Exchange Rates and Arbitrage

Joel Graham Joe Griner

Outline

What are Exchange Rates? Purchasing Power Parity History – Exchange Rate Systems Big Mac Index Cross Rates

Triangular Arbitrage

What are Exchange Rates?

The amount of currency that can be exchanged for a unit of another currency $1 us = ¥95

Example – Exchange Rate

Shoe Japan USA¥7,000 S&H $70.00 S&H

Exchange Rate?$1 = ¥100

This establishes the concept of purchasing power parity, a single product should be the same price both countries

Example - Continued

Is this assumption always true? What could cause prices to be

different? Economic Climate Government Policy Inflation

Example – Forward Rates

Shoe Japan USA¥7,000 S&H $70.00 S&H

6% -- Inflation -- 3%

What is the new price?¥7,420 S&H $72.10 S&H

Exchange Rate?$1 = ¥102.91

Forward Rate = Spot Rate x ( (1 + πfc) ÷ (1 + πdc) )

Purchasing Power Parity

Represents the real value of the currency within the country

PPP suggests that two different currencies should adjust so that items cost the same in both countries

PPP - Continued

Such adjustments occur through inflationary forces, causing the price of goods in one country to be higher than in the other

When this occurs, exchange rates must change in order to reflect the change in purchasing power between the two currencies

History of Exchange Rates

The gold standard Bretton Woods Fixed Exchange Rates End of Fixed Exchange Rates

The Gold Standard

For centuries the world’s currency was backed by gold.

In the 1930s, the US dollar was set to a fixed rate of 1 ounce of gold being worth 35 dollars.

The gold standard finally broke down in 1971 do to unstable governmental policies as well as high inflation.

Bretton Woods

Held in Bretton Woods, New Hampshire in July 1944.

The 44 allied nations met to discuss international monetary policies.

Created a pegged exchange rate that made the dollar as the reserve currency.

Fixed Exchange Rate

Countries pegged their currency against the US dollar which made the US dollar the reserve currency.

The US dollar was convertible into gold.

Countries were required to keep their exchange rate within +/- 1% of parity.

End of Fixed Rates

US was spending too much on the Vietnam War and social programs and the dollar was becoming way undervalued.

Too much gold was being exchanged for dollars which decreased the amount of gold in the US

In 1971, Nixon declared that dollars were no longer convertible to gold, which led to the establishment of the floating exchange rate system.

Big Mac Index

Since the purchasing power parity concept can be complex and difficult to measure, The Economist established a way to measure real-world PPP using MacDonald’s Big Mac hamburger

The Big Mac was chosen because of it’s availability in many countries around the world and the ability of franchisees in establishing input prices

BMI - Continued

The Big Mac PPP exchange rate is calculated between two countries by dividing the price of a Big Mac in country A by the price of a Big Mac in country B.

The Big Mac exchange rate is then compared with the actual market exchange rate

If the calculated rate is lower, then the currency is undervalued, if higher, than it is overvalued

BMI – Continued

It is effective in measuring PPP because it is a consistent good, with very few differences across countries

A simple basket of goods can vary greatly by culture, as basic goods defined here in the U.S are significantly different than those in other parts of the world such as in rural India

Big Mac Index: Feb 4th, 2009

Direct Quote

A direct quote is expressed as x amount of home currency units = one foreign currency unit

For example: $0.85 = €1

Indirect Quote

An indirect quote is simply the reciprocal of a direct quote, expressed as x amount of foreign currency units = one home currency unit

For example: ¥120 = $1

Quoting Terms

Quoting in terms of home currency (U.S. Dollars) per unit of foreign currency is called American Terms

Quoting in terms of # of foreign currency units per unit of home currency (U.S. Dollar) is called European Terms

$.20 = ¥1 American Terms

¥5 = $1 European Terms

Cross Rates

The exchange rate between two countries other than the home country can be inferred from their exchange rates with the home currency

Rates calculated in this way are referred to as theoretical cross rates

c$ / $ x € / c$ = € / $

Cross Rates - Example

1.08150 CAD per 1 USDX

0.646138 Euro per 1 CAD=

0.698798 Euro to 1 USD

If 0.698798 ≠ the reported Euro to USD exchange rate, an arbitrage opportunity exists

Triangular Arbitrage

Barring any government restrictions, riskless arbitrage will assure that the exchange rate between two countries will be the same in both countries

In reality, theoretical cross rates computed from exchange quotes, rarely differ from the actual cross rates quoted by dealers

In the event that an imbalance occurs, a riskless arbitrage opportunity arises

Triangular Arbitrage - Workout

$

€c$

Beginning with 20,000 USD

20,000 USD x 1.08150 CAD

21630 CAD

21630 CAD x 0.646138 Euro

13975.96494 Euro

13975.96494 Euro ÷ 0.698798 USD per Euro

20,000 USD

Triangular Arbitrage - Workout

$

€c$

Beginning with 20,000 USD

20,000 USD x 1.08150 CAD

21630 CAD

21630 CAD x 0.646138 Euro

13975.96494 Euro

13975.96494 Euro ÷ 0.690000 USD per Euro

20,225.02165 USD

Risk Free Profit of

$225.022

Triangular Arbitrage

As you can see, even with a difference of .008798 between the theoretical cross rate and the actual exchange rate for euro per dollar, risk free profit can be realized

As large and frequent transactions are carried out to exploit this opportunity, the difference between theoretical rates and reported rates will diminish

Questions?

Thank you!