Yield Measures, Spot Rates, and Forward Rates

Question 1

yield measures

Answer 1

1. based on certain assumptions, thereby limiting their use to gauge relative value accurately
2. include current yield, yield to maturity, yield to call, yield to put, yield to worst, and cash flow yield, expressed as a percent return.

Question 2

sources of return

Answer 2

1. coupon interest payments
2. capital gain or loss
3. income from reinvestment of interim cash flows

Question 3

Coupon Interest Payments

Answer 3

The main source of return on a bond is the periodic coupon interest payments, which are absent in case of zero-coupon instruments.

Question 4

Capital Gain or Loss

Answer 4

1. An investor can earn capital gain or loss, depending on the proceeds received while the bond matures, is called, or is sold. If the proceeds are more than the purchase price, a capital gain is generated, and vice versa.
2. A capital gain is observed in bonds held to maturity, if the bond is purchased below its par value, and in callable bonds if the call price is more than the purchase price.

Question 5

Reinvestment Income

Answer 5

1. derived from the interest and principal payments that can be reinvested before final maturity.
2. can make up a significant part of the total dollar return, and this is affected by reinvestment risk and interest rate risk

Question 6

Current yield

Answer 6

1. annual dollar coupon interest to a bond’s market price, calculated as annual dollar coupon interest/price.
2. greater than coupon rate for a bond selling at discount, equal for bond selling at par, and less for bond selling at premium.
3. only considers coupon interest and no other source of investor return

Question 7

Yield to Maturity

Answer 7

1. the most popular measure of yield and is the interest rate that makes the present value of a bond’s cash flows equal to its market price plus accrued interest.
2. found through trial and error IRR calculation.
3. usually annualized by doubling semiannual yield and is called bond-equivalent yield. (BOND)

Question 8

a bond-equivalent yield (YTM)

Answer 8

1. at par, coupon rate = current yield = yield to maturity;
2. at discount, coupon rate < current yield < yield to maturity;
3. at premium, coupon rate > current yield > yield to maturity.

Question 9

The Bond-Equivalent Yield Convention

Answer 9

involves doubling the semiannual yield to obtain an annual yield. However, investors should make sure to use the bond-equivalent yield measure properly

Question 10

Limitations of Yield-to-Maturity Measure

Answer 10

1. considers not only coupon income but also any capital gain or loss and timing of cash flows. It also assumes that coupon payments can be reinvested at an interest rate equal to the yield to maturity.
2. highlight the need to question their use in investment decisions.

Question 11

total dollar return

Answer 11

An investor’s total return is the sum of coupon payments, capital gain/loss, and reinvestment income.

Question 12

total future dollars

Answer 12

all the dollars an investor expects to receive including the recovery of the principal

Question 13

Factors Affecting Reinvestment Risk

Answer 13

the maturity length (the longer maturity, the higher the risk)

and the coupon rate (the higher, the more dependent on reinvestment; Zero-coupon bonds have no reinvestment risk if held to maturity)

Question 14

Comparing Semiannual-Pay and Annual-Pay Bonds

Answer 14

1. A bond-equivalent yield is computed for non-U.S. bonds that pay interest annually.
2. The bond-equivalent yield of an annual-pay bond is always less than the annual-pay bond’s yield to maturity.
3. To compare the yield on a U.S. bond issue with that on an annual-pay non-U.S. bond, an adjustment using the bond-equivalent yield is required

Question 15

Yield to Call

Answer 15

1. Callable bonds have a yield to maturity and a yield to call
2. assumes the bond will be called on a certain date at the price specified in the call schedule.
3. Yield to first call is computed for bonds not currently callable
4. yield to next call is computed for currently callable bonds.
5. Yield to refunding is used when bonds are currently callable but prohibited from being called using certain funds for a certain period
6. Bonds can be called with funds from other sources during the protected period.
7. To calculate, find the interest rate that makes the expected cash flows equal the price plus accrued interest
8. considers all potential returns from owning a bond, but it assumes unrealistic investor and issuer behavior.

Question 16

yield to call assumptions

Answer 16

1. the investor will hold the bond to the assumed call date
2. the issuer will call the bond on that date

Comparison of different yields to call with the yield to maturity is meaningless because the cash flows stop at the assumed call date.

Question 17

Yield to Put

Answer 17

the interest rate that will make the present value of the cash flows to the first put date equal to the price plus accrued interest.

Question 18

yield to worst

Answer 18

the lowest yield calculated for all possible call and put dates. It does not indicate potential return or recognize differing reinvestment risks.

Question 19

Cash flow yield

Answer 19

1. calculated for mortgage-backed and asset-backed securities by projecting cash flows based on an assumed prepayment rate.
2. Yield is the interest rate that makes the projected cash flows equal to the price plus accrued interest.

Question 20

Bond-Equivalent Yield (CFY)

Answer 20

annualized for bond-equivalent purposes by computing the effective semiannual yield from the monthly yield, doubling it, and then compounding it for six months

Question 21

Limitations of Cash Flow Yield

Answer 21

1. include the assumptions that coupon payments can be reinvested at the cash flow yield and that the security is held until final payoff.
2. Reinvestment risk is a significant factor for mortgage-backed and asset-backed securities given their monthly payments and dependence on prepayment rates.

Question 22

Spread for life

Answer 22

1. a margin measure used for floating-rate securities. It accounts for the accretion or amortization of the premium or discount and the quoted margin over the security’s remaining life
2. calculates accretion/amortization of discount/premium over the floater’s remaining term to maturity, but does not consider coupon rate or time value of money.

Question 23

Discount Margin

Answer 23

1. estimates the average margin over the reference rate that the investor can expect to earn over the life of the security. It involves determining cash flows, selecting a margin, discounting cash flows, and comparing present value with security’s price.
2. equal to the quoted margin in the coupon reset formula for a security selling at par.
3. assumes that reference rate will not change over the life of the security and does not factor in caps or floors.

Question 24

Yield on Treasury Bills

Answer 24

1. calculated using settlement price per $1 of maturity value and number of days to maturity. Convention is to calculate on a discount basis
2. Market participants make adjustments to make it comparable to that of a Treasury coupon security
3. To compare, the yield on a discount basis can be converted to a money market yield using a formula.

Question 25

THEORETICAL SPOT RATES

Answer 25

1. provide the appropriate set of interest rates to value default-free cash flows.
2. A default-free curve can be constructed from the observed Treasury yield curve.

Question 26

Bootstrapping

Answer 26

1. used to create a theoretical spot rate curve
2. starts with the yield for the on-the-run Treasury issues with no credit risk and liquidity risk.
3. issues only a limited number of instruments to construct the Treasury yield curve
4. may provide misleading yields for interim maturities when using linear interpolation.
5. The value of a Treasury coupon security should be equal to the package of zero-coupon Treasury securities that mimic its cash flows

Question 27

Normal spread

Answer 27

1. involves calculating the difference between the bond’s yield and the yield to maturity of a benchmark Treasury coupon security
2. provides compensation for credit risk, option risk, and liquidity risk of non-Treasury security investments when compared to those of Treasury securities with identical maturity

Question 28

Zero-Volatility Spread (Z-Spread/static spread)

Answer 28

1. calculated as the spread that renders the present value of cash flows from non-Treasury bonds equal to the bond’s price when discounted to the Treasury spot rate plus the spread.
2. It considers the entire Treasury spot rate curve, in contrast to the nominal spread
3. represents a spread over the entire Treasury spot rate curve and compensates for the non-Treasury security’s credit, liquidity, and option risk.

Question 29

Divergence Between Z-Spread and Nominal Spread

Answer 29

1. depends on the shape of the term structure of interest rates and security characteristics.
2. nominal spread assumes a flat yield curve where the same yield is used for each cash flow.
3. Z-spread and nominal spread will produce the same value with a flat yield curve and produce different results in a steep yield curve environment.

Question 30

Z-Spread Relative to Any Benchmark

Answer 30

1. The Z-spread can be calculated relative to any benchmark spot rate curve instead of the Treasury spot rate curve as a measure of liquidity and option risk
2. Vendors of analytical systems often allow users to select a benchmark spot rate curve, and investors should always ask what benchmark was used to compute the Z-spread

Question 31

Option-Adjusted Spread

Answer 31

1. a measure that incorporates the value of an embedded option in a security and adds it to the Z-spread to reflect the security’s true value
2. measures the spread over a spot rate curve, overcoming the shortcomings of the nominal spread and accounting for future interest rate volatility that can affect cash flows for bonds with embedded options.

Question 32

Valuation models

Answer 32

1. determine the fair price of a security, highlighting undervalued securities, and can convert price differences into yield spread measures.
2. OAS reconciles the fair price to market price by finding a return that equates the two, using a model-dependent trial and error procedure.
3. modeling differences in OAS: the assumptions of interest rate volatility and the benchmark used in the analysis.

Question 33

Why is the spread referred to as ‘‘option adjusted’’?

Answer 33

because the embedded option can change cash flows, whereas the Z-spread ignores the effect of interest rate changes on cash flows and assumes zero volatility

Question 34

Option Cost

Answer 34

1. can be obtained by calculating the difference between the OAS at the assumed interest rate volatility and the Z-spread.
2. positive for callable bonds and most mortgage-backed and asset-backed securities because the issuer’s ability to alter cash flows results in an OAS that is less than the Z-spread
3. a putable bond has a negative option cost because of the investor’s ability to alter cash flows

Question 35

Pitfalls of Nominal Spread

Answer 35

1. A high nominal spread may hide a high option cost.
2. While an investor may rely on the nominal spread, they may not be adequately compensated for the option risk associated with a security with an embedded option.

Question 36

Summary of Spread Measures

Answer 36

1. nominal; treasury yield curve (Benchmark); reflects compensation for credit risk, option risk and liquidity risk
2. zero-volatility spread; treasury spot rate curve (Benchmark); reflects compensation for credit risk, option risk and liquidity risk
3. option-adjusted spread; treasury spot rate curve (Benchmark); reflects compensation for credit risk and liquidity risk

Question 37

Forward rates

Answer 37

1. can be extrapolated from the default-free theoretical spot rate curve, and viewed as the market’s consensus of future interest rates, under certain assumptions
2. For different periods, can be calculated from the default-free theoretical spot rate curve using a bootstrapping methodology.
3. also known as implied forward rates and can be obtained for a LIBOR spot rate curve using the same method

Question 38

Deriving 6-Month Forward Rates

Answer 38

1. an arbitrage principle is used, where two investments with the same cash flows and risk have the same value.
2. the rate that equalizes the dollar return between buying a 6-month Treasury bill and a 1-year Treasury bill.

Question 39

Short-term forward rate curve

Answer 39

1. always lies above spot rate curve if the par yield curve is upward sloping
2. has an unusual shape, which is smoothed out by analysts using statistical techniques.