E Interest represented by “r3” is_ A B C D spot rate on a three-year investment (APR) spot rate on a two-year investment (APR) expected spot rate 2 years from today expected spot rate one year from today
The correct answer and explanation is :
The correct answer is: D. Expected spot rate one year from today
Explanation (300 words):
In finance, particularly in the context of fixed income and interest rates, “r₃” typically denotes a spot rate for a 3-year investment today. However, in the context of the question, “r₃” is used to represent a forward-looking interest rate, and the key lies in understanding forward rates vs spot rates.
Spot rates are the interest rates for an investment that starts today and matures in a specific number of years. For example, the spot rate for 3 years (r₃) is the yield on a 3-year zero-coupon bond bought today.
However, sometimes “r₃” is used in a forward rate context, especially when dealing with expectations of future interest rates. In that sense:
- Forward Rate (f₁,₂): This is the interest rate expected one year from now for a 2-year investment (year 1 to year 3).
- Forward Rate (f₂,₁): This would be the rate two years from now for one year (from year 2 to year 3).
In the given options, “r₃” is best interpreted as the forward rate expected one year from today (i.e., the rate that would apply in the future, not today). Specifically, it refers to the expected spot rate one year from now for a one-year investment — in forward rate notation, this would be f₁,₁.
This interpretation aligns with how economists and analysts use the expectations theory of the term structure of interest rates. According to this theory, longer-term interest rates (like the 2-year or 3-year spot rate) reflect a series of expected future short-term interest rates.
Therefore, “r₃” in this context reflects an expected short-term (1-year) interest rate beginning one year from today, making option D the most accurate.
