interest rate question

Martinghoul:

How do you arrive at the former conclusion (that B's ccy will appreciate vs A's) from interest rate parity?

tempaccount:

Both are correct (in theory), but the difference is one of time horizon as well as theory vs. practice.

In the short term and in practice after a rate announcement, higher interest rates encourage capital inflows, which drives the currency higher.

If you look at the pricing of any forward contract, the currency with the higher interest rate is expected to depreciate in order to satisfy the no-arbitrage condition. In other words, covered interest rate parity generally holds, because no bank is going to just give you the interest rate of the higher yielding currency without making you accept the exchange risk.

The theory of interest rate parity says that there would be an uncovered arbitrage if that higher yielding currency did not depreciate. Over a very long time horizon, that's probably true, but other factors besides interest rates affect the value of currencies in the meantime.

The mechanism by which a no-arbitrage condition is satisfied is arbitrage, meaning the theory assumes that speculators will buy the lower yielding currency because returns on cash should equalize. There are a few reasons this may not happen - arbitrage has limitations. Capital may not move freely between the two countries, and there may be persistent differences in the risk-return profile of each country's assets that justify a difference in rates. In a nutshell, that is why uncovered interest arbitrage is possible - sometimes (often, actually), the currency with the higher interest rate also has higher risk-adjusted return potential.

The way I like to think about this dynamic, and this is kind of my own theory, is that the short-term impact of a change in rates sets up the long-term arbitrage opportunity. This is related to Dornbusch's overshooting hypothesis, which you should read if you're interested in learning more about rates. Consider a thought experiment: two countries have perfectly equivalent economies, 0% interest rates, and a 1:1 exchange rate. All of a sudden, country A increases its interest rate to 5%. In the short term, the exchange rate appreciates in favor of country A as speculators move capital from country B to country A. All else equal, I would expect the exchange rate (expressed in number of units of A's currency one unit of B's currency is worth) to move to 1/1.05 = 0.95238. The one-year forward rate would be 1.0000, however. Why? Given perfect capital mobility and uncovered interest rate parity, that would set up a 5% yield on the now fundamentally undervalued currency B, to match the 5% yield in currency A. In practice it's never this neat, but that's the idea.

Great! This is exactly what I was wondering about!! I read somewhere else about the long term and short term effects but it wasnt very clear. Your explaination is much much better. Thank you! I understand that real life circumstances are different from this interest rate parity theory, it's just that the completely opporsite of my two assumptions bothers me. Now I fully understand the reason. Again, thank you so much for the help! Your own theory makes great sense,I really appreciate it!

tempaccount:

Both are correct (in theory), but the difference is one of time horizon as well as theory vs. practice.

In the short term and in practice after a rate announcement, higher interest rates encourage capital inflows, which drives the currency higher.

If you look at the pricing of any forward contract, the currency with the higher interest rate is expected to depreciate in order to satisfy the no-arbitrage condition. In other words, *covered* interest rate parity generally holds, because no bank is going to just give you the interest rate of the higher yielding currency without making you accept the exchange risk.

The theory of interest rate parity says that there would be an *uncovered* arbitrage if that higher yielding currency did not depreciate. Over a very long time horizon, that's probably true, but other factors besides interest rates affect the value of currencies in the meantime.

The mechanism by which a no-arbitrage condition is satisfied is arbitrage, meaning the theory assumes that speculators will buy the lower yielding currency because returns on cash should equalize. There are a few reasons this may not happen - arbitrage has limitations. Capital may not move freely between the two countries, and there may be persistent differences in the risk-return profile of each country's assets that justify a difference in rates. In a nutshell, that is why uncovered interest arbitrage is possible - sometimes (often, actually), the currency with the higher interest rate also has higher risk-adjusted return potential.

The way I like to think about this dynamic, and this is kind of my own theory, is that the short-term impact of a change in rates sets up the long-term arbitrage opportunity. This is related to Dornbusch's overshooting hypothesis, which you should read if you're interested in learning more about rates. Consider a thought experiment: two countries have perfectly equivalent economies, 0% interest rates, and a 1:1 exchange rate. All of a sudden, country A increases its interest rate to 5%. In the short term, the exchange rate appreciates in favor of country A as speculators move capital from country B to country A. All else equal, I would expect the exchange rate (expressed in number of units of A's currency one unit of B's currency is worth) to move to 1/1.05 = 0.95238. The one-year forward rate would be 1.0000, however. Why? Given perfect capital mobility and uncovered interest rate parity, that would set up a 5% yield on the now fundamentally undervalued currency B, to match the 5% yield in currency A. In practice it's never this neat, but that's the idea.

Wow, this is a great explanation. Short term money would flow into Country A, appreciating its currency. I could now get more of Country B currency for 1 dollar of Currency A due to the appreciation. Based on your calculation it should be 5% more, if it was more I could convert to B and gain a higher yield than the 5% interest rate in Country A, if it were less the opposite would happen (pocketing the difference between the interest rate and the exchange rate).

But why would the forward contract depreciate? Because its assuming that that at delivery the currency depreciation would equal the impact of the change in interest rate? I guess the opportunity here would be to speculate as to whether the movements in the exchange rate would happen before the delivery date.

This macro stuff is fascinating. There is still a part of me that would love to explore macro investing. As a value investor its tough to have such fluid, dynamic thesis that aren't derived on any concrete fundamental values for long. But I still think back to my university days when the genius of Soros & Druckenmiller inspired me to move into economics.

Great post again.