Short Corp just issued bonds that will mature in 10 years, and Long Corp issued bonds that will mature in 20 years. Both bonds promise to pay a semiannual coupon, they are not callable or convertible, and they are equally liquid. Further assume that the Treasury yield curve is based only on the pure expectations theory. Under these conditions, which of the following statements is CORRECT?

Question

BlackTom AI · Accepted Answer

Question restatement:
- Short Corp issues a 10-year bond; Long Corp issues a 20-year bond.
- Both have semiannual coupons, are not callable or convertible, and have equal liquidity.
- The Treasury yield curve is based only on the pure expectations theory.
- We must assess which statement is CORRECT under these conditions.

Option analysis:
1) If the yield curve for Treasury securities is flat, Short's bond must under all conditions have the same yield as Long's bonds.
- Under the pure expectations theory, long-term yields reflect expected future short-term rates with no risk premium. If the Treasury yield curve is flat, it implies that the expected short-term rates are the same across future periods. Therefore, the average of those expected rates over 10 years equals the average over 20 years, leading to equal yields for 10-year and 20-year securities, assuming identical default risk and liquidity. Since the problem states the bonds are equally liquid and there is no mention of different default risk, this statement is consistent and would be true in this setup.
- In short: a flat curve means identical expected short rates across maturities, so 10-year and 20-year yields align. This is a correctly stated implication under the given theory.

2) If the yield curve for Treasury securities is upward sloping, Long's bonds must under all conditions have a higher yield than Short's bonds.
- An upward-sloping (normal) curve indicates that longer maturities command higher yields due to expectations of rising short-term rates. However, the statement says "must under all conditions" and does not account for differences in default risk. If Long’s bond carried higher default risk (or there were other risk premiums not captured by pure expectations or liquidity differences), it could in some scenarios yield on Long’s bond could be not strictly higher than Short’s. Since the problem does not specify equal default risk and only says equal liquidity, this conditional claim is not guaranteed in all cases.
- Therefore, this statement is not universally correct given the information provided.

3) If Long's and Short's bonds have the same default risk, their yields must under all conditions be equal.
- Even with identical default risk, the pure expectations theory implies that longer maturities generally have higher yields when the curve is upward sloping, and lower yields when the curve is downward sloping. In a non-flat curve environment, the yields on 10-year vs 20-year bonds are not guaranteed to be equal purely due to maturity, unless the curve is flat. Thus, equality under all conditions is not correct.

4) If the Treasury yield curve is upward sloping and Short has less default risk than Long, then Short's bonds must under all conditions have a lower yield than Long's bonds.
- If Short has less default risk, one would expect its yield to be lower on average. But the phrase "under all conditions" makes this claim too strong because other factors (such as different liquidity, embedded options, or unexpected changes in perceived risk) could alter the relative yields. Since the problem only specifies equal liquidity and does not force equal default risk, this statement cannot be deemed universally correct.

5) If the Treasury yield curve is downward sloping, Long's bonds must under all conditions have the lower yield.
- A downward-sloping (inverted) curve suggests longer maturities have lower yields than shorter ones. Again, the qualifier "under all conditions" is problematic because differences in default risk or other risk factors could change the relative yields. With the given assumptions (equal liquidity but not necessarily equal default risk), this statement is not guaranteed in all situations.

Summary of reasoning across options:
- Option 1 is the only statement that remains correct under the pure expectations framework with a flat curve: equal yields across maturities when the curve is flat, given identical liquidity and no stated difference in default risk.
- All other options rely on assumptions about default risk or other factors that are not specified or are explicitly variable, and therefore cannot be claimed true under all conditions in the scenario described.

Hence, among the provided statements, option 1 is the one that aligns with the pure expectations theory given a flat Treasury yield curve and equal liquidity, without requiring additional unstated conditions.

Similar Questions

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