# Interest rate Parity Question

3 month treasury bill rates in the U.S. and Japn are 4% and 1%, respectively. The 3 month forward yen is 0.01015/yen and the spot exchange rate between the U.S. dollar and the yen is yen100/. Under these conditions, a currency arbitrageus would: A. DO nothing because there is no profitable arbitrage opportunity under these conditions B. Sell the yen forward and buy the spot yen C. Buy the yen forward and sell the spot yen D. Sell the yen forward and buy the spot U.S. dollar My thought process: Using interest rate parity, US foreign and Yen domestic, foward(DC/FC)/spot(DC/FC)=(1+rdom)/(1+rfor) 0.01015/(1/100) < 1.04/1.01 So \$0.01015/yen is too low, thus should buy the yen forward and sell the spot yen. C. But if you use forward premium concept, you get B. Any one can explain this?

For one thing, in the above problem since it is a annual rate, and you have a 90 day forward rate your 1+rd and 1 + rf should use 1.01 for the US and 1.0025 for the Japanese side. since rates are /Yen =Domestic, Yen=Foreign 1+rd = 1.01 F/S ( 1+rf) = .01015/0.01 * 1.0025 = 1.0175 > 1 + rd so borrow USD and sell Yen Forward because US rate is lower, is what I thought. I hope I did understand right what was written in the earlier post today. *Otherwise need to hit the books again, or some good samaritan will explain this step by step *** so I can remember it. Choice D

I hate decimal 0, I ll just set Yen as domestic. Patriotically, I won’t. f = 98.522 S = 100 1+rd = 1.01^0.25=1.00249 1+rf = 1.04^0.25 = 1.00985 f=(1+rd)*s / (1+rf) = 99.27091 --> forward is underpriced, then buy forward, sell spot. C

cpk123 Wrote: ------------------------------------------------------- > For one thing, in the above problem since it is a > annual rate, and you have a 90 day forward rate > > your 1+rd and 1 + rf should use 1.01 for the US > and 1.0025 for the Japanese side. > > since rates are /Yen =Domestic, Yen=Foreign > > 1+rd = 1.01 > > F/S ( 1+rf) = .01015/0.01 * 1.0025 = 1.0175 > 1 + > rd > > so borrow USD and sell Yen Forward because US rate > is lower, is what I thought. > > > I hope I did understand right what was written in > the earlier post today. > *Otherwise need to hit the books again, or some > good samaritan will explain this step by step *** > so I can remember it. > > > Choice D I got similar number. But I think after borrowing USD, need to buy yen using spot rate and also sell forward yen so that we can change back to USD. So I think it is B. Suppose borrow 1M U.S. dollar. Need to return 1.01 M in 3 months. Buy yen and exchange back to \$ after 3 months: 1M * 100 * (1.0025) * 0.01015 = 1,017,537.5. Arbitrage Profit: 7537.5

disptra a question for you. once we do the (1+rd) and the F/S ( 1+rf) what is the rule of thumb to apply. When 1+rd < F/S (1+rf) what should be done? When 1+rd > F/S (1+rf) then what should be done? If you could explain this, with reasoning. I am able to do the arbitrage problem, and arrive at the profit / loss per se. But when it comes to solving text driven Analysis problems which say Buy X, Sell Y or Sell Y Forward and Buy X Forward and things like that, I get a real blinder of a headache, (kind of blank out and then get to the good old guessing game). Thanks in advance. CP

I get B too borrow us dollars change in yen. deposit in bank and sell forward

When 1+rd < F/S (1+rf) what should be done? that means that adjusted foreign interest rate is higher than local. So borrow at local, change at spot , deposit in bank the foreign currency and sell it at forward price for domestic When 1+rd > F/S (1+rf) then what should be done? local interest rate is higher than adjusted one borrow at foreign, change into local, deposit in local bank and sell domestic currency for foreign at forward does it make sense?

answer is B According to the intreste rate parity, the annualized forward premium (discount) on the yen should approximately equal the difference between U.S. and Japanese interest rates. The annualized forward premium on the yen and the interest rate differential between the U.S. and Japan are forward premiums/yen=(F-S)/S * (360/tm)=[(0.1015-0.01)/0.01] (360/90)=6% rus-rjapan=3% since they are not equal, the forward premium must fall, which means the forward yen is overvalued. therefore, sell the overvalued forward yen and buy the spot yen. answer C is incorrect becasue the premium should decrease, which meanst he forward yen will fall in value. therefore, it would be unprofitble to buy it. anyone buying this?

I have struggled with this as well. I have read this part of book several times. I think florinpop’s method is good. First need to determine if borrow domestic or foreign currency. If 1 + rd < (F/S) (1+rf), borrow domectic. 1 + rd > (F/S) (1+rf), borrow foreign. i.e borrow at low interest rate and lend at higher rate. And it is always four step processes to complete the arbitrage: borrow, exchange at spot rate, lend, and sell forward contract.

I do this in a straight forward way: Assume you have 100 USD, or 10000 Yen at spot rate. Deposit 100 USD at 1% yield 101 USD 3 months later, Deposit 10000 Yen at 0.25% yield 10025 Yen 3 months later. Exchange that 10025 Yen into USD yields 101.75 USD. In real life, I would choose to deposit in Yen during the period. So, I will buy Yen, deposit it in the bank, and sell Yen 3 month later, pocket the difference. That is B.

C (ignore my previous post) I v been haunted by this problem for a few days. So I have done some extra thinking. here is my rules, hopefully you ll find helpful. 1. 1+rd > f/s (1+rf) --> borrow foreign, and invest domestically. now you need at spot rate, later you need to return f, need foward contract to sell . 2. 1+rd < f/s (1+rf) --> borrow domestically, invest in foreign country. now you need to sell for foreign currency, later you need to return , and need forward contract to buy \$. 1. always need the currency with greater “return” 2. figure out what currency you need now, get it with spot rate. 3. and the other one is what you need to return later, get it with forward rate.

I wanted to say B (ignore my previous post)

yepp i’m gonna get massacred on these questions

Arbitrage means no NET investment. So, since we know the forward yen is overpriced, we r interested in selling it forward (U’ll have to deliver YEN and recieve DOLLAR in 3 months). Say, we borrow 100USD, buy YEN (100*100 = 10,000). Recieve interest on that YEN (10,000 * 1.01/4 = 10,025). AFTER 3 months, u’ll recieve (10,025 * 0.01015 = USD 101.7538) . Pay back the loan with interest (100 * 1.01 = 101). UR risk-free profit = 101.7538 - 101 = USD 0.7538.