this is how i think about it - if a currency is overvalued (the dollar in this case), you always want to invest at that country’s risk free rate because it’s going to higher (leading their currency to depreciate). to get there, you always want to borrow the currency with the lower risk free rate (which caused the currency to appreciate).
Here is how I do it. We are comparing the fair price of forward vs observed price of forward. Keep in mind, we are not valuing dollar against yen. So stick with one currency and use the other currency as the “price” for the first currency. Either way you will end up with the same conclusion. Start with the observed "price" of dollar forward = 22.22Yen (1 / .045) and the fair "price" of dollar is 20Yen. Dollar forward is overvalued. To earn a risk-less profit, you would sell forward (agree to sell and receive Yen in the future) and buy spot. And since you will receive boatload and Yen at the contract expiration, you wanna borrow Yen right now to buy . So that in the future date when you sell to get Yen, you can use Yen to pay back your original loan. Start with Yen the observed forward “price” of Yen is .045 and the fair “price” is .05. Yen forward is undervalued. To earn a risk-less profit, you wanna buy Yen forward and sell Yen spot. After you shorted Yen on the spot, you will then convert your Yen into so that when your contract expires, you have to buy Yen and exit your position. Notice the two ways to execute this transaction: 1) Borrow yen to buy Sell forward Exchange for Yen at expiration Use Yen to pay off original loan. 2) Short Yen & convert Yen into Buy Yen forward Exchange $ for Yen at expiration. Use Yen to pay off original loan. You will end up with the same profit.
I do it simply like this: If forward is overpriced- sell it short…Anything overpriced should be sold short Yen will be cheap in future; so it is expensive today… So you borrow something expensive to pay it back when it is cheap… Think about a friend who has got gold today… I borrow it and sell it in market as i belive gold is expensive right now… Once gold price goes down, i buy it back and give it back to my friend… so you borrow something expesive…
Thanks man, it makes sense. > Yen will be cheap in future; so it is expensive today… In this example, yen will be expensive in the future. It’s fair price is $0.05 in the future, but it is selling for only $0.045 today (as a forward contract). Right? Now, try this: An arbitrageur observes that the spot rate is $1.2000/€, and the 6-month forward rate is $1.18000/€, with U.S rate =4% and EU rate=6%. If the arbitrageur has a $5,000,000 line of credit with a bank, which of the following best estimates the arbitrage’s risk-free profit and the flow of funds in the spot market? a. A profit of $71,600 and a flow of funds of €4.2 million from EU to U.S. b. A profit of $71,600 and a flow of funds of $5 million from U.S. to EU. c. A profit of $35,830 and a flow of funds of €4.2 million from EU to U.S.
c?
Either way, you need to show your method. Off for now.
is it B for the latest problem?
buy 5 Mill at 1.2 Spot = 4.166667 M Euro Need to repay 4.166667 \* 1.03 = 4.2916667 M Euro Convert to at spot = 5 Mill US Move forward: @ 1.02 = 5.1 Mill US Convert at forward price of 1.18 $/Euro = 4.322034 Mill Euro Arb profit = 0.03036722 M Euro = * 1.18 = 35830 USD profit and funds flow from EU to USD at Spot 4.16 Mill C)
Re: interest rate arbitrage, your way this makes me crave burger king. I want a flame broiled whopper (my way) right now.
Ah! this one killed me. i was ready for an answer that; Interest rate parity dictates that the forward rate will be $1.1888 per Euro, and the current forward rate is only $1.18 per Euro…IN other words, forward is underpriced. Hence, i would buy forward (go long the forward; or buy euro later for only $1.18); and at the same time sell Euro today as it is overpriced in spot… but this one asked for actual calculations… 
CPK, I got the correct answer. But I tend to get confused when I have to convert the rate: For example, if the full year rate is 4%, then should be us (1.04)^(0.5) for half year or should we just use (1.02). If makes a bit of difference in the answer.
Answer is like cpk did it.
I’m betting on C. forward rate is .045 per yen when it really should be .05/yen. So in this case, comparatively speaking, we established that the foward is overvalued To exploit that, we would want to short the foward (that leaves you with option A and C) Now the question is should we borrow or yen. Since we are basically shorting the in the future, we have to hedge our risk by holding current , which means, we need to borrow Yen to buy 's. If you prefer simple thinking, I think of it this way, we’re working with an currency interest rate arbitrage question, hint…we should include both currencies in the answer somehow~ c) Borrow yen today and sell the $ forward.