Suppose you live in period t (present) in a world where there are only 3 types of assets: 1-year T-bills, 2-year T-bills, and 6-year T-bills. For

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simplicity assume that people care about the next 6 years of their lives, and they cannot sell short. This means that if they buy a bond of maturity n, they have to keep it until period t + n (the maturity date). People can buy 1-year bonds in every single period (t, t + 1,...,t + 5). Also, they can buy 2-year bonds in period t (that mature in t+2), in period t+2 (that mature in t+4), and in t + 4 (that mature in t + 6). Throughout this problem please use notation similar to the one we used in the lecture (for example ie2,t+2 will be the expected interest rate of the 2-year bond that agents can buy in period t + 2).

a) Suppose these assets are perfect substitutes. What will happen to the interest rate of 2-year (i2,t) and 6-year (i6,t) T-bills bought in period t if the supply of 1-year T-bills shifts out? b) Now consider the other extreme: these assets are not substitutes at all. Is the interest rate (in period t) of 2-year bonds higher or lower than the one of 6-year bonds? How will an outward shift of the supply of 1-year T-bills in period t affect the interest rate of 6-year bonds?

Now consider an environment which is a combination of the ones described above. In particular, the assets are substitutes, but not perfect. People prefer short term bonds (because they are more liquid), but they would be willing to buy some bigger maturity bonds for the right return, a.k.a. premium. Let the premium of the asset of maturity n which is bought in period t be given by

ln,t = 0.01(n 1)

c) Suppose that the interest rate of 1-year bonds is expected to stay constant at 10 per cent over the next 5 years. Then calculate the interest rate (in period t) of 2-year and 6-year bills. Use your calculations to plot the yield curve of different maturity T-bills as of period t.