Reading 41: Introduction to Fixed-Income Valuation

51 questions available

Bond Valuation Fundamentals5 min
Valuation relies on discounting future cash flows. The primary method uses a single market discount rate (YTM) to value a bond. When the coupon rate equals the YTM, the bond trades at par. If the coupon is greater, it trades at a premium; if less, at a discount. The price-yield relationship is convex, meaning bond prices are more sensitive to yield decreases than increases. The 'constant-yield price trajectory' describes how a bond's price moves toward par as it approaches maturity, assuming the yield remains constant.

Key Points

  • Bond Price = Present Value of future cash flows.
  • Inverse relationship: Yields up, Price down.
  • Convexity: Price gain from yield drop > Price loss from yield rise.
  • Premium bond: Coupon > YTM; Discount bond: Coupon < YTM.
  • Constant-yield trajectory pulls price to par over time.
Spot Rates, Forward Rates, and Matrix Pricing6 min
Bonds can also be valued using spot rates, which are discount rates for single cash flows at specific times. This 'no-arbitrage' price prevents profit from stripping or reconstituting bonds. Forward rates represent interest rates for future periods. Spot rates can be derived from forward rates and vice versa. Matrix pricing estimates yields for illiquid bonds by interpolating yields of similar benchmark bonds based on maturity.

Key Points

  • Spot rates are zero-coupon rates for specific maturities.
  • No-arbitrage price uses spot rates for each cash flow.
  • Forward rates are implied rates for future lending/borrowing.
  • Matrix pricing uses interpolation for non-traded bonds.
  • (1 + S2)^2 = (1 + S1) * (1 + 1y1y).
Yield Measures and Spreads6 min
Different yield measures serve different purposes. YTM is the most common but assumes reinvestment at the same rate. Current yield measures income relative to price. Floating-rate notes use a reference rate plus a margin; the discount margin reflects the required return. Yield spreads (G-spread, I-spread, Z-spread) measure risk premiums over benchmarks. The Option-Adjusted Spread (OAS) removes the value of embedded options from the Z-spread to isolate credit and liquidity risk.

Key Points

  • Current Yield = Annual Coupon / Flat Price.
  • FRN: Quoted Margin used for payments; Discount Margin used for valuation.
  • Money Market: Discount basis (360 days) vs. Add-on (365 days).
  • Z-spread: Constant spread added to spot curve to match price.
  • OAS = Z-spread - Option Value (in basis points).

Questions

Question 1

An investor calculates the value of a 5-year, 6 percent annual coupon bond with a par value of 1,000. If the market discount rate is 8 percent, the value of the bond is closest to:

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Question 2

A bond has a coupon rate of 5 percent and a yield to maturity of 4 percent. This bond is trading at:

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Question 3

Which of the following statements regarding the price-yield relationship of a standard option-free bond is most accurate?

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Question 4

A 10-year zero-coupon bond with a par value of 1,000 and a required yield of 6 percent (semiannual basis) is priced closest to:

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Question 5

If a bond's yield to maturity remains constant over time, a bond trading at a discount will:

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Question 6

Given the following spot rates: 1-year = 3 percent, 2-year = 4 percent, 3-year = 5 percent. The price of a 3-year, 5 percent annual coupon bond with a par value of 1,000 is closest to:

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Question 7

Which of the following best describes the 'no-arbitrage price' of a bond?

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Question 8

A 4 percent semiannual coupon bond settles on June 15. The previous coupon was paid on April 15 (61 days ago). There are 183 days in the current coupon period. The accrued interest per 100 of par value is closest to:

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Question 9

The full price of a bond is calculated as:

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Question 10

In the context of bond trading, the 'clean price' refers to:

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Question 11

An analyst uses matrix pricing to estimate the required yield on a 4-year illiquid bond. A 3-year comparable bond yields 3.5 percent and a 5-year comparable bond yields 4.5 percent. The estimated yield for the 4-year bond using linear interpolation is:

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Question 12

Matrix pricing is best described as a method used to:

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Question 13

A bond with a periodicity of 2 has a yield to maturity of 4 percent. What is its effective annual yield?

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Question 14

A 20-year, 1,000 par value bond with a 6 percent annual coupon is trading at 802.07. The current yield is closest to:

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Question 15

The yield calculated using the stated coupon payment dates, ignoring weekends and holidays, is referred to as:

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Question 15

Which of the following yield measures allows an investor to choose the currency in which to be paid?

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Question 16

A callable bond has a yield-to-maturity of 5.5 percent and a yield-to-first-call of 5.2 percent. The yield-to-worst is:

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Question 17

The 'option-adjusted yield' for a callable bond will be:

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Question 18

For a floating-rate note (FRN), if the credit quality of the issuer decreases, the quoted margin will likely be:

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Question 19

A 90-day T-bill is priced with an annualized discount of 1.2 percent. The face value is 1,000. The price of the T-bill is closest to:

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Question 20

A money market instrument has an add-on yield of 1.4 percent based on a 365-day year. This yield is referred to as the:

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Question 21

The spot rate yield curve is also referred to as the:

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Question 22

A par bond yield curve is constructed from:

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Question 23

Forward rates are best described as:

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Question 24

If the current 1-year spot rate is 2 percent and the 1-year forward rate one year from now (1y1y) is 3 percent, the approximate 2-year spot rate is:

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Question 25

The notation '2y1y' refers to:

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Question 26

Using the geometric mean relationship, if the 1-year spot rate is S1 and the 2-year spot rate is S2, the 1-year forward rate one year from now (1y1y) satisfies:

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Question 27

A yield spread calculated by adding an equal amount to each benchmark spot rate to match a bond's market price is called the:

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Question 28

If a 5-year corporate bond yields 6.25 percent and the 5-year Treasury note yields 3.50 percent, the G-spread is:

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Question 29

The Option-Adjusted Spread (OAS) for a callable bond is typically:

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Question 30

If a bond's yield increases, its price will:

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Question 31

Which of the following yield curves is constructed from yields on government bonds trading at par?

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Question 32

An investor calculates a bond's value using forward rates. The value obtained should be:

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Question 33

A 'step-up note' is a type of bond where the coupon rate:

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Question 34

A deferred-coupon bond:

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Question 35

Which of the following is an advantage of a cap for a floating-rate note issuer?

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Question 36

The simple yield of a bond:

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Question 37

For a bond with a 5 percent annual coupon and a YTM of 7 percent, the price value of a basis point (PVBP) will generally be:

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Question 38

A 3-year bond has spot rates of S1=3 percent, S2=4 percent, S3=5 percent. The implied 1-year forward rate 2 years from now (2y1y) is closest to:

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Question 39

For a 180-day money market instrument quoted with a discount yield of 2 percent, the price per 100 par value is:

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Question 40

When the yield curve is upward sloping, the forward curve is typically:

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Question 41

Which spread measure is most appropriate for a bond with embedded options?

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Question 42

If a callable bond's Z-spread is 200 bps and the value of the call option is 50 bps, the OAS is:

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Question 43

The interpolated spread (I-spread) uses which of the following as a benchmark?

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Question 44

If the coupon rate of a bond is higher than the YTM, the bond is likely to have:

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Question 45

A bond pays interest semiannually. If the quoted annual yield-to-maturity is 8 percent, the periodic discount rate used for valuation is:

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Question 46

The 'street convention' yield differs from the 'true yield' because:

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Question 47

A 5-year zero-coupon bond is priced at 800. What is the approximate yield to maturity on an annual basis?

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Question 48

What does a negative Z-spread imply?

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Question 49

When estimating the price change of a bond for a given change in yield, convexity is used to:

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Question 50

A bond's price is 950. If the yield falls by 10 basis points, the price rises to 958. If the yield rises by 10 basis points, the price falls to 942. What is the approximate duration (PVBP perspective)?

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