 # Covered Interest Arbitrage

Hi al,

For covered interest arbirtrage, can anyone help simplify it for me (I have trouble with currency quotes for some reason in general…) And for this i know there are several steps but is there a way to simplify it or remember it?

“Williams has uncovered a potential arbitrage opportunity in the foreign exchange markets. The current spot rate is \$2.00 per BU. The Bundovianrisk-free interest rate is 3% and the one year forward rate is \$2.10 per BU. The uS Risk free rate is 5%”

Question :: The Maximum profit from covered interest arbitrage int he USD / BU market by borrowing \$1,000 or the bU equivalent is closes to :

A. \$19.05

B.\$ 31.50

C. \$72.50

Thanks guys!

Jason

1. Check what the forward should be worth: \$2/Bu * (1.05/1.03) = \$2.039

2. The market is saying that F1 = \$2.10/Bu… basically you can sign a contract today to sell 1 Bu for \$2.10, when in fact you should only get \$2.039.

3. So, you decide to buy the forward.

4. Borrow \$1000 at 5%, to pay \$50 later in the year.

5. Buy the Bu at the spot, you’ll get 500 Bu…then deposit at 3%, at end of year you’ll have 515 Bu.

6. Your contract guarantees \$2.10 per Bu, so you’ll get: 515 Bu * \$2/Bu = \$1081.50.

7. Deduct interest of \$50 on the dollars you borrowed, you’ll have \$1031.50 on you.

If you do this a few times, you’ll be able to do these steps quickly.

yep – except you sell the forward rather than buying it.

That’s right, typo there…if F > value calculated, sell it, else buy it.

just remember when the Spot rate is qouted \$/Fc then you set your equation up the same way…

So * (1+\$int rate/1+FcInt rate)=FP no Arb

if FP no Arb calcualted is > than quouted FP then buy the qouted mrkt FP

I wrote this in my notes in early months of studying.

“Short F = borrow base curency”

“If calculated = higher, short F”.

If F > calculated, it means I would be able to get more FC when the contract expires. It means I am effectively buying the forward so that I can use BU to exchange for USD at a higher rate than calculated.

Am I missing something here?

…probably…look, the quote F1 = \$2.10/Bu is just like a price tag that says \$2.10/Box, i.e., 1 box will cost you \$2.10. In this example you found that one box should sell for \$2.039, so clearly you do not want to buy it for \$2.10! You’d rather be the seller if that’s the case. So, you sell the forward contract. Don’t try to memorise it with base/FC/DC/American?British stuff…just think about it realistcialy.

Why would the dollar depreciate when its interest rate is higher? I thought higher interest rates mean more money pouring in?

If *real* interest rates are higher that will attract foreign money, but if it is a matter of the dollar appreciating to offset U.S. inflation, then it is no good to go for the greenback. If interest rate in Zambia is 20%, would you throw your money in Zambia? Probably not, because the exchange rate is expected to depreciate by about 18% (assuming U.S. rate of 2%) by year end.

But how are we supposed to know that based off of what is given?

I understand if the nominal is higher you wouldn’t invest. If the real is higher you would. But with this they just say rf rate. Are we to assume that’s the nominal?

If not told otherwise, it is nominal. If you are given price levels and expected inflation, you can calculate what the nominal rate should be. If you find that the nominal rate is more than what was expected, it would be because real interest rates moved higher, but that’s another topic in econ.

Why doesn’t this logic works?

\$2.10/BU -> 1 BU equals \$2.10 in the market

\$2.039/BU -> 1 BU equals \$2.039 according to your calculation.

So, why not go to the market with BU and exchange for higher \$ rate?

I’m just thinking aloud here. Seems like I am deviating…lets see how it goes.

Think I have figured it out.

Short forward = Sell the base currency.

\$2.10/BU -> 1 BU equals \$2.10 in the market.

Shorting this means you are selling the BU at a higher price compared to the no-arb price (overpriced).

Long means buying BU at a higher price which no one will do.

Thanks Dreary.