Question

9. Uncovered Interest Parity and Expectations Theory of interest rates Assume two countries, the U.S. and the UK. In the United States, there are 1-year bonds and 5-year bonds (denominated in dollars). In the United Kingdom, there are also 1-year and 5-year bonds (denominated in pounds). There is a spot market Mathematically, come up with one equation for the Spot Exchange Rate that satisfies (1) the uncovered interest parity condition; (2) the expectation theory for interest rates in the US; and (3) the expectation theory of interest rates in the United Kingdom. The EXPLAIN what your equation means.

Answer 1

Uncovered interest rate parity states that difference of interest rate between two countries is equal to the change in the foreighn exchange rates over the same period,if the uncovered parity is not true people can make risk free profit by using arbitrage.

Let investor considering investing between US and UK , let the interest rate in the U.S.,i$ and let the interest rate in united kingdom be ip.

there are two interest rates covered interest rates and uncovered interest rates.When uncovered interest rate parity holds, there can be no excess return earned from simultaneously going long a higher-yielding currency investment and shorting a different lower-yielding currency investment or interest rate spread.

Uncovered interest rate parity formula. = %Change in expected future spot price S($)/S(P) = I nt($) - I nt(P) --------------1)

S($) - SPOT PRICE of $

S(P) - Spot price of pound

i$ - interest rate of $

iP - interest rate of pound

The expectations theory uses long-term interest rates to predict future short-term interest rates.Investors estimate future interest rates when considering different investments. For example, an investor who’s deciding whether to buy a 5-year bond versus successive 1-year bonds might use the expectations theory to predict the prices.

In equation 1

the bond prices of 5 year for dollor and pound can be prtedicted by successive 1 year bond

where I nt($) = (It + It+1+ It+2 ... I t+4)/n

I nt(P)= (It + It+1+ It+2 ... I t+4)/n