25. What happens to a bond's YTM if it is purchased at a discount and held to maturity?

    YTM exceeds coupon rate due to accretion to par

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