Consider the following annual rates. 0i1 = 5%, 0i2 = 6%, 0i3 = 7%, 0i4 = 8% 2i2e=3%, 3i2e = 5.5%, Assume yearly compounding.

The notation follows the convention used in the course, where the first subscript is the start of the investment and the second subscript the length of the investment. These subscripts are expressed in number of years.

(a) Draw a unique timeline and indicate in different separate lines (just below the timeline) the 6 opportunities of investments starting today implied by the interest rates listed above. Make sure that you include the relevant interest rates for each year of each investment. (1 mark)

(b) Assuming expectations theory holds, calculate 0i5 . {Always use general formula with notation before plugging your numbers]. (1 mark)

(c) Assuming expectations theory holds, derive the implicit expectation 2i1e embedded in the yield curve. [Always use general formula with notation before plugging your numbers]. Is expectations theory a theory that explains the formation of expectations by investors? Explain your answer. (1.5 marks)

(d) With rigorous calculations, check whether expectations theory holds for 0i4. Explain your reasoning. [Always use general formula with notation before plugging your numbers]. Is there a liquidity premium? if yes, calculate its value and interpret it. If not, provide an interpretation. (2 marks)