FORWARD RATE AGREEMENT (FRA)


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1 FORWARD RATE AGREEMENT (FRA) 1. Terminology Hedging with FRAs Determination of Forward Interest Rates (FRA) The Principle of Forward Interest Rates Highest and Lowest FRA Price Limits The FRA Formula Calculating FRA Rates through Fwd/Fwd Rates FINANCE TRAINER International Forward Rage Agreement (FRA) / Page 1 of 18
2 FORWARD RATE AGREEMENT (FRA) The forward, or future rate agreement, is a contract between two parties to fix a future interest rate. This contract defines the interest rate for a future period based on an agreed principal. If on the agreed date (fixing date) the FRA rate differs from the current market rate (reference rate), a settlement payment depending on the difference must be paid by one of the contractors. The principal is not exchanged and there is no obligation by either party to borrow or lend capital. The FRA can be used by market participants who wish to hedge against future interest rate risks by setting the future interest rate today (Hedging). by market participants who want to make profits based on their expectations on the future development of interest rates (Trading). by market participants who try to take advantage of the different prices of FRAs and other financial instruments, e.g. futures, by means of arbitrage. FRAs are overthecounter (OTC) products and are available for a variety of periods: starting from a few days to terms of several years. In practice, however, the FRAmarket for 1year FRAs offers the highest liquidity and is therefore also regarded as a moneymarket instrument. The FRA is not an obligation to borrow or lend any capital in the future. At settlement date, the principal just serves as the basis to calculate the difference between the two interest rates, or rather the settlement payment that results from this difference. FINANCE TRAINER International Forward Rage Agreement (FRA) / Page 2 of 18
3 1. Terminology On 10th January the following FRA is dealt: FRA 6/12 spot Principal: EUR 100 m FRA rate: 4½ % + 6 mo  2 working days + FRA term t0 t1 t2 t3 t4 today value date spot 7/10 1/12 1/10 1/12 fixing date maturity date 7/12 settlement date t0 : trading date t1 : value date spot t2 : fixing date: the difference between contract rate and reference rate is determined 2 working days before settlement date. t3 : settlement date: the settlement payment is exchanged ("amount due") t4 : maturity date (final maturity): defines the end of the FRA period, there are no more payments to be made, but the exact term of the FRA is determined; final maturity settlement date = days of FRA term FRA rate The FRA rate is the interest rate stipulated in the contract, e.g. here 4½%. FRA term The FRA term is the period from settlement date until maturity date. For this period the interest rate has been fixed. E.g. the term of an 3/9 FRA is 6 months. FINANCE TRAINER International Forward Rage Agreement (FRA) / Page 3 of 18
4 Reference rate The reference rate is the rate which the FRA rate is compared to on the fixing date. The basis for the reference rate is agreed upon on the trade date. Usually for the main currencies (e.g. USD, GP, CHF, JPY, AUD, etc.) the LIOR calculated by A (ritish ankers Association) is used. For the EUR it is mostly EURIOR. For currencies where there is no LIOR calculated local fixings are used (e.g. WIOR for PLN, PRIOR for CZK, etc.). It has to be taken into account that all reference rates represent an offer side (LIOR, EURIOR, WIOR, etc.) and are therefore a rate for taking money (as market user), no matter if the FRA was traded in order to hedge a future borrowing or lending. FRA purchase (buy FRA) The buyer of an FRA receives the amount due if on the fixing date the reference rate is higher than the FRA rate. If the reference rate is below the FRA rate the buyer has to pay the amount due. An FRA can be purchased in order to speculate on rising interest rates in the future or as a hedge for a future short position in deposits and thus a protection against rising interest rates. FRA sale (sell FRA) The seller of an FRA receives the amount due if on the fixing date the reference rate is lower than the FRA rate. If the reference rate is above the FRA rate the seller has to pay the amount due. An FRA can be sold in order to speculate on falling interest rates in the future or as a hedge for a future long position in deposits and thus a protection against falling interest rates. Fixing date Usually the fixing date is 2 working days before settlement date. GP FRAs are settled on the sameday (not at value date after 2 days) and constitute therefore an exception. FINANCE TRAINER International Forward Rage Agreement (FRA) / Page 4 of 18
5 Amount due The amount due is the only cashflow that exists in an FRA and is due on the settlement date. The amount due is determined by the difference between FRA rate and reference rate multiplied by the amount of capital times the FRA term and is discounted to the settlement date (because the calculation would be due on maturity date). The formula to calculate the settlement payment is: AD REF FRA VOL D 1 REF D AD REF VOL FRA D = amount due = reference rate (e.g. LIOR) in decimals = volume of the FRA (+ = buy; = sell) = FRA rate in decimals = number of days of the FRA term = day basis of calculation You have sold the following FRA: EUR 100 m FRA 3/9 at 4.50% Days of FRA (interest period): months LIOR at fixing date: 4.75 % What is the amount due? ,000,000 AD , You have to pay EUR 122, value settlement date. FINANCE TRAINER International Forward Rage Agreement (FRA) / Page 5 of 18
6 Quotation FRA terms are usually labeled by a slash (3/9) or by a dot (3 6). The FRA terms most commonly used are terms of 3, 6, 9, or 12 months. 1/4 1/7 2/5 2/8 3/6 3/9 3/12 6/12 6/18 9/12 9/15 9/18 12/18 12/24 Usual FRA periods As FRAs are OTC instruments the maturities and the periods of FRAs can be freely agreed upon by the counterparties. For the standard periods like 3, 6 and 12 months market liquidity is the highest. Generally also an FRA with a e.g. 5months period (e.g. a 2/7 FRA) can be traded. Regarding the settlement date you have the following categories: Spot FRAs: the settlement date is exactely x full months after spot value roken dates: the settlement date is not exactely x full months after spot value IMM FRAs: the settlement date is a future maturity, i.e. on an IMM date (International Monetary Market). The IMM dates are always the 3rd Wednesday in March, June, September and December. Therefore IMM FRAs are a special kind of broken dates. trade date: Tue 22 nd Mar 2005 spot value: Thu 24 th Mar 2005 What is the term of a 3/6 spot, of a 3/6 over the 7th and of a 3/6 IMM FRA? 3/6 spot FRA: settlement: Fri 24 th Jun 2005 maturity: Mon 26 th Sep /6 over the 7 th : settlement: Tue 7 th Jun 2005 (=roken Date) maturity: Wed 7 th Sep /6 IMM: settlement: Wed 15 th Jun 2005 (3 rd Wed in June) maturity: Thu 15 th Sep 2005 FINANCE TRAINER International Forward Rage Agreement (FRA) / Page 6 of 18
7 Excerpt from a Reuters page for EUR Spot FRAs: Market liquidity and spreads FRAmarkets in USD, EUR and GP are the most liquid ones. As a rule: FRAs with MM futuresunderlying low spreads (e.g. EUR 6/12, Quotation ) FRAs without MM futuresunderlying greater spreads (e.g. HUF 6/12, quotation ) Regarding the maturity the liquidity of IMM FRAs is the highest followed by spot FRAs and broken dates. Therefore the spread for IMM FRAs is often only 1 P whereas for broken dates spreads of 35 P are common. Standard documentation The usual legal contract basis for FRAs are the socalled FRAA terms which are composed by the ritish ankers Association (A). FINANCE TRAINER International Forward Rage Agreement (FRA) / Page 7 of 18
8 Credit risk (Risk of Default) of an FRA The FRA comprises no exchange of principal. Therefore, the only risk is the nonfulfillment of the amount due at settlement date (replacement risk). The credit risk is thereby limited to the difference between FRA rate and the lockedin reference rate at settlement date. The credit line (partner limit) used by an FRA is therefore usually between 15 % p.a. of the principal amount (with regard to the term of the FRAperiod), from spot until settlement date. In addition one should also take into account the following factors: Period to settlement: the longer the period to settlement, the higher the risk that the reference rate differs strongly from the FRA rate which would lead to a higher amount due FRA period: the longer the FRA period, the stronger the impact of the interest rate differential on the amount due Volatility: the higher the statistical margin of deviation (=volatility), the higher the probability that the reference rate differs strongly from the FRA rate Ideally limitsystems guarantee a permanent marktomarketvaluation plus an addon factor for the remaining time until settlement which can be calculated with the Value at Risk (VAR) approach. FINANCE TRAINER International Forward Rage Agreement (FRA) / Page 8 of 18
9 2. Hedging with FRAs The main advantage of derivatives like FRAs is the separation of liquidity and interest rate risk. Thus the interest rate risk can be controlled more efficient, i.e. at more favourable prices (closer spreads) and by avoiding additional credit risk which would occur for controlling the interest rate risk with cash instruments. When hedging cash positions with derivatives you have to take into account that you always only hedge a reference rate (e.g. LIOR, EURIOR, etc.). For the total result the spreads to the reference rate that have to be paid in the cash market have to be considered. For example you cannot assume that you can lend at LIOR. For borrowings a premium on the LIOR (credit spread) has to be considered. Your position shows that you have to refinance EUR 100 m from 3 to 6 months. 3/6 FRA: % Your condition for refinancing: EURIOR + 25 P You are hedging your position with an FRA. What is your result assuming that the 3months EURIOR in 3 months will be 4.25%? You have the risk that the 3months EURIOR rises and therefore buy a 3/6 EUR FRA 100 m at 3.50% for hedging. After 3 months you refinance at the current rate of 4.50% (EURIOR credit spread). You receive a cash settlement of 0.75% (4.25%3.50%). Thus your total result is 3.75% ( = cash rate amount due). The 3.75% can also be interpreted as: FRA rate + spread EURIOR (= ). FINANCE TRAINER International Forward Rage Agreement (FRA) / Page 9 of 18
10 Your cash position shows a liquidity overhang from 3 to 6 months. You are hedging the interest rate by a 3/6 FRA sale at 3.46%. What is your result, assuming that you can lend cash at EURIOR  5 P? The result will be 3.41% (= FRA rate spread EURIOR = ). The following table shows the result for different interest rate scenarios: EURIOR in 3 months 3.00% 4.00% 5.00% Interest rate for lending (E 5 P) 2.95% 3.95% 4.95% Amount due (FRA  E) +0.46% 0.54% 1.54% Result (lending + amount due) 3.41% 3.41% 3.41% Remaining risks when hedging with derivatives LIOR risk: As shown in the example, the result remains the same and is therefore independent of the LIOR resp. EURIOR level. ut only assuming, that the cash transaction can be done exactely at LIOR plus a certain spread. Thus you have the risk that the market rate (at which you lend or borrow cash) does not comply with the LIOR. (e.g. LIOR has been fixed at 11:00 a.m. at 3%, you make the refinancing at 1:00 p.m. and the market has changed to 3.05%) Liquidity risk: Assuming that interest rates are unchanged, you still have the risk that the spread (at which you can lend or borrow cash) changes. In the example a credit spread of 25 P is calculated (LIOR + 25 P). You have the risk that this spread increases up to + 35 P, for example. Here liquidity risk is the risk of higher refinancing costs due to a widening of the credit spreads (e.g. because of a worsening of your own credit rating or because the market asks for higher premiums for the same credit ratings). FINANCE TRAINER International Forward Rage Agreement (FRA) / Page 10 of 18
11 3. Determination of Forward Interest Rates (FRA) 3.1 The Principle of Forward Interest Rates Forward interest rates can be derived from the current yield curve as you can always produce a forward deposit by means of 2 deposits with different terms. For example you can produce a forward borrowing from 6 to 12 months by borrowing for 12 months and lending for 6 months at the same time. The resulting interest rate depends on the costs resp. returns of the 2 deposits and therefore on the yield curve. Money market rates: 6 months: 4.00% 12 months: 4.50% How can you produce today the interest rate for a borrowing from 6 to 12 months? Answer: orrowing for 12 months at 4.50% and lending for 6 months at 4.00% at the same time Cashflows: orrowing 12 mo at 4.50% Lending 6 mo at 4.00% today 6mo 12mo % 102 You have a positive cashflow of +102 after 6 months (= borrowing of 102) and a negative cashflow of after 12 months (= paying back the principle plus 2.5 interest rate). Interest of 2.5 for half a year based on a starting capital of 102 results in an interest rate of 4.90% p.a. (see above calculation). Thus the forward interest rate is 4.90%. FINANCE TRAINER International Forward Rage Agreement (FRA) / Page 11 of 18
12 3.2 Highest and Lowest FRA Price Limits The highest resp. lowest FRA price limits are determined by the forward rates. A future interest rate can be produced (as shown above) by means of 2 deposits (forward deposit). ut it can also be produced by means of derivatives, e.g. FRAs. oth interest rates have to be linked to each other; otherwise it would be possible to profit from the price differences without any risk (= Arbitrage). The theoretical highest resp. lowest FRA price limits can be derived from the money market cash forward rates. Determination of the highest FRA price limit The question is: At what rate can a FRA sale position be closed in the cash market? The FRA price has to be lower than that synthetic cash price. Otherwise you could sell the FRA directly in the market and close the position by a synthetic FRA purchase in the cash market at the same time. Money market rates: 6 mo % (180 days) 12 mo % (360 days) What is the highest FRA price limit of a 6/12 FRA with the given yield curve? With a sold FRA you can fix a rate for a future lending. Therefore the FRA sale is equivalent to a future lending. Thus this interest rate position can be closed by fixing an interest rate for a future borrowing (= synthetic FRA purchase = borrowing 12 months + lending 6 months). The highest FRA price limit is therefore defined by the price of a synthetic FRA purchase. FINANCE TRAINER International Forward Rage Agreement (FRA) / Page 12 of 18
13 Cashflows: + spot (1) 100 (2) 1) borrowing 12 mo at 4.50% synthetic FRA 6/12 uy + 6 mo  2) lending 6 mo at 4.00% (3) at % mo  3) FRA sale at 4.90% same result for FRA 4.90% If the FRA can be sold above 4.90%, arbitrage is possible. Thus the highest FRA price limit is 4.90% and is equivalent to the price of a synthetic FRA purchase which can be produced by borrowing for the long period and lending for the short period (= take long + give short). Note: You have a remaining risk for the cash lending at LIOR in 6 months. In this example it is the risk at the FRA maturity date to give 6 months cash at LIOR (= LIOR risk). If you only get less, e.g. LIOR  10 P, your result is reduced. Determination of the lowest FRA price limit Here the question is: At what rate can an FRA long position be closed in the cash market? The FRA price has to be higher than that cash price. Otherwise you could buy the FRA directly in the market and close the position by a synthetic FRA sale in the cash market at the same time. FINANCE TRAINER International Forward Rage Agreement (FRA) / Page 13 of 18
14 Money market rates: 6 mo % (180 days) 12 mo % (360 days) What is the lowest FRA price limit of a 6/12 FRA with the given yield curve? With a bought FRA you can fix a rate for a future borrowing. Therefore the FRA purchase is equivalent to a future borrowing. Thus this interest rate position can be closed by fixing an interest rate for a future lending (= synthetic FRA sale = lending 12 months + borrowing 6 months). The lowest FRA price limit is therefore defined by the price of a synthetic FRA sale. Cashflows: + spot (1) 100 (2) 1) borrowing 6 mo at 4.10% synthetic FRA 6/12 Sell + 6 mo  2) lending 12 mo at 4.40% (3) at % mo  3) FRA purchase at % same result for FRA 4.606% If the FRA can be bought below 4.606%, arbitrage is possible. Thus the lowest FRA price limit is 4.606% and is equivalent to the price of a synthetic FRA sale which can be produced by lending for the long period and borrowing for the short period (= give long + take short). Note: You have a remaining risk for the cash borrowing at LIOR in 6 months. In this example it is the risk at the FRA maturity date to take 6 months cash at LIOR (= LIOR risk). If you pay more, e.g. LIOR + 10 P, your result is reduced. FINANCE TRAINER International Forward Rage Agreement (FRA) / Page 14 of 18
15 Consequences for the highest and lowest FRA price limits The FRA market prices should always lie between the price limits which are determined by the cash rates. In the above example this would be 4.60% and 4.90%. If the market prices were outside this range, arbitrage would be possible. The position of the FRA price within this range shows the market participants expectations. If the FRA rate is positioned just under the higher price limit, the market participants expect the rates to rise and therefore the demand for FRAs rises. Thus the FRA price rises though the cash rates are still unchanged, as these are mainly influenced by the liquidity situation resp. the central bank. Analogically, if the FRA rate is positioned just above the lower price limit, the market participants expect the rates to fall. 3.3 The FRA Formula For calculating FRA prices and forward deposit rates you have the following formulae: FRA bid r 1 r 1 L(bid) S(offer ) D L 1 D S D FRA FRA offer r 1 r 1 L(offer) S(bid) D L 1 D S D FRA r L r S D L D S D FRA = interest rate, longterm = interest rate, shortterm = day basis of calculation = number of days, longterm = number of days, shortterm = number of days, FRA Money market rates: 6 mo % (180 days) 12 mo % (360 days) FRA % FRA % offer bid FINANCE TRAINER International Forward Rage Agreement (FRA) / Page 15 of 18
16 Compare the FRA prices to the results of the calculation of the higher and lower FRA price limits! You will notice that the lower price limit (4.606%) complies with the bid side and the higher price limit (4.902%) complies with the offer side. The Connection between Yield Curve and FRA Rates As shown above, the FRA rates can be derived from the yield curve. The steeper the yield curve, the higher the FRA rates. The flatter the yield curve, the lower the FRA rates. For a normal yield curve FRA rates are higher than the interest rate level. For an inverse yield curve FRA rates are lower than the interest rate level. 3.4 Calculating FRA Rates through Fwd/Fwd Rates FRA rates can be calculated from cash and futures rates as well as from forward/forward swaps. EUR/USD spot: months forward rate: /6 forward/forward swap: (90 days) 3/6 EUR FRA: % (90 days) How can you compute the price for a 3/6 USD FRA purchase for 100 m USD synthetically? The purchase of a 3/6 FRA is equivalent to the interest rate of a future borrowing. This can also be produced by buying the USD in 3 months and selling the USD in 6 months (= Fwd/Fwd FX swap sell and buy EUR/USD). The EUR side of the swap has to be closed with a purchase of a 3/6 EUR FRA. The rate for the period 3/6 can be derived from the USD cashflows. FINANCE TRAINER International Forward Rage Agreement (FRA) / Page 16 of 18
17 Cashflows: 1) sell EUR at EUR  3 m. + USD % 2) buy EUR at EUR  6 m. + USD ) 3/6 Fwd/Fwd swap: sell EUR at 3months forward at ) 3/6 Fwd/Fwd swap: buy EUR at 6months forward at ( ) 3) uy 3/6 EUR FRA at 2.50% Result: ( ) / x 360/90 = % You can buy the 3/6 USD FRA synthetically at %. Note: In 3 months the short leg of the FX swap is delivered, i.e. you sell EUR and buy USD. These cashflows have to be closed again, e.g. with a 3months FX swap buy and sell EUR/USD. Formula for calculating FRA Rates from Fwd/Fwd Swaps A spot FX swap is derived from the interest rates of the two currencies. Therefore you can also derive the interest rates of the two currencies from the FX swap prices. As a Fwd/Fwd swap is a future FX swap, the interest rates are forward resp. FRA rates. According to this, the FRA rates can be calculated by means of an adapted formula for the calculation of interest rates out of FX swaps: FINANCE TRAINER International Forward Rage Agreement (FRA) / Page 17 of 18
18 FRA base currency FRA quote currency FRA D 1 FRA Q FWD Q FWD L S 1 D FRA Q D 1 FRA FWD FWD S 1 D L Q FWD = forward FX rate FRA Q = FRA p. a. in decimals, quote currency FRA = FRA p. a. in decimals, base currency Q = basis quote curreny (360 or 365) = basis base currency (360 or 365) D = days S = short period L = long period Excursus: With FRAs you can also extend the period of an FX Outright deal before maturity. This can be calculated with the normal forward rate formula (the spot rate is replaced by the forward rate and both deposit rates by the FRA rates): O long O short 1 FRA 1 FRA Q D Q D D = days O long = outright rate O short = spot rate FRA Q = FRA p. a. in decimals, quote currency FRA = FRA p. a. in decimals, base currency Q = basis quote curreny (360 or 365) = basis base currency (360 or 365) FINANCE TRAINER International Forward Rage Agreement (FRA) / Page 18 of 18
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