I am having a heck of a time with this topic. Any hints or ticks would be appreciated. I have no trouble identifying whether a arbitrage opportunity exists. But once I identify the opportunity I can never tell what currency I should borrow and lend in. Does anyone have any tricks for working through this?
aghhh. Just tried another problem and still can not figure out how to decide what currency to borrow in. Any help?
please post a problem or direct us somewhere- much more useful
I have USD:JPY spot at 116.35 and US Int rate of 4% and JPY Int rate of 1.5% Forward rate is USD:JPY 112.99 I have determined that the correct forward rate is 113.55 so it looks to me like the JPY is overvalued in the forward market and the USD is undervalued This is where I get fouled up. Now I have to decide if I should lend in JPY or lend in USD I think that that I should sell forward the JPY which means that I need to buy USD at the spot rate…but I am not sure
Here’s how I would do this: First, identify what is overvalued/undervalued: In this case, as you said, the Yen appears to be overvalued. Equivalently, the Dollar is undervalued. An arb opportunity exists on either side actually, long dollar or short yen. From a technical standpoint it doesn’t really matter. From a practical standpoint, lets take the perspective of our domestic currency, the Dollar (for me anyways). So we’ve identified the problem as being: The futures price is undervaluing the dollar. How can I take advantage of this? In this case, because the future is undervaluing the dollar, we want to buy the future. We have to keep in mind what this means: This means that I will be buying the dollar at the Futures price at maturity of the contract. In otherwords, I will have to have YEN to exchange for those dollars that I will be purchasing. Lets assume $1M notional principal. What I will do then is borrow 1M at 4%, convert it at spot of 116.35 to receive Y116,350,000, and invest it at 1.5%. (NOTE: I have 0 risk here because I am long the forward which guarantees me that I can convert the YEN that I now have into 's at a pre-set rate) Now here’s how this goes down: - At maturity, my YEN investment pays off Y118,095,250. - Next, I will convert my Y118,095,250 into $ at the contract rate of 112.99 for $1,045,183.20 - I will now pay off my obligation to the bank that lent me the original $1M which is $1,040,000. And I’ve pocketed the difference of $5,183.20 Points to keep in mind: 1. Identify overpriced/underpriced 2. Sell overpriced/Buy underpriced 3. Remember that in an arb situation, there should be no money out of pocket (why i borrowed 1m from the bank instread of fronting it) 4. Work backwards. We knew I wanted to buy the forward, which meant I needed YEN. This further meant that I needed 's to convert into Yen at the current rate. Since I needed $, I borrowed them. We’re given the interest rates in the problem. It makes complete sense that I would borrow at my rate, and since I now posess YEN, I would invest them at the Japanese rate. 5. Work out what happens at maturity. My YEN’s pay off (principal X (1+r)). My YEN is exchanged at the contract rate, and then my obligation (principal X (1+r)) gets settled. Hope this helps! Donnie
I prefer working with the individual units in the question and then just multiplying the final answer by the total units given Here is how I do it Yo know the fwd is undervalued, so the trade is sell the spot and buy the forward To identify which currency to sell and which one to buy know your Num/Deno regardless of which one is your DC or FC as the assumption in all problems is there are no transaction costs, limitless borrowing, etc. So your original quote is JPY/USD (the denominator is what you are buying and selling) in this case is the USD, if the quote was USD/JPY then you would buy and sell the JPY SO moving from that Borrow 1USD @ 4% to owe 1.04 in a year sell the spot (1USD) to ger JPY 116.35 Invest JPY 116.35 @ 1.015 to get JPY 118.095250 in 1 year convert back to USD in a year @ fwd of 112.99 i.e. 118.095250/112.99 = USD 1.045183 Pay back the USD 1.04 you owe to net USD 1.045183 - USD 1.04 = USD.005183 Now multiply by the amount inthe problem so for USD 1 MM the profit is .005183*1,000,000 = $5,183 Another logical way(without worrying about the DC, FC) of understanding this to spot check your answer is : country with low int rate will appreciate and the one with high int rate will depreciate so USD will depreciate and JPY will appreciate so you want to invest in JPY by selling the USD (this always works)
Ok, I think I have it now. The point you made about needing the Yen to exchange for USD in the future makes sense. Now that I think about it the only way I would have Yen would be if my loan paid off in Yen. So that means if if I loaned in Yen I must have borrowed in USD. I will run through some questions tonight. Thanks much
The part I like about arbitrage… IF you do it the wrong direction (borrow the wrong thing and invest in the wrong thing). You lose money. So try it the other way. Generic form of all arbitrages: Borrow-invest-payoff loan-leftover is arbitrage profit. Keys to “risk-free” arbitrage: At time 0, borrow and lock in investment returns (with derivative instruments usually) At time future, pay off loan and keep profit Its risk free because your returns are known and you are not relying on a theoretical parity. It does not mean that its credit risk free. Beware of Bid-Ask spreads. Its really not any more difficult but it will seem more complicated. Without a bid-ask, arbitrage profit = loss of doing it the wrong way. So one direction you make money, the other you lose. With Bid-Ask - Only one way MIGHT make a profit but you can lose money both directions if the dealers spread wipes out an arbitraging opportunities.