Interpret Bond Yield Measures - Series 65

1. What is the relationship between coupon rate and YTM when a bond trades at par value?

   Par bond: $\text{YTM}=\text{coupon rate}$. At par, the yield equals the coupon rate since there is no price adjustment to maturity.

2. Find the current yield for a $4\%$ annual coupon bond priced at $102$ (par $=100$).

   $\text{Current yield}=\frac{4}{102}\approx^3.92\%$. For a premium bond, current yield is below the coupon rate due to the elevated market price.

3. Identify the relationship among coupon rate, YTM, and price when a bond trades at a discount to par.

   Discount bond: $\text{YTM}>\text{coupon rate}$. Bonds trading below par require a higher YTM to compensate for the price discount through maturity.

4. What yield measure includes both coupon income and price accretion or amortization to par at maturity?

   Yield to maturity (YTM). YTM accounts for both periodic interest and the convergence of price to par at maturity.

5. What is yield to call (YTC) conceptually for a callable bond expected to be redeemed at the call date?

   IRR on cash flows to the call date using call price as final value. YTC computes the return if the bond is called at the earliest date, replacing maturity value with call price.

6. Identify whether YTM is greater than, less than, or equal to coupon rate for a bond priced at $90$ (par $=100$).

   $\text{YTM}>\text{coupon rate}$. Discount bonds have YTM exceeding coupon rate to account for price appreciation to par.

7. Identify the relationship among coupon rate, YTM, and price when a bond trades at a premium to par.

   Premium bond: $\text{YTM}<\text{coupon rate}$. Bonds above par have lower YTM as the premium amortizes down to par over time.

8. Identify what happens to a bond's price when market yields rise, holding all other features constant.

   Price falls when yields rise (inverse price-yield relationship). Higher yields increase the discount rate, reducing the present value of future cash flows.

9. What yield measure ignores price change and uses only annual coupon divided by current market price?

   Current yield. Current yield focuses solely on coupon income relative to market price, excluding price changes.

10. Identify the yield measure investors often focus on for a callable bond: the lower of YTM and YTC.

    Yield to worst (YTW) $=\min(\text{YTM},\text{YTC})$. YTW conservatively estimates the lowest possible yield outcome for callable bonds.

11. What is yield to maturity (YTM) conceptually for a bond held to maturity with all payments reinvested?

    IRR on all cash flows to maturity at the purchase price. YTM represents the total return assuming the bond is held until maturity with coupons reinvested at the same rate.

12. Compute the present value of $50$ annually for $2$ years at $5\%$ using the annuity PV factor.

    $PV=50\times\frac{1-(1.05)^{-2}}{0.05}\approx92.97$. Using the annuity PV formula at 5% for two periods yields the discounted value of payments.

13. State the present value formula for a level annuity with payment $PMT$, rate $r$, and $n$ payments.

    $PV=PMT\times\frac{1-(1+r)^{-n}}{r}$. The formula sums the present values of equal periodic payments discounted at the given rate.

14. Identify the yield measure that is typically lower for a premium callable bond when the call is likely: YTM or YTC?

    YTC is typically lower than YTM for a premium callable bond. For premium callable bonds, early call amortizes the premium faster, resulting in lower yield.

15. Compute the present value of $100$ received in $3$ years discounted at $5\%$ annually.

    $PV=\frac{100}{(1.05)^3}\approx86.38$. The formula compounds the discount rate over three periods to find present value.

16. Find the current yield for a $6\%$ annual coupon bond priced at $95$ (par $=100$).

    $\text{Current yield}=\frac{6}{95}\approx^6.32\%$. Current yield divides the annual coupon payment by the bond's market price to express income return.

17. Compute the present value of an annuity paying $100$ annually for $3$ years at $10\%$.

    $PV=100\times\frac{1-(1.10)^{-3}}{0.10}\approx248.69$. The annuity factor discounts three equal payments at 10% to compute total present value.

18. What yield measure is most relevant when a callable bond is likely to be redeemed before maturity?

    Yield to call (YTC). YTC provides the expected return if the issuer exercises the call option prior to maturity.

19. State the present value formula for a single future cash flow $FV$ discounted at rate $r$ for $n$ periods.

    $PV=\frac{FV}{(1+r)^n}$. This discounts a lump-sum future payment back to present using compound interest.

20. Compute the present value of $1{,}000$ received in $2$ years discounted at $10\%$ annually.

    $PV=\frac{1000}{(1.10)^2}\approx826.45$. Discounting at 10% for two years reduces the future value to its equivalent current amount.

21. State the bond pricing equation that defines YTM for price $P$, coupon $C$, par $F$, yield $y$, and $n$ periods.

    $P=\sum_{t=1}^{n}\frac{C}{(1+y)^t}+\frac{F}{(1+y)^n}$. The equation discounts all coupons and par value at YTM to equal the bond's current price.

22. State the bond pricing equation that defines YTC for price $P$, coupon $C$, call price $CP$, yield $y$, and $n$ to call.

    $P=\sum_{t=1}^{n}\frac{C}{(1+y)^t}+\frac{CP}{(1+y)^n}$. For YTC, the formula discounts coupons to the call date and uses call price as the terminal value.

23. Identify whether YTM is greater than, less than, or equal to coupon rate for a bond priced at $110$ (par $=100$).

    $\text{YTM}<\text{coupon rate}$. Premium bonds yield less than coupon rate as price depreciates to par at maturity.

24. What is the formula for current yield on a bond using annual coupon and current market price?

    $\text{Current yield}=\frac{\text{annual coupon}}{\text{current market price}}$. This formula calculates the bond's annual interest return as a percentage of its prevailing market value, ignoring capital gains or losses.

25. State the discounted cash flow (DCF) valuation formula for any asset with cash flows $CF_t$ and discount rate $r$.

    $PV=\sum_{t=1}^{n}\frac{CF_t}{(1+r)^t}$. DCF values an asset by discounting each expected cash flow to present at the appropriate rate.

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