using interest rate futures with index futures

8/14/2019 Using Interest Rate Futures With Index Futures

1/8

RESEARCH AND pRoDuCt DEVELopMENt

Imrving Eqiy Index Fres

tracking and perfrmancewih Ineres Rae Fres

By Richard Co, Research and Product Development

May 2008


2/8

The valuation o any equity index utures contract requires consideration

o the interest rate environment. Portolio managers who neglect this may

be met with unwelcome tracking errors, which arise naturally rom the

interaction o short-term interest rate movements with daily marks-to-

market on utures.

One can bring these tracking errors under control through judicious use o

interest rate utures. This document reviews various strategies or doing so.

The discussion is organized into ve parts: Part one outlines how interest

rate movements generate tracking errors that may undermine equity

utures perormance. Parts two and three explore how CME Group 30-day

Fed Funds rate (FF) utures and Eurodollar (ED) utures, respectively,

may be used to control this source o risk or, alternatively, to exploit it as a

potential source o incremental return. Part our considers combinations

o FF and ED utures. Part ve measures the added transaction costs that

a user would incur by combining interest rate utures with a core equity

index utures position.

par I: tracking Errrs De Shr Rae Mvemens

Consider January 2008. Countering a sharp deterioration in credit market

conditions, the FOMC made an ad hoc cut o 75 basis points (bps) in

its ed unds rate target, ollowed by another reduction o 50 bps at its

ensuing regularly scheduled meeting. Tracking errors due to interest

rate movements were severe, as evidenced by Exhibit 1, which compares

perormance o an S&P 500 cash portolio and a synthetic portolio built

with S&P 500 Index utures over the course o the month.

EXHIBIt 1:

S&P 500 Index: CME Group futures vs. cash, Jan 08.

(See footnote 1 for details of Total Return calculation.)

Dec 31 07 Jan 31 08priceRern

talRern1

S&p 500

Futures 1477.20 1379.60 -6.61% -6.27%

Cash Index 1468.36 1378.55 -6.12% -6.00%

Futures Premium 8.84 1.05

Finance Rae 4.648% 3.174%

The drop in interest rates a total o 147 bps rom the beginning o the

month to the end o the month drove a wedge o 27 bps per annum

between the total return on the synthetic portolio and the total return

on the cash portolio. This dierential maniests as an unexpectedly rapid

erosion in the cash-utures price premium.

Suppose the cash component o the synthetic utures structure had been

invested so as to earn a suitable money market interest rate over the term

until utures expiration. The drop in interest rates would have generatedgains which, in turn, would have closed the perormance gap between the

synthetic utures portolio and the cash portolio.

Combining a long position in equity index utures with a money market

instrument paying the overnight interest rate eectively amounts to the

ollowing:

Lng Eqiy Index Fres

ReceiveperformanceofIndex

Payxedinterestrateonnotionalvalue

Mney Marke Insrmen

Receiveovernightrateonnotionalvalue

Commitnotionalvalueincash

This set up makes the synthetic portolio managers problem easy to spot.

The objective is to commit cash and receive the perormance o the Index

via S&P 500 Index utures. Implicit in this synthetic structure is a notional

position in an overnight index swap (OIS) that pays xed interest or the

interval until utures expiry and receives oating interest. Regardless

o whether this notional OIS produces a avorable outcome, it is an

unintended eature o the synthetic portolios structure, and thereore an

unintended source o risk. The challenge is to nd the means to control it.

cmegroup.com

This article discusses

how to maximize returns

onanequityindexfutures

strategybyusinginterest

rate futures to reduce

trackingerrorsfrom

short-rate movements.


3/8

TheFFfuturespositionwouldhaveearned$88,166.67.Thisis

approximately17.6bpsperannumon$50millionnotionalvalue,

enough to narrow the overall total return shortall (Exhibit 1,

right-hand column) to within 10 bps.

The147bpsdropintheovernightnancingrateaccounteddirectly

or around 20 bps o the total 27 bps tracking error between the cash

portolio and the synthetic utures structure. I we use this as the basis

o comparison (instead o the ull 27 bps dierential between cashtotalreturnandfuturestotalreturn),thenthe17.6bpsgainontheFF

utures hedge would have reduced the pertinent portion o the tracking

error to just 2.4 bps.

Basisriskexplainsmuchofthe2.4bpsresidual.InlateDecember2007

FFfuturesimpliedanaverageovernightratearound4.063percent

or the period ending with the equity index utures expiry. At the same

time, the implied term nancing rate or S&P 500 Index utures was

4.648percent,58.5bpshigher.BytheendofJanuary2008,thespread

betweenthesetworateshadnarrowedto29.6bps.Inotherwords,

the spread between the hedge (the FF contract rate) and the hedge

object (the implied nancing rate) shited by 29 bps over the course

o the month.

EXHIBIt 2:

UsingFFfuturestolayoriskfortheembeddedOIS.

Dec 31 07 Jan 31 08

FF Fres price

Jan 08 95.840 96.065

Feb08 95.980 97.045

Mar 08 96.065 97.245

Imlied Rae 4.063 2.878

Finance Rae 4.648 3.174

Rae Sread 58.5 29.6

ImprovingEquityIndexFuturesTrackingandPerformancewithInterestRateFuture

par II: Fed Fnds Fres as an oIS Srrgae

CME Group Fed Funds utures2 have a monthly listing/expiry cycle. Each

contract reerences the calendar-month average o the eective overnight

ederal unds rate during the contracts named expiry month. The pricing

convention is 100-minus-rate, where rate is the average ed unds rate

during the contract expiry month. Thus, an unexpected decrease in the ed

unds rate or the contract expiry month takes the orm o an increase in

the utures contract price, and vice versa. Each contract has a notional value

ofapproximately$5million.Accordingly,eachonebpmoveinthecontract

referencerateisworth$41.67($5,000,000x0.0001x30/360).

Strips o FF utures are ideally suited or controlling the xed-rate component

o the notional OIS embedded in the synthetic equity index portolio.

Continuingwiththepreviousexample,considera$50millionnotional-value

position in Mar 08 S&P 500 Index utures on December 31, 2007. These

contracts expired on March 20, 2008. To lay o the notional xed-rate

nancing exposure embedded in the synthetic portolio, one could have

purchased a properly sized strip o Jan 08, Feb 08 and Mar 08 FF utures:

FF Cnrac NmberExiry Mnhs f Cnracs

Jan 08 10

Feb08 10

Mar 08 7

Note that the Mar 08 component o the strip must be scaled down so that

the basis point value o the hedge matches the interest rate sensitivity o the

xed-rate leg o the notional OIS3.

Exhibit 2 shows FF utures month-end settlement prices or Dec 07 and

Jan 08. Not surprisingly, FF utures prices rose sharply over this interval.

When applied to the FF utures strip specied earlier, these price gains

would have oset much o the interest-rate related erosion in the S&P 500cash-utures spread shown in Exhibit 1.


4/8

cmegroup.com

This hedging strategy is static.4 At the end o the month, the Jan 08

FF contracts expire5, leaving the outstanding Feb 08 and Mar 08

contracts in place. Within the month o January, a Jan 08 FF contract

can be viewed as consisting o two parts: One reecting the month-

to-date path o realized values o the eective ed unds rate, the other

reecting market expectations or the balance o the month. Because

the FF contract settles to the arithmetic average o overnight rates

over the entire month, the inuence o the second anticipative partgradually shrinks. This means that, even i the hedge position had

been initiated during the month o January, the number o Jan 08 FF

contracts would not need to be reduced (unlike the scaling that is

required or the Mar 08 component o the strip).

By way o caveat, it bears repeating that the spread between the FF

utures contract rate and the nancing rate implied by the equity index

utures calendar spread can, on occasion, eature enough volatility

to blunt the eectiveness o the FF hedge. With this in mind, the

practitioner should always take account o the extent to which basis risk

could undermine the perormance o the FF utures hedge.

par III: Erdllar Fres and Calendar Sreads

Rather than ocus on reducing tracking error due to unwanted interest

rate exposure, one might instead greet this exposure as a potential source

o extra alpha. For equity portolio managers who are also close students

o the money market, a potentially ruitul approach is to trade the equity

nancing rate implied in the quarterly calendar spread in equity index

utures.

One can view this implied nancing rate as the sum o two components:

(i) the corresponding three-month LIBOR, and (ii) the spread between

three-month LIBOR and the implied nancing rate. For market participants

who conne themselves to trading only equity index utures calendar

spreads, these two components are inextricably linked. By contrast,

those who are willing to add an ED utures overlay can isolate the spread

component a distinct advantage insoar as the spread component

requently emerges as a source o trading opportunities.

The most obvious time to spot such opportunities, and to exploit them,

is during the quarterly roll, when trafc in equity index utures calendar

spreads is naturally quite high. For example, an investor holding a long

position in Mar S&P 500 Index utures who wants to maintain her long

exposure into the next utures expiry would do so by buying the Mar-Jun

calendar spread (i.e., by selling Mar utures and buying Jun utures). By

taking a position in this utures calendar spread, either long or short, she

Thespreadcomponentfrequently

emergesasasourceoftrading

opportunitiesparticularlyduring

thequarterlyrollperiod.

implicitly takes a view on the rate at which market participants can nance

a notional S&P 500 Equity portolio or the three-month interval between

utures expiries. To the extent that this is either a low priority or a matter o

indierence to many equity index investment managers, a det speculator

can prot by taking the other side o the trade.

Exhibit 3 illustrates this point by comparing intra-day movements in

the nancing rate implied by calendar spreads in E-mini S&P 500 Index

utures during the Mar-Jun 08 roll against intra-day movements in various

Eurodollar (ED) utures contract rates. Three eatures warrant mention:

Throughouttherollperiod,theshort-terminterestratecurvewas

inverted. Rates implied by Mar 08 ED utures were higher than those

implied by Apr 08 ED utures. (note that Mar 08 ED utures expired on

March 17, 2008)

RollingalongpositioninE-miniS&P500Indexfuturesentaileda

simultaneous sale o Mar 08 contracts and purchase o Jun08 contracts

As noted above, the long utures position implicitly extends the

notional equity portolio exposure or three months, at an implied

nancing rate that spans the term between utures expiry dates. This

interval sits between the three-month periods reerenced by Mar 08

and Apr 08 ED contracts. Not surprisingly, the implied nancing rate

tends to be bracketed by the Mar 08 and Apr 08 ED contract rates.

Exhibit3revealsconsiderablemovementinthespreadbetweenthe

implied nancing rate and ED contract rates. On volatile days, the

spreads range approaches 10 bps.

Against this backdrop, consider an example in which you are approaching

a quarterly roll with a 100-contract long position in the nearby E-mini

S&P 500 Index utures. Assume moreover that you intend to roll this

position into the deerred utures. As already noted, the calendar spread

between the expiring contract and the deerred contract incorporates an

assumption that you are paying a xed nancing rate over the three-month


5/8

Consectetuer adipiscing elit

morbi posuere elis euerat etiam lectus massa iacu-

lis in ultrices a, convallis id,

tortor. Quisque convallis

libero nec arcu.

ImprovingEquityIndexFuturesTrackingandPerformancewithInterestRateFutures

2.90

2.80

2.70

2.60

2.50

2.40

2.30

2.20

2.10

2.00

3/10/08 3/11/08 3/12/08 3/13/08 3/14/08 3/17/08 3/18/08 3/19/08

CalendarSpreadImpliedRates/EurodollarFutures

FOMC

Implied

EDH8

EDJ8

EDK8

EXHIBIt 3:

TheMar-Jun08Roll:FinancingratesimpliedinE-miniS&P500Indexfuturescalendarspreadsvs.Eurodollarfuturescontractrates.Notethattherollperiodendedonedayearlierthaniscustomary,duetotheGoodFridaymarketholiday.

interval between utures expiry dates. To lay o the LIBOR component o

this nancing rate (and thereby to isolate the spread), you would buy ED

utures. To determine the appropriate scale o the ED utures position, rst

compute the dollar value o a 1 bp move in the implied nancing rate or

100 E-mini S&P 500 utures calendar spreads:

NotionalValuex0.0001x90/360or,morespecically,

100x$50xLeadFuturesPricex0.0001x(90/360)

Thus, or example, i the nearby utures price is 1400, each 1 bp move

intheimpliednancingrateisworth$175.6 Because ED utures7 have a

constantbasispointvalueof$25,thesizeofthelongEDfuturespositionis

7contracts=$175/$25.

To make protable opportunistic use o this combination, you would buy

the calendar spread in equity index utures and buy ED utures when

the implied nancing rate is low relative to the ED utures contract rate.

Conversely, you would unwind the ED utures position whenever the

nancing rate implied in your equity index utures calendar spread is high

relative to the ED utures contract rate.

In theory, the order o execution does not matter. For example, nothing

prevents you rom opportunistically locking in the ED contract rate rst, then

locking in the equity index nancing rate (by buying the equity index utures

calendar spread) later. In practice, however, the utures expiry calendar

constrains your choice o timing. Given that ED utures expire on the Monday

prior to the third Wednesday o the month, while S&P 500 Index utures

expire on the third Friday o the month, the expiring ED utures tend to

cease trading earlier than the expiring equity index utures.8 Thus, i you use

ED utures with the same expiry month as the nearby leg o the equity index

utures calendar spread, your exibility in timing would typically be conned

to the rst week o the quarterly roll (as Exhibit 3 illustrates).

You can loosen this constraint by using an ED contract with a later expiry

say, Apr 08 instead o Mar 08 in this example. The cost o doing so,

however, may be less liquidity. ED utures with standard quarterly expiries

(i.e., Mar, Jun, Sep or Dec) tend to trade more deeply than contracts with

serial expiries. Given this, you would need to assess (among other things)

whether your ED position is so large as to make these dierences in

liquidity a material concern.


6/8

FF Cnrac NmberExiry Mnhs f Cnracs

Mar 089 3

Apr 08 10

May08 10

Jun 08 7

Recall that we are assuming the notional portolio positions to be

collateralized ully in money market instruments paying the overnight

interest rate. Thus, we care relatively less about the precise level at which

the FF utures strip is booked.

Far more important is the spread between FF and ED contract rates. The

usual rule o thumb applies: Buy the spread when it is cheap. Exhibit 4

shows the FF-ED spread or the rst two weeks in March 2008. With

interest rates as volatile as they have been in recent months, this spread

is capable o swinging 15 bps during the roll enough to make ample

opportunity or alpha pick-up.

Here too, the sequence by which one legs into this spread does not matter.

You might sell the equity index utures calendar spread rst, then sell the

FF-ED spread, or vice versa. The objective is to stitch the trade together as

cheaply as possible.

par IV: Crssing over frm ED FF

Recall that the synthetic investment strategy achieves equity market

exposure via equity index utures while earning the overnight interest rate

on investors cash. As noted on page one, a crucial eature o the strategy is

that it embeds an implicit overnight equity index swap in which the portolio

pays a xed rate, via the term equity nancing rate, while receiving a oating

rate. This suggests another approach to picking up incremental alpha, in

which the core equity index utures position is augmented by the FF-ED

spread that lays o both legs o the embedded OIS.

Thus, returning to the earlier Mar-Jun roll example, assume you plan to roll

$50millionnotionalofS&P500Indexfutures.ThecompanionEDfutures

position would be long 50 contracts. Suppose that you incorporate an

appropriately scaled FF utures strip covering the interval between Mar08

and Jun08 Index utures expiries. Its conguration would be as shown on

page six. Importantly, the dollar value o a 1 bp change in money market

interest rates is identical or both legs o the spread. For ED, (50 contracts)

x($25perbppercontract)=$,1250.ForFF,(30contracts)x($41.67per

bppercontract)=$,1250.Thus,thisinterestratefuturesspreadexactly

replicates the spread between overnight ed unds and three-month LIBOR

or the targeted time interval.

76

74

72

70

68

66

64

62

60

58

56

54

3/3/08 3/4/08 3/5/08 3/6/08 3/7/08 3/10/08 3/11/08 3/12/08 3/13/08 3/14/08

Fed

Fund/Eu

rodollarSpread

(bps)

EXHIBIt 4:

Intra-daygraphofthespreadbetweentheFFfuturesstripandMar08EDfutures.


7/8

Fr mre infrmain ab CME Gr Eqiy rdcsvisi www.cmegr.cm/eqiies.

Written by Richard Co, Research & Product Development, CME Group. You can contact the author at [email protected] or 312-930-3227.

1 For the cash index, the total return calculation assumes that the ex-dividend amount is added at the end o the month. For utures, total return assumes the ull notional value is invested at theeective overnight ederal unds rate throughout the month.

2 For a complete description o the terms and conditions o 30-Day Federal Funds utures, please visit www.cmegroup.com.

3 Because o the S&P 500 Index utures in this example expire on March 20, 2008, a 1 bp move in the average interest rate level in March would exert impact or only 20/31 o the month. Thus, oneshould scale back the number o Mar 08 FF utures to two-thirds o portolio notional value in this case 7 contracts instead o 10. Note that this step hinges on the correlation amongst the ratesthroughout the month.

4 Certainly, i gains or losses on the stock index were so large as to change signicantly the notional value o the position, then the size o the FF utures hedge position might require adjustment.

5 More precisely, the contract is marked to the nal settlement price on the rst business day o the next calendar month, due to the timing o the publication o eective overnight ed unds rate data.

6 Tokeepthingssimple,weassume90daysbetweenindexfuturesexpirydates.Foralargeposition,anactualdaycountwouldusefullyimprovetheprecisionofthecalculation.

7 For a complete description o terms and conditions or Eurodollar utures, please visit www.cmegroup.com.

8 For equity index utures and ED utures that expire in the same month, a little calendar arithmetic reveals that Index utures expire earlier in approximately 28 out o every 100 cases.

9 As beore, the odd amounts in the Mar 08 and Jun 08 contracts reect the portions o those months covered by the time span between Mar 08 and Jun 08 equity index utures expiries: Roughly thelast third o March and the rst two thirds o June.

10 RecallthatthebasispointvalueofanE-miniS&P500calendarspreadis$1.75=$50xLeadFuturesPricex0.0001x90/360,wheretheleadfuturesarepricedat1400.Thetickincrementinthe

spreadis0.05indexpoint,or$50x0.05=$2.50.Assumingaone-tickmarket,thebid/askspreadisequivalentto$2.50/$1.75=1.43basispoints,expressedinimpliednancerateterms.

par V: Execin Css

Aside rom the extra commission charges, the equity investor considering

these interest rate overlays should take account o slippage costs.

Fortunately, the interest rate utures involved in these strategies are very

liquid. During the equity index utures roll month, the applicable ED

utures typically eatures a bid/ask spread o bp. Given that the same ED

utures would be bought and sold in two separate trades, the cost o entry

and exit would be the entire bid/ask spread o bp. FF utures trade in

increments o bp. Since these positions are put on and held until expiry,

however it would be hal the bid/ask spread, or bp. The combined cost or

both legs o the spread would be bp, plus brokerage.

To put this in perspective, the typical bid/ask spread in the S&P 500 Index

utures calendar spread is 0.05 index points, equivalent to 1.43 bps10,

making entry costs or a buy and hold equal to approximately bp. That

is, the slippage cost or the interest rate overlay would be less than the

hal spread that one would spend in entry cost on the equity index utures

calendar spread itsel. Given the potential or alpha pick-up, this might be

money well spent.

Alternatively, the trade could be structured in simpler orm, by spreading

the equity index utures calendar spread directly against the weighted

FF utures strip. This would save bp in bid/ask spread costs plus the

commission on the ED utures leg. The expiration schedule o the ED

utures would no longer enter as a source o intererence. The downsidewould be the merging o the two rate spread opportunities.

Cnclsin

The interest rate risks identied above are embedded in equity index

utures and in equity index utures calendar spreads, regardless o whethermarket participants choose to address them explicitly. The tools presented

here enable the practitioner to disassemble the interest rate risk into its

various components and then to address each individually.

Lets grant that the oregoing examples are drawn rom a period o

extraordinary volatility in both money market interest rates and in the

spread relationships among them. Nevertheless, the basic motivation and

structure o the strategies presented here remain valid in calmer waters. In

nearly all seasons, judicious application should improve the tracking and

perormance o standard equity index utures strategies.

Innearlyallenvironments,judicious

application of interest rate futures

shouldimprovetrackingand

performanceofequityindexfutures.


8/8

EQ196/700/0808

CME Group hE adquartErs

20SouthWackerDrive

Chicago,Illinois60606

cmegroup.com

CME Group Global offiCEs

Ccg

312 930 1000

[email protected]

syney

61 2 9231 7475

[email protected]

hng Kng

852 31017696

[email protected]

tky

81 3 5403 4828

[email protected]

lnn

44 20 7796 7100

[email protected]

Wngn d.C.

312 930 1000

[email protected]

CME Group,theGlobeLogo,CME, E-miniandGlobexaretrademarksofChicagoMercantileExchangeInc.S&P500isatrademarkofTheMcGraw-HillCompanies,Inc.

Copyright2008CMEGroup.Allrightsreserved.

using interest rate futures with index futures

Documents