Commerce 4FJ3

Fixed Income Analysis

Week 10

Interest Rate Futures

2

Forward Contracts

• Any contract that legally binds two parties to engage in a specific transaction at some point in the future at a pre-specified price is a forward contract

• Can be negotiated individually

• Not usually transferable

• Subject to counterparty risk

3

Forward Payoff

• A forward contract does not have a direct payoff, the transaction that was negotiated takes place

• Implied payoff or cost; the company has agreed to sell a bond forward for $1,160 and the bond is selling at $1,200 at the time of delivery, there is an opportunity cost of $40

4

Futures

• Similar to a forward contract in the fact that it binds both parties to a specific transaction in the future… but– A futures contract is standardized with respect

to the quantity, quality, time, and location– Contracts are traded on organized exchanges– No specific link between the buyer and seller– Gains or losses are realized on a daily basis

5

Futures Trading

• When a futures contract is traded on an exchange the price is recorded as well as the identities of the two parties

• The link between buyer and seller is broken

• The buyer now has a contract to buy the asset from the clearinghouse and the seller has a contract to sell to the clearinghouse

6

Futures Trading

• If either party takes the opposite position later that position is netted against their previous contract and their position is reversed or closed out

• A trader that sells an asset is said to be short in that asset while a buyer is referred to as long in the asset

7

Delivery

• If a contract is held to maturity (less than 1% on average are), the clearinghouse matches buyers and sellers based on their stated preferences for delivery options and informs each party of the delivery details

• Often closed out before maturity to allow the investor to set their own details

8

Marking to Market

• To protect against the credit risk, futures contracts are marked to market at the end of each trading day

• This rewrites the contract so that the price is set to the settlement price and any gain or loss is paid in cash

• The settlement price is usually the closing price of that contract but may differ if a contract has very low volume

9

Marking to Market Example

• You enter a futures contract to buy a bond issued by XYZ for $95.20/$100 face value

• The settlement price is $95.00 (FV=$1,000)– your contract is rewritten to buying at $95.00– you must pay the difference of $2.00 to the

clearinghouse

• The next day price rise to $95.75 you will be paid $7.50 by the clearinghouse

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Reason for Marking to Market

• Marking to market significantly reduces the counter-party risk (one party being unable or unwilling to fulfil their obligations)

• To be able to meet the marking to market requirements investors are required to maintain a margin account

• Margin requirements are typically 5-10%

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Margins

• Initial margin: how much you must deposit when you open a position

• Maintenance margin: the lowest level that your margin account can fall to before you are required to deposit more

• Variation margin: the amount that you must deposit within 24 hours or your position will be closed out

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Leverage

• Consider two investment options– buy 1 bond for $1,000, cost = $1,000– enter futures contracts for $20,000 face value of

those bonds, initial margin = $1,000

• Return if price rises to $1,025– $25 increase in market value: 2.5% return– $500 net marking to market: 50% return

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Use of Leverage

• Can be used by speculators

• Can be used to offset price risk– A portfolio has a potential large loss if interest

rates increase– The portfolio can be rebalanced to reduce the

price risk, at the cost of transaction costs– Selling a few bond futures could generate large

profits if interest rates increase

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Currently Traded Contracts

• A few of the most traded contracts are– US T-Bill futures– Eurodollar CD futures– US treasury bond futures– US treasury note futures– US agency note futures– CBOT 10-year municipal note index futures

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US T-Bill futures

• Traded on the International Money Market of the Chicago Mercantile Exchange (IMM)

• Underlying asset is a US T-bill with a face value of $1,000,000 and a maturity of 13 weeks (typically 91 days) from the delivery date

• The delivered T-bill can either be newly issued or seasoned

• Delivery dates are synchronized with regularly scheduled T-bill auctions

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Quoted Yields

• T-bills are quoted on the annualized yield on a bank discount basis

360

360

tFYD

tF

DY

d

d

maturity toDays

valueFace

discountDollar

decimal a as yield Annual

t

F

D

Yd

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T-Bill Futures Prices

• Quoted on an index basisindex price = 100 - (Yd x 100)

• Given a current quote of 3.75% for T-bills index price = 100 - (3.75) = $96.25

• Given a futures price of $92.50 the yield is

%5.7075.0100

50.92100

100

priceindex 100

dY

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Invoice Price

• This is how much is paid for the t-bill if it is delivered

• Invoice price = $1,000,000 - D

• Find the invoice price if the final settlement price is $92.50

67.041,981000,000,1$

33.958,18$360

91000,000,1$075.0

DInvoice

D

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Price of a Basis Point

• The change in price of the underlying bond for a change of one basis point is: 0.0001 x $1,000,000 x 91/360 = $25.28

• Market participants often refer to the value of a basis point as $25 in spite of the fact that the typical T-Bill has a maturity of 91 days

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Eurodollar CD Futures

• Traded on both the IMM of the Chicago Mercantile Exchange, and the London International Financial Futures Exchange

• Debt obligation tied to foreign banks instead of US treasury

• Discount is based LIBOR, London interbank offered rate

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Eurodollar Futures

• Also $1,000,000 face value and quoted on an index basis, but standardized at 90 days

• Value of a basis point = $25

• Cash settlement contract, no delivery if held to maturity, parties settle in cash

25$360

900001.0000,000,1$

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Treasury Bond Futures

• Underlying asset; hypothetical $100,000 face value, 20-year, 6% coupon bond

• Physical settle; The CME Group allows the seller to deliver one of several Treasury bonds that the CME Group declares is acceptable for delivery, with adjustments– List is printed before trading begins

Exhibit 26-1 Treasury Bonds Acceptable for Delivery and Conversion Factors

CouponMaturityDate

Mar.2011

Jun.2011

Sep.2011

Dec.2011

Mar.2012

Jun.2012

Sep.2012

Dec.2012

Mar.2013

6 3/4 08/15/26 1.0741 1.0735 ----- ----- ----- ----- ----- ----- -----

6 1/2 11/15/26 1.0500 1.0494 1.0490 ----- ----- ----- ----- ----- -----

6 5/8 02/15/27 1.0630 1.0625 1.0618 1.0613 ----- ----- ----- ----- -----

6 3/8 08/15/27 1.0385 1.0382 1.0377 1.0375 1.0370 1.0368 ----- ----- -----

6 1/8 11/15/27 1.0130 1.0127 1.0127 1.0125 1.0125 1.0123 1.0123 ----- -----

5 1/2 08/15/28 0.9466 0.9472 0.9475 0.9481 0.9485 0.9490 0.9494 0.9500 0.9504

5 1/4 11/15/28 0.9194 0.9200 0.9208 0.9213 0.9221 0.9227 0.9235 0.9242 0.9250

5 1/4 02/15/29 0.9187 0.9194 0.9200 0.9208 0.9213 0.9221 0.9227 0.9235 0.9242

6 1/8 08/15/29 1.0136 1.0136 1.0134 1.0134 1.0132 1.0132 1.0130 1.0130 1.0127

6 1/4 05/15/30 1.0281 1.0278 1.0277 1.0274 1.0273 1.0270 1.0269 1.0265 1.0264

5 3/8 02/15/31 0.9281 0.9287 0.9291 0.9297 0.9301 0.9307 0.9311 0.9318 0.9322

4 1/2 02/15/36 0.8078 0.8087 0.8095 0.8105 0.8113 0.8123 0.8132 0.8142 0.8151

4 3/4 02/15/37 ----- ----- ----- ----- 0.8398 0.8406 0.8413 0.8421 0.8427

5 02/15/37 ----- ----- ----- ----- ----- 0.8718 0.8725 0.8730 0.8737

4 3/8 02/15/38 ----- ----- ----- ----- ----- ----- ----- ----- 0.7918

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Treasury Bond Futures Details

• Price quoted per $100 of face value

• Price quoted in $1/3296-13 means $(96 + 13/32) = $96.40625

• Invoice price = Contract size (face value) x settlement price x conversion factor + accrued interest

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Treasury Bond Delivery Example

• Settlement price = $102-12

• Conversion factor of delivered bond = 1.157

• Invoice price = 100,000 x 102.375 x 1.157 + accrued interest = $118,447.88 + accrued interest

• The buyer does not know the exact price they have to pay until the bond is delivered

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Treasury Bond Delivery Options

• The seller has a few options when actually delivering the bond– Quality option (swap option): can deliver one

of the listed acceptable bonds– Timing option: can deliver on any day of the

contract delivery month– Wild card option: notice of intent to deliver,

must be given 1 day in advance, as late as 8:00 p.m. Chicago time

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1Cost

Invoice 365

t

Cheapest to Deliver

• Given a choice sellers will want to figure out which issue is the cheapest to deliver

• Face value of issue is set at $100,000 but actual price is affected by conversion ratio

• Find implied repo rate

• Highest repo rate is the cheapest to deliver

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US Treasury Note Futures

• 2, 5, and 10 year maturity contracts

• Underlying asset; $100,000 face value or $200,000 for 2 year, 6% coupon rate

• Smaller basket of acceptable bonds available due to more restrictive definitions of an acceptable issue

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US Agency Note Futures

• Traded on CBOT and CME (2006)

• Underlying asset is $100,000 debenture from either Fannie Mae or Freddie Mac

• Both exchanges have 5 & 10 year maturities

• Coupon rate: 6% on CBOT, 6.5% on CME

30

Municipal Index Futures

• CBOT 10-year municipal note index futures

• Mentioned on page 596, 8th Edition

• Underlying asset; a basket of up to 250 municipal bonds which meet certain rules, 10-40 years remaining maturity, coupon rate between 3% and 9%, etc.

• Cash settlement contract

31

Pricing of Futures Contracts

• Theoretical model based on carry cost pricing and arbitrage arguments

• Tactic:– buy the underlying asset using borrowed funds– enter a futures contract to fix the selling price– sell at delivery date and repay the loan– if money can be made, there will be excess

demand for the bond and supply of the future

32

Cash and Carry Trade Example

• 20-year, 12% coupon par bond, borrowing rate of 8%, futures price of $107 for delivery in 3 months– No cost to establish: borrow to buy bond– Invoice price = $107 + 3 (accrued interest)– Bank loan = $100 + 2 (interest)– Net profit = 110 - 102 = $8 per $100 of face

33

Theoretical Price

• Assuming short sales, we can also do the reverse, so we can get a theoretical price

• profit = 0 = proceeds - outlay• F = P(1 + t(r - c))

F = futures price P = Current bond pricet = time to deliveryr = financing costc = current yield on underlying bond

• (r - c) called cost of carry

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Theoretical Price Problems

• Interim cash flows from marking to market make the strategy risky

• Financing rate; borrowing and lending rates may be different

• Multiple issues may be deliverable• Delivery date unknown• Underlying may be a basket of bonds,

tracking error may result

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Adjusted Model

• The simple model may be adjusted to handle some of those problems

• P(1 + t(rb - c)) ≥ F ≥ P(1 + t(rl - c))to account for different rates

• F = P(1 + t(r - c)) - delivery optionsto account for delivery options

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Bond Portfolio Management

• The bond portfolio manager can use future contracts to:– Speculate on the movement of interest rates– Control the interest risk of a portfolio– Create synthetic securities for yield

enhancement– Create a temporary substitute for rebalancing or

switching from bonds to stocks

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Controlling the Duration of a Portfolio

• Instead of rebalancing a manager can use futures to match duration

• The contract size and duration must be known to find the hedge ratioDollar duration = Duration x $value of portfolio

portfolio target dollar duration portfolio current dollar durationdollar duration of futures contract

Hedging

• Hedging is nothing more than a special case of interest rate risk management where the target duration is zero

• In hedging an individual bond position with futures, the hedger is taking a futures position as a temporary substitute for transactions to be made in the cash market at a later date

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Hedging Risks

• The difference between the cash price and the futures price is the basis. The risk that the basis will change in an unpredictable way is called basis risk

• Typically, the bond to be hedged is not identical to the bond underlying the futures contract. This type of hedging is referred to as cross hedging

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Bonds vs. Stocks

• A pension fund manager wanting to change the allocation between stocks and bonds can:– Buy bonds and sell stocks– Use interest-rate futures and stock index futures

• transactions costs are lower

• market impact costs are avoided or reduced

• activities of the portfolio managers employed by the pension fund manager are not disrupted