International Arbitrage- Chapter 7
Types of Arbitrage
1. Location: involves spot currency rates- Different
2. Triangular: spot rates, with three currencies
3. Interest- involves spot, forward and interest rates
Example of Location Arbitrage
Location A quotes Location B quotes
What would you do?
Actually, nothing you can do! No arbitrage is possible
Location A quotes Location B quotes
Here, one could buy from “A” at $1.61 and sell to “B” at
$1.62, making $0.01 in the process
Determine the cross rate between Yen, $, and BP, i.e.,
determine the Yen/BP rate, using the Yen/$ and $/BP rate.
These rates are given as follows:
Yen/$ = 120, $/BP = 1.60
To get Yen/BP = (Yen/$)*($/BP)
Or: 120*1.6 = Yen 192/BP
This was we know that the equilibrium cross-rate between
the three currencies are (with the two given above) is 192.
Deviation from this rate would lead to TRIANGULAR
Using the above example, suppose that $/BP is 1.60, the
Yen/$ rate is 120, and the Yen/BP is 180. How can you
take advantage of this situation?
If we adopt the direction that follows $---BP---Yen, then no
matter if we start from $, BP or Yen, we end up short.
If we, on the other hand adopt the direction: $---Yen---BP,
we end up higher.
Clearly, this illustrates, that the mistake is not in the $/BP
or between $/Yen (both are directly quoted). The mistake
is in the Yen/BP quote, which leads to the “triangular”
Interest rate Parity
Chapter 7 Real-Time Web Project
To recognize the relationship between interest rates and the forward (or
futures) discount, use the following 3 websites. First, go to
determine the prevailing interest rate in Brazil. Second, go to
http://www.bloomberg.com and click on Treasuries to determine the
prevailing U.S. interest rate. Third, determine the futures price of the
Brazilian real to the prevailing spot rate (go to http://www.bloomberg.com
and click on Currencies. Take the reciprocal of the Bloomberg exchange rate
so that you can compare it to the futures price quoted in dollars.)
1. What is the difference between the annualized interest rate of Brazil
versus the annual interest rate in the U.S.? Now, go to
http://www.cme.com/trading/dta/del/rth.html to assess futures
contract prices on the Brazilian real (expressed in dollars per real).
2. Does the futures price exhibit a premium or a discount? Compare the
futures premium or discount with the interest differential. According
to interest rate parity, a foreign currency with a high interest rate
should have a discount in its futures price. Does that relationship exist
here? Does this relationship hold here? Use the interest rate parity
formula to determine the magnitude of a forward (or futures) premium
or discount. Does it appear that interest rate parity holds here? If not,
do you think that the discrepancy allows for covered interest arbitrage,
or is it due to transactions costs and data limitations?
What is the lesson?
The ability to “look forward” in the FX markets takes shape
by way of the Monetary markets- Interest rates.
Thus for there to be an equilibrium between the SPOT,
FORWARD and or the FUTURES rate, they have to align
with the interest rate differentials.
That is the Forward discount/premium must be equal to the
interest rate differential.
This relationship is called CIRP
Have $800K to invest. Spot rate = $1.60 and the F = $1.60,
90 day $ rate = 2%, 90 day Pound rate = 4%. Is arbitrage
Step 1: Determine the forward premium/discount
(F – S/S )*(90/360) = 0
Step 2: determine the differential interest rate
Ih – If = 2-4% = -2%
Step 3: compare the two steps. If equal no arbitrage,
Step 4: Determine who can conduct arbitrage?
Home/Foreign? In this case:
In this case, -2% corresponds to the a point on the vertical
Step 5: After making the determination of direction, spot
Step 6: Invest in MM market = ₤5M*1.04 =₤5.20M
Step 7: Reconvert using forward
₤5.20M*1.60 = $832K
Step 8: Determine the borrowed obligation
$800K*1.02 = $816K
Step 9: Determine the profit
$832k - $816k = $16k = 2%
conclusions from CIRP
1. Points off the chart are arbitrage points
2. points to the left of the line are good for foreign
3. points to the right of the line are arbitrage points for
the domestic investors.
4. points off the chart may be within the transaction cost
1) $1M/C$0.80 = C$1.25M
2) Invest: C$1.25M*1.04 = C$1.30M
3) Reconvert: C$1.30M*$0.79 = $1.027M
4) Yield = ($1.027M-$1M)/$1M = 2.7% per 90 days
5) Compare that to 2.5% if invested in U.S. over 90 days
6) Annual arbitrage = 2.7 -2.5 = 0.2%*4 = 0.8%/Yr
1. No; 2. If more competition
P = (1.01/1.014) – 1 = -0.0039448
Actual premium = $1.6435- $1.65/$1.65 = -0.003939