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An analyst on the emerging markets fixed-income desk of an investment bank has been asked to construct a term structure model of interest rates for one of the countries the desk covers. After conducting initial research, the analyst assumes that the 1-year spot rate for each of the next 3 years is expected to be 17.00% and that the interest rate process can be represented by the following risk-neutral interest rate tree:
Year 0 Year 1 Year 2 Year 3
17.00%
/ \
19.00% 15.00%
/ \ / \
19.00% 17.00% 17.00% 15.00%
/ \ / \
21.00% 13.00% 19.00% 11.00%
/ \ / \
23.00% 15.00% 13.00% 11.00%
Year 0 Year 1 Year 2 Year 3
17.00%
/ \
19.00% 15.00%
/ \ / \
19.00% 17.00% 17.00% 15.00%
/ \ / \
21.00% 13.00% 19.00% 11.00%
/ \ / \
23.00% 15.00% 13.00% 11.00%
(Note: Each node branches with probability 0.5 to up or down rates)
Which of the following correctly describes the shape of the term structure that will result from the given interest rate tree?
A
Slightly downward sloping, since discounting the terminal cash flow over longer time periods when interest rates exhibit volatility results in slightly lower spot rates.
B
Flat, since the interest rate tree is based on the assumption that all expected 1-year spot rates are equal.
C
Slightly upward sloping, since there is an opportunity cost associated with long-term interest rates.
D
Steeply upward sloping, since investors will demand higher long-term interest rates as compensation for interest rate volatility.