If i (2020) denotes the annual interest rate on 2-year bonds issued in 2020 and i (2020) and 2 1
I (2021) represent interest rates on 1-year bonds purchased in 2020 and 2021, the
1
Equilibrium relationship between the 2-year bond and the two 1-year bonds is:
A)i (2020) = i (2020) + i (2021). 2 1 1
B)i (2020) = (1/2)[i (2020) + i (2021)].
C)i (2020) = (1/2)[i (2020) - i (2021)]. 2 1 1
D)i (2020) = 2·[i (2020) + i (2021)]. 2 1 1

Question

Quizplus · Accepted Answer

The equilibrium relationship between the 2-year bond and the two 1-year bonds is based on the idea of no-arbitrage, meaning that an investor should be indifferent between buying the 2-year bond or buying a combination of the two 1-year bonds. 
If the interest rates on the two 1-year bonds purchased in different years are not equivalent, then there is an opportunity for arbitrage (profit without risk). 
In order to eliminate the opportunity for arbitrage, the interest rates on the two 1-year bonds should be combined in a way that is equivalent to the interest rate on the 2-year bond. 
The correct equation is i (2020) = (1/2)[i (2020) + i (2021)], which represents a weighted average of the interest rates on the two 1-year bonds, with equal weighting based on the assumption of no-arbitrage.

If I (2020) Denotes the Annual Interest Rate on 2-Year