Short- and Long-Run Exchange Rate Risk Exercise

Worksheet (v1.2)

In this exercise you are asked to choose a currency in which it is assumed you have foreign exchange exposure both in trade (short-run) and investment (long-run). In this exercise you are asked to find both spot and forward exchange rates for a chosen currency and also inflation rates associated with that currency. You are encouraged to read through the exercise first before choosing your currency to ensure the requested data is accessible via the links provided.

Short-Run Exchange Rate Risk

Assume you have a trade receivable denominated in a foreign currency of your choice that is payable to you by your customer in 6 months. At the current spot rate the trade receivable is worth the equivalent of US$5,000,000. To find the current spot rate for the chosen currency pair go to http://www.hsbcnet.com/gbm/fxcalc-disp.[1] Enter 5,000,000 in the âConvertâ box, United States dollar in the âFrom:â box, and your chosen currency in the âTo:â box. Click on âGoâ for the spot rate, which will be expressed in European terms, that is, units of foreign currency per one US dollar. Enter the name of the chosen currency, the date the site is accessed, and the spot rate in European terms in the table below.

To find a 180 day forward rate for the currency pair, go to http://www.hsbcnet.com/gbm/fwcalc-disp#. For âAmountâ you can just enter 1 and enter US dollars in the âBuyâ box and the foreign currency in the âSellâ box. For âValue Dateâ enter â6 Monthsâ and click âGoâ for the forward rate. (Clicking on the Inverse box will switch the rate from European to American terms.) Enter the one-year forward rate in the table below. Make sure the forward rate is expressed in the same way as the forward rate, that is, in European terms.

Foreign Currency	Date	Current Spot Rate in European terms: FX per 1 US dollar	Six -Month Forward Rate in European terms: FX per 1 US dollar

Based on the data above, answer the following questions:

At the current spot rate how much in the foreign currency are you owed in 6 months?

Assuming you fully hedge your FX exposure in the forward market, how many US dollars will you receive in 6 months?

Is the foreign currency selling in the forward market at a premium, i.e. it appreciates relative to the spot rate, or a discount, i.e., it depreciates relative to the spot rate? Provide numbers to support your answer.

Long-Run Exchange Rate Risk

Assume you have undertaken a 3-year investment abroad with expected cash flows denominated in your chosen currency. At the current spot rate those cash flows are expected to provide a positive net present value (NPV) in US dollar terms. Based on relative purchasing power parity you are asked to estimate future spot rates over the next three years based on comparative inflation data.[2] With that data complete the table below.

S₀ = Current Spot Rate in European Terms (Foreign currency per US dollar)	E(S_t) = Expected Exchange Rate Spot Rate in t Years in European Terms (Foreign currency per US dollar)	h_US= Annual Inflation Rate in the United States	h_FC = Annual Foreign Country Inflation Rate

Using the data above and textbook equation (18.3) E(S_t) = S₀ â [1 + (h_FC - h_US)]^t and assuming the estimated inflation rate in Year 1 also holds for Years 2 and 3, please respond to the following:

Based on relative purchasing power parity, estimate S_1.

Based on relative purchasing power parity, estimate S_2.

Based on relative purchasing power parity, estimate S_3.

Based on relative purchasing power parity, has the foreign currency appreciated or depreciated against the US dollar? Explain.

Based on relative purchasing power parity, has the NPV of the investment project increased or decreased in US dollar terms? Explain.

[1] Please note currencies are grouped according to their region: Americas (where the United States dollar may be found), Asia-Pacific, Europe, and MENA. Please advise your instructor should this or any other link in the assignment be broken.

[2] Sources of Inflation data include http://stats.oecd.org/ for OECD countries and http://data.worldbank.org/indicator/FP.CPI.TOTL.ZG at the World Bank site. It is viewed important to be consistent in the definition and source of inflation numbers for the US and the other currency that you use for the relative PPP equation. The most basic definitions of inflation are consumer price index (CPI), producer price index (PPI), and GDP deflator. Estimates of the next yearâs inflation are preferred but it is also common to use the past yearâs inflation as the best estimate of next yearâs and subsequent yearsâ inflation. You are encouraged to share any useful websites for this data you find with the class.

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Please read the article and answer these questions. Thanks.

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. Whatâs that about?

Itâs 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 âForget the G7, Watch the C6.â

So now weâre 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 Mehrlingâs 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?

4. Why would a commercial bank borrow foreign currency from its own central bank, rather than using a foreign exchange swap for the purpose?