# Which currency to borrow/sell.

This has always given me problems and I am a retaker. When you are doing a question where there is an arbitrage oppurtunity, currency forwards etc. Can some one please explain how do you know which currency to borrow or sell. I can calculate the arbitrage profit from there but I am always clueless on when to borrow/sell. An answer will be greatly appreciated as this will also clear up some covered arbitrage issues in econ as well.

please provide an example problem and we can walk through the solution… that is more helpful, than talking in the air.

Most of the time its borrow domestic, cash to foreign, invest at foreign rate, cash to domestic and subtract out the domestic borrowed plus interest. If its a negative number, go the other way…

I will type two different questions in the EOC’s The euro currently trades at \$1.0231. The dollar rfr is 4% and the euro rfr is 5%. Six month forward contracts are quoted at a rate of \$1.0225. Indicate how you might earn a risk free profit in a forward contract. Cearly outline your steps you undertake to earn the profit The JPY currently trades at \$0.00812. The US rfr is 4.5%and the Jpanaese rfr is 2.0%. Three month forward contracts on the yen are quoted at \$0.00813. Indicate how you might earn a risk free profit in a forward contract. Cearly outline your steps you undertake to earn the profit The CFAI answers both these questions by giving a rate of return and state it is in excess of the market rate. Please do not answer it for me this way but rather provide the arbitrage profit in nominal value. Thx

buy low sell high!!! just think of everything that way.

Ok, let’s put it this way: When the currency forward is overvalued, you’d want to sell it right? So you sell it AND you have the obligation to deliver the foreign currency at expiration (T). Discount the amount to be delivered to PV using the FOREIGN interest rate and you will have the amount of FOREIGN currency you need to buy TODAY. Use the spot rate TODAY to calculate the amount of domestic currency you have to buy TODAY. When undervalued, you’d want to buy the currency forward and short sell the foreign currency. That’s my 2 cents, please confirm my thoughts.

First one: 1.0231 /Euro \* (1.04/1.05)^180/365 = 1.01828 Forward is at 1.0225 So forward is overpriced. So borrow domestic, convert to spot say 1000 -> convert to Euros at Spot => 977.41 Euro Lend forward at 5% for 180/365 -> becomes 1001.22 Euro Convert to at forward price -\> \*1.0225 = 1023.75 You need to return 1000 * 1.04^(180/365) = 1019.53\$ Profit = 1023.75 - 1019.53 = 4.22\$ 2nd one: Spot: 0.00812\$ / Yen Forward = 0.00812 * (1.045/1.02)^(90/365) = 0.00817 /Yen Forward is priced at 0.00813 /Yen Forward is underpriced. So you would buy the Forward. Short sell the Yen today. And buy the Forward today. Sell 1000\$ worth of Yen today at 0.00812\$/Yen and buy the forward => 123152.71 Yen. Move forward 123152.71 * 1.02^(90/365) = 123755.51 Yen Convert to at the forward price \*0.00813-\> 1006.13 You have earned a profit of 6.13 \$

CPK - If you short sell the Yen today don’t you need to borrow \$'s to do that? so the first step would be to borrow \$1000 for 3-mo @ 4.5% which would cause you to have to pay: 1000[1 + .045(90/365)] = \$1011.10 Therefore wiping out the profit and causing a loss of 1011.10 - 1006.13 = 4.97 B/c of the loss I went the opposite way: Borrow Yen 1,000 owe 1004.93 Buy Fwd contract to be able to convert to Yen @ .00813 /Yen in 3 mo convert to @ spot for \$8.12 invest \$8.12 @ 4.5% for three mo. to get 8.21 convert \$8.21 @ Fwd rate for 1,009.85Yen 1009.85 yen - 1,004.93 yen = 4.92yen profit.

I always think to myself buy low, sell high. After that determine which currency is undervalued forward, and which is overvalued forward. Once you know this, you know which currency you are buying forward. Do the opposite to your forward, on a spot basis. Example, FC is overvalued forward, DC is undervalued forward. 1) Buy DC/Sell FC forward. 2) Borrow DC and exchange to FC spot. 3) Earn interest on FC, when forward expires exchange all of it back to DC. 4) Repay the DC you borrowed, plus the interest. 5) Go to the bank with your \$\$\$ profit.

I use the interest rates to guide me rather than the currencies. Currencies are too confusing. Borrow in currency where interest rates are too low. Lend in currency where interest rates are too high.

If (R domestic - R foreign) < F-S/S then borrow domestic lend foreign i got this from a qbank answer

After all of this I am more clear but still not 100% sure. I think soddy 1979 generic answer has helped me most but my general sticking point is determining which currency is over/under valued CP in the second example, the no arbitrage forward price is greater than the (\$0.00817) is greater than the 3 month forward contract (\$0.00813) I just want you to let me know if my thinking below is correct. I am using the simplest currency quotation so it is clear. JPY:US = 1:\$0.00817 NO ARBITRAGE PRICE JPY :US = 1:\$0.00813 forward contract Therefore JPY is undervalued in the forward market since it is below the no arbitrage price. Therefore I should enter into a forward contract to buy JPY in three months time @\$0.00813. At the same time i should sell JPY now. In order to sell JPY I would need to be holding JPY. Therefore the steps i thought were 1. Borrow 1000 JPY, this is worth 1000 x(1.02)^0.25 in three months = 1004.96 JPY 2. Sell 1000 JPY now and buy \$US = \$8.12 3. Invest \$us at US rfr =\$8.12 x (1.045)^0.25= \$8.21US 4. Buy forward contract with \$8.21US = 8.21/0.00813 =1009.84jpy 5. Profir = 1009.84-1004.96 = 4.88 JPY The yield on the transaction would be the solution to 1000 X (1+I)^0.25 = 1009.84 This is equalt to 3.93% > 2%.

you are right Jeff. My mistake… I went the wrong way around on that one.