# Interest Rate Parity

Came upon the post below (bottom of this post) on Level III forum searching under Interest Rate Parity. The problem is as follows: If two countries have different risk free rates the currency of the country with the lower risk free rate is supposed to appreciate vs. the currency of the country with the higher risk free rate (as measured by forward rate vs. spot rate ) unless such happens there is an arbitrage opportunity. This reasoning is given by both Schweser and CFA texts Doesn’t this run contrary to the logic of the previous reading (balance of payments) where it is stated that: if a country has a high risk free rate investors will flock to there hence putting upward pressure on the demand for that coutries currency strengthening it against the currencies of the countries with lower risk free rates. There were replys to that original post but I am still not sure I got the whole picture. Can somebody please shad some light on this? Domestic risk free = 4%; Foreign risk free = 4.8% Fwd differential = -0.8%, which means foreign currency is expected to depreciate by 8%. Example on page 208 of Schweser Note Bk3. Shouldn’t foreign currency be expected to appreciate? Since foreign rate is higher, investors would want to invest in foreign, thus demanding more foreign currency. Can somebody explain? Thanks.

wiredkris Wrote: ------------------------------------------------------- > Came upon the post below (bottom of this post) on > Level III forum searching under Interest Rate > Parity. > > The problem is as follows: > If two countries have different risk free rates > the currency of the country with the lower risk > free rate is supposed to appreciate vs. the > currency of the country with the higher risk free > rate (as measured by forward rate vs. spot rate ) > unless such happens there is an arbitrage > opportunity. This reasoning is given by both > Schweser and CFA texts > This isn’t exactly right. The currency isn’t “supposed” to do anything, however the forward exchange rate is completely determined by the nominal interest rates. If the forward rate is different than the rate implied by the interest differential that is available in risk-free interest rates, there is an arbitrage. This has nothing to do with economics or currency demand or anything else except the two interest rates. The arbitrage implies that the forward market says that the lower yielding currency is expected to appreciate. Then there is the question of whether or not the Expected(spot rate) = forward rate. There’s a ton of research on this and mostly it’s pretty close. If it was decidedly different or you could figure out when it would be different you could make arbitrarily much money by doing carry trades and trading currency markets. > Doesn’t this run contrary to the logic of the > previous reading (balance of payments) where it is > stated that: if a country has a high risk free > rate investors will flock to there hence putting > upward pressure on the demand for that coutries > currency strengthening it against the currencies > of the countries with lower risk free rates. > This is mostly about changes in real interest rates, not the absolute level of nominal interest rates. If a country raises its real interest rates then all else equal investors may want to put their money there. Investors need to believe that the increased interest rate is not because of increased risk and that it represents an increased real rate. This effect is not within 100 miles as strong as the arbitrage pricing ofcurrency forwards. > There were replys to that original post but I am > still not sure I got the whole picture. Can > somebody please shad some light on this? > > > > > > Domestic risk free = 4%; Foreign risk free = 4.8% > > Fwd differential = -0.8%, which means foreign > currency is expected to depreciate by 8%. > Example on page 208 of Schweser Note Bk3. > > Shouldn’t foreign currency be expected to > appreciate? Since foreign rate is higher, > investors would want to invest in foreign, thus > demanding more foreign currency. Can somebody > explain? Thanks.

get a good handle on this. This was all over the material last year in the PM and Econ sections and can rear its head on exam day in a variety of ways.

Joey, Budfox, Many thanks for your replys. IRP pirnciple and why would an arbitrage opportunity present itself if low rate currency (or rather the forward exchange rate) weren’t to appreciate against the high interest rate currency is clear in academic and logical sense. What’s confusing is that say if GBP rate were 4% vs. 7% in US\$ IRP predicts GBP would strengthen against the US\$ while in reality probably the opposite would be the case. This diametral difference between the IRP based prediction of interest rate movement with what’s happening in reality (Denmark, Hungary etc. raising rates to support local currencies) is something I haven’t been able to get my head around so far

“while in reality probably the opposite would be the case” is just not so. If you think so, try trading currency futures.

Thanks but no thanks. I rather stick with doing stuff that I actually understand. Your claim that “it just isn’t so” may indeed be the case but that’s not the point. The point I am making is that reading on BOP tells a story very different from IRP conclusion. Thanks for sharing your vision of this relationship though, opened up a new, interesting angle. I’ll be looking into this some more it seems.

wiredkris Wrote: ------------------------------------------------------- > Thanks but no thanks. I rather stick with doing > stuff that I actually understand. Your claim that > “it just isn’t so” may indeed be the case but > that’s not the point. The point I am making is > that reading on BOP tells a story very different > from IRP conclusion. This is not so. Reread above. It’s important to straighten this out. > Thanks for sharing your > vision of this relationship though, opened up a > new, interesting angle. I’ll be looking into this > some more it seems.

OK thanks. I’ll look into it

I have a similar question regarding the exchange rate/interest rate. The first question on Reading 19 states: Question: Consider two contries, A and B, whose currencies are a and b, respectively. The interest rate in A is greater than the interest rate in B. Which of the following is true according to the expected exchange rate movement relationship and interest rate parity, respectively? The Answer given is C: a is expected to depreciate relative to b, and a trades with a forward discount. I can certainly do all the calculations to get the answer. However, base on the intuition, if interest rate in A is higher, people will buy a currency to invest in A country, this will lead a to appreciate instead depreciate. Why is it opposite?

when people buy a currency - its demand increases. that causes a drop in price (all else equal) is that what happens? so it depreciates. eco is one subject I cannot put my arm around most of the time. so please ignore me and enlighten me if I am wrong.

cpk123: “when people buy a currency - its demand increases. that causes a drop in price (all else equal)” … ?? Increasing demand generally causes price to increase (all else equal). If there are 30 people bidding on one shovel, the guy who pays the highest price for the shovel gets to dig the hole. A higher nominal interest rate in Country A will result in people purchasing currency “a” in order to get A’s higher interest rate. In the short-term, currency “a” will definitely APpreciate relative to currency “b” as more people hunt the higher rate. When they unwind in one year, they will sell currency “a” in order to get back to their home currency. You have to understand whether you are using the formula constructed from a direct quote or an indirect quote perspective. The old Solnik material does a lousy job of indicating whether formulas have been constructed from a direct or indirect perspective. For example: F / S0 = (1 + rDC) / (1 + rFC) using units of domestic currency per one unit of foreign currency (represented in old Solnik as DC/FC and new Solnik as FC:DC or FCDC… all of which are “FC in terms of DC” or a direct quote perspective). F / S0 = (1 + rFC) / (1 + rDC) using the indirect quote perspective (FC/DC). You can see from the indirect quote perspective that F increases as rFC increases, all else equal. That is, the number of FC/DC units required at the end of the forward period increases as the FC interest rate increases. Why? Because you have to unwind the trade. The number of FC units required to buy a DC unit increases when the trade unwinds because investors have to repatriate their money back to DC units, thus bidding up the price of DC in terms of FC. Forward discount/premium: s = (F / S0) - 1. If we use indirect quote perspective, there will be a forward currency PREMIUM; i.e., more units of FC forward than FC spot per unit of DC. This is a DEPRECIATION because it takes more FC units to purchase a DC unit. Net message is that FC APpreciates short term as people buy FC with DC to invest in FC’s higher interest rate, but DEpreciates long term when investors repatriate FC for DC.

Should clarify second to last paragraph: This is a FC DEPRECIATION (DC APPRECIATION) because it takes more FC units to purchase a DC unit.

Insiderman Wrote: ------------------------------------------------------- > cpk123: “when people buy a currency - its demand > increases. that causes a drop in price (all else > equal)” > > … ?? > > Increasing demand generally causes price to > increase (all else equal). If there are 30 people > bidding on one shovel, the guy who pays the > highest price for the shovel gets to dig the > hole. > The difference is there is essentially an unlimited amount of currency. > A higher nominal interest rate in Country A will > result in people purchasing currency “a” in order > to get A’s higher interest rate. You must not have been around for awhile as that is categorically untrue. Higher nominal interest rates shouldn’t impress anyone and, in particular, when interest rates get really high there is usually an exodus of capital and everything else from a country. Really high nominal interest rates are very often the sign of impending hyperinflation, currency devaluation, or general economic chaos. > In the > short-term, currency “a” will definitely > APpreciate relative to currency “b” as more people > hunt the higher rate. No chance > When they unwind in one > year, they will sell currency “a” in order to get > back to their home currency. > I don’t know what one year has to do with anything, but “carry trades” have all kinds of risk. > You have to understand whether you are using the > formula constructed from a direct quote or an > indirect quote perspective. The old Solnik > material does a lousy job of indicating whether > formulas have been constructed from a direct or > indirect perspective. > Silly. I don’t even remember which is which, but currency appreciation or depreciation is unambiguous. > For example: > > F / S0 = (1 + rDC) / (1 + rFC) using units of > domestic currency per one unit of foreign currency > (represented in old Solnik as DC/FC and new Solnik > as FC:DC or FCDC… all of which are “FC in terms > of DC” or a direct quote perspective). > So? > F / S0 = (1 + rFC) / (1 + rDC) using the indirect > quote perspective (FC/DC). > > You can see from the indirect quote perspective > that F increases as rFC increases, all else equal. A higher interest rate in a foreign currency means it sells at a forward dsicount in the currency market. This is covered interest rate arbitrage. > That is, the number of FC/DC units required at > the end of the forward period increases as the FC > interest rate increases. Why? Because you have > to unwind the trade. The number of FC units > required to buy a DC unit increases when the trade > unwinds because investors have to repatriate their > money back to DC units, thus bidding up the price > of DC in terms of FC. > No. It has to do with a simple arbitrage. > Forward discount/premium: s = (F / S0) - 1. If we > use indirect quote perspective, there will be a > forward currency PREMIUM; i.e., more units of FC > forward than FC spot per unit of DC. This is a > DEPRECIATION because it takes more FC units to > purchase a DC unit. > > Net message is that FC APpreciates short term as > people buy FC with DC to invest in FC’s higher > interest rate, but DEpreciates long term when > investors repatriate FC for DC. Not close and you need to check thsi out more.

To JoeyDVivre. Thanks for the update, but saying something is wrong is not a refutation. Also, you may need to know how to use those formulas to pass the exam. They’re in the book, by the way. "> When they unwind in one > year, they will sell currency “a” in order to get > back to their home currency. > I don’t know what one year has to do with anything, but “carry trades” have all kinds of risk. " But they don’t have interest rate risk and, if you lock them in with a forward contract, they don’t have currency risk. "> You have to understand whether you are using the > formula constructed from a direct quote or an > indirect quote perspective. The old Solnik > material does a lousy job of indicating whether > formulas have been constructed from a direct or > indirect perspective. > Silly. I don’t even remember which is which, but currency appreciation or depreciation is unambiguous. " So how do you GET to the appreciation or depreciation (forward premium or discount) without the formula? And knowing how to use the formula depends on whether you get direct quote information or indirect quote information (which currency you’re talking about exchanging). "> That is, the number of FC/DC units required at > the end of the forward period increases as the FC > interest rate increases. Why? Because you have > to unwind the trade. The number of FC units > required to buy a DC unit increases when the trade > unwinds because investors have to repatriate their > money back to DC units, thus bidding up the price > of DC in terms of FC. > No. It has to do with a simple arbitrage. " The “simple arbitrage” is the mechanism by which the forward discount offsets the interest rate differential. It is not the cause of the process but the solution to the imbalance. “> Forward discount/premium: s = (F / S0) - 1. If we > use indirect quote perspective, there will be a > forward currency PREMIUM; i.e., more units of FC > forward than FC spot per unit of DC. This is a > DEPRECIATION because it takes more FC units to > purchase a DC unit. > > Net message is that FC APpreciates short term as > people buy FC with DC to invest in FC’s higher > interest rate, but DEpreciates long term when > investors repatriate FC for DC. Not close and you need to check thsi out more.” And why is it incorrect? And real world doesn’t matter here. It’s about the exam and the theory. Cheers.