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# Inter-Market Arbitrage

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“Inter-Market Arbitrage”

## 1 Inter-Market Arbitrage

The question posed is to examine whether a trader with \$1 million can profit from inter-market arbitrage. The following facts are available: – New York Citibank: \$ 1.2223/ London Barclays Bank:\$ 1.8457/A£ Frankfurt Deutsche Bank: 1.5100/A£ To resolve the question, the commencement of the process is to begin with calculating the a cross rate, which is arrived at by calculating the ratio of the exchange rate of currency A to the dollar divided by the exchange rate B to the dollar (Copeland 2002, p.7). Using the above information between Citibank and Barclays, we need to calculate the dollar cross rate. Step 1. Citibank\$1.2223 / =0.6622 Barclays\$1.8457 / A£ Step 2 Take \$1 million to Deutsche and exchange for A£’s: – \$1,000,000=A£662,252 1.5100/ A£ Step 3 Exchange A£’s for Dollars at Barclays Bank: – A£662,250 x 1.8457 =\$1,222,318

The Trader’s profit therefore is \$222,318 The concept of triangular arbitrage is based the ability to be able to capitalise on a discrepancy that exists on the international financial markets between three cross exchange rate (Moosa 2003). The opportunity exists where these rates are different to those one would achieve when calculations are based on spot rates. The art is to use three banks in different locations with differing exchange rates, as in the above case \$ to  and A£ to \$. By selling the dollar to the expensive  and converting to the A£ where it is cheap, a profit is derived from the transaction. The main attraction of triangular arbitrage is that it allows investors to seek out the most advantageous of the world’s financial markets to achieve a profitable return on their investments even when achieving this within the domestic market may prove difficult.

## 2 Currency exchange rates

In essence, the exchange rate between the currency of one country and that of another is simply a matter of price (Copeland 2003, p.3). For example, if one has A£100 and want to buy products at A£50, two units can be brought for this investment. If the product price falls to A£25 per unit, four can be purchased, therefore meaning that the exchange rate of the unit has depreciated, or the investment value has appreciated. The same scenario is true for currency. For example, if the value of the Japanese Yen against the dollar, there is a appreciation of the Yen and a resultant depreciation of the Dollar. For example, if the Yen exchange rate against the dollar rises from \$0.0074079 to \$0.00850, there has been an appreciation of the Yen and depreciation of the dollar, which in percentage terms can be defined as follows: – Yen Appreciation = 0.001092 x 100 / 0.007408 represents an appreciation of 14.74237% Dollar depreciation = 0.001092 x 100 /0.00850 represent a depreciation of 12.84824%

## 3 Currency forward rates

 Country Currency symbol US\$ equivalent Currency per US\$ Japan (yen) 1 month forward 3 month forward 6 month forward JPY JPY JPY JPY 0.009189 0.009215 0.009271 0.009360 108.83 108.52 107.86 106.84

The above table provides an example of a forward exchange rate contract at given points in the future (Copeland 2004, p.8). In this case the first line represents today’s exchange price for the currency and the other represent the contact price at which bank offering these rates is prepared to exchange yen for dollars at the defined forward dates. For example, if the contract is for one month, the bank will guarantee to exchange yen for dollars at a rate of 0.009215. The forward contract is used by organisations as a hedge against an adverse future currency movement (Moosa 2003). For example if a supplier agrees a future price based upon today’s exchange rate and by the date of payment that exchange rate has depreciated, there would be a financial loss. Therefore, the future contract, which guarantees a pre-determined future rate, is used to mitigate these potential losses. However, there will be a need for the contract purchaser, in this case the Japanese yen, to ascertain whether they are selling at an annualised premium or discount. The equation for calculating a premium or discount is as follows (Mossa 2003): – Forward rate – spot ratex 12x 100 Spot rateNo. of mths Therefore, based on the above table, the following will be the result.

 1 month 3 months 6 months Forward rate 108.5200 107.8600 106.8400 Minus spot rate 108.8300 108.8300 108.8300 -0.3100 -0.9700 -1.9900 Divided by spot rate -0.0028 -0.0089 -0.0183 Times twelve divided by months -0.0342 -0.0357 -0.0366 Times 100 -3.4182 -3.5652 -3.6571

This suggests that the yen is being sold at a discount

## 4 Rates relationship

There is a distinct relationship between spot rates, forward rates, inflation rates and interest rates, although they each perform a separate task (Copeland 2004).

• Spot rates relate to the price at which a currency or stock can be purchased at a given time in the present, for example today (Moosa 2003).
• Forward rates are those that are anticipated and are expectations based upon the current spot rate. It is the rate at which the parties will agree to exchange different currencies at a set future date, which is usually 30, 60, 90 or 180 days.

The formula for calculating the theoretical future forward rate uses the interest rates of the two currencies as a guide. An example of this calculation is as follows: – Spot rate = 1.94UK\$/Us\$ UK Libor= 4.5%90 day US Libor= 3.75%90 day (Note – libor is the interest rate at which banks lend to each other (Moosa 2003)). The calculation for the 90 forward rate would be: – 1.94 x(1+((90/365)*.045))= 1.9433 (1+((90/360)*.0375)) This formula shows the link and relationship that exists between interest, spot and interest rates.

• Inflation rates

Inflation rates reflect the average percentage increase in the price of goods and services (Cuthbertson Nitzsche 2001). It is usually linked to a nation’s retail price index. It is primarily based upon the level of supply and demand that this is in the economy. If demand increases so do prices, thereby leading to an inflationary episode. There is a direct link between inflation rates and interest rates. Governments tend to use interest rates to control inflation, for example raising interest rates to reduce demand and therefore the inflation rate.

• Interest rates

Interest rates are essentially related to the cost of borrowing. In effect they are a charge that is levied by the lender to compensate them a) for the risk they are taking with their capital and b) for the loss of capital growth or income they could have received from that money if invested elsewhere (Elton and Gruber 2002). The other relationship between interest rates and inflation is used when assessing the real rate of interest. This method takes into account the depreciation of the value of money. For example, in the value of the A£ had decreased by 2% in a year the interest rate was 5%, the real rate of interest is 3% (Interest rate 5% – inflation rate 2% = real interest rate 3%) There is a mutual connection between all of these rates. For example, we could extend the equation used within forward rates to take account of all the rates as follows: – Spot rate = 1.94UK\$/Us\$ UK Libor= 4.5%90 dayUK Inflation rate 2% US Libor= 3.75%90 dayUS Inflation rate 1.5% (Note – libor is the interest rate at which banks lend to each other (Moosa 2003)). The calculation for the 90 forward rate using this formula would be: – 1.94 x_(1+((90/365)*(.045-.02))_= 1.941041 (1+((90/360)*(.0375-.015))

## 5 Future exchange rates

The expected future value of currency is not something that can be accurately predicted (Pilbeam 2005). Therefore in order to calculate the future exchange rate value, the financial markets have to base their expectations upon known variables. The following example shows how this is equation is carried out in practice, using the following data: – Swiss Franc-One year interest rate= 4% US dollar-One year interest rate=13% Current exchange rate-SFR 1 = \$0.63 From this, the following equation needs to be resolved: – Forward exchange rate = S(1 + rq)n=0.63(1+.04)=0.57982 (1+rb)n (1+.13) If there was a change in expectations resulting from future US inflation which caused the future spot price to rise to US \$0.70, this would have the following impact upon the above equation: – Forward exchange rate = S(1 + rq)n=0.70(1+.04)=0.6442 (1+rb)n (1+.13) However, it is likely that the US would increase interest rates to address the inflationary pressures. For example, if these were increased to 15%, this would have the following influence upon the previous equation: – Forward exchange rate = S(1 + rq)n=0.70(1+.04)=0.6330 (1+rb)n (1+.15)

## Bibliography

Cuthbertson, Keith and Nitzsche (2001). Investments: Spot and Derivatives Markets. John Wiley & Sons Ltd. Chichester, UK. Eales, B. A. and M. Choudhry (2003), Derivative Instruments: A guide to Theory and Practice, Butterworth Heinemann Finance. Oxford, UK. Elton, Edwin J and Gruber, Martin J (2002). Modern Portfolio and Investment Analysis. 6th Edition. John Wiley & Sons Inc. New York, US. Pilbeam, Keith (2005). Finance and Financial Markets. 2nd Rev. edition. Palgrave Macmillan. London. UK. Copeland, Laurance (2004). Exchange Rates and International Finance. 3rd Edition. Pearson Education, Harlow UK Moosa, Imad A (2003). International Financial Operations: Arbitrage, Hedging, Speculation, Financing and Investment. Palgrave MacMillan, Edinburgh, UK

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