Implied Financing in S&P 500 Futures
August 9, 2012

Page 1 of 3

A confluence of market shaking events have cometogether to introduce significant volatility in thedomestic equity and other markets in recentmonths.
These events include the European
sovereign debt crisis, the ongoing fiscal debate in
the U.S. and a general shift in the nexus of
economic activity from the developed to theemerging economies.
As a result, we have witnessed some pricing
anomalies in various markets including CME Group’s
flagship E-mini Standard & Poor’s 500 (S&P 500)
futures. In particular, the financing rates implicit in
the September/December 2011 “roll” or spread in Emini S&P 500 futures have fallen all the way down to27 basis points below prevailing LIBOR rates.
S&P 500 and VIX Indexes

1,400

40%

1,300

30%

VIX

35%

1,250

25%

1,200

20%

1,150

15%

1,100
9/7

8/24

8/10

7/27

7/13

6/29

6/15

6/1

10%

Standard & Poor's 500

VIX Volatility Index

This article is intended to review this situation anddiscuss how one may monitor it using CME Group’sEquity Quarterly Roll analyzer. 1Calculating Roll Value –Many asset managers
routinely buy and hold a passive position in stockindex futures. This tactic allows one to secure thereturns in the underlying stock index such as theS&P 500, which is often regarded as the benchmark
or bogey against which asset manager performance
may be measured.
Such tactics are commonplace in the context of“portable alpha” programs which attempt to securecore or “beta” returns in the benchmark and, inaddition, enhance overall portfolio returns bylayering on an additional trading strategy in pursuitof excess or “alpha” returns.
1Thus, asset managers passively holding longpositions in an expiring contract must “roll forward”
their positions. This is accomplished by selling theexpiring contract and reestablishing their longpositions in the next contract month.
“Roll” ForwardSell Nearby & Buy
Deferred Futures

The price at which one may roll forward is easilyfound in the spread between nearby and deferred
futures contracts.
𝑅𝑜𝑙𝑙 = 𝐷𝑒𝑓𝑒𝑟𝑟𝑒𝑑 𝐹𝑢𝑡𝑢𝑟𝑒𝑠 − 𝑁𝑒𝑎𝑟𝑏𝑦 𝐹𝑢𝑡𝑢𝑟𝑒𝑠

45%

1,350

S&P 500

50%

But, unlike equities, futures are not perpetual innature but rather expire on a periodic basis. Of
course, the convention in stock index futures is toprovide for a quarterly expiration on the 3rd Friday ofMarch, June, September and December.

CME Group Equity Quarterly Roll Analyzer may be
www.cmegroup.com/trading/equityaccessedat:index/paceofroll/main.html

E.g., assume that Sep-11 E-mini S&P 500 futures
are at 1,176.00 while Dec-11 E-mini S&P 500
futures are at 1,170.25. Thus, the roll may bequoted as the spread or -5.75 index points (=1,170.25 – 1,176.00).
𝑅𝑜𝑙𝑙 = 1,170.25 − 1,176.00 = −5.75 𝑖𝑛𝑑𝑒𝑥 𝑝𝑜𝑖𝑛𝑡𝑠

Positive and Negative Carry – While the roll may
readily be calculated, the next question is whether
or not it fairly reflects prevailing market conditions.
As a general rule, the “fair value” of a stock index
futures contract (FVfutures) may be calculated byreference to “cost of carry” considerations. In otherwords, what would it cost to buy and carry until
term an equity portfolio that reflects the value of theunderlying index (Spot).
We assume that one finances the portfolio atprevailing short-term rates, such as LIBOR rates(R); and, benefits from the accrual of dividend
income measured in index points (Div) over so manydays (days) until futures maturity.
𝐹𝑉𝑓𝑢𝑡𝑢𝑟𝑒𝑠 = 𝑆𝑝𝑜𝑡 + 𝐹𝑖𝑛𝑎𝑛𝑐𝑖𝑛𝑔 − 𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑𝑠
𝑑𝑎𝑦𝑠= 𝑆𝑝𝑜𝑡 𝑥 �1 + 𝑅 �� � − 𝐷𝑖𝑣360

E.g., assume that the S&P 500 is at 1,176.80, shortterm LIBOR rates are at 0.39%, there are 112 days
until expiration and we expect 7.90 index points ofdividend accrual until futures contract expiration.
Thus, we may calculate the fair value of a futurescontract at 1,170.22.

Implied Financing in S&P 500 Futures
August 9, 2012

Page 2 of 3

112
𝐹𝑉𝑓𝑢𝑡𝑢𝑟𝑒𝑠 = 1,176.80 𝑥 �1 + 0.36% �� � – 7.90
360
= 1,170.22

Where the cost of financing exceeds the expected
receipt of dividend income, stock index futures
should trade at premium to the spot index value. As
a result, deferred futures should generally trade at apremium to nearby futures and the roll is quoted asa positive number. This is a condition known as“negative carry” in futures markets because
financing costs exceed dividend receipts. Negative
carry is the condition normally expected in stockindex futures.
But sometimes, the anticipated dividend stream
exceeds financing costs. This is the case currently
as short-term interest rates, driven fundamentallyby Fed monetary policy, are at historically all-timelows with target Fed Funds at 0-0.25%. As such,deferred futures should trade at discount to nearby
futures and the roll is quoted as a negative number.
This is a circumstance known as “positive carry”
because dividend receipts exceed financing costs.
Positive and Negative Carry
60

Negative
Carry

40

200

Positive
Carry-20-40-60

t+0

t+1t+2t+3t+4t+5t+6t+7Implicit Financing – How might one determine
whether the “roll” is cheap or rich? One might
attempt to calculate the fair value associated with
the nearby and deferred futures contracts. Or, one
might get to the heart of the matter by calculating
the financing rate implicit (Imp Fin) in the value ofthe roll (Roll).
In order to calculate this value, we also need toknow the price of nearby futures (Futuresnearby); thenumber of days between expiration of nearby anddeferred futures (Daysbetween). Finally, we need toestimate the dividends that will accrue between theexpiration of the nearby and deferred futures(Divbetween) as well as dividends that will accrue until
expiration of the nearby futures contract (Divtonearby).
360
𝑅𝑜𝑙𝑙 + 𝐷𝑖𝑣𝑏𝑒𝑡𝑤𝑒𝑒𝑛
𝐼𝑚𝑝 𝐹𝑖𝑛 = ����𝑑𝑎𝑦𝑠𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝐹𝑢𝑡𝑢𝑟𝑒𝑠𝑛𝑒𝑒𝑎𝑟𝑏𝑦 + 𝐷𝑖𝑣𝑡𝑜 𝑛𝑒𝑎𝑟𝑏𝑦

E.g., assume the roll is at -5.75 index points, there
are 91 days between the nearby and deferred
futures contract expiration dates, and nearby futures
are at 1,176.00. We estimate that there will be 6.75
index points in dividends accrued between
expirations and an additional 1.15 index points individends accrued until expiration of nearby futures.
The implicit financing rate is calculated as 0.336%.
−5.75 + 6.75
360��
� = 0.00336 𝑜𝑟 0.336%
𝐼𝑚𝑝 𝐹𝑖𝑛 = �
91 1,176.00 + 1.15

We can compare this implied financing rate of
0.336% to prevailing financing rates to determine
whether the Roll appears rich or cheap.
E.g., assume that prevailing rates are at 0.43%
while the implied financing rate is at 0.336% or 9.4
basis points below prevailing rates. This suggeststhat the Roll is rather low or cheap. Thus, it may be
an opportunity time to “buy the roll” by buying
deferred and selling nearby futures.
E.g., assume that the implied financing rate is at0.52% while prevailing rates are at 0.43%. This
would suggest that the Roll is rather high or rich.
Thus, it may be more opportune to “sell the roll” buyselling deferred and buying nearby futures.
Implicit Financing< Prevailing Rate

Roll is “Cheap”

Implicit Financing>Prevailing Rate

Roll is “Rich”

Most Recent Roll – As suggested earlier, asset
managers notably including portable alpha managers
follow the value and pace of the roll closely. They
do so because a passive long strategy requires thatthey execute a roll transaction on a regular quarterly
basis.
Thus, it is often interesting to monitor how muchopen interest has rolled or transferred from theexpiring or nearby contract month to the deferredmonth.
CME Group’s Quarterly Roll Analyzer
provides this information in graphic form beginningapproximately one month prior to the expiration of aquarterly futures contract.

Implied Financing in S&P 500 Futures
August 9, 2012

Page 3 of 3

Our graphic depicts how the roll progressed relative
to historic averages during September 2011.
Inparticular, we depict the percentage of aggregate
open interest held in the expiring and first deferred
quarterly contracts that has rolled.

September to a sizable discount to December. Thus,
these shorts did not have an opportunity to roll theirshort positions in December at attractive values.

Beyond that, the Quarterly Roll Analyzer provides
information regarding the implicit financing rate andcompares it to prevailing LIBOR rates. During theSeptember 2011 roll period as open interest
transferred from nearby September 2011 to thedeferred December 2011 futures contract, we notethat implicit financing rates declined sharply during
the last few days immediately preceding expiration
on September 16th (or the 3rd Friday of the contract
month).

0.45%(Sep-11 E-mini S&P 500 Roll)

0.40%
0.35%
0.30%
0.25%
0.20%
0.15%
0.10%
0.05%

Pace of E-mini S&P 500 Roll

Implied Finance Rate

60%
50%

9/15

9/13

9/11

9/9

9/7

9/5

9/3

9/1

8/30

8/26

70%

8/28

0.00%

(Sep-11)80%

Implied vs. Prevailing Rates

Prevailing LIBOR Rate

As such, this situation was reminiscent of conditions
in late 2008 and into 2009 near the height of thesubprime mortgage crisis when bearish sentiment
likewise weighed heavily on the marketplace.

40%
30%
20%
10%

Sep-11 Roll

9/15

9/13

9/11

9/9

9/7

9/5

9/3

9/1

8/30

8/28

8/26

0%

Historic Average

Note that the implicit financing rate fell to some 27
basis points below prevailing LIBOR rates.
Thissuggests that the roll became cheap and presented
an opportune moment to buy the roll (buy deferredand sell nearby futures).
Events including the prospects of weak domestic
growth on the back of the recent fiscal debate,
coupled with flare-ups in the European sovereign
debt situation weighed heavily on equity markets
during recent weeks.
As a result, shorts
aggressively sold the nearby contract, pushing

Concluding Note – Once again, we suggest thatinterested parties consult our website to access ourEquity Quarterly Roll Analyzer. Specifically, the tool
is found at www.cmegroup.com/trading/equityindex/paceofroll/main.html. It represents a valuableand popular way of monitoring activity during a
critical period of market activity.
For more information, please contact …
Richard Co, Director
Equity Products
312-930-3227, Richard.co@cmegroup.com
John W. Labuszewski, Managing Director
Research & Product Development
312-466-7469, jlab@cmegroup.com

Copyright 2011 CME Group All Rights Reserved. CME Group™, the Globe Logo, Globex® and CME® are trademarks of Chicago
Mercantile Exchange Inc. CBOT® is the trademark of the Board of Trade of the City of Chicago. NYMEX is trademark of New York
Mercantile Exchange, Inc. The information herein is taken from sources believed to be reliable. However, it is intended for purposes ofinformation and education only and is not guaranteed by CME Group Inc. or any of its subsidiaries as to accuracy, completeness, nor any
trading result and does not constitute trading advice or constitute a solicitation of the purchase or sale of any futures or options.
Unless otherwise indicated, references to CME Group products include references to exchange-traded products on one of its regulated
exchanges (CME, CBOT, NYMEX, COMEX). Products listed in these exchanges are subject to the rules and regulations of the particularexchange and the applicable rulebook should be consulted.