Currency Futures and Swaps

International ‐ 04 Outline

1. The Market for Futures 2. Markets for Currency Swaps is not Perfect

There are two key imperfections in forward contracts:

1. Default risk:

a. the customer fails to deliver ‐ the bank withholds the

payment , b. the customer fails to buy ‐ the bank sells at spot ⟹ in both cases the net opportunity loss is , Ways of reducing default risk: • the right to offset –bank withdraws at the client’s default without breaching contract • credit lines (when dealing with banks) & credit agreements • restricted applications & shorter lives w/ to rollover Forward Contract is not Perfect

• in the form of interest‐baring deposit or of securities – form of collateral • the initial margin is posted ⟶ if market value of forward contract < 0 bank ask for additional margin ⟶ if customer fails to provide it, the bank seizes the margin and closes out • periodic reconstructing ‐ market value is computed every day – the party w/ negative value buys back the contract and new contract is signed ‐ if the loser fails to settle the value, the bank seizes the initial margin and closes out the contract

2. Illiquidity ‐ the lack of the secondary market prevents to easily sell forward contracts before maturity Futures contracts: alternative to forward contracts • Futures are forward transactions with standard contract sizes and maturity dates • Futures are standardized and are usually traded on an exchange created for this purpose (Chicago Mercantile/International Money Market is the largest one) • The average contract length is roughly 3 months. Futures contracts: , sizes

• USD/GBP – 65,500 GBP at IMM • USD/EUR – 125,000 EUR at IMM • EUR/USD – 50,000 USD at Stockholm, EUREX • USD/CHF – 125,000 CHF at IMM • USD/AUD, USD/NZD – 100,000 AUD‐NZD at IMM‐NZFE • USD/JPY – 12,500,000 JPY at IMM • USD/CAD – 100,000 at IMM Features of Future Contract A contract's characteristics: • the initial value is zero • it stipulates delivery of a known number of FC units on a known future date T

• the HC payment for the FC is known amount , & paid later

Definition: buying a contract (purchase transaction) customer will get FC and pay it with HC Terminology: going long in FC / going long forex Features of Future Contract

1. Marking to market: measuring and recording a fair market value of asset (whose value changes over time)

• we have daily cash flows , , with final payment , = ST

• if , , < 0 buyer pays the seller

• if , , > 0 seller pays the buyer • the payments are done through a clearing house • futures are similar to periodic reconstructing as in case of forward contract • but in forward contract changes are discounted, in futures not • in case of default, the loss is a one‐day marked‐to‐market outflow: all previous losses have already been settled Features of Future Contract Example: Implication of marking to the market

At investor A buys EUR 1m at , = USD/EUR 0.960

At , = USD/EUR 0.890

At , = USD/EUR 0.889 and the investor A defaults Futures at investor A pays 1m (0.960 0.890) = USD 70000 as amarked‐to‐market cash flow.

Because of default at , A does not pay 1m (0.890 0.889) = USD 1000 Forward the loss for the seller is

1m ( ) = 1m (0.960 0.889) = USD 71000 Features of Future Contract 2. Margin requirements • a buyer and seller should put up initial security that almost for sure covers a one‐day loss • initial margin • maintenance margin ‐ the minimal level of the margin; if reached margin call ‐ request to " the margin • failure to make a margin payment your position is liquidated • if you bought, the contract will be sold • if you were , the contract will be bought • the loss or gain is subtracted from your margin Margin requirements also decrease the loss in case of default Features of Future Contract 3. Organized markets • forward contracts initiated over‐the‐counter and held until maturity • futures are traded on organized exchanges w/ specific terms of contracts, w/ an active secondary market 4. Standardized contracts • a future is standardized in size and date • a forward contract is unique in size and expiry date Features of Future Contract 5. Clearing corporation • futures are not initiated between agents A and B, • but either party has a contract w/ a futures clearing corporation or clearing house • sale from A to B: A sells to clearing house clearing house sells to B • while in forward contracts , A sell to B directly Hedging with Future Contract Problems: • contract size is fixed it is unlikely to match the position to be hedged • the expiration dates of futures rarely match those of currency inflows/outflows which should be hedged • the choice of underlying assets in futures is limited – the currency one wished to may not have a future contract the need for imperfect hedge: • cross‐hedge ‐ the currencies do not match • delta‐hedge ‐ the maturities do not match • cross‐and‐delta hedge ‐ currencies and maturities mismatch Generic Problem for Hedging w/ Futures We want to minimize the variance of the hedged cash flow 1. There is 1 unit of FC e ("exposure") to be received at time and will be converted into HC w/ spot rate . 2. The is available for a "related" currency h ("hedge") w/ expiration at 3. The size of the futures contract is 1 unit of FC h Generic Problem for Hedging w/ Futures 4. Contracts are infinitely divisible ‐ the fixed‐contract‐ size problem is ignored So, we want to minimize the variance of

, , Where –the number of contract sold, – change in the prices btw t & , , Generic Problem for Hedging w/ Futures So

slope coefficient from ,

, , , Where , Perfect Match There is a perfect match if

• future contract expires at (that is, = ) • e = h • : on the last day of trading , the future price equal the spot rate 1 ‐ sell forward one for one Currency‐Mismatch Hedge or Cross‐Hedge

• Future contract expires at (that is, = ) • e h • : on the last day of trading the future , price equal the spot rate

In reality to run ∆ ´∆ ´, where ∆ denotes change of variable over time Currency‐Mismatch Hedge or Cross‐Hedge

Since distribution of ∆S is still not constant, you might run the regressions with percentages " ", where ∆/ and use (by definition and ∆ ) ∆ / and is the cross rate • You assume that not but is constant / • Practitioners often guess 1 ⟹ • This rule is biased, but has zero sampling error Delta‐Hedge

• Future contract does not expire at (that is, ) • e = h Since futures and forwards are almost indistinguishable

1 , 1 , ⟹ , , 1, 1, !!! ‐ interest rates are not know ahead of time now Delta‐Hedge

The rule of thumb that there is no uncertainty abut interest rates and you assume some level of ratio 1 / 1

⟹ , ⟹ a is like the forward‐looking regression coefficient of on The rule of thumb ‐ set the hedge ratio = the forecast ratio 1 / 1 • you can use the current n days rates or • forecast implicit on forward interest rates Cross‐and‐Delta Hedge

The rule of thumb / • set the hedge ratio = x / • hedge ratio equals the current cross rate times the forecast ratio Adjusting for the Size of the Spot Exposure and the Future Contract

So far we assume • exposure was 1 unit of currency j • the size of futures contract is 1 unit of FC i

• if the exposure is a larger number, , the number of contracts one needs to sell obviously goes up proportionaly

• if the size of the futures contract is rather than unity, the number of futures contracts goes down

⟹ the number of contracts to be sold in order to hedge units

of currency j using a futures with size units of currency iis given by Pros and Cons of Futures Contracts Relative to Forwards

Pros: • because of institutional arrangement in futures markets, the default risk is low even relatively small players can trade in the future markets • because of standardizations futures markets have low transaction costs small contracts can be arranged • because of the liquidity of the secondary market, futures positions can be closed out earlier Pros and Cons of Futures Contracts Relative to Forwards

Cons: • because of standardization the hedge is almost sure imperfect: cheap future imperfect hedge vs expensive hedge in the • future contracts exist only for a few high‐turnover exchange rates for most exchange rates the hedger has to choose btw forward contracts or money‐market hedges, or across‐hedge in the futures markets, which is less effective Fixed‐for‐Fixed Currency Swaps

A fixed‐for‐fixed currency is a transaction where two parties • two parties at the time of contract initiation, exchange the to principals • these two principals are denominated in different currencies, but have roughly the same market value • two parties return the principals when the contracts expires • in addition, they periodically pay a normal interest to each other on the amount borrowed • swap interest rate ‐ yield at par for near‐riskless bonds with the same maturities as the swap Why Are Swap Rates almost Riskless? • The risks in case of default are limited by the right‐to‐ offset clause • if one counterparty defaults the right‐to‐offset provides the other party the right not to full its obligation under the contract • The probability of default is low because the customers are screened Why Are Swap Rates almost Riskless? • Many swaps have a credit trigger clause • if the customer's credit trigger clause is downgraded the financial institution can terminate the swap & settle for the swap's market value at that moment • The uncertainty about bank's inflow is the same as uncertainty about the bank's outflows the risks virtually cancel out each other Swap Costs • The swapping bank charges a small annual commission for each payment to be made • The bank's commission can be also up‐front commission • if commission fee per payment is X, then up front commission will be calculated as X a(r ,n), where a(r ,n) the present value of a n‐year unit annuity discounted at a rate r Swap Costs • Sometimes bank's fee is build into the interest rates, which would increase or decrease the quoted rates by a few basis points • if a swap dealer quotes USD 3.15‐3.19% & EUR 3.88‐3.92% and in under your contract you "borrow„ EUR & "lend" USD you pay 3.95% on the EUR and receive 3.13% on the USD Note(!!!): do not confuse price and commission • you pay commission regardless whether you go long or short • you pay the price if you buy & get the price if you sell Example of Fixed‐for‐Fixed

The Japanese company wants to borrow (bullet) cheaply in HC and then swap the loan into USD • bullet loan ‐ a loan that requires a balloon payment at the end of the term Steps: • borrow JPY 1000m from the house bank at 1% (the actual loan rate) • " relend" these JPY 1000m to the swap dealer, at 0.6% (the JPY swap rate) • ... who in return " lends"USD 10m to the rm at 3% (the USD swap rate) Example of Fixed‐for‐Fixed Currency Swap

The cash flows from swapping (<●> means outflow) Swap Loan JPY 1000 JPY 1000 lent USD 10m Combined borrowed at 1% At 0.6% Borrowed at 3% Principal at tJPY 1000m USD 10m USD 10m JPY 6m Interest (p.a.) Principal at T JPY 1000m From the last column, we can see that the ultimately: • the company borrows USD 10m • annual interest payments consist of • the USD risk‐free rate (3%) • the risk spread on JPY loan from the house bank: 1%‐0.6%=0.4% Valuing an Outstanding Fixed‐for‐Fixed Currency Swap

The swap is like a portfolio consisting of • a loan • an investment in long‐term deposit we can value a swap as the difference btw the market value of the loan and the market value of the investment Valuing an Outstanding Fixed‐for‐Fixed Currency Swap

Example: Two years ago, a bank swapped a company loan (asset) of USD 100m for GBP for seven years. The swap rates are 4% on the USD leg and 5% on the GBP leg. The spot rate was USD/GBP 2. Now the five‐year USD swap rate is 2.5%, the five‐year GBP swap rate is 4%, and the spot rate is USD/GBP 1.7. Valuing an Outstanding Fixed‐for‐Fixed Currency Swap

Solution: The company's USD outflows are valued as 0.04 ∗ 100 100 106, 968, 742.74 1 0.025 1 0.025 The GBP inflows are worth 0.05 ∗ 50 50 52, 225, 911.17 1 0.04 1 0.04 At the current spot rate is USD 88,784,047.98. ⟹ the contract is the net liability w/ value USD 88,784,047.98‐ USD Interest Rate Swaps • There is still an exchange of the service payments on 2distinct loans • 2 loans differ not in the currency but in the method of determining the interest payments • because both loans in the same currency, there is no initial exchange of principals and no final amortization • two loans are notional (fictitious or theoretical) • The only cash flows that are swapped are the interest streams on each of the notional loans Interest Rate Swaps: Coupon Swaps (Fixed‐for‐Floating) For the floating‐rate leg of the swap, the rate is traditionally Libor or similar market rate For the fixed‐rate leg is the same as the N‐year swap rate used in fixed‐for‐fixed currency swaps Example: A company wants to borrow NZD to finance its investment. As NZD interest rates are rather volatile, the company prefers fixed‐ rate loans. But the eurobanks dislike fixed‐rate loans. The company's alternatives are the following: • a ‐NZD xed‐rate bond issue would be possible only at 7%, which represents a hefty 2% spread above the NZD swap rate of 5% • from a London bank, the company can get an NZD floating‐ rate bank loan at Libor + 1% Interest Rate Swaps: Coupon Swaps (Fixed‐for‐Floating) Answer: • the company borrows NZD at the NZD Libor +1 % • swaps this into a fixed‐rate NZD loan at the 5% swap rate Swap Loan NZD 1 NZD 1 lent NZD 1 Combined borrowed at at Libor % borrowed at Libor + 1% 5% Principal at NZD1 NZD1 NZD1 t Interest <5%+1%=6 (p.a.) +1%> %> Principal at NZD1 T Interest Rate Swaps: Valuing Coupon Swaps (Fixed‐for‐Floating)

To value fixed‐rate payment stream • discount the known cash flows using the prevailing swap rate till time to maturity To value floating‐rate part

,

, where FV ‐ face value, ‐ the last reset data, ‐ the next reset date, t ‐ present date ( < t < ) Interest Rate Swaps: Valuing Coupon Swaps (Fixed‐for‐Floating)

Intuition:

• at the initial investment FV will grow to

FV(1 + , ) • but in terms of today money, we have to discount it

using the prevailing interest rate or by 1 + ,

MV of a coupon swap = MV incoming stream MV outgoing stream where MV = market value Other Interest Rate Swaps

Base Swaps • the parties swap two streams of floating‐rate interest payments • each stream is determined by a different base rate • e.g. a Libor‐based revolving loan can be swapped for a US T‐bill‐based revolving loan Cross‐currency (circus) swaps • currency swap + (floating vs fixed rate)