# Interest-Rate Arbitrage: Essential Information for Arbitrageurs (2008)

## G. Stolyarov II

Note from the Author: I was commissioned to write this article by Associated Content (which subsequently became Yahoo! Voices) in 2008, for the benefit of investors seeking to benefit from interest-rate arbitrage between US dollars and Indian rupees. The article expresses some good general advice and concepts, as well as a simplified mathematical model of interest-rate arbitrage, though many of its particulars are relevant to the context in which it was written in 2008 and are likely obsolete now. The article has enjoyed some popularity and has received over 7,000 views to date. Still, for the historical record, due to the closure of Yahoo! Voices in 2014, I render this article permanently available on this page.

~ G. Stolyarov II, July 21, 2014

An arbitrage opportunity is a chance to generate risk-free profit when the market in general has, for some reason, mispriced some assets - including currencies - and most individuals in the market have overlooked the true value of those assets. Although theoretical models of interest rate behavior often assume away the existence of arbitrage, such opportunities do occur quite frequently in the real world.

To understand interest rate arbitrage, it is first necessary to define a few terms and understand at least a little bit of the mathematics behind it. If you wish to personally take advantage of interest rate arbitrage, at least an elementary knowledge of the mathematics and the concepts it is based on is essential. Investors who know none of the relevant math will always lose money in the long run, because of the presence of numerous capable investors who know a lot of math.

First, and quite obviously, we have two currencies and interest rates denominated in those currencies. Let us call those currencies A and B. We let iAA be the currency-A denominated interest rate and let iBB be the currency-B denominated interest rate. For instance, iAA can be the interest rate in terms of U. S. dollars (USD) and iBB can be the interest rate in terms of the Indian rupee (INR).

Now we also need two different kinds of exchange rates. First, we have the spot exchange rate or S. This is the exchange rate at which you can trade one currency for another right now. For instance, according to Dollars2Rupees.com, on May 2, 2008, one U. S. dollar traded for 40.55 rupees. So the rupee-denominated spot exchange rate for the dollar was 40.55 INR/USD. On the other hand, the dollar-denominated spot exchange rate for the rupee on May 2, 2008 was 0.0247 USD/INR. The spot rate you will be concerned about will depend on which currency you are holding (your "domestic currency") and which currency you are thinking about acquiring (your "foreign currency"). The spot exchange rate you will be concerned with will be the price of one unit of your "foreign currency," expressed in terms of your "domestic currency."

The other rate you need to know is the forward exchange rate or F. A forward exchange rate is a rate given now for an exchange of currencies that will occur later at some specified time. To find the forward exchange rates for rupees in terms of dollars for various time periods, take a look at OFX.com, where you can find forward exchange rates for any major currency in terms of any other major currency.

If no arbitrage existed, we would have a condition called interest rate parity, where (1 + iA) = (F/S)(1 + iB). Parity means that there is no opportunity iA make a risk-free profit by holding and investing one of these currencies over the other.

But what happens if the parity equation does not hold? If it is the case that (1 + iA) < (F/S)(1 + iB), then this means that it is more advantageoiA to hold curreiBy B. You could borrow money in terms of currency A (say, dollars) and convert it to currency B (say, rupees). Then, you could invest money in India and earn a higher interest rate than you have to pay on your dollar-denominated loan. On the other hand, (1 + iA) > (F/S)(1 + iB), then you should borrow currency B (say, rupees) and convert it into currency A (say, dollars) and invest money in the United States, repaying the rupee-denominated loan while earning a higher interest rate on the money you borrowed and invested. To find which of these relationships hold, you will need to know the prevailing interest rates in terms of each currency, as well as the relevant spot and forward exchange rates.

However, be warned: this is an extremely simplified view of matters that does not take many complicating factors into account. If you observe a deviation from interest rate parity in the real world, this may not necessarily mean that arbitrage opportunities exist. The presence of transaction costs - such as commissions and bid-ask spreads - as well as higher taxation of interest in one country as opposed to another - could account for deviations from parity. Also, remember that real-world interest rates carry a component of risk. That is, if the rupee-denominated interest rate is higher than the dollar-denominated interest rate, this might not mean that arbitrage actually exists; it might simply mean that you would run a greater risk losing your money altogether if you invested in India - and you get paid a premium to compensate you for the risk of loss. Of course, having been paid a slight premium for a few months is no comfort to someone who has lost an entire investment. I am not suggesting that this is necessarily the case with investments made into India today; but you need to consider it as a possibility, and if you reject that possibility, you need to have a good reason for doing so.

The foremost piece of advice for anybody who wishes to take advantage of interest rate arbitrage is to become highly informed about the particulars of the transaction one wishes to enter into. For instance, if you have connections to India - friends, relatives, or business associates - then they might have some highly particular and highly useful information that you would not find on the news or on the Internet. Ask them about taxes and transaction costs in India and how safe an investment made in rupees might be. Also research the volatility of interest rates - how much they fluctuate over time - in India and in the United States. After all, if interest rates are highly volatile, a perceived arbitrage opportunity might simply be random noise, and in a few months, the arbitrage inequality will be altogether reversed. If you are taking a long-term arbitrage position, make sure that the interest rates you are investing into are stable.

It is true that interest rates in the United States have been falling considerably as a result of reckless rate-cutting by the U. S. Federal Reserve - a trend that has not occurred in India and in many other countries. Markets do not adjust to such changes instantaneously, and there may be a time window in which arbitrage is possible. But remember, no arbitrage exists when the market has already recognized a change and anticipated it or reacted to it. To find out whether you can borrow dollars, convert them to rupees, and invest them profitably in India, you will need to know about the transaction costs of doing so, the taxes India's government levels on interest rates, and the historical volatility of interest rates in India. Also, remember that you will be investing your money in some particular financial institution within India. Find an honest, reliable Indian bank with a history of paying out the promised returns. Ask your friends and relatives for any information that might help you with this search. Above all, be skeptical of supposed arbitrage claims made on the major media networks. Once the media catches on to a profit opportunity, chances are that the time window for taking advantage of it has already passed. Think for yourself and find out as much as you can that might decrease your risks. That is the surest way to benefit from interest rate arbitrage.

Gennady Stolyarov II (G. Stolyarov II) is an actuary, science-fiction novelist, independent philosophical essayist, poet, amateur mathematician, composer, and Editor-in-Chief of The Rational Argumentator, a magazine championing the principles of reason, rights, and progress.

In December 2013, Mr. Stolyarov published Death is Wrong, an ambitious children’s book on life extension illustrated by his wife Wendy. Death is Wrong can be found on Amazon in paperback and Kindle formats.

Mr. Stolyarov has contributed articles to the Institute for Ethics and Emerging Technologies (IEET), The Wave Chronicle, Le Quebecois Libre, Brighter Brains Institute, Immortal Life, Enter Stage RightRebirth of Reason, The Liberal Institute, and the Ludwig von Mises Institute.

In an effort to assist the spread of rational ideas, Mr. Stolyarov published his articles on Associated Content (subsequently the Yahoo! Contributor Network and Yahoo! Voices) from 2007 until Yahoo! closed this venue in 2014. Mr. Stolyarov held the highest Clout Level (10) possible on the Yahoo! Contributor Network and was one of its Page View Millionaires, with over 3,175,000 views. Mr. Stolyarov’s selected writings from that era have been preserved on this page.

Mr. Stolyarov holds the professional insurance designations of Associate of the Society of Actuaries (ASA), Associate of the Casualty Actuarial Society (ACAS), Member of the American Academy of Actuaries (MAAA), Chartered Property Casualty Underwriter (CPCU), Associate in Reinsurance (ARe), Associate in Regulation and Compliance (ARC), Associate in Personal Insurance (API), Associate in Insurance Services (AIS), Accredited Insurance Examiner (AIE), and Associate in Insurance Accounting and Finance (AIAF).

Mr. Stolyarov has written a science fiction novel, Eden against the Colossus, a philosophical treatise, A Rational Cosmology,  a play, Implied Consent, and a free self-help treatise, The Best Self-Help is Free. You can watch his YouTube Videos.Mr. Stolyarov can be contacted at gennadystolyarovii@gmail.com.

This TRA feature has been edited in accordance with TRA’s Statement of Policy.

Learn about Mr. Stolyarov's novel, Eden against the Colossus, here.

Read Mr. Stolyarov's new comprehensive treatise, A Rational Cosmology, explicating such terms as the universe, matter, space, time, sound, light, life, consciousness, and volition, here.

Read Mr. Stolyarov's new four-act play, Implied Consent, a futuristic intellectual drama on the sanctity of human life, here.