S&P Systematic Global Macro Index (S&P SGMI) Methodology

Transcription

1 S&P Systematic Global Macro Inex (S&P SGMI) Methoology May 2014 S&P Dow Jones Inices: Inex Methoology

2 Table of Contents Introuction 3 Overview 3 Highlights 4 The S&P SGMI Methoology 4 Inex Family 5 Inex Constituents an Weightings 6 Overview of the Inex Constituent Determination Process 6 General Eligibility Requirements 6 Liquiity Requirement 8 The S&P SGMI Select Sectors 11 Position Direction 11 Weighting Scheme 14 Rebalancing 18 Sources of Information 18 Inex Maintenance 20 Inex Calculation 22 Spot Calculation 22 Total Dollar Weight Calculation 23 Contract Weight 24 Contract Roll Weights Logic 24 Normalizing Constant 25 Excess Return Calculation 25 Contract Daily Return Calculation 26 Total Dollar Weight Obtaine 26 Total Dollar Weight Investe 27 Total Return Calculation 28 S&P Dow Jones Inices: S&P Systematic Global Macro Inex (S&P SGMI) Methoology 1

3 Glossary 29 Inex Data 30 Inex Governance 31 Inex Committee 31 Inex Business Committee 31 Inex Policy 32 Holiay Scheule 32 Inex Dissemination 33 Tickers 33 Appenix 34 Position Determination 34 Number of Contracts 35 Cash Weight Calculation 37 Precisions for Calculation 37 S&P Dow Jones Inices Contact Information 38 Inex Management 38 Prouct Management 38 Meia Relations 38 Client Services 38 Disclaimer 39 S&P Dow Jones Inices: S&P Systematic Global Macro Inex (S&P SGMI) Methoology 2

4 Introuction Overview The objective of the S&P Systematic Global Macro Inex (S&P SGMI) is to measure statistically relevant price trens of certain globally trae liqui future contracts by systematically investing with long, short or no positions. The strategy is meant to represent the general level of volatility taken by managers in the global macro an manage futures/commoity Traing Avisor (CTA) universe, while still being subject to leverage constraints. The inex follows a quantitative methoology to track the prices of a globally iversifie portfolio of over three ozen commoity, foreign exchange an financial futures contracts. Each contract (also calle a constituent) may be in a long, short, or no investment position epening upon a trening signal generate by a regression of its historical prices. The constituents are groupe into six of the most significant sectors trae in the global macro universe. Since the inex is unbiase towars any particular futures contract or sector, the weighting is base on the premise that each position has an equal probability of success. So, each sector is allocate an equal risk capital allowance with the unerlying constituents within each sector evenly weighte as well. The resulting portfolio is, then, leverage in such a way that the effects of iversification among the various constituents are taken into account. Finally, the weights are ajuste to fit within the leverage constraints. The S&P SGMI is calculate an maintaine by S&P Dow Jones Inices. It is esigne as a leverage inex, comprise of traable constituents, which can easily form the basis of futures proucts. This methoology was create by S&P Dow Jones Inices to achieve the aforementione objective of measuring the unerlying interest of each inex governe by this methoology ocument. Any changes to or eviations from this methoology are mae in the sole jugment an iscretion of S&P Dow Jones Inices so that the inex continues to achieve its objective. S&P Dow Jones Inices: S&P Systematic Global Macro Inex (S&P SGMI) Methoology 3

5 Highlights The key characteristics of the S&P SGMI inclue: Currently 37 constituents (futures contracts) are groupe into six sectors. Risk capital allowances for the constituents are allocate evenly within their respective sectors. Risk capital allowances for the sectors are allocate evenly in the portfolio, with the total risk capital etermine by the target volatility. Constituent position is etermine by a regression of historical prices. Constituent selection is etermine every two years. Sectors an constituents are rebalance monthly. The S&P SGMI Methoology The S&P SGMI was evelope in coorination with Thayer Brook Partners LLP (TBP) exclusively for S&P Dow Jones Inices. On any given S&P SGMI business ay, the composition of the S&P SGMI an its value, as etermine an publishe by S&P Dow Jones Inices, are ispositive. This ocument escribes the methoology use by S&P Dow Jones Inices in etermining such composition an calculating such value. Neither this methoology nor any set of proceures, however, are capable of anticipating all possible circumstances an events that may occur with respect to the S&P SGMI an the methoology for its composition, weighting an calculation. Accoringly, a number of subjective jugments are mae in connection with the operation of the S&P SGMI that cannot be aequately reflecte in this ocument. All questions of interpretation with respect to the application of the provisions of this methoology, incluing any eterminations that nee to be mae in the event of a market emergency or other extraorinary circumstances, are resolve by S&P Dow Jones Inices in consultation with the Inex Committee, or the Inex Avisory Panel where appropriate. S&P Dow Jones Inices is committe to maintaining the S&P SGMI as an inex comprise of traable constituents that serves as a principal measure for futures investing. We also recognize that the etaile rules-base approach containe in the methoology may not, at all times, reflect the unerlying liquiity an conition of a specific market, particularly in perios of extraorinary market volatility or rapi technological change. Therefore, S&P Dow Jones Inices may etermine that a given Contract that satisfies the eligibility criteria set forth in this methoology shoul, nevertheless, be exclue from the S&P SGMI if inclusion of such Contract is inconsistent with, or woul unermine, the purposes of the S&P SGMI as a measure for futures market performance an an inex comprise of traable constituents. Further, moifications to the methoology use to calculate the S&P SGMI may be necessary from time to time. S&P Dow Jones Inices reserves the right to make such changes or refinements to the methoology set forth in this ocument as it believes necessary in orer to preserve an enhance the utility of the S&P SGMI as a measure for futures market performance an the traability of the S&P SGMI constituents. S&P Dow S&P Dow Jones Inices: S&P Systematic Global Macro Inex (S&P SGMI) Methoology 4

6 Jones Inices also reserves the right to take any action with respect to the S&P SGMI, as it eems necessary or appropriate, in orer to aress market emergencies or other extraorinary market events or conitions. Wherever practicable, any such changes or actions are publicly announce prior to their effective ate. This methoology uses various terms an efinitions similar to the S&P GSCI Inex Methoology. Where not specifically note otherwise in this ocument, the rules of the S&P GSCI Methoology will prevail. Where the terms in this ocument are also efine in the S&P GSCI Methoology, the efinitions in this ocument prevail. Inex Family S&P Dow Jones Inices also calculates two stanalone sub-inices representing the components of the S&P SGMI. These are the S&P SGMI Commoity (reflecting the physical commoity futures components of the S&P SGMI) an the S&P SGMI Financial (reflecting the financial futures components of the S&P SGMI) Inices. Excess an Total Return sub-inices are calculate an publishe for each of these two market sectors. The S&P SGMI Commoity an S&P SGMI Financial inices are completely inepenent stanalone inices that follow the S&P SGMI methoology. Currency of Calculation The S&P SGMI is calculate only in US ollar. The unerlying futures contracts prices are collecte in the local currencies. Using WM/Reuters spot exchange rates, these local prices are converte to US ollar. Exchange Rates Real-time Forex rates, as supplie by WM/Reuters, are use for ongoing inex calculation. The inex s final closing values convert all unerlying contracts prices use in the inex calculation at the spot exchange rates provie by WM/Reuters at Lonon 04:00 PM Greenwich Mean Time. S&P Dow Jones Inices: S&P Systematic Global Macro Inex (S&P SGMI) Methoology 5

7 Inex Constituents an Weightings Overview of the Inex Constituent Determination Process The Contracts inclue in the S&P SGMI are etermine every two years an must satisfy several eligibility criteria. First, S&P Dow Jones Inices ientifies those contracts that meet the general criteria for eligibility. Secon, the Contract liquiity requirements are applie. The list of Designate Contracts for the relevant S&P SGMI Years is, then, complete an the process moves to the etermination of the constituents weights iscusse below. General Eligibility Requirements These criteria are intene only to ientify Contracts with characteristics that facilitate the calculation of the S&P SGMI an are consistent with the general purpose of the S&P SGMI as an inex comprise of traable constituents. This process generally prouces a substantial list of Contracts eligible for inclusion; the list is narrowe through the application of the more specific criteria escribe below. Physical Commoities, Financial, an Foreign Exchange Futures. To be eligible for inclusion in the S&P SGMI, a Contract must be on a physical commoity, financial instrument, currency, interest rate or an equity inex. The Contracts nee not require physical elivery by their terms in orer for a commoity to be consiere a physical commoity. Certain Contract Characteristics. In orer for a Contract to be eligible for inclusion in the S&P SGMI, the following criteria must be satisfie: (i) the Contract must have a specifie expiration or term, or provie in some other manner for elivery or settlement at a specifie time, or within a specifie time perio, in the future; (ii) the Contract must, at any given point in time, be available for traing at least five months prior to its expiration or such other ate or time perio specifie for elivery or settlement; an (iii) the Traing Facility on which the Contract is trae must allow market participants to execute sprea transactions between the pairs of Contract Expirations inclue in the S&P SGMI that, at any given point in time, are involve in the rolls effecte uring the next three Roll Perios. The requirements set forth in this section reflect the fact that some of the proucts, from time to time, trae on or through Traing Facilities, in particular certain electronic platforms, may not isplay traitional characteristics of a futures contract, such as particular contract months. While it is not necessary for a Contract Expiration to be expresse as a calenar month, the S&P SGMI an its unerlying methoology are premise upon the existence of specifie ates or time perios for elivery or settlement. S&P Dow Jones Inices: S&P Systematic Global Macro Inex (S&P SGMI) Methoology 6

8 It is assume that Contracts trae on contract markets, exempt electronic traing facilities, erivatives transaction execution facilities, exempt boars of trae an foreign boars of trae (as such terms are efine in the U.S. Commoity Exchange Act an the rules an regulations promulgate there uner) will generally satisfy the above requirements, unless S&P Dow Jones Inices etermines that any such Contract oes not satisfy the foregoing criteria. The requirement that the specific Contract month be available for traing at least five months prior to its expiration is esigne to ensure that a genuine traing market in the Contract exists prior to the time establishe for elivery or settlement, when traing conitions can be affecte by the impening expiration of the Contract. The final requirement in this Section, regaring execution of sprea transactions, is esigne to allow market participants to effect the rolling of contracts inclue in the S&P SGMI more efficiently. Denomination an Geographical Requirements. To be eligible for inclusion in the S&P SGMI, a Contract must be trae on or through a Traing Facility that has its principal place of business or operations in a country that is a member of the Organization for Economic Cooperation an Development (OECD) uring the relevant Annual Calculation Perio or Interim Calculation Perio. This assures that the S&P SGMI is limite to those futures for which there are Traing Facilities in inustrialize countries. Availability of Daily Contract Reference Prices. For a Contract to be eligible for inclusion in the S&P SGMI, Daily Contract Reference Prices generally must have been available on a continuous basis for at least two years prior to the propose ate of inclusion. In appropriate circumstances, S&P Dow Jones Inices may etermine that a shorter time perio is sufficient or that historical Daily Contract Reference Prices for a given Contract may be erive from Daily Contract Reference Prices of a similar or relate Contract. At an after the time a particular Contract is inclue in the S&P SGMI, the price must generally be available to all members of, or participants in, such Facility (an S&P Dow Jones Inices) on the same Contract Business Day from the Traing Facility or through a recognize thir-party ata venor. Such publication must inclue, at all times, Daily Contract Reference Prices for at least one Contract Expiration that is five months or more from the ate the etermination is mae, as well as for all Contract Expirations uring such five-month perio. The requirement that a Contract have a continuous price history of at least two years is intene to ensure the reliability an availability of the prices necessary to enable S&P Dow Jones Inices to calculate the S&P SGMI. In aition, in orer to calculate the S&P SGMI on an ongoing basis, S&P Dow Jones Inices must be able to obtain Daily Contract Reference Prices for certain Contract Expirations with respect to each Designate Contract prior to the S&P SGMI Settlement Time on each Contract Business Day. This requirement is intene to assure that the value of the S&P SGMI can be reliably calculate on the basis of prices that are both announce an, in general, reaily available to the members of, or participants in, the relevant Traing Facility (an S&P Dow Jones Inices). S&P Dow Jones Inices: S&P Systematic Global Macro Inex (S&P SGMI) Methoology 7

9 Availability of Volume Data. For a Contract to be eligible for inclusion in the S&P SGMI, volume ata with respect to such Contract must be available from sources satisfying the criteria specifie uner Sources of Information below, for at least two years immeiately prior to the ate on which the etermination to inclue the contracts is mae. The S&P SGMI etermination ate is the same as the S&P GSCI for annual volume ata, the 12-month perios from September through August. Other Requirements with respect to the Traing Facility. The Traing Facility on or through which a Contract is trae must (i) make price quotations generally available to its members or participants (an to S&P Dow Jones Inices) in a manner an with a frequency that is sufficient to provie reasonably reliable inications of the level of the relevant market at any given point in time; (ii) make reliable traing volume information available to S&P Dow Jones Inices with at least the frequency require by S&P Dow Jones Inices to make the monthly eterminations escribe uner Sources of Information below; (iii) accept bis an offers from multiple participants or price proviers (i.e., it must not be a single-ealer platform); an (iv) be accessible to a sufficiently broa range of participants. Such access may be provie either (a) by the Traing Facility making clearing services reasonably available, thereby eliminating counterparty creit consierations, or (b) by a network of brokers or ealers who are willing to intermeiate transactions with thir parties, thereby enabling such thir parties to enter into transactions base on prices poste on such Facility. These requirements are intene to establish certain minimum stanars for Traing Facilities. If traing in certain futures is shifte to electronic platforms that are largely unregulate, or subject to ifferent levels or types of regulation than traitional exchanges, these stanars serve to ensure that the S&P SGMI inclues only Contracts for which sufficient an reliable ata an, in particular, price ata evelope in a competitive process, are available. It is assume that contract markets an foreign boars of trae (as such terms are efine in the U.S. Commoity Exchange Act an the rules an regulations promulgate there uner) will generally satisfy the above requirements, unless S&P Dow Jones Inices etermines otherwise. Contract Traing Hour Requirements. S&P Dow Jones Inices may exclue a Contract from the S&P SGMI that otherwise satisfies the criteria an conitions for inclusion if, in its reasonable jugment, such Contract's Overall Traing Winow is insufficient to support the traability of the S&P SGMI taken as a whole. This requirement is intene to support an enhance the traability of the S&P SGMI constituents, by ensuring that all Designate Contracts are available for traing uring at least a minimum perio of time. Liquiity Requirement The S&P SGMI is limite to those Contracts that are actively trae in orer to assure that the prices generate by the markets for such Contracts represent reliable, competitive prices. Liquiity is an inication both of the significance of a particular market an the ability to trae with minimal market impact. Liquiity is etermine by the annual Total Dollar Value Trae (TDVT). The Contracts that satisfy the general eligibility requirements set forth in General Eligibility Requirements above must, therefore, also satisfy the liquiity requirements escribe below before being inclue in the S&P S&P Dow Jones Inices: S&P Systematic Global Macro Inex (S&P SGMI) Methoology 8

10 SGMI. Exhibit 1 on the following page isplays the most liqui contracts from each sector that are inclue accoring to these criteria. S&P Dow Jones Inices: S&P Systematic Global Macro Inex (S&P SGMI) Methoology 9

11 EXHIBIT 1: CONTRACT INCLUSION CRITERIA Sector Constituent Exchange Sector Currency Energy Energy Commoities Commoity - Softs & Livestock Commoity - Grains Commoity - Metals Fixe Income Natural Gas NYMEX E USD Heating Oil #2 NYMEX E USD Gas Oil ICE E USD Crue Oil NYMEX E USD Brent Crue ICE E USD Gasoline NYMEX E USD Sugar #11 NYBOT C USD Live Cattle CME C USD Coffee "C" NYBOT C USD Cotton #2 NYBOT C USD Soybeans CBOT C USD Corn CBOT C USD Wheat CBOT C USD Copper NYMEX C USD Gol (100 oz.) COMEX C USD Silver COMEX C USD Top from the 3 regions Greater than 3yr maturity Inclusion Criteria TDVT>$5B Top 6 Top 4 Top 3 Top 3 T-Notes (10-year) CBOT FI USD Fixe Income - U.S. T-Notes (5-year) CBOT FI USD Top 3 T-Bons (30-year) CBOT FI USD Fixe Income - Euro-Bun EUREX FI EUR Europe Euro-Bobl EUREX FI EUR Top 2 Fixe Income - Asia JGB TSE FI JPY Top 2* Foreign Exchange Top 6 OECD only US Exch Only Euro FX CME FX USD Japanese Yen CME FX USD British Poun CME FX USD Foreign Exchange Australian Dollar CME FX USD Top 6 US Canaian Dollar CME FX USD Swiss Franc CME FX USD Top 2 in each of 3 regions Equity (Inst w/ mini are aggregate for Volume purposes) Equity - U.S. Equity - Europe Equity - Asia STIR Nasaq Complex CME SI USD S&P 500 Inex Complex CME SI USD Euro Stoxx 50 EUREX SI EUR Dax EUREX SI EUR Kospi 200 KE SI KRW Nikkei 225 Futures OSE SI JPY 4th Quarterly Contract in each region STIR - U.S. Euroollars (3-month) CME STIR USD STIR - Europe 3 Month Euribor LIFFE STIR EUR STIR - Asia 3 Month Euroyen TFX STIR JPY *STIR stans for Short Tem Interest Rate Top 2 Top 2 Top 2 S&P Dow Jones Inices: S&P Systematic Global Macro Inex (S&P SGMI) Methoology 10

12 The S&P SGMI Select Sectors The six S&P SGMI sectors are categorize into two subsets: the financial select sector an the commoities select sector. For each of these two select sectors, sub-inices are compute using the same methoology as the S&P SGMI. Exhibit 2 shows the various parameters for the S&P SGMI composite an select sectors inices. EXHIBIT 2: COMPARISON SGMI Composite SGMI Financials SGMI Commoities Number of Sectors Number of Constituents Target Inex Volatility 17.5% 17.5% 17.5% Leverage Constraint 3X 3X 3X The four sectors inclue in the S&P SGMI Financials are Equity, Fixe Income, Foreign Exchange an Short Term Interest Rates (STIR). There are six constituents in each of the Equity, Fixe Income an Foreign Exchange sectors, an three constituents in STIR. The two sectors inclue in the S&P SGMI Commoities are Energy an Commoities. There are six constituents in the Energy sector, an ten constituents in the Commoities sector. Within each of the sub-inices, the risk capital allocations are carrie out evenly first at the sector level, then again evenly within the iniviual sectors, in accorance with the S&P SGMI methoology. Position Direction In orer to reflect the measure of the global macro an manage futures/commoity Traing Avisor (CTA) universe, the S&P SGMI must take irectional positions that are long or short in orer to represent the positions of the general market. If there is a positive tren, then the position will be long; conversely, if there is a negative tren, then the position will be short. Determining whether the tren is negative or positive for each constituent each month is epenent upon a series of steps that must be followe to evelop a vali time-series regression moel where the slope (positive/negative) acts as the position irection (long/short) inicator. In orer to establish whether a constituent is currently in an upwar or ownwar tren we compute a linear regression of the constituent returns against time. This is an approach that is wiely aopte by traitional technical analysts. If the regression line has a positive slope then the conclusion is that the market is currently trening upwars, S&P Dow Jones Inices: S&P Systematic Global Macro Inex (S&P SGMI) Methoology 11

13 an if the slope of the regression line is negative then the conclusion is that the market is trening ownwars. The first step in eveloping a constituent s vali time series regression is to collect its aily historical price ata an calculate a cumulative return for each ay. At least 256 ata points must be available or else the weight cannot be calculate, so there woul be no position. However, since a historical return is often epenent on the prior return, known as autocorrelation, the return ata alone is not sufficient to prouce a vali moel with a constant mean an variance. For example, the mean an variance may be increasing over time in an unajuste moel, so that any preicte value will be too low. Because the time tren may vary through history, the analysis will use only the most recent perio of time when the tren was stable. To etermine this time perio an initial assumption is mae that the tren was stable over the most recent 22 ays an then tests in five ay increments until the longest stability perio is iscovere. To check for stability the hypothesis that two variances are equal is teste. Equality inicates a stable tren an the longest perio of stability ening with the current ate is use for the position irection ecision. The two variances are (1) the variance of the aily returns an (2) the variance of resiuals of an Orinary Least Squares (OLS) linear regression of the cumulative return (y) on time (t). The statistical test that we use to test the valiity of the linear regression moel is the F- test (or variance ratio test), which tests whether the variance of the linear regression resiuals (ajuste for autocorrelation) is the same as the variance of the first ifferences of cumulative returns series. This is the null hypothesis. Equality of variances inicates that the linear regression moel is a goo fit for the ata. If the variance of the resiuals (ajuste for autocorrelation) is significantly larger than the variance of the first ifferences then this inicates that the linear moel is not a goo fit for the ata which is likely to be ue to non-linearity e.g. a change in the tren. If the test cannot reject the null hypothesis that the two variances are equal, the time perio is increase by five ays an the variances are recompute an reteste. If the null hypothesis is rejecte, inicating the variances are not equal, then the sign of the slope coefficient in the regression is use to etermine the position: positive = long, negative = short an 0 = no position. Again, as the resiuals are likely to be autocorrelate an uncorrecte F-test is oversensitive. To correct for this oversensitivity, the variance of the resiuals are ajuste by a factor of (1- ρ 2 ), where ρ is the autocorrelation lag at 1. Once F is too large, the regression is no longer as goo at e-trening as the first ifferences, showing the resiuals have more noise than the series itself. The autocorrelation of the resiuals is compute as follows: ρ = n 1 1 ( yt µ )( yt+ 1 µ ) ( n 1) t= 1 + (1/ n) Var( y ) t S&P Dow Jones Inices: S&P Systematic Global Macro Inex (S&P SGMI) Methoology 12

14 where: y t = the resiual at time t µ = the mean of the resiuals (1.., n), an n = the number of ays in the relevant perio. 1/n is inclue to correct for a negative bias in the autocorrelation of a short time series. As the time series gets longer, this term becomes less relevant. F is then efine as: 2 Var( resiuals) * (1 ρ ) F = Var( FD) where FD = the first ifferences of the aily cumulative percentage return series use in the regression. resiuals= resiuals of the OLS. Finally, the iterative process base on the continuous cumulative component returns an a confience interval of 95% is run to establish the irection base on the slope of the regression. This is referre to as the F-Inverse function (F inv ). The process starts at the present an works backwars until: F inv > F ( 95%, n 3, n 2) where n = the number of ays looking back note: the F-Inverse function is roune to 2 ecimal places to assure that the algorithm is easily repeatable. More specifically, the algorithm starts by regressing the past 22 ays, beginning with the rebalancing reference ate. If F < Finv (95%, 19, 20), the process continues by aing five ays of history with each iteration until F > Finv ( 95%, n 3, n 2). Once F > Finv ( 95%, n 3, n 2), the sign of the slope etermines the market position. If the slope is negative (ownwar sloping) then the market position for that component is short. Conversely, if the slope is positive (upwar sloping) then the market position for that component is long. For more information on position irection, please refer to the Appenix. S&P Dow Jones Inices: S&P Systematic Global Macro Inex (S&P SGMI) Methoology 13

15 Weighting Scheme The intention of the S&P SGMI weighting scheme is to create an inex where each of the sectors is allocate the same risk capital allowance, with each of the constituents allocate the same risk capital allowance within its sector. The iea is that no single sector or constituent shoul rive the volatility of the inex. It is important to note that the goal of the weighting methoology is to allocate the risk capital allowance as evenly as possible. The S&P SGMI is a leverage prouct an, as such, is not trying to minimize volatility for a given investment. It has been specifically esigne to be mathematically vali without being overly epenent on the iniviual elements of the cross-correlation matrix. The S&P SGMI methoology creates a consistent an efficient portfolio by first proucing a set of relative weights which creates the iversifie portfolio. To take avantage of this iversification, leverage management then occurs by scaling the portfolio to the target volatility by using a factor which is solely epenent upon the overall average of the cross-correlation matrix an not the iniviual elements of that matrix. The overall portfolio average is more stable than the iniviual elements an, thus, ultimately facilitates the calculation of a portfolio that is leverage to achieve a given target volatility. In orer to apply this concept to the S&P SGMI, the number of contracts nees to be etermine for each constituent, so it is necessary to choose a ollar amount an target inex volatility. The ollar amount or assets uner management (AUM) is arbitrary but the target volatility level is currently set to 17.5%, an is meant to represent the average volatility of the global macro manage futures/commoity Traing Avisor (CTA) universe. From the AUM an target volatility, a US$ aily risk allowance is calculate for the entire inex by multiplying the AUM by the aily target volatility. US$ Daily Risk Allowance Inex = Target Volatility AUMUS $ * 256 It represents the total ollar risk the inex is allowe to take in one ay. The next step is to etermine the aily risk allowance for each constituent. Again, the iea is for each sector to have an equal ollar risk allowance where each constituent in the sector also has an equal ollar risk allowance. US$ Daily Risk Allowance Constituent = US$ Daily Risk Allowance Inex *(1/N)*(1/M) *CF where: N = number of sectors in the inex M = the number of constituents in its sector CF = the correlation factor. S&P Dow Jones Inices: S&P Systematic Global Macro Inex (S&P SGMI) Methoology 14

16 The correlation factor nees to be taken into account in orer to properly assess the risk allowance for each constituent. If the correlations were not consiere or were just assume to be 1, then the aily risk allowance woul be too low to hit the chosen target volatility. In orer to compute the correlation factor, a correlation matrix of aily returns of all constituents is run an the average of the lower left triangle is calculate (AC). CF = Q ( 1+ (( Q 1) * AC)) which allows the inex to allocate over the AUM (apply leverage) with the intention of reaching the target volatility. where: Q = the number of total constituents in the inex Once each constituent s US$ aily risk allowance is etermine, the number of contracts neee to fill the position is calculate by iviing the aily risk allowance by the US$ ollar risk of one contract. For each constituent, the US$ ollar risk of one contract is measure by multiplying the stanar eviation of the first ifferences of local prices by the local value of the contract tick an then by the exchange rate to the US$. So, all else being constant, higher volatility of a constituent will yiel a higher US$ ollar risk of one contract so fewer contracts will be neee to fill the total risk allowance for the constituent. Conversely, if the volatility is too low, too many contracts woul be require to fill the total risk allowance or it might not be possible at all. The inex solution for this problem is to set a threshol of 0.125% as a lower limit to a ratio that tests whether there is enough volatility for the contract size. Ratio = US$ risk * m m * P * tick * FX where: US$risk = US$ risk per constituent contract m = number of contracts P = last local contract price Tick = the local value of a contract tick FX = exchange rate to the US$ Note: the enominator in the equation above measures the nominal value of the constituent in US$ If this ratio is less than 0.125%, then no position is taken so the weight of the constituent will be zero. Again, since the correlation factor allows for an allocation greater than the AUM, also known as leverage, the inex nees to ajust so that the leverage is never greater than 3x or 300% total nominal exposure. If the total nominal exposure of the inex is greater than 300%, then 300% is ivie by the total nominal exposure of the inex to create a scale- S&P Dow Jones Inices: S&P Systematic Global Macro Inex (S&P SGMI) Methoology 15

17 back factor. This ratio will be applie to the number of contracts for each constituent to reuce the inex to 300% of total nominal exposure. Please see the formulas below that show the mathematical concept behin using the Correlation Factor (CF) in the weighting scheme. This illustration is for the simplifie case where all iniviual constituents are allocate equally, which iffers slightly from the aopte allocation scheme. Although the moel is not exact, our stuies show that the practical benefits erive from correlation stability far outweigh the mathematical rigor of a full scale moel. By efinition, the variance of the portfolio returns is etermine as the sum of the iniviual variances plus a cross-correlation factor. This is shown in the formula below: m i= 1 where, Var( ) + ρ σ σ x i ρ = correlation σ = stanar eviation m = number of constituents Since each risk unit, by esign, has the same expecte stanar eviation, the equation can be rewritten as: mvar( x) + Var( x) ρ m 1, i j i, j The equation for the portfolio variance can now be restate as: m 1 mvar( x) 1 + ρ i, m 1, i j m 1, i j The size, N, of the correlation matrix is: ij i j j N 2 = ( m m) = m( m 1) Thus the average of the correlation matrix, ρ, is given by the following ientities, ρ = ρ ij ρ i j N i j ij = m( m 1) An so it follows that: S&P Dow Jones Inices: S&P Systematic Global Macro Inex (S&P SGMI) Methoology 16

18 1 m ρ i j ij = ρ( m 1) Substituting the above equation into the equation for the portfolio variance, we get: ( + ( m 1) ) mvar( x) 1 ρ An it follows that the scaling factor is only proportional to the average of the crosscorrelation matrix: Var( portfolio) = (1 + ( m 1) m Var( x) 2 ρ ) / m Therefore, the size of each risk unit can be compute irectly from the target volatility: Var( portfolio) m Var ( x) = 2 m 1+ ( m 1)ρ Or, taking the square root of this equation we arrive at: σ per risk unit σ = aily target m m 1 + ( m 1) ρ Thus, the size of each risk unit is equal to the risk capital allocate to the constituent multiplie by the Correlation Factor (CF). The number of contracts which can be trae to create a single risk unit is: σ σ per risk unit per contract At the en of each month, the USD stanar eviation of each component is sample σ per contract over the past 60 traing ays, to yiel the which is use with the preceing formula to etermine the number of contracts in a risk unit for any given component. Accoring to the representative volatility of managers in the CTA universe as etermine by TBP, the target S&P SGMI annualize volatility is set to 17.5%, before any restriction on exposure. If a component s USD stanar eviation ivie by its nominal size is less than 0.125%, then there is no position for that contract. If the gross exposure of the inex is greater than 300%, each contract is scale back proportionately such that the overall gross exposure is 300%. S&P Dow Jones Inices: S&P Systematic Global Macro Inex (S&P SGMI) Methoology 17

19 Thus the number of contracts for any given component is compute using the formula: C = 17.5% 256 m σ 1+ ( m 1)ρ per contract m For more information on the weighting scheme, please refer to the Appenix. Rebalancing Monthly Rebalancing for Component Weights. Components are rebalance accoring to the signals generate by the algorithm run after the close of the last business ay of each month. The rebalancing reference position implementation perio is the secon (2 n ) through the sixth (6 th ) S&P SGMI business ays of the month. Bi-Annual Rebalancing for Component Weights. At the beginning of every other year, each of the constituents is evaluate for liquiity to ensure only the most liqui is inclue in the inex as etermine by the TDVT. Sources of Information The following are the sources of the information use to etermine the eligibility of Contracts for inclusion in the S&P SGMI pursuant to the requirements set forth in General Eligibility Requirements. If any of the sources ientifie below is unavailable, with respect to the etermination of the S&P SGMI for a particular S&P SGMI Year, S&P Dow Jones Inices will ientify appropriate alternative sources an the composition of the S&P SGMI for such year will be base on such alternative sources. In aition, if S&P Dow Jones Inices, in its reasonable jugment, believes that one or more of the sources ientifie below contains a manifest error, it may use an alternative source to obtain the necessary information. Any such alternative sources use by S&P Dow Jones Inices will be publicly isclose at the time that the composition of the S&P SGMI for the next S&P SGMI Year is announce. General Eligibility Requirements. The ientification of those futures that satisfy the general eligibility requirements set forth in General Eligibility Requirements is base on (1) the FIA (Futures Inustry Association) Reports that are publishe at the time of the relevant Annual Calculation Perio or Interim Calculation Perio, an (2) the most recent version of the Futures an Options Fact Book, publishe by the Futures Inustry Institute. The etermination as to whether a particular Traing Facility has its principal place of business or operations in an OECD country is base on the most recent ata publishe by the OECD. Contract Volume an Liquiity Requirements. In orer to etermine whether a particular Contract satisfies the volume an liquiity requirements escribe above, S&P Dow Jones Inices may use any available sources that it believes to be reasonably reliable incluing, but not limite to, ata containe in the FIA Reports. In the event of S&P Dow Jones Inices: S&P Systematic Global Macro Inex (S&P SGMI) Methoology 18

20 manifest error, S&P Dow Jones Inices may supplement, an make corrections to, any such ata. S&P Dow Jones Inices: S&P Systematic Global Macro Inex (S&P SGMI) Methoology 19

21 Inex Maintenance The S&P SGMI is a strategy of capturing futures contract price trens even though futures contracts have limite urations. Consequently, for the inicator to be calculate through time it must change (or roll) from tracking contracts that are approaching expiration to tracking new contracts. Each contract has its own roll pattern base on historical liquiity as etermine by the Total Dollar Value Trae (TDVT) an open interest. Exhibit 3 is a scheule of the active contracts use for price inputs of the Inex. EXHIBIT 3: SCHEDULE OF CONTRACT MONTHS S&P SGMI Designate Contract Roll Scheule - Designate contract month the inex rolls into at the beginning of each month. JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC Australian Dollar H H M M M U U U Z Z Z H British Poun H H M M M U U U Z Z Z H Canaian Dollar H H M M M U U U Z Z Z H Euro H H M M M U U U Z Z Z H Japanese Yen H H M M M U U U Z Z Z H Swiss Franc H H M M M U U U Z Z Z H 10 Year Note H M M M U U U Z Z Z H H Treasury Bon H M M M U U U Z Z Z H H 5 Year Note H M M M U U U Z Z Z H H Coffee "C" H K K N N U U Z Z Z H H Sugar #11 H K K N N V V V H H H H Cotton #2 H K K N N Z Z Z Z Z H H Crue Oil H J K M N Q U V X Z F G Heating Oil H J K M N Q U V X Z F G Unleae Gasoline H J K M N Q U V X Z F G Natural Gas H J K M N Q U V X Z F G Corn H K K N N U U Z Z Z H H Soybeans H K K N N X X X X F F H Wheat (Chicago) H K K N N U U Z Z Z H H Copper (COMEX) H K K N N U U Z Z Z H H Live Cattle J J M M Q Q V V Z Z G G Gol J J M M Q Q Z Z Z Z G G Silver H K K N N U U Z Z Z H H GasOil H J K M N Q U V X Z F G Brent Crue J K M N Q U V X Z F G H Euro-Bun H M M M U U U Z Z Z H H Euro-Bobl H M M M U U U Z Z Z H H JGB H M M M U U U Z Z Z H H Nasaq 100 Inex H H M M M U U U Z Z Z H S&P 500 Inex H H M M M U U U Z Z Z H Euro Stoxx 50 H H M M M U U U Z Z Z H Dax H H M M M U U U Z Z Z H Kospi 200 H M M M U U U Z Z Z H H Nikkei 225 H M M M U U U Z Z Z H H Euroollars (3-month) Z Z H H H M M M U U U Z Euribor (3-month) Z Z H H H M M M U U U Z Euroyen (3-month) Z Z H H H M M M U U U Z S&P Dow Jones Inices: S&P Systematic Global Macro Inex (S&P SGMI) Methoology 20

22 EXHIBIT 4: MONTH LETTER CODES LETTER F G H J K M N Q U V X Z CONTRACT EXPIRATION JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC The risk of aberrational liquiity or pricing of a commoity futures contract aroun the maturity ate is greater than in the case of cash-settle futures contracts because (among other factors) a number of market participants take elivery of the unerlying commoities. Spot markets in commoities occasionally have elivery problems relate to, for example, weather conitions isrupting transportation of cattle to a elivery point. Such a elay coul cause the spot market to move significantly, while latter-ate futures contracts are little change. The strategy avois elivery issues by owning contracts that are outsie of nearby elivery. S&P Dow Jones Inices: S&P Systematic Global Macro Inex (S&P SGMI) Methoology 21

23 Inex Calculation Please note, for all calculations below the formulae inclue the contract rolls that occur uring the monthly rebalancings. During the remainer of each month, only one contract will be in effect, so the irrelevant portions of some equations will not apply. Spot Calculation On a given S&P SGMI business ay,, the spot price (SPOT) of the inex containing i number of Components (c) is calculate as follows: SPOT where i c= i i c= i = i TDW1+ SC1 NCol + c= 1 c= 1 i TDW 2 + SC2 NCnew TDW1 = The sum of the Total Dollar Weight (TDW) of each Component s (c s) Current Contract. TDW 2 = The sum of the TDW of each Component (c s) next SC1 = SC2 = NC ol Contract The Short Component effective uring the last month, expresse in the same terms as the Contract Weights, CWs. The Short Component effective in the current month, expresse in the same terms as the CWs. = Normalizing Constant effective uring the last month NC new = Normalizing Constant effective uring this month The Short Component (SC) is allocate to the amount of weight remaining in the Inex after the weights of each component has been efine base on the long an short positions an their respective percentage weights. Aing the weight of the Short Component to the sum of the weights of the Components make the weight in the Inex sum to 100%. S&P Dow Jones Inices: S&P Systematic Global Macro Inex (S&P SGMI) Methoology 22

24 The Short Component is calculate as follows: SC = NumberofContracts * CRW where c * Position CRWc = Contract Roll Weights for Future c on ay Position is set as efine in the Appenix. Please see the contract roll weights table on the next page for the CRW on ay. Total Dollar Weight Calculation On a given S&P SGMI business ay,, the Total Dollar Weight (TDW) for Future c is the prouct of its Contract Weight, Contract Roll Weight, Daily Contract Reference Price an US$ exchange rate for the current an next contracts, respectively. TDWc i = c= 1 TDWc 1 * ( CRWc / CRWc 1) + ( CWc * CRWc * ( DCRPc DCRPc 1)* FXc ) On the roll start ate for the contract rolling in an on the base ate for the contract rolling out, the TDW is as follows: TDWc = CWc * CRWc * DCRPc * FXc After the completion of the roll, for the current contract, the TDW is as follows: TDWc i = c= 1 TDWc 1 + ( CWc * CRWc * ( DCRPc DCRPc 1)* FXc ) where TDWc = Total Dollar Weight for Future c on ay. TDWc -1 = Total Dollar Weight for Future c on the S&P SGMI business ay prior to ay. CWc = Contract Weight for Future c set on ay. CRWc = Contract Roll Weights for Future c on ay CRWc -1 = Contract Roll Weights for Future c on the S&P SGMI business ay prior to ay. DCRPc = Daily Contract Reference Price for Future c on ay DCRPc -1 = Daily Contract Reference Price for Future c on the S&P SGMI business ay prior to ay. FXc = Foreign Exchange Rate for Future c on ay S&P Dow Jones Inices: S&P Systematic Global Macro Inex (S&P SGMI) Methoology 23

25 Contract Weight Contract Weights (CWs) are etermine on the last S&P SGMI business ay of each month. Effective for the following roll start ate. The CW value is calculate as follows: CW = Multiplier * Number of Contracts * Position Multiplier = the value of a point For etermination of the Number of Contracts an Position please refer to the Appenix. Contract Roll Weights Logic On a given non-roll ay, CRW1 = 1 an CRW2 = 0 During the Roll Perio the CRW value is compute as follows: For the S&P SGMI the number of roll ays is five (5). CRW = 100% number of roll ays = 20% Since the number of roll ays is five, 20% of its component will roll in an roll out aily, keeping the aggregate Component s weight total of 100%. ay CRW1 CRW S&P Dow Jones Inices: S&P Systematic Global Macro Inex (S&P SGMI) Methoology 24

26 Normalizing Constant In orer to assure continuity of the S&P SGMI an to allow comparisons of the value of the S&P SGMI to be mae over time, it is necessary to make an ajustment to the calculation of the S&P SGMI each time the CWs are change. The factor use to make this ajustment is the Normalizing Constant (NC) an is use in the same manner as similar factors applie to the calculation of other publishe financial market inices. The NC is etermine each time the composition of the S&P SGMI is change pursuant to the proceures set forth in this methoology. NC new = NC ol * ( CW 2 * DCRP1 + CW 2 * DCRP2 ) + SC1 ( CW1* DCRP1 + CW1* DCRP2 ) + SC2 where CW1 = Last month s Contract Weight CW2 = This month s Contract Weight SC1 = Short Component effective uring the last month, expresse in the same terms as Contract Weights, CWs SC2 = Short Component effective in the current month, expresse in the same terms as CWs DCRP1 = Current contract price on ay DCRP2 = Next contract price on ay NC ol = Normalizing Constant effective as of the last month Excess Return Calculation On a given S&P SGMI business ay,, the S&P SGMI Excess Return (ER) inex level is equal to the prouct of the S&P SGMI ER inex level on the immeiately preceing S&P SGMI business ay multiplie by one plus the Contract Daily Return as of that ay. The Inex is calculate to a seven (7) igit precision. ER = ER * 1+ where 1 [ CDR ] ER = Excess Return Value for S&P SGMI Business Day. ER-1 = Excess Return Value as on the S&P SGMI business ay prior to ay. CDR = Contract Daily Return of the Inex on the S&P SGMI business ay prior to ay. S&P Dow Jones Inices: S&P Systematic Global Macro Inex (S&P SGMI) Methoology 25

27 Contract Daily Return Calculation The Contract Daily Return (CDR) on any S&P SGMI Business Day,, is equal to the ratio obtaine by iviing the Total Dollar Weight Obtaine by the Total Dollar Weight Investe on the immeiately preceing S&P SGMI Business Day, minus one. CDR = TDWO TDWI 1 where TDWO = Total Dollar Weight Obtaine for S&P SGMI Business Day. TDWI = Total Dollar Weight Investe for S&P SGMI Business Day. Total Dollar Weight Obtaine On a given S&P SGMI business ay,, the Total Dollar Weight Obtaine (TDWO) is the amount obtaine from an investment on the immeiately preceing ay. The TDWO for a given ay is calculate using the Component Weights an Contract Roll Weights in effect on the immeiately preceing ay, -1, an the Daily Contract Reference Prices use to calculate the S&P SGMI Inex on ay. NCnew TDWO = * ( TDWI1 + TDWO2) NCol TDWO1 = i c= 1 TDW1 1 + ( CW1c * CRW1c 1* ( DCRP1c DCRP1c 1) * FXc) + SC1 TDWO2 = i c= 1 where TDW 2 ( 2 * 2 * ( 1 + CW c CRW c 1 DCRP c DCRP2c 1) * FXc) + SC2 TDWO1 = Total Dollar Weight Obtaine of the current contract on ay TDWO2 = Total Dollar Weight Obtaine of the next contract on ay CW1 = Contract Weight of the current contract on ay CW2 = Contract Weight of the next contract on ay CRW1-1 = The roll-out percentage of the Contract Roll Weight on the S&P SGMI business ay prior to ay. 2 S&P Dow Jones Inices: S&P Systematic Global Macro Inex (S&P SGMI) Methoology 26

28 CRW2-1 = The roll-in percentage of the Contract Roll Weight on the S&P SGMI business ay prior to ay. DCRP1 = Current contract price on ay DCRP2 = Next contract price on ay SC1 = Short Component effective last month SC2 = Short Component effective in the current month. NC ol = Normalizing Constant effective as of the last month NC new = Normalizing Constant effective uring this month Total Dollar Weight Investe On a given S&P SGMI business ay,, the Total Dollar Weight Investe (TDWI) is equal to the Total Dollar Weight of the immeiate preceing S&P SGMI business ay -1 an is calculate as follows: NCnew TDWI = * ( TDWI1 + TDWO2) NCol TDWI1 = TDW1 i c= 1 TDWI2 = TDW 2 where i c= SC1 1 + SC2 TDWI1 = Total Dollar Weight Investe of the current contract on ay TDWI2 = Total Dollar Weight Investe of the next contract on ay TDW1-1 = Total Dollar Weight of the of the current contract on the S&P SGMI business ay prior to ay. TDW2-1 = Total Dollar Weight of the next contract on the S&P SGMI business ay prior to ay. SC1 = Short Component effective last month SC2 = Short Component effective in the current month. NC ol = Normalizing Constant effective as of the last month NC new = Normalizing Constant effective uring this month S&P Dow Jones Inices: S&P Systematic Global Macro Inex (S&P SGMI) Methoology 27

29 Total Return Calculation On any given calenar ay,, the Treasury Bill Return (TBR) is equal to an amount etermine in accorance with the following formula: TBR = *TBAR 1 1 / 91 1 where: TBAR -1 = The 3 month T-Bill Rate available on the S&P SGMI business ay prior to ay.. On a given S&P SGMI business ay,, the value of the S&P SGMI Total Return (TR) Inex is equal to the prouct of (i) the value of the S&P SGMI TR on the immeiately preceing S&P SGMI Business Day, (ii) one plus the sum of the Contract Daily Return an the Treasury Bill Return on the ay on which the calculation is mae, an (iii) one plus the Treasury Bill Return for each non S&P SGMI Business Day since the immeiately preceing S&P SGMI Business Day. The result of the foregoing calculation is, then, roune to seven (7) igits of precision. The calculation of the S&P SGMI TR for any S&P SGMI Business Day,, is obtaine by rouning the expression below to seven igits of precision. ays SPSGMITR SPSGMITR * (1 + CDR + TBR )* (1 TBR ) where = 1 + SPSGMITR -1 = S&P SGMI TR Inex value on the S&P SGMI business ay prior to ay. CDR = The Contract Daily Return on ay. TBR = Treasury Bill Return on ay. Days = Number of non S&P SGMI business ays since the last immeiate preceing S&P SGMI Business Day. S&P Dow Jones Inices: S&P Systematic Global Macro Inex (S&P SGMI) Methoology 28

30 Glossary Term CDR CRW CW DCRP Active Contract Contract Expiration NC Roll Perio ER Inex Spot Inex TR Inex Treasury Bill Rate TDW TDWO TDWI TBR Description Contract Daily Return Contract Roll Weight Contract Weight Daily Contract Reference Price A liqui, actively trae Contract with respect to a Designate Contract, as efine or ientifie by the relevant Traing Facility or, if no such efinition or ientification is provie by the Traing Facility, as efine by stanar custom an practice in the inustry. A ate or term specifie by the Traing Facility on or through which a Contract is trae as the ate or term on, uring or after which such Contract will expire, or elivery or settlement will occur. The contract expiration may, but is not require to, be a particular contract month. Normalizing Constant With respect to any Designate Contract, the perio of five S&P SGMI Business Days beginning on the 2 n S&P SGMI Business Day of each calenar month an ening on the 6 th S&P SGMI Business Day of such month. Excess Return Inex, which is the accretion of the Contract Daily Return inexe to a normalize value The inex that reflects the price levels of the Designate Contracts an the CPW of each such Contract. The Total Return Inex incorporates the returns of the ER Inex an the Treasury Bill Return. Treasury Bill Rate (TBAR-1). On any S&P SGMI Business Day,, the 91-ay iscount rate for U.S. Treasury Bills, as reporte by the U.S. Department of the Treasury s Treasury Direct service at on the most recent of the weekly auction ates prior to such S&P SGMI Business Day,. Total Dollar Weight Total Dollar Weight Obtaine Total Dollar Weight Investe Treasury Bill Rate S&P Dow Jones Inices: S&P Systematic Global Macro Inex (S&P SGMI) Methoology 29

31 Inex Data In orer to reflect the performance of a total return investment in futures, three separate but relate inices have been evelope base on the S&P SGMI. 1. The S&P SGMI Spot Inex, which is base on price levels of the contracts inclue in the S&P SGMI. 2. The S&P SGMI Excess Return Inex (S&P SGMI ER), which incorporates the returns of the S&P SGMI Spot Inex as well as the iscount or premium obtaine by rolling hypothetical positions in such contracts forwar as they approach elivery. 3. The S&P SGMI Total Return Inex (S&P SGMI TR), which incorporates the returns of the S&P SGMI ER an interest earne on hypothetical fully collateralize contract positions on the futures inclue in the S&P SGMI. S&P Dow Jones Inices: S&P Systematic Global Macro Inex (S&P SGMI) Methoology 30

32 Inex Governance Inex Committee The S&P SGMI is overseen by the S&P Dow Jones Inices Commoities Inex Committee, which is responsible for all analytical methoologies an calculation of the inices. The Inex Committee may revise inex policy covering rules for selecting futures, or other matters. The Inex Committee consists solely of full-time employees of S&P Dow Jones Inices. S&P Dow Jones Inices consiers information about changes to its inices an relate matters to be potentially market moving an material. Therefore, all Inex Committee iscussions are confiential. Inex Business Committee S&P Dow Jones Inices has establishe a Business Committee to assist with the operation of the S&P SGMI. The Business Committee meets on an annual basis an at other times, if neee. The principal purpose of the Business Committee is to review the performance of the S&P SGMI against the business plan for the immeiately preceing financial year, approve the business plan for the SGMI business for the next financial year, an to iscuss prouct an competitor strategy an general business evelopment. The Business Committee may iscuss such other matters as S&P Dow Jones Inices in its sole iscretion will ecie. The Business Committee is comprise of four members, with three members appointe by S&P Dow Jones Inices an one member appointe by TBP. One of the S&P Dow Jones Inices members serves as the Chairman of the Business Committee. The Business Committee shall not have any formal ecision making power an no confiential or material non-public information is provie to the Business Committee. As the Business Committee is avisory, formal votes are not taken. The Business Committee acts solely in an avisory an consultative capacity; the Inex Committee makes all ecisions with respect to the composition, calculation an operation of the S&P SGMI. For information on Quality Assurance an Internal Reviews of Methoology, please refer to S&P Dow Jones Inices Commoities Inices Policies & Practices ocument locate uner the Resource Center on our Web site, S&P Dow Jones Inices: S&P Systematic Global Macro Inex (S&P SGMI) Methoology 31

33 Inex Policy Holiay Scheule The S&P SGMI is calculate aily base on the same holiay scheule as the S&P GSCI which follows the official NYSE holiay scheule. The Inex is calculate when the majority of the S&P SGMI futures contracts are open for official traing an official settlement prices are provie, excluing holiays an weekens. For information on Calculations an Pricing Disruptions, Expert Jugment, Data Hierarchy an Unexpecte Exchange Closures, please refer to S&P Dow Jones Inices Commoities Inices Policies & Practices ocument locate uner the Resource Center on our Web site, S&P Dow Jones Inices: S&P Systematic Global Macro Inex (S&P SGMI) Methoology 32

34 Inex Dissemination Complete ata for inex replication (incluing tickers an ata on inex levels an returns) are available through S&P Dow Jones Inices inex ata group for subscription via FTP. Tickers Inex Bloomberg Reuters S&P Systematic Global Macro Inex ER SPSGMIP.SPSGMIP S&P Systematic Global Macro Inex TR SPSGMITR.SPSGMITR S&P Systematic Global Macro Commoities Inex ER SPSGMICP.SPSGMICP S&P Systematic Global Macro Commoities Inex TR SPSGMICT.SPSGMICT S&P Systematic Global Macro Financials Inex ER SPSGMIFP.SPSGMIFP S&P Systematic Global Macro Financials Inex TR SPSGMIFT.SPSGMIFT S&P Dow Jones Inices: S&P Systematic Global Macro Inex (S&P SGMI) Methoology 33

35 Appenix Inex values an ivisors are calculate every S&P SGMI business ay. Along with the aily inex calculations, the position etermination an number of contracts (weights) calculations are mae once a month on the Rebalancing Reference ay. Position Determination Position refers to either a long, a short or no position for each futures contract. The position will be use for calculating each component s aily Total Dollar Weight. Position Value Position Type 1 Long -1 Short 0 No Position For performing position etermination S&P Dow Jones Inices requires at least 256 ays of historic closing price ata. Steps for Position etermination: 1. Beginning with the latest ay, calculate the return for the contract for that ate. The return is calculate by taking the current ay s (t) contract closing price an calculating the return for it using the previous ay s (t-1) closing price. During roll perios, contracts use in return calculations will change. For example, assuming we are rolling from a March to a June contract: On the Roll start ate: Price of March Contractt - Price of March Price Return t = Price of March Contractt On the ay after the Roll: Contractt - 1 Price of June Contractt - Price of June Contractt - 1 Price Return t = Price of June Contractt 2. Calculate the cumulative returns for each ay using the formulae above. 3. Create a time-series of aily cumulative returns. 4. Take the last 22 cumulative returns an calculate the resiuals from an Orinary Least Square (OLS) regression curve. 5. Compute the autocorrelation ajuste variance of the resiuals (AAVR). S&P Dow Jones Inices: S&P Systematic Global Macro Inex (S&P SGMI) Methoology 34

36 AAVR = Variance of Covariance of Resiuals 1 Resiuals* 1 + Variance of Resiuals n 2 This ratio is ρ, the autocorrelation lag at Calculate the aily ifferences for the cumulative returns. 7. Calculate the variance of the ifferences calculate in step 6 for the 22 ays over which the OLS was calculate. 8. Calculate the Variance Ratio using the AAVR an variance of ifferences calculate in steps 5 an 7. Variance Ratio =AAVR/Variance of ifferences 9. Calculate the F-Inverse function (FINV) using a probability =.05 (a 95% confience internal), Degree of Freeom1 = n-3 an Degree of Freeom2 = n-2, where n= If Variance Ratio FINV then increase the sample size by going back 5 more ays an repeating steps 4 through Once Variance Ratio > FINV, then the breakpoint has been reache. The slope is calculate base on the cumulative returns from the breakpoint to the rebalancing reference ay. The position value of a futures contract is, then, calculate using the Slope o If slope > 0, then Position Value=1 (Long) o If slope < 0, then Position Value=-1 (Short) o If slope = 0, then Position Value=0 12. If all historic contract prices are use an Variance Ratio is still less than FINV then the contract start ate become the breakpoint. The slope an positions are calculate as mentione in Step 11. Number of Contracts The following calculation is one once every month to etermine the number of contracts for each inex component. 1. The following parameters are use for the calculation of the number of contracts i. Assets Uner Management (AUM). This is a constant (US$ 10 billion) use to calculate the number of contracts. For example a ifferent number of contracts woul be purchase in the inex for US$ 10 million versus if there were US$ 100m. The weights will be the same but the number of contracts will be ifferent. ii. Target Volatility (17.5%) iii. Local Currency Per Unit for all futures contracts present in the inex iv. Threshol Floor (0.125%) v. Threshol Ceiling (300%) S&P Dow Jones Inices: S&P Systematic Global Macro Inex (S&P SGMI) Methoology 35

37 2. The following calculations are one to arrive at the number of contracts i. Volatility Per Day = Target Volatility 256 ii. Daily Risk Allowance = Volatility Per Day * AUM iii. Compute the average correlation factor using the last 256 aily returns of each instrument iv. Calculate the stanar eviation of the price ifferences for each instrument for the last 60 ays v. For each instrument, US Dollar Risk = Local Currency Per Unit * St Deviation of Price Differences * Fx Rate vi. For each Instrument, Risk Allowance = Sector Weight * Instrument Weight * Daily Risk Allowance where 100% Sector Weight = Number of Sectors Instrument Weight = vii. For each instrument, SectorWeight Number of Instruments in the Sector Final Risk Allowance = Risk Allowance * Correlation Factor (roune to 1 ecimal) viii. Contract Size = Final Risk Allowance ; (roune to 0 ecimals) US Dollar Risk ix. Nominal Value in Dollars = Local Currency Per Unit * FX Rate * Contract Size * Instrument s Last Closing Price Volatility x. Ratio Nominal = US Dollar Risk *Contract Size Nominal Value in Dollars Volatility xi. If the Ratio is less than the Threshol Floor then the Contract Size Nominal is 0, otherwise it is as calculate in step viii xii. Nominal Value as a Percent of AUM = Nominal Value in Dollars AUM S&P Dow Jones Inices: S&P Systematic Global Macro Inex (S&P SGMI) Methoology 36

38 xiii. Total Nominal Exposure= ( Nominal Value as a Percent of AUM) for all futures in the inex xiv. If Total Nominal Exposure > Threshol Ceiling then, o Scale Back = o Scale Back = 1 Cash Weight Calculation Threshol Ceiling Total Nominal Value, else o Number Of Contracts = Scale Back * Contract Size; roune to 0 ecimals Cash Weight= AUM Total Dollar Weight ( Open of the Rebalancing Reference Day) The Rebalancing Reference Day is the close of business of the last traing ay of each month. The Rebalancing Day is the secon traing ay of each following month (this is also the contract Roll Start ate). Precisions for Calculation The following are the precisions use for calculations OLS 15 Decimals FINV 2 Decimals Variance Ratio 2 Decimals Correlation Factor 1 Decimal Stanar Deviation 14 Decimals Contract Size (Instrument Weight) Roune to Nearest Whole Number Cash Weight 14 Decimals S&P Dow Jones Inices: S&P Systematic Global Macro Inex (S&P SGMI) Methoology 37

39 S&P Dow Jones Inices Contact Information Inex Management Davi M. Blitzer, Ph.D. Managing Director & Chairman of the Inex Committee Mark Berkenkopf Associate Director Prouct Management Joi Gunzberg Vice Presient Marya Alsati-Mora Associate Director Meia Relations Davi Guarino Communications Client Services Beijing Dubai Hong Kong Lonon New York or Syney Tokyo S&P Dow Jones Inices: S&P Systematic Global Macro Inex (S&P SGMI) Methoology 38

40 Disclaimer S&P Dow Jones Inices LLC, a part of McGraw Hill Financial All rights reserve. Stanar & Poor s an S&P are registere traemarks of Stanar & Poor s Financial Services LLC ( S&P ), a part of McGraw Hill Financial. Dow Jones is a registere traemark of Dow Jones Traemark Holings LLC ( Dow Jones ). Traemarks have been license to S&P Dow Jones Inices LLC. Reistribution, reprouction an/or photocopying in whole or in part are prohibite without written permission. This ocument oes not constitute an offer of services in jurisictions where S&P Dow Jones Inices LLC, Dow Jones, S&P or their respective affiliates (collectively S&P Dow Jones Inices ) o not have the necessary licenses. All information provie by S&P Dow Jones Inices is impersonal an not tailore to the nees of any person, entity or group of persons. S&P Dow Jones Inices receives compensation in connection with licensing its inices to thir parties. Past performance of an inex is not a guarantee of future results. It is not possible to invest irectly in an inex. Exposure to an asset class represente by an inex is available through investable instruments base on that inex. S&P Dow Jones Inices oes not sponsor, enorse, sell, promote or manage any investment fun or other investment vehicle that is offere by thir parties an that seeks to provie an investment return base on the performance of any inex. S&P Dow Jones Inices makes no assurance that investment proucts base on the inex will accurately track inex performance or provie positive investment returns. S&P Dow Jones Inices LLC is not an investment avisor, an S&P Dow Jones Inices makes no representation regaring the avisability of investing in any such investment fun or other investment vehicle. A ecision to invest in any such investment fun or other investment vehicle shoul not be mae in reliance on any of the statements set forth in this ocument. Prospective investors are avise to make an investment in any such fun or other vehicle only after carefully consiering the risks associate with investing in such funs, as etaile in an offering memoranum or similar ocument that is prepare by or on behalf of the issuer of the investment fun or other vehicle. Inclusion of a security within an inex is not a recommenation by S&P Dow Jones Inices to buy, sell, or hol such security, nor is it consiere to be investment avice. These materials have been prepare solely for informational purposes base upon information generally available to the public from sources believe to be reliable. No content containe in these materials (incluing inex ata, ratings, creit-relate analyses an ata, moel, software or other application or output therefrom) or any part thereof (Content) may be moifie, reverse-engineere, reprouce or istribute in any form by any means, or store in a atabase or retrieval system, without the prior written permission of S&P Dow Jones Inices. The Content shall not be use for any unlawful or unauthorize purposes. S&P Dow Jones Inices an its thir-party ata proviers an licensors (collectively S&P Dow Jones Inices Parties ) o not guarantee the accuracy, completeness, timeliness or availability of the Content. S&P Dow Jones Inices Parties are not responsible for any errors or omissions, regarless of the cause, for the results S&P Dow Jones Inices: S&P Systematic Global Macro Inex (S&P SGMI) Methoology 39

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