joel graham joe griner. what are exchange rates? purchasing power parity history – exchange...
TRANSCRIPT
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Exchange Rates and Arbitrage
Joel Graham Joe Griner
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Outline
What are Exchange Rates? Purchasing Power Parity History – Exchange Rate Systems Big Mac Index Cross Rates
Triangular Arbitrage
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What are Exchange Rates?
The amount of currency that can be exchanged for a unit of another currency $1 us = ¥95
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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
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Example - Continued
Is this assumption always true? What could cause prices to be
different? Economic Climate Government Policy Inflation
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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) )
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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
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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
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History of Exchange Rates
The gold standard Bretton Woods Fixed Exchange Rates End of Fixed Exchange Rates
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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.
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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.
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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.
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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.
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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
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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
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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
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Direct Quote
A direct quote is expressed as x amount of home currency units = one foreign currency unit
For example: $0.85 = €1
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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
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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 = $1 European Terms
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Cross Rates
The exchange rate between two countries other than the home country can be inferred from their exchange rates with the home currency
Rates calculated in this way are referred to as theoretical cross rates
c$ / $ x € / c$ = € / $
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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
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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
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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
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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
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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
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Questions?
Thank you!