Given Eng’s expectation for spot rates, the first-year return on a 3-year zero-coupon bond is closest to:
A. 0.75%.
B. 1.45%.
C. 1.95%.
Why is (A) wrong? The answer key states that (A) is wrong because " 1. Incorrect because this is the 1-year spot rate. This rate would only have been achieved if the spot rates evolved as implied by the current forward curve. This is not the case under Eng’s expectation of an unchanged spot curve."
Can someone help me understand the significance of an unchanged spot curve in this question?
Michael expects that the spot rates one year from today will remain the same as they are today, rather than evolving to what is implied by the forward rates.
This allows him to earn a higher return by rolling down the yield curve. This means that if the investor has a holding period of one year, they can earn a higher yield by buying a bond with a longer maturity and selling it in one year, rather than buying a bond that matures in one year.
If the investor buys a one-year bond and holds it to maturity, then they yield 0.75%.
If the investor instead buys a 3-year bond and sells it in one year, then he should instead earn a 1.95% yield.
The math looks as follows:
Buy 3-Year Bond: $100 / (1.0145)^3 = $95.773
After 1 year, it becomes a 2-Year Bond: $100 / (1.012)^2 = $97.643
($97.643 / $95.773) - 1 = 1.95%
