Using Interest Rate Futures With Index Futures

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Improving Equity Index Futures tracking and performance with Interest Rate Futures
By Richard Co, Research and Product Development May 2008

This article discusses how to maximize returns on an equity index futures strategy by using interest rate futures to reduce tracking errors from short-rate movements.

The drop in interest rates – a total of 147 bps from the beginning of the month to the end of the month – drove a wedge of 27 bps per annum between the total return on the synthetic portfolio and the total return on the cash portfolio. This differential manifests as an unexpectedly rapid erosion in the cash-futures price premium.
EXHIBIt 1: S&P 500 Index: CME Group futures vs. cash, Jan 08.
Dec 31 07 S&p 500 … Futures … Cash Index … Futures Premium Finance Rate 1477.20 1468.36 8.84 4.648% 1379.60 1378.55 1.05 3.174% -6.61% -6.12% -6.27% -6.00% Jan 31 08 price Return total Return1

The valuation of any equity index futures contract requires consideration of the interest rate environment. Portfolio managers who neglect this may be met with unwelcome tracking errors, which arise naturally from the interaction of short-term interest rate movements with daily marks-tomarket on futures. One can bring these tracking errors under control through judicious use of interest rate futures. This document reviews various strategies for doing so. The discussion is organized into five parts: Part one outlines how interest rate movements generate tracking errors that may undermine equity futures performance. Parts two and three explore how CME Group 30-day Fed Funds rate (FF) futures and Eurodollar (ED) futures, respectively, may be used to control this source of risk or, alternatively, to exploit it as a potential source of incremental return. Part four considers combinations of FF and ED futures. Part five measures the added transaction costs that a user would incur by combining interest rate futures with a core equity index futures position. part I: tracking Errors Due to Short Rate Movements Consider January 2008. Countering a sharp deterioration in credit market conditions, the FOMC made an ad hoc cut of 75 basis points (bps) in its fed funds rate target, followed by another reduction of 50 bps at its ensuing regularly scheduled meeting. Tracking errors due to interest rate movements were severe, as evidenced by Exhibit 1, which compares performance of an S&P 500 cash portfolio and a synthetic portfolio built with S&P 500 Index futures over the course of the month.

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

Suppose the cash component of the synthetic futures structure had been invested so as to earn a suitable money market interest rate over the term until futures expiration. The drop in interest rates would have generated gains which, in turn, would have closed the performance gap between the synthetic futures portfolio and the cash portfolio. Combining a long position in equity index futures with a money market instrument paying the overnight interest rate effectively amounts to the following:
Long Equity Index Futures • Receive performance of Index • Pay fixed interest rate on notional value Money Market Instrument • Receive overnight rate on notional value • Commit notional value in cash

This set up makes the synthetic portfolio manager’s problem easy to spot. The objective is to commit cash and receive the performance of the Index via S&P 500 Index futures. Implicit in this synthetic structure is a notional position in an overnight index swap (OIS) that pays fixed interest for the interval until futures expiry and receives floating interest. Regardless of whether this notional OIS produces a favorable outcome, it is an unintended feature of the synthetic portfolio’s structure, and therefore an unintended source of risk. The challenge is to find the means to control it.

Improving Equity Index Futures Tracking and Performance with Interest Rate Futures

part II: Fed Funds Futures as an oIS Surrogate CME Group Fed Funds futures2 have a monthly listing/expiry cycle. Each contract references the calendar-month average of the effective overnight federal funds rate during the contract’s named expiry month. The pricing convention is 100-minus-rate, where “rate” is the average fed funds rate during the contract expiry month. Thus, an unexpected decrease in the fed funds rate for the contract expiry month takes the form of an increase in the futures contract price, and vice versa. Each contract has a notional value of approximately $5 million. Accordingly, each one bp move in the contract reference rate is worth $41.67 ( ≈ $5,000,000 x 0.0001 x 30/360). Strips of FF futures are ideally suited for controlling the fixed-rate component of the notional OIS embedded in the synthetic equity index portfolio. Continuing with the previous example, consider a $50 million notional-value position in Mar 08 S&P 500 Index futures on December 31, 2007. These contracts expired on March 20, 2008. To lay off the notional fixed-rate financing exposure embedded in the synthetic portfolio, one could have purchased a properly sized strip of Jan 08, Feb 08 and Mar 08 FF futures:
FF Contract Expiry Months Jan 08 Feb 08 Mar 08 Number of Contracts 10 10 7

EXHIBIt 2: Using FF futures to lay off risk for the embedded OIS.
Dec 31 07 FF Futures price … Jan 08 … Feb 08 … Mar 08 Implied Rate Finance Rate Rate Spread 95.840 95.980 96.065 4.063 4.648 58.5 96.065 97.045 97.245 2.878 3.174 29.6 Jan 31 08

• The FF futures position would have earned $88,166.67. This is approximately 17.6 bps per annum on $50 million notional value, enough to narrow the overall total return shortfall (Exhibit 1, right-hand column) to within 10 bps. • The 147 bps drop in the overnight financing rate accounted directly for around 20 bps of the total 27 bps tracking error between the cash portfolio and the synthetic futures structure. If we use this as the basis of comparison (instead of the full 27 bps differential between cash total return and futures total return), then the 17.6 bps gain on the FF futures hedge would have reduced the pertinent portion of the tracking error to just 2.4 bps. • Basis risk explains much of the 2.4 bps residual. In late December 2007, FF futures implied an average overnight rate around 4.063 percent for the period ending with the equity index futures expiry. At the same time, the implied term financing rate for S&P 500 Index futures was 4.648 percent, 58.5 bps higher. By the end of January 2008, the spread between these two rates had narrowed to 29.6 bps. In other words, the spread between the hedge (the FF contract rate) and the hedge object (the implied financing rate) shifted by 29 bps over the course of the month.

Note that the Mar 08 component of the strip must be scaled down so that the basis point value of the hedge matches the interest rate sensitivity of the fixed-rate leg of the notional OIS3. Exhibit 2 shows FF futures month-end settlement prices for Dec 07 and Jan 08. Not surprisingly, FF futures prices rose sharply over this interval. When applied to the FF futures strip specified earlier, these price gains would have offset much of the interest-rate related erosion in the S&P 500 cash-futures spread shown in Exhibit 1.

This hedging strategy is static.4 At the end of the month, the Jan 08 FF contracts expire5, leaving the outstanding Feb 08 and Mar 08 contracts in place. Within the month of January, a Jan 08 FF contract can be viewed as consisting of two parts: One reflecting the monthto-date path of realized values of the effective fed funds rate, the other reflecting market expectations for the balance of the month. Because the FF contract settles to the arithmetic average of overnight rates over the entire month, the influence of the second “anticipative” part gradually shrinks. This means that, even if the hedge position had been initiated during the month of January, the number of Jan 08 FF contracts would not need to be reduced (unlike the scaling that is required for the Mar 08 component of the strip). By way of caveat, it bears repeating that the spread between the FF futures contract rate and the financing rate implied by the equity index futures calendar spread can, on occasion, feature enough volatility to blunt the effectiveness of the FF hedge. With this in mind, the practitioner should always take account of the extent to which basis risk could undermine the performance of the FF futures hedge.
part III: Eurodollar Futures and Calendar Spreads Rather than focus on reducing tracking error due to unwanted interest rate exposure, one might instead greet this exposure as a potential source of extra alpha. For equity portfolio managers who are also close students of the money market, a potentially fruitful approach is to trade the equity financing rate implied in the quarterly calendar spread in equity index futures. One can view this implied financing rate as the sum of two components: (i) the corresponding three-month LIBOR, and (ii) the spread between three-month LIBOR and the implied financing rate. For market participants who confine themselves to trading only equity index futures calendar spreads, these two components are inextricably linked. By contrast, those who are willing to add an ED futures overlay can isolate the spread component – a distinct advantage insofar as the spread component frequently emerges as a source of trading opportunities. The most obvious time to spot such opportunities, and to exploit them, is during the quarterly roll, when traffic in equity index futures calendar spreads is naturally quite high. For example, an investor holding a long position in Mar S&P 500 Index futures who wants to maintain her long exposure into the next futures expiry would do so by buying the Mar-Jun calendar spread (i.e., by selling Mar futures and buying Jun futures). By taking a position in this futures calendar spread, either long or short, she

The spread component frequently emerges as a source of trading opportunities – particularly during the quarterly roll period.
implicitly takes a view on the rate at which market participants can finance a notional S&P 500 Equity portfolio for the three-month interval between futures expiries. To the extent that this is either a low priority or a matter of indifference to many equity index investment managers, a deft speculator can profit by taking the other side of the trade. Exhibit 3 illustrates this point by comparing intra-day movements in the financing rate implied by calendar spreads in E-mini S&P 500 Index futures during the Mar-Jun 08 roll against intra-day movements in various Eurodollar (ED) futures contract rates. Three features warrant mention: • Throughout the roll period, the short-term interest rate curve was inverted. Rates implied by Mar 08 ED futures were higher than those implied by Apr 08 ED futures. (note that Mar 08 ED futures expired on March 17, 2008) • Rolling a long position in E-mini S&P 500 Index futures entailed a simultaneous sale of Mar 08 contracts and purchase of Jun08 contracts. As noted above, the long futures position implicitly extends the notional equity portfolio exposure for three months, at an implied financing rate that spans the term between futures expiry dates. This interval sits between the three-month periods referenced by Mar 08 and Apr 08 ED contracts. Not surprisingly, the implied financing rate tends to be bracketed by the Mar 08 and Apr 08 ED contract rates. • Exhibit 3 reveals considerable movement in the spread between the implied financing rate and ED contract rates. On volatile days, the spread’s 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 futures. Assume moreover that you intend to roll this position into the deferred futures. As already noted, the calendar spread between the expiring contract and the deferred contract incorporates an assumption that you are paying a fixed financing rate over the three-month

Improving Equity Index Futures Tracking and Performance with Interest Rate Futures

interval between futures expiry dates. To lay off the LIBOR component of this financing rate (and thereby to isolate the spread), you would buy ED futures. To determine the appropriate scale of the ED futures position, first compute the dollar value of a 1 bp move in the implied financing rate for 100 E-mini S&P 500 futures calendar spreads: Notional Value x 0.0001 x 90/360 or, more specifically, 100 x $50 x Lead Futures Price x 0.0001 x (90/360) Thus, for example, if the nearby futures price is 1400, each 1 bp move in the implied financing rate is worth $175.6 Because ED futures7 have a constant basis point value of $25, the size of the long ED futures position is 7 contracts = $175/$25. To make profitable opportunistic use of this combination, you would buy the calendar spread in equity index futures and buy ED futures when the implied financing rate is low relative to the ED futures contract rate. Conversely, you would unwind the ED futures position whenever the financing rate implied in your equity index futures calendar spread is high relative to the ED futures contract rate.

In theory, the order of execution does not matter. For example, nothing prevents you from opportunistically locking in the ED contract rate first, then locking in the equity index financing rate (by buying the equity index futures calendar spread) later. In practice, however, the futures expiry calendar constrains your choice of timing. Given that ED futures expire on the Monday prior to the third Wednesday of the month, while S&P 500 Index futures expire on the third Friday of the month, the expiring ED futures tend to cease trading earlier than the expiring equity index futures.8 Thus, if you use ED futures with the same expiry month as the nearby leg of the equity index futures calendar spread, your flexibility in timing would typically be confined to the first week of the quarterly roll (as Exhibit 3 illustrates).

Consectetuer adipiscing elit morbi posuere felis eu erat etiam lectus massa iacuYou can loosen inconstraint by using an EDconvallis expiry lis this ultrices a, contract with a later id, – say, Apr 08 instead of Mar 08 in this example. The cost of doing so, however,tortor. Quisque convallisexpiries may be less liquidity. ED futures with standard quarterly (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) libero nec arcu. whether your ED position is so large as to make these differences in
liquidity a material concern.

The Mar-Jun 08 Roll: Financing rates implied in E-mini S&P 500 Index futures calendar spreads vs. Eurodollar futures contract rates. Note that the roll period ended one day earlier than is customary, due to the Good Friday market holiday.

Calendar Spread Implied Rates / Eurodollar Futures






2.20 Implied EDH8 EDJ8 EDK8 3/10/08 3/11/08 3/12/08 3/13/08 3/14/08 3/17/08 3/18/08 3/19/08






part IV: Crossing over from ED to FF Recall that the synthetic investment strategy achieves equity market exposure via equity index futures while earning the overnight interest rate on investors’ cash. As noted on page one, a crucial feature of the strategy is that it embeds an implicit overnight equity index swap in which the portfolio pays a fixed rate, via the term equity financing rate, while receiving a floating rate. This suggests another approach to picking up incremental alpha, in which the core equity index futures position is augmented by the FF-ED spread that lays off both legs of the embedded OIS. Thus, returning to the earlier Mar-Jun roll example, assume you plan to roll $50 million notional of S&P 500 Index futures. The companion ED futures position would be long 50 contracts. Suppose that you incorporate an appropriately scaled FF futures strip covering the interval between Mar08 and Jun08 Index futures expiries. Its configuration would be as shown on page six. Importantly, the dollar value of a 1 bp change in money market interest rates is identical for both legs of the spread. For ED, (50 contracts) x ($25 per bp per contract) = $,1250. For FF, (30 contracts) x ($41.67 per bp per contract) = $,1250. Thus, this interest rate futures spread exactly replicates the spread between overnight fed funds and three-month LIBOR for the targeted time interval.

FF Contract Expiry Months Mar 089 Apr 08 May 08 Jun 08

Number of Contracts 3 10 10 7

Recall that we are assuming the notional portfolio positions to be collateralized fully in money market instruments paying the overnight interest rate. Thus, we care relatively less about the precise level at which the FF futures strip is booked. Far more important is the spread between FF and ED contract rates. The usual rule of thumb applies: Buy the spread when it is cheap. Exhibit 4 shows the FF-ED spread for the first two weeks in March 2008. With interest rates as volatile as they have been in recent months, this spread is capable of swinging 15 bps during the roll – enough to make ample opportunity for alpha pick-up. Here too, the sequence by which one legs into this spread does not matter. You might sell the equity index futures calendar spread first, then sell the FF-ED spread, or vice versa. The objective is to stitch the trade together as cheaply as possible.

EXHIBIt 4: Intra-day graph of the spread between the FF futures strip and Mar 08 ED futures.
76 74 72

Fed Fund/Eurodollar Spread (bps)

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

part V: Execution Costs Aside from the extra commission charges, the equity investor considering these interest rate overlays should take account of slippage costs. Fortunately, the interest rate futures involved in these strategies are very liquid. During the equity index futures roll month, the applicable ED futures typically features a bid/ask spread of ∑ bp. Given that the same ED futures would be bought and sold in two separate trades, the cost of entry and exit would be the entire bid/ask spread of ∑ bp. FF futures trade in increments of ∂ bp. Since these positions are put on and held until expiry, however it would be half the bid/ask spread, or ∑ bp. The combined cost for both legs of the spread would be ∂ bp, plus brokerage. To put this in perspective, the typical bid/ask spread in the S&P 500 Index futures calendar spread is 0.05 index points, equivalent to 1.43 bps10, making entry costs for a buy and hold equal to approximately ∆ bp. That is, the slippage cost for the interest rate overlay would be less than the half spread that one would spend in entry cost on the equity index futures calendar spread itself. Given the potential for alpha pick-up, this might be money well spent. Alternatively, the trade could be structured in simpler form, by spreading the equity index futures calendar spread directly against the weighted FF futures strip. This would save ∑ bp in bid/ask spread costs plus the commission on the ED futures leg. The expiration schedule of the ED futures would no longer enter as a source of interference. The downside would be the merging of the two rate spread opportunities.

In nearly all environments, judicious application of interest rate futures should improve tracking and performance of equity index futures.
Conclusion The interest rate risks identified above are embedded in equity index futures and in equity index futures calendar spreads, regardless of whether market 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. Let’s grant that the foregoing examples are drawn from a period of extraordinary volatility in both money market interest rates and in the spread relationships among them. Nevertheless, the basic motivation and structure of the strategies presented here remain valid in calmer waters. In nearly all seasons, judicious application should improve the tracking and performance of standard equity index futures strategies.

For more information about CME Group Equity products visit
Written by Richard Co, Research & Product Development, CME Group. You can contact the author at [email protected] or 312-930-3227. 1 2 3 For the cash index, the total return calculation assumes that the ex-dividend amount is added at the end of the month. For futures, total return assumes the full notional value is invested at the effective overnight federal funds rate throughout the month. For a complete description of the terms and conditions of 30-Day Federal Funds futures, please visit Because of the S&P 500 Index futures in this example expire on March 20, 2008, a 1 bp move in the average interest rate level in March would exert impact for only 20/31 of the month. Thus, one should scale back the number of Mar 08 FF futures to two-thirds of portfolio notional value – in this case 7 contracts instead of 10. Note that this step hinges on the correlation amongst the rates throughout the month. Certainly, if gains or losses on the stock index were so large as to change significantly the notional value of the position, then the size of the FF futures hedge position might require adjustment. More precisely, the contract is marked to the final settlement price on the first business day of the next calendar month, due to the timing of the publication of effective overnight fed funds rate data. To keep things simple, we assume 90 days between index futures expiry dates. For a large position, an actual day count would usefully improve the precision of the calculation. For a complete description of terms and conditions for Eurodollar futures, please visit For equity index futures and ED futures that expire in the same month, a little calendar arithmetic reveals that Index futures expire earlier in approximately 28 out of every 100 cases. As before, the odd amounts in the Mar 08 and Jun 08 contracts reflect the portions of those months covered by the time span between Mar 08 and Jun 08 equity index futures expiries: Roughly the last third of March and the first two thirds of June.

4 5 6 7 8 9

10 Recall that the basis point value of an E-mini S&P 500 calendar spread is $1.75 = $50 x Lead Futures Price x 0.0001 x 90/360, where the lead futures are priced at 1400. The tick increment in the spread is 0.05 index point, or $50 x 0.05 = $2.50. Assuming a one-tick market, the bid/ask spread is equivalent to $2.50/$1.75 = 1.43 basis points, expressed in implied finance rate terms.

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