Part 1"According to the expectations theory of the term structure, it is better to invest in one-year bonds, reinvested over two years, than to invest in a two-year bond, if interest rates on one-year bonds are expected to be the same in both years." Is this statement true, false, or uncertain? A. False: These investments are almost of the same profitability. B. True: The expected return on one-year bonds, reinvested over two years, is always higher at amount i Subscript t minus i Subscript t plus 1 Superscript eit−iet+1. C. Uncertain: The answer depends on whether we can ignore the left parenthesis i Subscript 2 t Baseline right parenthesis squaredi2t2 and i Subscript t minus i Subscript t plus 1 Superscript eit−iet+1 values.

Question

Part 1​"According to the expectations theory of the term​ structure, it is better to invest in​ one-year bonds, reinvested over two​ years, than to invest in a​ two-year bond, if interest rates on​ one-year bonds are expected to be the same in both​ years." Is this statement​ true, false, or​ uncertain? A. ​False: These investments are almost of the same profitability. B. ​True: The expected return on​ one-year bonds, reinvested over two​ years, is always higher at amount i Subscript t minus i Subscript t plus 1 Superscript eit−iet+1. C. ​Uncertain: The answer depends on whether we can ignore the left parenthesis i Subscript 2 t Baseline right parenthesis squaredi2t2 and i Subscript t minus i Subscript t plus 1 Superscript eit−iet+1 values.

BlackTom AI · Accepted Answer

The question asks us to evaluate the statement within the expectations theory of the term structure.
Option A restates the claim that investing in one-year bonds and rolling them over for two years yields almost the same profitability as a direct two-year bond when one-year rates are expected to be the same across the two years. Under the expectations theory, the two-year rate is determined by the expected path of one-year rates: if the expected one-year rate in year 1 equals the expected one-year rate in year 2, then the return from a two-year bond should equal the product of two successive one-year investments, i.e., the same overall yield. Therefore, this option is consistent with the theory that the two strategies have the same expected return when future one-year rates are expected to be constant.

Option B claims that the rollover strategy always yields a higher return, citing the expression i_t − i_{t+1}^{e} (and a symbolized e). This is not aligned with the core idea: if the expected future one-year rate equals the current rate, there is no guaranteed extra gain from rolling over; the expected return should match the two-year bond's return, not exceed it. The use of a difference or an extra exponent does not reflect the standard expectation framework and introduces a misinterpretation of how expected rates aggregate over time.

Option C argues that the conclusion is uncertain and depends on ignoring certain squared terms and e-values (some ad hoc notation). The standard expectation theory does not hinge on such neglected terms; the core result about equivalence of returns under a flat (unchanged) expected path is straightforward. Introducing these ignored terms adds unnecessary ambiguity and misrepresents the model, making this option incorrect.

To summarize: Option A aligns with the equal-returns implication of the expectations theory when future one-year rates are expected to be the same; Options B and C introduce erroneous interpretations or unnecessary complexities that contradict the basic logic of the theory.

Quiz:Quiz 1

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