Question

In: Finance

Forward rates in standard swaps are set relative to spot rates to eliminate arbitrage opportunities.

 

Article:

TESTING THE GLOBAL CENTRAL BANK SWAP NETWORK

In the last few weeks, the ECB has been drawing on its liquidity swap line with the Fed, first $308 million for a week, then $658 million for a week, and last week back down to $358 million. What’s that about?

It’s not such a large amount. Bank of Japan borrowed more in the past, $810 million in March and $1528 million in January. But the question then repeats, what was that about?

Both of these drawings are part of the new set of central bank swap lines linking what I call the C6: the Fed, ECB, Bank of Japan, Bank of England, Swiss National Bank, and Bank of Canada. On October 31, 2013these lines were made permanent and unlimited; contract details may be found here. Ever since then I have had a slide in my powerpoints saying “Forget the G7, Watch the C6.”

So now we’re watching. What are we seeing?

Central bank swaps are in some ways quite similar to a standard commercial FX swap, but the differences are important and significant.

A standard swap involves exchange of two currencies today at the spot exchange rate prevailing today, plus a promise to reverse the transaction at maturity using the forward exchange rate prevailing today. Suppose that forward rate is calculated using covered interest parity as

F = S(1+r)/(1+r*)

where r and r* are respectively the dollar and foreign interest rate for a given term T, s is the spot exchange rate and f is the forward exchange rate for date T.

In this case, the exposure of the standard swap contract is identical to a swap of IOUs between the contracting parties at the prevailing interest rates in their respective currencies. One party borrows dollars at rate r and the other party borrows euros at the rate r*.

Central bank swaps are different. First, the forward rate in the contract is usually exactly the same as the current spot exchange rate. This means that central banks are never in the position of realizing profits or losses from the swap (although of course there will be implicit profits and losses), that come from deviation between the agreed forward rate and the spot rate at expiry.

Second, the interest rate on the contract is negotiated rather than calculated from market prices. But, given the choice of forward rate, the analogous commercial contract would call for payment of the interest differential, so anything different from that is significant. Significantly, the documentation of the current C6 swap line leaves open the question of who pays interest to who, and how much.

Usual practice has been for the party who draws on the line to pay interest on the line at some penalty rate. Thus the May 9, 2010 swap agreement between the Fed and ECB called for the ECB to pay the USD Overnight Index Swap Rate plus 100 basis points on its dollar borrowing, and the Fed to pay nothing on its euro borrowing. In effect, the ECB was simply borrowing dollars at the discount window, like any other bank, but with its own monetary liability serving as collateral instead of some financial asset.

This kind of arrangement is still in effect a swap of IOUs but at a price that is away from the market. Central bank swap lines thus in effect operate as a kind of outside spread providing bounds within which normal commercial dealing takes place. So long as prices stay at or near CIP, private agents prefer to do business directly with each other. But when CIP comes under pressure, because of one-sided liquidity flows, the central bank moves from backstop to market-maker and the outside price becomes the market price.

The ECB is borrowing dollars from the Fed and lending them on to banks in Europe who have dollar liquidity needs. Here is the tender documentation. Presumably it is doing this for banks who are unable, for whatever reason, to access dollar funding in the open market, or only at a premium that is higher than the ECB charges.

During the financial crisis, dollar funding needs like this got met by central bank liquidity swaps that rose almost to $600 billion, raising questions in Congress. Now, in normal times, smaller sums are becoming a routine way of handling the normal stresses and strains of world funding flows.

For lack of a world central bank, we have a network of central bank liquidity swaps.

(Council on Foreign Relations has a fun interactive app that shows the rest of the emerging swap network as well.)

Questions:

2. Forward rates in standard swaps are set relative to spot rates to eliminate arbitrage opportunities. Using a numerical example, demonstrate that an arbitrage opportunity would exist if a forward exchange rate quote differed from the formula given in Mehrling’s article.

3. How do swap lines between central banks differ from standard foreign exchange swap contracts? How are forward rates set? How are interest rates determined?

Solutions

Expert Solution

2) Forward rates in standard swaps are set relative to spot rates to eliminate arbitrage opportunities. the calculation of forward rate is by use of formula ; F = S(1+r)/(1+r*) ; to eliminate artbitrage opportunity in such contract.

For numerical example , Spot rate US$/CAD is 1.2500 CAD ,risk-free interest rate is 4% for USD and 3% for CAD. one year forward

for forward rate = 1.2500(1+3%)/(1+4%) =1.2380 CAD.

If actual forward rate would hinger or lower than the above calculated rate , it will create a arbitrage opportunity for investors.

3) The central bank swap line differ from standard normal market foreign exchange swap contract , as

  • the forward rate in the contract is usually exactly the same as the current spot exchange rate. This means that central banks are never in the position of realizing profits or losses from the swap (although of course there will be implicit profits and losses), that come from deviation between the agreed forward rate and the spot rate at expiry.
  • the interest rate on the contract is negotiated rather than calculated from market prices. But, given the choice of forward rate, the analogous commercial contract would call for payment of the interest differential, so anything different from that is significant.

The interest rate in such arrangement is decided by  the party who draws on the line to pay interest on the line at some penalty rate.

The interest is such swap arrangement is based on contrcat arrangement for example  swap agreement between the Fed and ECB called for the ECB to pay the USD Overnight Index Swap Rate plus 100 basis points on its dollar borrowing, and the Fed to pay nothing on its euro borrowing.

The forward rate in the contract is usually exactly the same as the current spot exchange rate. This means that central banks are never in the position of realizing profits or losses from the swap .


Related Solutions

Definitions: Forward ERs, Swaps, Triangle arbitrage, Covered interest arbitrage, Carry trade
Definitions: Forward ERs, Swaps, Triangle arbitrage, Covered interest arbitrage, Carry trade
Explain spot exchanges rate, forward exchanges rates and currency swaps with example? Which strategy is more...
Explain spot exchanges rate, forward exchanges rates and currency swaps with example? Which strategy is more suitable to reduce risk and losses from changes in exchange rates?
2) Forward exchange rates under no-arbitrage a) Find the five-year forward AUD/JPY exchange rate under no-arbitrage...
2) Forward exchange rates under no-arbitrage a) Find the five-year forward AUD/JPY exchange rate under no-arbitrage if the spot exchange rate is 80 yen per Australian dollar, and the five-year risk-free interest rates in Australia and Japan are 4% and 6% per annum, respectively. (1 point) b) Choose a forward exchange rate that is greater than the no-arbitrage exchange rate you found in (a), and describe the arbitrage strategy you would use to exploit this situation. Calculate your profits from...
Covered interest arbitrage and IRP. What is the relationship between forward rates and interest rates? If...
Covered interest arbitrage and IRP. What is the relationship between forward rates and interest rates? If ? = ? and ?௛ ≠ ?௙, is arbitrage possible? a. Assume the following information: You have $1,000 to invest: Current spot rate of Australian dollar = $0.95 180-day forward rate of Australian dollar = $0.94 6-month deposit rate in U.S. = 4% 6-month deposit rate in Australia = 6% If you use covered interest arbitrage for a 180-day investment, what will be the...
Spot and forward exchange rates for the British pound are as follows: Spot exchange rate =...
Spot and forward exchange rates for the British pound are as follows: Spot exchange rate = 1.4500 USD/GBP, 90-day forward exchange rate =1.4416 USD/GBP, 180-day forward exchange rate = 1.4400 USD/GBP. Additionally, a 180-day European call option to buy 1 GBP for USD 1.42 costs 3 cents, and a 90-day European put option to sell 1 GBP for USD 1.49 costs 3 cents. Which of the following is the correct arbitrage strategy? Select one: Buy the 90-day forward contract and...
Why must the relationship between spot rates and forward rates hold? A) Because there is an...
Why must the relationship between spot rates and forward rates hold? A) Because there is an assumption of arbitrage-free valuation in the market. B) Because we need a reliable yield curve to price fixed-income securities C) Because investors require multiple methodologies to invest their savings D) Because the law of one price does not hold in all situations
you have the following assumptions and spot rates - solve for the implied forward rates
you have the following assumptions and spot rates - solve for the implied forward ratest0t1t2t3One-year rate1.330%?????????Two-year rate1.590%??????Three-year rate1.810%Four-year rate2.030%Implied forward 1 year ratet+1f1 X   at time t+1 (in one year)Implied forward 1 year ratet+2f1 xat time t+2 (in two years)Implied forward 2 year ratet+1f2 xat time t+1 (in one year)Implied forward 1 year ratet+3f1 xat time t+3 (in three years)Implied forward 2 year ratet+2f2 xat time t+2 (in two years)
Discuss IRP, the IFE, and international arbitrage opportunities with interest and currency exchange rates.
Discuss IRP, the IFE, and international arbitrage opportunities with interest and currency exchange rates.
Suppose that the spot and the forward exchange rates between the UK pound (£) and the...
Suppose that the spot and the forward exchange rates between the UK pound (£) and the Euro (€) are S0=0.5108 £/€ and Ft=3 months=0.5168 £/€. The time to maturity of the forward contract is 3 months. The annual interest rate of £-denominated Eurocurrency market deposits is 4.08%. The annual interest rate of €-denominated, 3-month Eurocurrency market deposits is 3.15%. a) Examine whether there exists an arbitrage opportunity. b) Devise an arbitrage strategy. Describe the transactions and calculate the arbitrage profits.
Based on the pure expectations theory, if the implied forward rates under the no-arbitrage condition are...
Based on the pure expectations theory, if the implied forward rates under the no-arbitrage condition are lower than spot rates of matching maturities, then the spot rate curve is most likely Group of answer choices flat downward sloping upward-sloping
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT