Description
This is a PPT explaining Foreign Exchange market Problem Set.
Vishwanath S R
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Interpret dealer quotes Discover and exploit triangular opportunities Calculate outright forward quotes Calculate forward premiums and discounts Design covered interest arbitrage transactions Determine a means of exploiting expected changes in interest rate differences between two countries in the foreign exchange markets
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Whether a quote is direct or indirect depends on one’s perspective From a dollar perspective, the British pound and the SDR are direct quotes because they expressed in terms of USD per unit of currency French Franc, DM and Yen are indirect quotes because they are in units of foreign currency per USD If the perspectives were reversed direct would become indirect and vice-versa
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To resolve this perspective problem, convention holds that all quotes except for sterling, SDRs, ECU and certain Commonwealth country currencies be made using European terms i.e. number of units of currency per dollar That is, dollar becomes the traded commodity The exceptions are quoted in American terms i.e. dollars per unit of currency
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DM is quoted in European terms; a spot sale of DM 1m for dollar would yield DM 1m/2.0320= 492,126 Note that the quote used is the dealer’s asking price since the seller of deutsche marks is effectively buying USD
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Triangular arbitrage opportunities can be spotted by comparing theoretical cross exchange rates (i.e. those that should prevail given spot rates against USD) to actual rates. Theoretical rates can be calculated by taking the ratio of, say, the French Franc bid for dollars to the DM bid and the Ffr ask to DM ask This would yield the FF/DM bid and ask cross exchange rates respectively
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By inverting these quotes and swapping the bid and ask, one obtains the DM/FF cross rates Note that since the market will always require a positive spread between bid and ask it is helpful first to compute cross rates by using that currency with the widest percentage spread in the numerator of the cross rate ratio and the currency with the smallest % spread in the denominator (e.g. FF/DM) If the ratio is inverted remember to switch the bid and ask rates to preserve the spread
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The cross exchange rates for DM, FF, and yen are in TN-1 By comparing this to Ex 2 one can observe that the quoted FF/Yen cross rate, 4.3365/84, is substantially out of line with the theoretical rate Specifically, the Yen is too expensive in terms of FF or alternatively the franc is cheap in terms of Yen This situation can be arbitraged away in a number of ways, but any approach must eventually involve selling Yen for Francs
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A dollar oriented arbitrageur could: 1) use dollars to buy Yen at 154.2 2) convert Yen to Francs at a cross rate of 23.06 and 3) convert the Francs back to USD at a spot rate of 6.6625. The profit per dollar would be $0.00366. A $5m transaction would net $18,299
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The SDR is quoted in American terms, i.e. dollars per SDR Therefore the formula for calculating % change in the dollar value of the SDR is: S(t+1)/S(t) * 100=% change Given the present SDR bid of 1.2141, the new SDR bid can be calculated as: [S(t+1) – 1.2141/1.2141]* 100 = 15% S(t+1) = 1.2141 * 1.15 = 1.3962
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The second part of the question asks for the SDR/$ offer. This is just the inverse of the $/SDR bid. So, the new offer rate would be 1/1.3962 = 0.7162 This can be shown more formally by using the formula for calculating premiums and discounts appropriate for European quotes (i.e. currency per dollar) Given a current SDR/$ offer of 1/1.2141 = 0.8237 we have:
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[S(t)-S(t+1)]/S(t+1) * 100 = % change 0.8237-S(t+1)/S(t+1) * 100 = 15% S(t+1) = 0.8237/1.15 = 0.7162 The point to note here is that there are two formulas for calculating forward premiums or discounts, or anticipated % changes in currency’s value. American quotes require the first formula; European quotes require the second
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To say that a currency is a “dollar discount” implies that the dollar is depreciating against this currency. This is in contrast to the statement “the currency is at a discount to the dollar”, which implies the opposite Similarly, a currency at a dollar premium implies that the dollar is appreciating against the currency Yen and DM are at dollar discounts (they are appreciating against USD), while the other currencies are at a premium
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The outright quotes for the pound and the FF, along with annualized % forward discounts, are as follows: TN-2 The outright quotes are determined by adding or subtracting the forward points to the spot bid and ask rates according to whether the bid points are less than or greater than forward ask points respectively The annualized % discounts are calculated using the mid point of the bid-ask spread and the appropriate formula as shown above
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To speculate on yen in the spot market, one could borrow yen, convert to USD, and invest the dollars, using the future proceeds of the dollar investment to repay the Yen loan. A million dollar transaction might be structured as follows: 1) Borrow Yen 154,300,000 for 3 months @ 4.8125%/4 = 1.2031% 2) convert the yen to dollars @154.3 receiving $1m
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3) Invest the dollars for 3 months @5.5%/4=1.375% 4) Repay the yen loan in 3 months by converting sufficient dollars at the anticipated new spot rate of 154.2/(1-0.07)=165.81 This would require Yen 154.3m(1.0120)/165.81=941750 5) expected USD profit = $1m (1.01375) – 941750 = $72000
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To speculate against the yen in the forward market, one should sell yen forward and hope to cover it in the spot market at a lower price than the forward sale price The yen can be sold forward three months at 154.3-0.27 = 154.03 Thus, a million dollar position would entail selling 154.03m forward 3 months. Assuming a 7% depreciation against the dollar, one could expect to purchase yen spot in 3 months at 165.81.
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The expected profit would be: [154.03m/154.03] - [154.03m/165.81] = $71045 The profits are virtually identical. The actual choice depends on ability to borrow in yen, to secure a forward contract in the amount and for the duration desired, and to close positions quickly.
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The treasurer can hedge the anticipated Sterling receipt using either a money market hedge or a forward hedge The latter can be implemented by selling 2m pounds forward at 1.4835 = (1.4890-0.0055) The nominal cost of the hedge expressed as an annualized % would be: [(1.4835-1.4890)] *12 * 100 = 4.4325% The dollar cost would be [(1.4835-1.4890)] * 2m pounds = $11,000
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The money market hedge would be implemented by borrowing sterling at 10.1875%, converting spot to dollars at 1.4890 and investing the dollars at 5.6875% The amount of sterling to be borrowed would be such that £2m would completely cover principal plus interest to be paid in 30 days. This is calculated as: 2m/(1+0.101875/12) The amount of sterling to be borrowed would be such that 2m (1+ 0.101875/12) = £ 1,983,164
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The nominal cost of the hedge is the spread between the borrowing and lending rates or (5.6875-10.1875)=(4.5%) The dollar cost is reflected in the dollars obtained in thirty days from the deposit relative to the amount that could be had if the entire £2m were converted today. That is, £1983164 * 1.4890 * (1+ 0.56875/12) - £2m * 1.4890 = $(11073)
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The cost of the two hedges are virtually identical because the forward discount on the pound is nearly equal to the interest rate difference Note that neither hedge eliminates currency losses; they just lock in a known loss
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Using mid-points of the bid ask spread the 1 year forward discount on the French Franc is (6.6600-6.78725)/ 6.78725 = (1.87)% The Eurodeposit spread (using mid points) (5.6875-7.3125) = (1.625)% The difference between the forward discount and the interest rate spread appears large enough to offer an arbitrage opportunity A FF10m arbitrage can be executed as follows:
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1) Borrow FF10m for one year @7.3750% 2) Sell FF10m spot @ 6.6625; receive 1,500,938 3) invest the dollars @ 5.625 for one year 4) Buy FF 10,737,500 forward one year @ 6.7769 to repay the FF loan with interest when it matures
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Profit = dollar received from investing in Eurodeposit – dollar needed to deliver against the forward purchase of francs $1500938 * 1.05625 – FF 10,737,500 /6.7769 = 939.26
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If the pound’s spot rate and the 6 month Eurodollar deposit rate remain unchanged in half a year, but the 6 month Euro sterling rate changes, the new 6 month forward rate on sterling required to eliminate covered interest arbitrage opportunities can be calculated by solving the following equations: Bid: F= 1.4890 * [(1+0.055/2)/(1+0.100625/2)]= 1.4567
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Ask: F = 1.4900 * [(1+0.05625/2)/(1+0.10/2)]= 1.4590 To calculate forward bid we multiply the spot bid times the ratio of dollar LIBID to Sterling LIBOR To calculate forward ask we multiply the spot ask times the ratio of dollar LIBOR to Sterling LIBID This reflects the fact that arbitraging using the spot bid rate requires one to borrow sterling and invest in dollars The opposite is true on the ask side
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Given the speculator’s expectations sterling looks cheap both 6 months and 12 months forward. Buy that forward contract that appears the cheapest and sell the other In this example, the six month contract is comparatively cheapest: it would be covered spot 6 months later at an expected gain of 1.48901.4611 = 0.0279, whereas the 12 month contract would have to be covered 6 months later at the new 6 month forward rate of 1.4567, generating an expected gain of 1.4567-1.4377 = $0.019
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The speculator’s transactions would be as follows: Buy pounds 6 months forward @ 1.4611 and sell pounds 12 months forward @ 1.4330 6 months later sell pound spot @ 1.4890 and buy pounds 6 months forward to cover the outstanding 12 month contract @ 1.4590 Gain on the 6 month contract = 0.0279; loss on 12 month contract = -0.0260; on £5m this translates into £9500
doc_208824952.pptx
This is a PPT explaining Foreign Exchange market Problem Set.
Vishwanath S R
? ? ? ? ?
?
Interpret dealer quotes Discover and exploit triangular opportunities Calculate outright forward quotes Calculate forward premiums and discounts Design covered interest arbitrage transactions Determine a means of exploiting expected changes in interest rate differences between two countries in the foreign exchange markets
? ?
?
?
Whether a quote is direct or indirect depends on one’s perspective From a dollar perspective, the British pound and the SDR are direct quotes because they expressed in terms of USD per unit of currency French Franc, DM and Yen are indirect quotes because they are in units of foreign currency per USD If the perspectives were reversed direct would become indirect and vice-versa
?
?
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To resolve this perspective problem, convention holds that all quotes except for sterling, SDRs, ECU and certain Commonwealth country currencies be made using European terms i.e. number of units of currency per dollar That is, dollar becomes the traded commodity The exceptions are quoted in American terms i.e. dollars per unit of currency
?
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DM is quoted in European terms; a spot sale of DM 1m for dollar would yield DM 1m/2.0320= 492,126 Note that the quote used is the dealer’s asking price since the seller of deutsche marks is effectively buying USD
?
?
?
Triangular arbitrage opportunities can be spotted by comparing theoretical cross exchange rates (i.e. those that should prevail given spot rates against USD) to actual rates. Theoretical rates can be calculated by taking the ratio of, say, the French Franc bid for dollars to the DM bid and the Ffr ask to DM ask This would yield the FF/DM bid and ask cross exchange rates respectively
?
?
?
By inverting these quotes and swapping the bid and ask, one obtains the DM/FF cross rates Note that since the market will always require a positive spread between bid and ask it is helpful first to compute cross rates by using that currency with the widest percentage spread in the numerator of the cross rate ratio and the currency with the smallest % spread in the denominator (e.g. FF/DM) If the ratio is inverted remember to switch the bid and ask rates to preserve the spread
?
?
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The cross exchange rates for DM, FF, and yen are in TN-1 By comparing this to Ex 2 one can observe that the quoted FF/Yen cross rate, 4.3365/84, is substantially out of line with the theoretical rate Specifically, the Yen is too expensive in terms of FF or alternatively the franc is cheap in terms of Yen This situation can be arbitraged away in a number of ways, but any approach must eventually involve selling Yen for Francs
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A dollar oriented arbitrageur could: 1) use dollars to buy Yen at 154.2 2) convert Yen to Francs at a cross rate of 23.06 and 3) convert the Francs back to USD at a spot rate of 6.6625. The profit per dollar would be $0.00366. A $5m transaction would net $18,299
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The SDR is quoted in American terms, i.e. dollars per SDR Therefore the formula for calculating % change in the dollar value of the SDR is: S(t+1)/S(t) * 100=% change Given the present SDR bid of 1.2141, the new SDR bid can be calculated as: [S(t+1) – 1.2141/1.2141]* 100 = 15% S(t+1) = 1.2141 * 1.15 = 1.3962
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The second part of the question asks for the SDR/$ offer. This is just the inverse of the $/SDR bid. So, the new offer rate would be 1/1.3962 = 0.7162 This can be shown more formally by using the formula for calculating premiums and discounts appropriate for European quotes (i.e. currency per dollar) Given a current SDR/$ offer of 1/1.2141 = 0.8237 we have:
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[S(t)-S(t+1)]/S(t+1) * 100 = % change 0.8237-S(t+1)/S(t+1) * 100 = 15% S(t+1) = 0.8237/1.15 = 0.7162 The point to note here is that there are two formulas for calculating forward premiums or discounts, or anticipated % changes in currency’s value. American quotes require the first formula; European quotes require the second
?
?
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To say that a currency is a “dollar discount” implies that the dollar is depreciating against this currency. This is in contrast to the statement “the currency is at a discount to the dollar”, which implies the opposite Similarly, a currency at a dollar premium implies that the dollar is appreciating against the currency Yen and DM are at dollar discounts (they are appreciating against USD), while the other currencies are at a premium
?
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The outright quotes for the pound and the FF, along with annualized % forward discounts, are as follows: TN-2 The outright quotes are determined by adding or subtracting the forward points to the spot bid and ask rates according to whether the bid points are less than or greater than forward ask points respectively The annualized % discounts are calculated using the mid point of the bid-ask spread and the appropriate formula as shown above
?
?
?
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To speculate on yen in the spot market, one could borrow yen, convert to USD, and invest the dollars, using the future proceeds of the dollar investment to repay the Yen loan. A million dollar transaction might be structured as follows: 1) Borrow Yen 154,300,000 for 3 months @ 4.8125%/4 = 1.2031% 2) convert the yen to dollars @154.3 receiving $1m
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3) Invest the dollars for 3 months @5.5%/4=1.375% 4) Repay the yen loan in 3 months by converting sufficient dollars at the anticipated new spot rate of 154.2/(1-0.07)=165.81 This would require Yen 154.3m(1.0120)/165.81=941750 5) expected USD profit = $1m (1.01375) – 941750 = $72000
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To speculate against the yen in the forward market, one should sell yen forward and hope to cover it in the spot market at a lower price than the forward sale price The yen can be sold forward three months at 154.3-0.27 = 154.03 Thus, a million dollar position would entail selling 154.03m forward 3 months. Assuming a 7% depreciation against the dollar, one could expect to purchase yen spot in 3 months at 165.81.
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The expected profit would be: [154.03m/154.03] - [154.03m/165.81] = $71045 The profits are virtually identical. The actual choice depends on ability to borrow in yen, to secure a forward contract in the amount and for the duration desired, and to close positions quickly.
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?
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The treasurer can hedge the anticipated Sterling receipt using either a money market hedge or a forward hedge The latter can be implemented by selling 2m pounds forward at 1.4835 = (1.4890-0.0055) The nominal cost of the hedge expressed as an annualized % would be: [(1.4835-1.4890)] *12 * 100 = 4.4325% The dollar cost would be [(1.4835-1.4890)] * 2m pounds = $11,000
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The money market hedge would be implemented by borrowing sterling at 10.1875%, converting spot to dollars at 1.4890 and investing the dollars at 5.6875% The amount of sterling to be borrowed would be such that £2m would completely cover principal plus interest to be paid in 30 days. This is calculated as: 2m/(1+0.101875/12) The amount of sterling to be borrowed would be such that 2m (1+ 0.101875/12) = £ 1,983,164
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The nominal cost of the hedge is the spread between the borrowing and lending rates or (5.6875-10.1875)=(4.5%) The dollar cost is reflected in the dollars obtained in thirty days from the deposit relative to the amount that could be had if the entire £2m were converted today. That is, £1983164 * 1.4890 * (1+ 0.56875/12) - £2m * 1.4890 = $(11073)
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The cost of the two hedges are virtually identical because the forward discount on the pound is nearly equal to the interest rate difference Note that neither hedge eliminates currency losses; they just lock in a known loss
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Using mid-points of the bid ask spread the 1 year forward discount on the French Franc is (6.6600-6.78725)/ 6.78725 = (1.87)% The Eurodeposit spread (using mid points) (5.6875-7.3125) = (1.625)% The difference between the forward discount and the interest rate spread appears large enough to offer an arbitrage opportunity A FF10m arbitrage can be executed as follows:
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1) Borrow FF10m for one year @7.3750% 2) Sell FF10m spot @ 6.6625; receive 1,500,938 3) invest the dollars @ 5.625 for one year 4) Buy FF 10,737,500 forward one year @ 6.7769 to repay the FF loan with interest when it matures
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Profit = dollar received from investing in Eurodeposit – dollar needed to deliver against the forward purchase of francs $1500938 * 1.05625 – FF 10,737,500 /6.7769 = 939.26
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If the pound’s spot rate and the 6 month Eurodollar deposit rate remain unchanged in half a year, but the 6 month Euro sterling rate changes, the new 6 month forward rate on sterling required to eliminate covered interest arbitrage opportunities can be calculated by solving the following equations: Bid: F= 1.4890 * [(1+0.055/2)/(1+0.100625/2)]= 1.4567
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Ask: F = 1.4900 * [(1+0.05625/2)/(1+0.10/2)]= 1.4590 To calculate forward bid we multiply the spot bid times the ratio of dollar LIBID to Sterling LIBOR To calculate forward ask we multiply the spot ask times the ratio of dollar LIBOR to Sterling LIBID This reflects the fact that arbitraging using the spot bid rate requires one to borrow sterling and invest in dollars The opposite is true on the ask side
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Given the speculator’s expectations sterling looks cheap both 6 months and 12 months forward. Buy that forward contract that appears the cheapest and sell the other In this example, the six month contract is comparatively cheapest: it would be covered spot 6 months later at an expected gain of 1.48901.4611 = 0.0279, whereas the 12 month contract would have to be covered 6 months later at the new 6 month forward rate of 1.4567, generating an expected gain of 1.4567-1.4377 = $0.019
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The speculator’s transactions would be as follows: Buy pounds 6 months forward @ 1.4611 and sell pounds 12 months forward @ 1.4330 6 months later sell pound spot @ 1.4890 and buy pounds 6 months forward to cover the outstanding 12 month contract @ 1.4590 Gain on the 6 month contract = 0.0279; loss on 12 month contract = -0.0260; on £5m this translates into £9500
doc_208824952.pptx