750 840003 rm rjs v interest rate forwards and futures

Derivatives and Risk ManagementBy Rajiv SrivastavaCopyright Oxford University Press

Forward Rate Agreement (FRA) Interest Rate Futures on T-Bills Euro-Dollar Futures Treasury Bonds Futures

Chapter 6 Interest Rate Forwards and Futures

Derivatives and Risk ManagementBy Rajiv Srivastava 2

Copyright Oxford University Press

Interest Rate Derivatives

Interest rate derivatives have some benchmark interest rate as underlying asset.

Derivatives on interest rates are used for covering the risk of changing interest rates.

Most business face risk of changing profit due to changes in the interest rates.

For some organizations like banks, construction companies are extremely prone to changing interest rates.




FRA The Product Pricing FRA Hedging With FRA Speculation with FRA Arbitrage with FRA




Forward Rate Agreement

Forward rate agreement, commonly referred as FRA is a contract to deposit or borrow a notional sum in future for a specified maturity at interest rate fixed now.

FRA as a product is specified as follows:



Quotation of FRA

INR 3/9 months 6.00 6.50%

Currency Deposit LendingRate Rate

Commencement Maturity of of deposit/lending deposit/lending (Bid Rate) (Ask Rate)


Borrowers FRA

Firms need to borrow capital. Such firms need protection against rising

interest rate. By booking FRA at ask rate they can freeze

the interest rate and hence the cost of borrowing.




Investors FRA

Firms surplus with capital need to lend funds. Such firms need protection against falling

interest rate. By booking FRA at bid rate they can freeze

the interest rate and hence the revenue from lending.




Settlement of FRA Settlement of FRA is done by exchanging the differential

cash flow of contracted interest rate and the actual benchmark on the notional principal.

With r = settlement rate, f = FRA rate, d = Nos of days in FRA contract, and P = notional principal amount, the settlement amount for investor and borrower FRA are

The amount to be received under the borrowers 3/9 FRA at 6.5% with actual interest rate at 7% would be Rs 2,40,907:



P x 365d

x f)-x(rd/365) x r+(11

=FRA) s(Borrower' flow Cash

P x 365d

x r)-x(fd/365) x r+(11

=FRA) s(Investor' flow Cash

2,40,907 Rs=1.0349

2,49,315=

01,00,00,00 x 365182

x 0.065) -x(0.07182/365) x 0.07+(1

1=received be to Amount


Pricing FRA Term structure of interest rate implies forward interest

rates and forms the basis of pricing of FRA. Assume following term structure up to 12 months:

3-m interest rate expected to prevail after 3 months used as a guide to quote 3/6 FRA. Mathematically,(1+ 0r3)(1+3r6) = (1+0r6) or (1+3r6) = (1+0r6)/(1+ 0r3)



Investment Horizon (months) 3 6 9 12Yields (% annualised) 5.00 5.30 5.60 6.00

5.53%=r annualised to equivalent or 0.01383,=r gives

1.01383;=1.01251.0265

=

36090

x 0.050+1

360180

x 0.053+1=)r(1+

6363

63


Hedging with FRA

FRA is an independent contract that delinks the actual investing or borrowing and serves as effective tool for hedging.

FRA provides hedging against1. Rising Interest Rates for borrowers, and 2. Falling Interest Rates for investors

Borrowers FRA is a contract that covers risk of rising interest rate while investors FRA protects against the falling interest rates.




Hedging Rising Interest Rates EXCEL Industries Ltd (EIL) would have a shortfall of Rs

500 lacs after 6 months for next 6 months. EIL have been availing loan at MIBOR currently at 9%. The borrowing cost is 10%.

The interest rates are expected to go up in next 6 months.

To hedge against rising interest rates, EIL buys a MIBOR based 6/12 FRA from another bank, Forward Bank (FB) at 9.25% for notional principal of Rs 500 lacs.




Hedging Rising Interest Rates We present the position of EIL under two situations after 6 months of

MIBOR being more than and less than the FRA contracted rate: When MIBOR goes beyond the FRA contracted rate of 9.25% up to 10% FB would pay EIL the differential of current MIBOR and agreed rate of

9.25% on notional principal of Rs 500 lacs for 180 days, discounted at 10%. The amount to be paid by FB is

1. Interest cost for loan from CB = 5,00,00,000 x 0.10/2 = Rs 25,00,0002. Maturity amount of FRA at 10% = 1,78,571 x 1.05 = Rs 1,87,5003. Effective interest amount paid = Rs 23,12,5004. Effective borrowing cost = 23,12,500/5,00,00,000 = 0.04625

equivalent to 9.25% p.a



571 1,78, Rs=1.05

1,87,500=

05,00,00,00 x 360180

x 0.0925) -(0.10 x 180/360) x 0.10+(1

1=firm to flow Cash


Hedging Rising Interest Rates When MIBOR falls below the FRA contracted rate to 8.60% In case the benchmark rate falls to 8.60% EIL would have to pay FB the

differential of actual and contracted rate as follows:

1. Interest cost for loan from CB = 5,00,00,000 x 0.086/2 = Rs 21,50,0002. Maturity amount of FRA at 10% = 1,55,800 x 1.043 = Rs 1,62,5003. Effective interest amount paid = Rs 23,12,5004. Effective borrowing cost = 23,12,500/5,00,00,000 = 0.04625

equivalent to 9.25% p.a



1,55,800 Rs -=1.043

1,62,500 -=

05,00,00,00 x 360180

x 0.0925) -(0.0860 x 180/360) x 0.086+(1

1= firm to flow Cash


Hedging Falling Interest Rates

Investing companies earn revenue by lending.

While rising interest rates are welcome by them a fall in interest rate is detrimental.

They need to protect against the expected fall in yields.

Investing companies can lock-in the yield offered by FRA just in the same manner as the borrowers lock-in the cost of borrowing.




Speculation with FRA

If one is neither an investor nor a borrower, then position in FRA is speculative.

The rates offered by FRA are reflecting the future expected rates of interest.

If one has a different view of future interest rate than the one reflected by FRA, then If future interest rate expected to be > FRA rate:

Book Investors FRA If future interest rate expected to be < FRA rate:

Book Borrowers FRAChapter 6

Interest Rate Forwards and FuturesDerivatives and Risk ManagementBy Rajiv Srivastava 15


Futures Contract on T-Bills Pricing T-Bills Quoting T-Bills Futures Hedging with Futures on T-Bills Speculation with T-Bills Futures Arbitrage with T-Bills Futures

Implied Repo Rate Pricing T-Bills Futures




Futures on T - Bills

A futures contract on T-bills on expiry calls for delivery of T-bills maturing 91 days thereafter.

The price of T-bill, a function of interest rate determines the price of futures on it.



Futures Contract on T-Bills

t = 0 t = T (Maturity) t = T + 91 days

Futures position Futures contract matures T-Bill maturesInitiated T-Bill delivered

T-Bill


Why Futures on T-Bills

One determinant of interest rate is the default risk. The yields on corporate debt (bonds) also include the risk premium for default.

T-bills is sovereign debt and can be assumed to have no risk of default.

Also the liquidity in the sovereign debt is high as compared to corporate bonds.

T-bills serve as an ideal instrument as an underlying asset for interest rate futures.




Pricing T-Bills T-Bills are issued at discount to face value and

redeemed at face value on maturity. For discount yield of 6% the amount of discount,

D on the T-bill with 90 days to maturity would be:

The purchase price of T-bill, P would be:P = Face value, V Discount, DThe price of the T-bill with 6% yield would be 100 1.50 = Rs 98.50.



1.50 Rs=360

90 x 0.06 x 100=

360T x d

x V=D


Quoting T-Bills Futures

Futures on T-bills are priced on index basis because of Inverse relationship of price with interest rate, and Convention of long position gaining with price rise

in other futures markets. Futures Price, F is stated as 100 I The quoted price of futures on Tbill of Rs 92

implies a yield of 8%.




Quoting T-Bills Futures

With 8% yield on T-bills the futures price would be Rs 92.

If hypothetically we assume one futures contract for Rs 10 lacs of face value of T-bills the discount would be 2% (8 x 90/360).

For a long position on futures the buyer has to pay 10 x (1 - 0.02) = Rs 9.80 lacs.



360T x Yield bill-T=D or

360 x 100T maturity, to days of Nos x F) Price, Futures - (100=D


Hedging with T-Bills Futures

T-bill futures are used to hedge the short term interest rate risk.

Depending upon the position of funds one may need protection against rising or falling interest rates.




Hedge Against Falling Yields

As prospective investor one faces the risk of falling interest rates.

Rather than investing funds today (invest in T-bills) one can buy futures on T-bills.

One is short on funds and to hedge investor takes opposite position in futures i.e. go long on T-bill futures.




Hedge Falling Yield - Example You have to invest Rs 10 crore after 3 months from now

fro next 3 months. The current yield on T-bills is attractive 7.80% and is likely to fall. Futures on T-bill is at 92.20. Size of the contract is Rs 10 lacs.

To hedge you can buy a futures contract on T-bills and lock-in the yield of 7.80%. Nos of contracts bought = 1000 lacs/10 lacs = 100 Amount committed to pay = 100 x 9,80,500 = Rs 9,80,50,000

By buying 100 futures contract on T-bills you have undertaken to pay Rs 9,80,50,000 and receive T-bills with face value of Rs 10 crore (100 contracts x Rs 10 lacs per contracts)




Hedge Falling Yield - ExampleHEDGING INVESTMENT RETURN WITH INTEREST RATE FUTURES

Scenario Yield falls to 7.00% Yield rises to 8.50%T-bill futures price 93.00 91.50Futures contract sold at 93.00 91.50Implied yield 7.00% 8.50%Price of contractValue to be received on the futures contracts sold Rs 9,82,50,000 Rs 9,78,75,000Amount to be received (+) /paid (-) on futures contracts

Rs 2,00,000 - Rs 1,75,000

Amount of interest earned on actual deployment of Rs 10 crore in T-bills

0.07 x 90/360 x 10,00,00,000 = Rs 17,50,000

0.085 x 90/360 x 10,00,00,000 = Rs 21,25,000

Actual earnings after adjusting for profit/loss on T-bill futures (ignoring time value of the gain/loss on futures)

Rs 19,50,000 Rs 19,50,000

Effective yield 7.80% 7.80%Chapter 6



Hedging Rising Interest Cost

Protection against falling interest rate is covered by buying interest rate futures, while rising interest rate scenario is hedged by selling them.

It is called short hedge. By going short on T-bill futures the yield in

the futures price can be locked as the cost of borrowing irrespective of the interest rate scenario at the time of actual borrowing.




Speculation : T-Bill Futures

SITUATION STRATEGY

When interest rates are expected to go up more than what futures market suggests The price of underlying asset as well as futures on them would fall

Sell futures now and buy later

When interest rates are expected to go down more than what the futures market suggests The price of underlying asset as well as futures on them would go up

Buy futures now and sell later



The strategies of speculators are summarised as below:


Arbitrage : T-Bill Futures

If futures are mispriced one can execute cash and carry or reverse cash and carry arbitrage as follows:



OVER PRICED FUTURES - CASH AND CARRY ARBITRAGEToday On Maturity

Sell the future Buy the underlying asset Borrow equivalent sum

Deliver asset against the futures contract Receive value equal to futures price Repay borrowing along with cost of borrowing

UNDER PRICED FUTURES - REVERSE CASH AND CARRY ARBITRAGEToday On Maturity

Buy the future Sell the underlying asset Lend equivalent sum

Acquire asset against the futures contract Receive the funds lent with interest Pay for the asset as agreed in futures contract


Implied Repo Rate

Futures contracts on interest rate are like repo transactions and therefore futures price imply a repo rate.

The repo rate implied in futures price is

Arbitrage with interest rate futures is determined by the implied repo rate and the actual yield in the market.



futures for remaining days of Nos365x

Price SpotPrice Spot-Price Futures=

Rate Repo Implied


Computing Implied Repo Rate Consider T-bill futures sells for Rs 90.00. Note that

Contract has exactly 90 days to mature. It warrants delivery of T-bills that have 90 days to mature. Hence 180-day T-bill is the deliverable Yield of 180-day bill is relevant spot price.

180-day T-bill is quoting with yield of 8%. The prices of 180-day T-bill and the futures contracts would be: Price of 180-day T-bill = 100 0.08 x 180/360 = Rs 96.00 Invoice price of futures contract = 100 - 0.10 x 90/360 = Rs 97.50

The implied repo rate is 6.25%



%25.60625.0=90360

x96.00

96.00 -97.50=Rate Repo Implied


Arbitrage : T-Bills Futures If implied repo rate is different than the actual repo rate it

presents an arbitrage opportunity either way. No arbitrage condition forces the implied repo rate to

converge to actual repo.



ARBITRAGE WITH INTEREST RATE FUTURESCash And Carry ArbitrageWhen Implied Repo Rate > Financing Cost, Say 4%

Reverse Cash And Carry ArbitrageWhen Implied Repo Rate< Financing Cost, Say 8%

Action Cash flow Action Cash flowTodaySell the Interest rate futures Buy 180-day T-bill in cash Borrow equivalent sum

-- 96.00+ 96.00

TodayBuy the Interest Rate FuturesSell 180-day T-bill in cash Lend equivalent sum

-+ 96.00- 96.00

Cash flow today 0.00 Cash flow today 0.00On maturity after 90 daysDeliver T-bill and realise futures contract valueRepay borrowing with interest

+97.50- 96.96

On maturity after 90 daysAcquire T-bill and pay futures contract valueReceive funds lent with interest

- 97.50+97.92

Cash flow on maturity + 0.54 Cash flow on maturity + 0.42Copyright Oxford University Press

Eurodollars Futures Contract on Eurodollars Pricing Eurodollar Futures Hedging with Eurodollar Futures




Eurodollars Eurodollar deposit is the US dollar deposit held by banks

outside USA by non USA banks or foreign branches of US banks.

Eurodollar deposits came into existence when during 1950s and 1960s the erstwhile USSR and East European countries parked their US dollar deposits with banks in London, Paris and other non US locations for they could not be confiscated by USA.

Eurodollars are not subject to regulation and control by US government.

These made Eurodollar deposits and lending rates purely determined by market forces;




Futures on Eurodollar Like contract on futures on T-Bill requires

seller to deliver T-bills that matures 91 days thereafter, a future contract on Eurodollar should have required delivery of deposit that matures 3 months thereafter.

Eurodollar deposits are not deliverable being non-transferable.

However, we use Eurodollar futures for hedging, speculation and arbitrage in the same way as futures on T-bills.




Eurodollar & T-Bill Futures

There are two key differences between the futures contracts on T-bills and Eurodollar deposits as below: Eurodollar deposits are non-transferable and

hence cannot be delivered. Therefore futures on Eurodollar deposits are necessarily cash settled.

Yield on Eurodollar deposit is on add-on basis. Add-on yield is related to discount yield is



T360

xPrice

Yield Discount=Yield on-Add


Actual and Discount Yield

With discount yield of 10% the current price of the T-bill maturing after 90 days would be

The actual yield would be:

If yield mentioned on add-on basis is 10% it simply means that if the current price is Rs 100, after 90 days one would get Rs 102.50.



97.50 Rs=360

90 x 0.10 x100 x 100=bill-T of Price

10.526%=90360

x97.50

97.50-100=Yield Actual


Pricing of Eurodollar Futures

Like futures on T-bills the futures on Eurodollar deposits too are quoted on index basis. Price of Eurodollar futures is given by:Eurodollar Futures Price, F =

100 3-m LIBOR rate Because of free pricing futures contract on

Eurodollars are extremely popular in international markets




Settlement: Eurodollar Futures Eurodollar futures are necessarily cash

settled i.e. difference of initial price F0 and final price F1 exchanged in cash.

The cash profit/loss for long and short position is given by:



36090

x 100

F-F x 1,000,000 $ =position short initial For

36090

x 100

F-F x 1,000,000 $ =position long initial For

Futures Eurodollar on sProfit/los

10

01


Hedging : Eurodollar Futures 3 months from now DFL needs to raise US $ 2

million for 6 months. Current LIBOR is 6.50% and the Eurodollar futures contract with 3 months to expire is quoted at 93.00. DFL expects the interest rate to rise to 8%. 1. How can DFL hedge against rising interest

rates? 2. What would be the effective cost if the interest

rate actually rises to 8%. 3. Also analyse the interest cost if LIBOR actually

falls to 6%.Chapter 6



Hedging Strategy DFL faces risk of rising interest rate for its

contemplated borrowing 3 months. Since futures contract provides cash flow based

on 3 months and loan required is for 6 months the compensation would be equal if the exposure in futures is for twice the actual borrowing.

DFL can therefore sell 4 futures contracts on Eurodollar futures equivalent to $ 4 million.




Hedging OutcomeIf LIBOR rises to 8% Eurodollar price would fall to 92.00. The profit of each futures is

The borrowing cost for 6-m loan on $ 2 million = 2 m x 0.08 x 180/360 = $ 80,000

Less: Profit earned from 4 Eurodollar futures contracts = 2,500 x 4 = $ 10,000

Effective interest paid = $ 70,000

This is the rate implicit in the futures contract now that can be locked in.



5002= ,$36090

x 100

92.00-93.00 x 1,000,000 $ =

36090

x 100

F-F x 1,000,000 $ =

Position) Short (For Futures Eurodollar on sProfit/los

10

7.00%=180360

x 2,000,000

70,000=Rate Interest Effective


Hedging OutcomeIf LIBOR falls to 6% Eurodollar price would rise to 94.00. The loss of each futures is

The borrowing cost for 6-m loan on $ 2 million= 2,000,000 x 0.06 x 180/360 = $ 60,000

Loss from 4 Eurodollar futures contracts = 2,500 x 4 = $ 10,000Effective interest paid = $ 70,000

With fall in the interest rates the firm would not benefit. It still has to pay the same cost of 7% the rate implicit in the futures contract now.



5002= ,$-36090

x 100

94.00-93.00 x 1,000,000 $ =

36090

x 100

F-F x 1,000,000 $ =

Position) Short (For Futures Eurodollar on sProfit/los

10

7.00%=180360

x2,000,000

70,000=Rate Interest Effective


Pricing T-Bonds Futures Contract on T-Bonds Pricing T-Bond Futures

Conversion Factor Cheapest-To-Deliver Bonds

Hedging Principle Duration and Modified Duration Duration Based Hedging




Treasury Bond Futures Futures contracts on treasury bonds are used for

hedging long term interest rate risk, while futures on T-bills cover interest rate risk over short term.

Like T-bills these bonds are also regarded as free of default risk.

The futures contract on T-bonds would require delivery of an equivalent government security, during the delivery period specified.

However, settlement by delivery may not arise because most contracts would be negated by the offsetting contracts prior to the maturity.




Pricing Treasury Bonds Following is term structure

The value of the GoI security with 8% semi-annual with 3 years to maturity is given by:

The price of the security is Rs 102.63



33

6

12/t

2/t

t0 )r1(

R)r1(

CP+

++

=

102.63 Rs=(1.072)

104.00+

(1.069)4.00

+(1.067)

4.00+

(1.064)4.00

+(1.060)

4.00+

(1.057)4.00

=P 3.02.52.01.51.00.50

Investment Horizon(m) 6 12 18 24 30 36Yields (%) 5.70 6.00 6.40 6.70 6.90 7.20


Futures on T-Bonds

Futures contract on treasury bonds requires delivery of a long term bond with minimum specifications decided by the exchange.

Different exchanges adopt different practices for delivery of the underlying instrument on which the prices are quoted.

Any instrument meeting minimum specification can be delivered by the seller of futures contracts on treasury bonds.




Pricing T-Bond Futures

The price of a futures contract on T-Bond uses the concept of cost of carry, as is the case with pricing of other futures contracts.

However, in case of T-bonds we also earn the dividend in the form of accrued interest.

Fair price of futures on T-Bonds must reflect true cost of financing.

Fair Price of futures = Spot price + Cost of financing Accrued interest




Fair Price of T-Bond Futures Futures contract price represents a repo transaction;

selling a security and buying it later at the price determined today.

Assume 8% GoI security sells for 96.0291 at YTM of 8.60%. Financing cost is 10%. Futures with 45 days to maturity sells for Rs 96.5000.Then we have:

Spot price of the bond (at YTM of 8.60%) = Rs 96.0291Accrued interest for 45 days = 4 x 45/182 = Rs 0.9890Cost of financing for 45 days = 96.03 x 0.10 x 45/365 = Rs 1.1839Net amount to be paid = 95.66 + 1.1794 0.4931 = Rs 96.2240Amount receivable against the futures contract sold = Rs 96.5000Arbitrage profit = Rs 0.2760




Implied Repo Rate

For no arbitrage: Futures fair price

= Spot price + Cost of financing Accrued interest. The repo rate implied in the futures price is 12.33%

while the actual financing cost is 10%



12.33% 0.1233=45365x

95.660.9890 + 96.02-96.50=

futures for remaining days of Nos365x

Price SpotAIPrice Spot-Price Futures=Rate Repo Implied

+


Underlying Asset For financial futures market the requirement of the

delivery forces the convergence of futures price to spot price.

The futures contract on any long term securities would warrant a delivery of the underlying asset.

Government securities issued at various points of time have different coupon rates and maturities.

Futures exchange would need to identify some government security on which the futures contracts may be traded.

This standardized futures contract on specific security would be notional and not available for delivery.




Deliverable Bonds

While the futures is quoted on a notional asset, the asset actually may not be existing and hence is non-deliverable.

Instead there are many other securities that may be deliverable.

Despite same face/nominal value the YTMs of securities would not be same as these securities issued at different points of times have varying coupon rates and maturities.




Conversion Factor Price of the bonds is dependent upon, interalia, on the

coupon rate and the time remaining for maturity. A bond with higher coupon is worth more than the bond

with lower coupon given all other features of the two bonds same.

For example if the futures contract requires delivery of bond with 6% coupon the seller who chooses to deliver a bond with 8% coupon would need adjustment of price for making the contract good.

The seller who delivers high coupon rate bond needs to be compensated more than the one who chooses to deliver the bond with lower coupon.




Conversion Factor The conversion factors for deliverable bonds are

determined against the standard bond with 6% coupon rate. It is greater than 1.00 when coupon is more than 6% lesser than 1.00 when coupon is less than 6%.

Conversion factor of the deliverable bond is its value relative to the notional bond underlying the futures contract.

Conversion factor for each deliverable security is computed by the exchange prior to maturity of contracts.




Cheapest-To-Deliver Bond

Of the many deliverables the seller has to choose which bond must be delivered.

Not all deliverable bonds would have same value.

The seller would like to deliver the one which costs him the least i.e. identify the cheapest-to-deliver (CTD) bond.

Profit/loss = Invoice amount cost of acquisition = Settlement price x conversion factor

Current market price Chapter 6



Hedging with T-Bond Futures

Hedging principle with futures on T-bonds remains same, i.e. taking opposite position in the futures to that of in the spot market.

One who is long on portfolio would need to go short on futures.

The value of portfolio falls with rise in yields. Risk from rising yield causing portfolio value

to fall can be covered by going short on interest rate futures.




Hedge Ratio To what extent the loss in the value of the portfolio would

be offset by the gains in the futures position depends upon the positions in the futures and portfolio value.

Hedge ratio depends upon the sensitivities of the portfolio and the futures with respect to changes in the interest rates. Where asset underlying the futures contract and cash

position is same the optimal hedge ratio is unity. In case of portfolio of bonds, due to different

sensitivities of the values of the assets underlying the futures contract and those in the cash position the optimal hedge ratio is would not be equal to 1.




Duration of Bond Portfolio Duration of the bond is the measure of sensitivity of its

value with respect to changes in the interest rates. Duration of the bond is computed by dividing the time

weighted cash flows of the bond by its current value.

Modified duration is more accurate measure of sensitivity of bond prices given by:



0

t

PDCF x t D bond, the of Duration =

r/21DMD

and 2m payment annual-semi Forr/m1DMD Duration, Modified

+=

=+

=


Computing Duration

A bond with three years remaining for maturity bearing a semi-annual coupon of 10% is trading at YTM of 12%. Find out the value of the bond, its duration and modified duration.



Period, t 1 2 3 4 5 6 TotalCash flow 5.00 5.00 5.00 5.00 5.00 105.00Present Value at 12%, DCF 4.7170 4.4500 4.1981 3.9605 3.7363 74.0209 95.0827t/2 x DCF 2.3585 4.4500 6.2971 7.9209 9.3407 222.0626 252.4299Value of the Bond 95.0827Duration 2.6548Modified Duration 2.5046


Hedge Ratio

Optimal hedge ratio for position in long term futures depends upon the duration of bonds portfolio and the duration of perceived CTD bond in the futures contract.

The optimal hedge ratio would be one that offsets the changes in the value of the portfolio of bonds. It may be expressed as:Change in value of bond portfolio

= h x Change in value of T-bond futures




Duration Based Hedging

Change in value of bond portfolio, B= Value x rB x Modified duration= B x rB x MDB= B x rB x DB/(1+rB/mB)

Change in the value of CTD bond (Govt Security), G

= Value x rG x Modified duration= G x rG x MDG= G x rG x DG/(1+rG/mG)




Hedge Ratio and Duration

Hedge ratio for portfolio of bonds

Ignoring differences in the coupon payments



Factor Conversion x )/mr(1)/mr(1x

D x r x GD x r x B

Factor Conversion x GB

FB

bondsT on futures of value in Changeportfolio bond of value the in ChangeRatio Hedge

BB

GG

GG

BB

++

=

=

=

=

Factor Conversion x )r(1)r(1x

D x GD x BRatio Hedge

B

G

G

B

++

=


Bond Futures in India Interest Rate Futures Contract Specifications

Underlying10 Year Notional Coupon bearing Government of India (GOI) security.(Notional Coupon 7% with semi annual compounding.)

Tick size Rs 0.0025 Contract trading cycle Four fixed quarterly contracts for entire year ending March, June, September and December.Last trading day Seventh business day preceding the last business day of the delivery month.

SettlementDaily settlement MTM: T + 1 in cashDelivery settlement : In the delivery month i.e. the contract expiry month.

Daily settlement price Closing price or Theoretical price.Mode of settlement Daily Settlement in CashDeliverable Grade Securities GOI securities

Conversion FactorThe conversion factor would be equal to the price of the deliverable security (per rupee of principal) on the first calendar day of the delivery month, to yield 7% with semi-annual compounding

Invoice Price Daily Settlement price times a conversion factor + Accrued InterestSource: www.nseindia.com on August 28, 2009




http://www.nseindia.com/marketinfo/ird/tracker/htms/irf_goilistsec.pdfhttp://www.nseindia.com/marketinfo/ird/tracker/htms/irf_goilistsec.pdfhttp://www.nseindia.com/

Hedging with T-Bond Futures

EXAMPLE A mutual fund is holding bonds worth Rs 5.00 crore.

YTMs in next 3 months are expected to rise. The portfolio of bonds has duration of 6.63 years. Futures contract on notional 10-year, 7% semi-annual Government of India (GoI) security is trading at Rs 104.3425. The cheapest-to-deliver GoI security is expected to have duration of 7.72 years.

How many contracts should the mutual fund trade to hedge against the risk of rising yields? Assume that the YTMs of the CTD bond and the portfolio are same.




Hedging with T-Bond Futures Price in the futures market for bond

with face value of Rs 100 = 104.3425 Value of one futures contract

(Bonds with face value of Rs 2,00,000) = 104.3425 x 2,000 = Rs 2,08,685

Therefore the number of interest rate futures contracts that must be booked:



scontract 206 say 205.7667.72 x 2,08,685

6.63 x 05,00,00,00)r(1)r(1x

D x FD x BRatio Hedge

B

G

G

B

=

=

++

=


CHAPTER 6Interest rate Forwards and FUTURESINTEREST RATE FORWARDS AND FUTURESInterest Rate DerivativesFORWARD RATE AGREEMENTForward Rate AgreementBorrowers FRAInvestors FRASettlement of FRAPricing FRAHedging with FRAHedging Rising Interest RatesHedging Rising Interest RatesHedging Rising Interest RatesHedging Falling Interest RatesSpeculation with FRAFUTURES ON T - BILLSFutures on T - BillsWhy Futures on T-BillsPricing T-BillsQuoting T-Bills FuturesQuoting T-Bills FuturesHedging with T-Bills FuturesHedge Against Falling YieldsHedge Falling Yield - ExampleHedge Falling Yield - ExampleHedging Rising Interest CostSpeculation : T-Bill FuturesArbitrage : T-Bill FuturesImplied Repo RateComputing Implied Repo RateArbitrage : T-Bills FuturesEURO DOLLAR FUTURESEurodollarsFutures on EurodollarEurodollar & T-Bill FuturesActual and Discount YieldPricing of Eurodollar FuturesSettlement: Eurodollar FuturesHedging : Eurodollar FuturesHedging StrategyHedging OutcomeHedging OutcomeTREASURY BOND FUTURESTreasury Bond FuturesPricing Treasury BondsFutures on T-BondsPricing T-Bond FuturesFair Price of T-Bond FuturesImplied Repo RateUnderlying AssetDeliverable BondsConversion FactorConversion FactorCheapest-To-Deliver BondHedging with T-Bond FuturesHedge RatioDuration of Bond PortfolioComputing DurationHedge RatioDuration Based HedgingHedge Ratio and DurationBond Futures in India Hedging with T-Bond FuturesHedging with T-Bond Futures

750 840003 rm rjs v interest rate forwards and futures

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