2 Forward Rate Agreement

Forward rate Agreement (OTC Derivative)

CA. Nagendra Sah Page 1

OTC Derivative:

OTC (Over-the-counter) contract is a contract which is privately negotiated between two parities.

OTC derivative is a derivative which is not traded on an exchange and it is being traded over-the-

counter (i.e. privately negotiated).

Derivative are traded in two kinds of market: (i) Exchange (ii) OTC Market

OTC Market Vs Exchange

OTC market is an informal market consisting of dealers or market makers who privately

negotiate transactions over electronic communication networks.

Example of OTC market in India:– OTCEI (Over the counter exchange of India)

It is an electronic stock exchange based in India and it has no central place of exchange (i.e.

no trading house) and all the trading is done through electronic network.

Example of OTC market abroad:– NASDAQ (National Association of Securities Dealers Automated Quotation System)

Exchange means Stock exchange. Stock exchange has been defined in the SCRA 1956 (For more

discussion on stock exchange see theory of chapter-Indian capital market.

Future contract traded OTC is a forward contract and the Forward contract traded in an

exchange is a future contract. However, Option traded in exchange or traded OTC both is called

Option.

In exchange trading, clearing houses guarantees the contract performance. However, in OTC

market there exist risks of default because contracts are privately negotiated.

OTC derivative

Forward contract: For discussion on forward contract see FOREX and derivative contract.

For Understanding forward rate agreement first we have to understand forward interest rate

or Implied Forward rate (Calculation of forward rate is based on expectation theory).

Implied Forward Interest rate: [M-10-New-8 M] [N-08-New-4 M] [RTP- N-09-New]

Forward interest rate is the interest rate (It is different from the forward exchange rate which we studied in FOREX) that we

expect to prevail in the market after certain period. For calculation of implied (i.e. Fair) forward rate,

first know some terms which are discussed below:

Meaning of 1st year Forward rate (Also known as 1 Year forward rate as of today)

It is an interest rate that we expect at beginning of 1st year for the borrowing/deposit made for 1

year period.

Today 1 Year

Borrowing/deposit period

Expected interest

Rate as on today for this

Forward Rate

agreement

Interest rate

swap

Caps, floor

and Collar

Forward

Contract

Summary of OTC derivatives


Meaning of 2nd year Forward rate (Also known as 1 Year forward rate 1 year from Now)

It is an interest rate that we expect to prevail at beginning of 2nd year for the borrowing/deposit to

be made for 1 year period after 1 year time.

Today 1 Year 2 Year

Borrowing/deposit period

Expected interest rate

at 1 year time for this

Meaning of 6 month Forward rate 3 month from now (Also known as 6 month forward rate 3

month forward)

It is an interest rate that we expect to prevail at 3 month time for the borrowing/deposit to be made

for 6 month period after 3 month time.

Today 3 month 9 month

Borrowing/deposit period 6 month

Expected interest rate

at 3 month time for this

How to calculate Forward interest rate (not forward exchange rate)?

Suppose 9 month LIBOR is 12% p.a. and 3 month LIBOR is 8% p.a. We can calculate 6 month forward

rate (i.e. 6 m implied forward rate/6m fair forward rate) 3 month from now as follows:


8% (i.e. 2% for 3 m) 6 month fair forward rate (Say ‘R’)

A

1 1.02 1.02

B 12% (i.e. 9% for 9 month)

1 1.09

If calculated 6 month forward rate (R) is Fair rate, then an investor would be at indifference between:

A. investing @ 8% p.a. for first 3 month and re-invest it @ R% p.a. for further period of 6 month

and

B. investing @ 12% p.a. for 9 month period.

It means, 1.02

= 1.09

Or,

=

or, R = (1.06863 – 1)

Hence, R = 0.1373 (i.e. 13.73%)

Mathematically, we can calculate forward rate using following formula:

(1+ 3 month rate) (1+ 6 month forward rate 3 month forward) = (1+ 9 month rate)



Forward Rate Agreement (FRA): [CS-June-2009-4 Marks]

Forward rate agreement is an OTC (Over the counter) contract between two parties, one is buyer of

FRA and another is seller of FRA, to fix a future interest rate.

This contract fixes the interest rate for future deposit/borrowing based on notional principal

because there is no actual borrowing/deposit under FRA.

FRA contract is to be settled on settlement date by payment of settlement amount. Settlement

amount is the discounted value of differential interest on notional principal.

Parties to FRA:

1. Buyer of FRA (Future borrower):

(i) A FRA buyer is a future borrower who is seeking to protect itself against future rise in

Interest rate.

(ii) Example-1: Suppose CA. Garib, an IDT teacher, will have to buy a car at 3 month time.

But he will get money from his student at 9 month time. In such situation, he has one

option that, he will take loan of 5,00,000/- at 3 month time and repay borrowing at 9

month time after getting money from student.

Now, borrowing rate is 10% p.a. but this rate is likely to be higher at 3 month time. What

CA. Garib will do, to protect his future borrowing rate?


Buy 3 9 FRA Borrowing period

now @ 10%

CA. Garib will buy 3 9 FRA @ 10% for notional amount 5,00,000 to protect interest rate.

In this case, doesn’t matter what will be the actual interest rate at 3 month time, he will incur

net interest cost @ 10%.

Remember that actual borrowing will not take place under FRA. It is settled by interest rate

differential. CA Garib has to take borrowing from market for buying Car at actual rate which

will prevail at 3 month.

We will complete the whole procedure of this transaction (in subsequent page) after knowing

the various term related to FRA.

(iii) The FRA buyer receives money from the FRA seller if actual Interest rate at 3 month time is above

the contract rate (i.e. 10%).

(iv) The FRA buyer pays money to the FRA seller if actual Interest rate at 3 month time is below the

contract rate (i.e.10%).

2. Seller of FRA (Future Lender/depositor):

(i) A FRA Seller is a future depositor who is seeking to protect itself against future decrease

in Interest rate.

(ii) Example-2: Suppose Mr. Lazy will receive 1,00,000/- from his father after 1 month as a

gift of passing IPCC. He is thinking to buy one diamond ring after 7 month for his

girlfriend and hence this amount will be surplus with him for 6 month. Now he is

planning to deposit it for 6 month time after 1 month when he receives money from his

father.

Today’s deposit rate is 8% p.a. but this rate is likely to be decrease at 1 month time. What

Mr. Lazy will do, to protect his future deposit rate?


Sell 1 FRA Deposit period

now @ 8%



-Mr. Lazy will sell 1 FRA @ 8% now for notional amount 1,00,000 to protect interest rate.

-In this case, doesn’t matter what will be the actual interest rate at 1 month time, he will get net

interest income @ 8%.

-Remember that actual deposit will not take place under FRA. It is settled by interest rate

differential.

(iii) The FRA seller receives money from the FRA buyer if actual Interest rate at 1 month time is below

the contract rate (i.e. 8%).

(iv) The FRA seller pays money to the FRA buyer if actual Interest rate at 1 month time is above the

contract rate (i.e.8%).

Summary of Payment structure:

Actual rate/Reference rate

Contract rate/Agreed rate

Actual rate/reference rate

FRA Quotation:

Suppose: 3 9 FRA = 8% - 10%

(Quoted by bank)

Lending rate Borrowing rate

FRA selling rate FRA buying rate

for customer for customer

FRA buying rate FRA selling rate

for bank for bank

Meaning of 3 9 FRA (It is also denoted by 3Vs9 FRA, 3-9 FRA, 3/9 FRA, 3.9 FRA): FRA contract to

be entered today for 6 month (i.e.9-3) borrowing/deposit to be placed after 3 month time. See example-1

discussed earlier for more clarity.


3 month Borrow/deposit period (6 month)

Meaning of 1 7 FRA (It is also denoted by 1Vs7 FRA, 1-7 FRA, 1/7 FRA, 1.7 FRA): FRA contract to

be entered today for 6 month (i.e. 7-1) borrowing/deposit to be placed after 1 month time. See example -2

discussed earlier for more clarity.

Various Rates used in FRA:

Contract rate (also known as fixed rate/agreed rate/FRA rate): It is a fixed interest rate on which

contract is agreed.

Actual Rate (also known as reference rate/settlement rate/floating rate): It is an actual EURIBOR (EURO Interbank offering rate) or LIBOR (London Interbank offering rate) rate at fixing date (two days prior to settlement date).

FRA Buyer FRA Seller

FRA Seller FRA Buyer



Various Dates used in FRA:

3 month 6 month (i.e. contract period)

2 Days 2 Days

Transaction Start Fixing Contract Settlement Maturity

Date Date Date Date Date

Today Spot date Value date B/D maturity date

Settlement amount payable/receivable by parties to contract

Settlement amount =

Note: For EUR and USD this is generally the number of days divided by 360, for GBP it is the number

of days divided by 365 days

For example-1 above

(i) Situation-1: Suppose actual rate on fixing date is 12%.

Settlement amount :

=

= 4,716 (appx)

Hence CA. Garib (FRA buyer) will receive 4,716 at 3 month time (i.e. on settlement date)

from bank (FRA seller).

(ii) Situation-2: Suppose actual rate on fixing date is 9%.

Settlement amount:

=

= 2,392 (appx)

Hence CA. Garib (FRA buyer) will pay 2,392 at 3 month time (i.e. on settlement date) to

bank (FRA seller).

For example-2 above

(i) Situation-1: Suppose actual rate on fixing date is 7%.

Settlement amount:

=

= 2,415 (appx)

Hence Mr Lazy (FRA seller) will receive 2,415 at 1 month time (i.e. on settlement date)

from bank (FRA buyer).

(ii) Situation-2: Suppose actual rate on fixing date is 11%.

Settlement amount:

=

= 1,422 (appx)

Hence CA. Garib (FRA buyer) will pay 1,422 at 1 month time (i.e. on settlement date) to

bank (FRA seller).



Concept of formula for settlement amount:

3 month 6 month (i.e. contract period)

2 Days 2 Days

Transaction Start Fixing Contract Settlement Maturity

Date Date Date Date Date

Discounted value

Arbitrage in FRA: [May-2010-New-8 Marks]

It is an arbitrage in Interest rate. Arbitrage in interest rate is possible when borrowing rate is less

than deposit rate.

Action for arbitrage:

(i) Borrow at low rate and

(ii) Deposit at High rate

Example -1:

Suppose, 3 month borrowing rate = 8% and 3 month deposit rate = 6%.

In this case arbitrage is not possible.

Example-2:


In this case arbitrage is possible, if one will borrow at 10% for 3 month and deposit it at 12% for 3

month and repay borrowing after 3 month from the receipt of deposit amount.

Example-3:


Is there is any arbitrage possibility?

NO, Arbitrage is not possible, even deposit rate is greater than borrowing rate.

0 Period 3month 6month

It is not possible to repay loan at 3 month because he will not receive deposit money at that date.

In above example-3 if we will get “3month forward rate 3 month forward” then we can check

arbitrage opportunity.

Differential Interest on

notional principal is

due on Maturity date

Settlement amount is payable on settlement date. Hence discount it for the

contract period at actual rate prevailing in the market.

For discounting do not use contract rate because discount rate is the rate at which

future value of money is converted at today’s money term and money is growing in

market at actual rate (i.e. current rate) prevailing in market.

Settlement amount

Take Loan for

3 month

Repay loan

at 3 month

Receive deposit

at 6 month

Make deposit

for 6 month

How will he repay

loan amount?



Example-4:

Suppose, 3 month borrowing/deposit = 8%

6 month borrowing/deposit = 10%

3month FR 3 month forward = 12%

0 Period 3Month 6 Month

A B/D rate = 8% Actual 3M FR 3MF = 12% for both B/D

Fair 3M FR 3MF = 11.76% for both B/D

B/D Rate = 10%

First calculate ‘implied 3 month forward rate 3 month forward’ and compare it with actual rate.

=

Hence, Fair 3M FR 3MF (R assumed) = 11.76% (annual rate)

Here, actual rate is higher than that of fair rate hence:

(i) make deposit in part A above (i.e. deposit for first 3 month @ 8% and re-investment it at

3 month time @ 12% for further 3 month); and

(ii) take borrowing in part B above (i.e. borrowing for 6 month @ 10%)

Calculation of Arbitrage gain: (Assuming Arbitrageur borrow 100)


1. Take borrowing

2. Make deposit for 3 month

3. Make further deposit at 3 month time for further 3 month

4. Repay borrowing from receipt of deposit

5. Calculate arbitrage gain = receipt from deposit – repayment of bowing

In our example arbitrage gain = 105.06 – 105 = 0.06 for borrowing of 100.

Concept for arbitrage in FRA:

Is the 3M forward rate 3 month forward (in our above example 4) is today’s rate? No, it is rate at 3

Month time.

Who know that this rate will actually prevail at 3 month time? None of the person knows it.

It may be or may not be.

B

@8% @12% 102

105.06

105

100

100

Borrowing

Deposit

@10%

Repay

Surplus Amt. is

arbitrage gain



Then how it will became risk free profit calculated in example -4 (Arbitrage gain)? No, this is not risk

free profit. We calculated it, only to understand the whole procedure and steps.

Yes, Above calculated gain will be Arbitrage gain if 3 month forward rate 3 month forward is a

3 6 FRA selling rate. Because FRA attracts fixed interest cost (@ contracted rate) for future period

even actual rate in future is either high rate or low.

Example-5: [based on Q-60] [M-10-8Marks]

The 6 & 12 months LIBOR are 5% and 6.5% respectively. A bank is quoting 6/12 FRA at 6.5%-6.75%.

Fair 6 month forward rate 6 month forward is 7.81%. Check for arbitrage possibility.

Checking for possibility of Arbitrage using FRA selling rate of customer 6.5% (i.e. deposit rate)


B/D rate = 5% Actual 6M FR 6MF = 6.5% for Deposit.


B/D Rate = 6.5%

Analysis: Actual rate is lower than fair rate hence one has to borrow at 6.5% (lower rate) for arbitrage gain but

given rate is 6.5% for Deposit. Thus, No arbitrage gain is possible in above case.

Checking for possibility of Arbitrage using FRA buying rate of customer 6.75% (i.e. borrowing

rate)


B/D rate = 5% Actual 6M FR 6MF = 6.75% for Borrow.


B/D Rate = 6.5%

Analysis: Actual rate is lower than fair rate hence one has to borrow at 6.75% (lower rate) for arbitrage gain

and the given rate 6.75% is also for Borrowing. Thus, arbitrage gain is possible in above case.

If given 6 month LIBOR 5% is deposit rate (not borrowing/deposit) then arbitrage gain is not possible even in this

situation also.

Example-6

The 6 & 12 months LIBOR are 5% and 6.5% respectively. A bank is quoting 6/12 FRA at 6.5% - 8.5%.

Fair 6 month forward rate 6 month forward is 7.81%. check for arbitrage possibility.

Using FRA selling rate for customer 6.5% arbitrage is not possible. It is same situation as above.

Using FRA buying rate of customer 8.5% (i.e. borrowing rate)


B/D rate = 5% Actual 6M FR 6MF = 8.5% for Borrow.


B/D Rate = 6.5%

Analysis: Actual rate is higher than fair rate hence one has to deposit at 8.5% (higher rate) for

arbitrage gain but the given rate 8.5% is for Borrowing. Thus, arbitrage gain is not possible in above

case.

For Caps, Floor and Collar and Interest rate swap see further notes:

Documents

2 Forward Rate Agreement