International monetary economics

International Monetary Econ

The rates obtained were as of market close on November 25, 2011. Historical rates are difficult to obtain online so this approach is more realistic. The spot rate for USD/JPY is 77.13 and the spot rate for USD/GBP is 0.64399 (Oanda.com, 2011).

The six-month forward rate for USD-JPY is 75.39 and for USD-GBP is 0.6279. The 6-month T-bill rates are for the U.S. 0.05%; for the UK 0.53% and for Japan 0.0%.

If covered interest rate parity holds, then there should be no arbitrage opportunity in trading forwards of these currencies. So for USD-GBP we have the following:

(1 + r£)/(1+r$) = (£/$f)/(£/$s)

For this relationship, interest rate parity does not hold. For the USD-JPY relationship we have the following:

r¥)/(1+r$) = (¥/$f)/( ¥/$s)

/ 1.0005 = 75.39/77.13

0.999 = 0.977

For this relationship, covered interest rate parity also does not hold.

If I have $10,000, my rate of return on U.S. T-bills (assuming this means 6-month) is going to be 0.05%, or $2.50.

If I buy six-month JPY, I will first convert to yen, giving me ¥771,300. This will earn nothing, so in six months I will also have ¥771,300. Using a six-month forward, this would be worth $10,230.80, as follows:

771,300/75.39

If I buy six-month GBP bonds I will start with £6640 and in six-month's time I will have £6457. Using the six-month forward rate this will convert back to $10,283.59.

3. With the JPY scenario, $10,000 would start with ¥771,300. This would be worth the same thing in six months. This would then convert back to USD as $10,016.88:

¥771,300 / 77 = $10,016.88

With the GPB scenario, $10,000 would start with £6640. In six months this will be worth £6457. This would be converted back to $10,249.21:

£6457 * 1.587 = $10,249.21

In both of these scenarios, the covered strategy is the more lucrative strategy, offering the highest return. There are a couple of possible reasons for this. One is that the expected rates are not as reliable as the forward rates. As such, they do not accurately reflect the interest rate parity.

However, the current forward rates also do not reflect interest rate parity. The Japanese six-month treasuries pay nothing and the U.S. treasuries pay almost nothing, yet the market is pricing in a weakening of the U.S. dollar over the next six months. There may be an expectation that the U.S. interest rates will be increased in the next six months at some point, perhaps if inflation edges too high and the economy shows some signs of life.

The same can be said about the USD-GBP pairing. The market appears to be pricing in an expected increase in the U.S. interest rates at some point in the next six months, or in this case a decrease in UK interest rates might also be the factor. However, given that the Japanese treasury rates cannot go lower, it is reasonable that the market is pricing in a U.S. rate increase, and that is affected the six-month forward rates for both currencies.

This exercise also illustrates that in the scenario given the covered interest rate strategy has the better payoff. As an investment strategy, the returns are greater, because of the expected changes in interest rates. The spot rates expected are simply less accurate numbers, which means that they may be less reliable to use for estimating investment returns.