International Arbitrage- Chapter 7 Types of Arbitrage 1. Location: involves spot currency rates- Different locations 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 $1.60-$1.61 $1.61-$1.62 What would you do? Actually, nothing you can do! No arbitrage is possible Location A quotes Location B quotes $1.60-$1.61 $1.62-$1.63 Here, one could buy from “A” at $1.61 and sell to “B” at $1.62, making $0.01 in the process Triangular arbitrage Example: 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 ARBITRAGE. Triangular arbitrage: 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? $ BP Yen 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” arbitrage. 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 http://www.latin-focus.com/latinfocus/countries/brazil/brazil.htm and 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 An example Have $800K to invest. Spot rate = $1.60 and the F = $1.60, 90 day $ rate = 2%, 90 day Pound rate = 4%. Is arbitrage possible? 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, otherwise possible. Step 4: Determine who can conduct arbitrage? Home/Foreign? In this case: Interest rates=ih-if Discount Premium X In this case, -2% corresponds to the a point on the vertical axis. Step 5: After making the determination of direction, spot conversion $1M------= ₤5M 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 investors 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 bounds. Examples No 6. 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 Small business 1. No; 2. If more competition P = (1.01/1.014) – 1 = -0.0039448 Actual premium = $1.6435- $1.65/$1.65 = -0.003939 Close enough!
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