Question

1. Explain the logic of the Pure Expectations Theory: what does it claim about the relationship between long and short rates (the pure expectations hypothesis) and how does this follow from the assumptions that the theory makes?

Answer 1

Pure expectations theory assumes that the term structure of an interest contract only depends on the shorter term segments for determining the pricing and interest rate of long term maturities. It envision that that yields at higher maturities correspond to future realized rates, and are compounded from the yields on short period maturities. In other words, buying a ten year bond is equal to buying a series of two five year bonds in successive manner . you’re as safe in a ten-year as in a five-year bond. For the government securities in U.S. the only risk and rewards are born of the womb of the interest rate return on the lent amount. There is no significant risk of default associated with this transaction. The pure expectations theory is in some ways similar to the efficient market hypothesis, which assumes a perfect market environment where expectations are the cheif determinant s of future prices.
Example
To calculate the yields on a 4 year bond, for example, all that you need to do is to take the geometric mean of one-year yields on the first, second, third and fourth years; there’s no external component independent of the yields that determines the yield curve. The term structure is substitutable. A contract on a four year term serves exactly the same purpose as one on 4-months aside from the difference in interest rates, and as such, it is valued as if made of successive , periodical contracts combined to form the rate on the fourth year. You can either buy 2 two-year bonds or a series of four one year bonds successively, the result will be the same with respect to return.