Question

Assuming that the Market Expectations theory is the correct theory of the term structure, calculate the interest rates in the term structure for maturities of one to five years, for the following series of one –year interest rates;

a. 5%, 7%, 7%,7%,7%

b. 5%, 4%, 4%, 4%, 4%

Answer 1

As per the Market Expectations theory, the long term interest rates are calculated as the average of short term interest rates.So, given the one-year interest rates, the respective yields can be found as:

a).

Year (n)	1-year interest rate (r)	Formula	Yields
1	5%	r1	5.00%
2	7%	(r1+r2)/2	6.00%
3	7%	(r1+r2+r3)/3	6.33%
4	7%	(r1+r2+r3+r4)/4	6.50%
5	7%	(r1+r2+f3+r4+r5)/5	6.60%

b).

Year (n)	1-year interest rate ('r)	Formula	Yields
1	5%	r1	5.00%
2	4%	(r1+r2)/2	4.50%
3	4%	(r1+r2+r3)/3	4.33%
4	4%	(r1+r2+r3+r4)/4	4.25%
5	4%	(r1+r2+f3+r4+r5)/5	4.20%