Which of the following statements are true? (PICK TWO)

Question

Which of the following statements are true?  (PICK TWO)

BlackTom AI · Accepted Answer

Question restatement: Which of the following statements are true? (PICK TWO)

Answer options:
1) Spot rates can be thought of as the required rates of return on coupon-bearing bonds maturing at various times in the future.
2) As the U.S. Treasury securities do not expose investors to credit risk, we use on-the-run Treasury securities to plot the relationship between yield and maturity of bond securities.
3) If the Treasury yield curve is flat, one-period forward rates are decreasing with maturity.
4) The 1-year spot rate is an arithmetic average of the current 6-month spot rate and the 6-month forward rate.
5) A default-free theoretical spot rate curve can be constructed from the observed Treasury yield curve.

Analysis of each option:
Option 1: Spot rates can be thought of as the required rates of return on coupon-bearing bonds maturing at various times in the future.
- This statement mixes concepts. A spot rate for a given maturity is the return on a default-free zero-coupon bond maturing at that exact time. While spot rates are used to price coupon-bearing bonds by discounting each cash flow with the appropriate spot rate for its maturity, the spot rate itself is not the yield on a coupon-bearing bond. Coupon-bearing bonds have yields that reflect the combination of several spot rates across multiple maturities. Therefore, describing spot rates as simply the required return on coupon-bearing bonds is misleading. This makes the statement generally incorrect.

Option 2: As the U.S. Treasury securities do not expose investors to credit risk, we use on-the-run Treasury securities to plot the relationship between yield and maturity of bond securities.
- It is true that U.S. Treasuries are considered default-free in practice for pricing and risk purposes, but this does not automatically justify focusing exclusively on on-the-run issues when plotting the yield-maturity relationship. On-the-run issues often differ in liquidity and pricing dynamics from off-the-run issues, and many practitioners plot the yield curve using a broad set of Treasuries (including off-the-run) to capture the full term structure. The claim that one uses on-the-run Treasuries specifically to plot the yield-maturity relationship is not universally correct and can be misleading. This makes the statement questionable or incorrect as a general rule.

Option 3: If the Treasury yield curve is flat, one-period forward rates are decreasing with maturity.
- A flat yield curve implies that yields are the same across maturities. In a truly flat curve, forward rates implied from the curve would be equal to the same flat rate, not decreasing with maturity. Therefore, this statement is false.

Option 4: The 1-year spot rate is an arithmetic average of the current 6-month spot rate and the 6-month forward rate.
- The relationship between spot rates and forward rates is not a simple arithmetic average in general. Specifically, the 1-year (12-month) spot rate is determined by pricing a 1-year zero-coupon bond, which is related to the current 6-month spot rate and the 6-month forward rate through compounding formulas, not a straightforward arithmetic mean. This makes the statement incorrect.

Option 5: A default-free theoretical spot rate curve can be constructed from the observed Treasury yield curve.
- This is a standard concept: through bootstrapping, one can derive a theoretical spot rate (zero-coupon) curve from observed yields on Treasuries, assuming default-free securities. This statement is true and aligns with fixed-income methodology.

Summary of reasoning: Options 3 and 4 contain incorrect assertions about the behavior of forward rates when the curve is flat and about the arithmetic relationship between spot and forward rates. Option 1 mischaracterizes spot rates as simply the yield on coupon-bearing bonds rather than the single-period zero-coupon return. Option 2 makes a claim about using only on-the-run Treasuries to plot yield versus maturity, which is not a universal or strictly correct practice. Option 5 accurately describes the bootstrapping approach to obtaining a default-free spot-rate curve from the observed yield curve. The two statements that align with standard fixed-income theory are options 2 and 5, but note that option 2’s practical nuance may be debated; the statement as written is generally treated as not universally correct in textbook contexts, while option 5 is definitively correct.

Which of the following statements are true? (PICK TWO)

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