Replicating & Outperforming GSCI

There are many options available to the institutional investor who seeks to gain exposure to the GSCI® Total Return Index (GSCI-TR). One popular alternative is to utilize the GSCI futures contracts traded at Chicago Mercantile Exchange® (CME). This affords the investor a liquid market with transparent pricing, flexibility to adjust exposure on a daily basis, and the opportunity to closely track the GSCI-TR and potentially outperform it.

This paper will briefly discuss the components of return that make up the GSCI-TR, examine how CME GSCI futures can be used to reproduce that return and review a few basic strategies for outperforming the benchmark.

Investors should obtain copies of the CME publication GSCI Futures & Options Information Guide as well as the Goldman, Sachs GSCI Manual, 2001 Edition. Both these publications are referenced below.

Return Components of the GSCI Total Return Index
The GSCI-TR measures the total return of a hypothetical investment in the commodity futures market with the following basic characteristics:

26 constituent commodity futures contracts, supporting 21 commodities, where each commodity is weighted according to world production. [When more than one futures contract supports an individual commodity, such as crude oil, the futures contracts are weighted according to relative liquidity (see The GSCI Manual, 2001 Edition)];

Futures position maintained in the first or second nearby contract of each underlying commodity;

Futures position rolled forward on the 5th through 9th business days of the month for each underlying contract expiring in that month, one fifth of position rolled each day; and

Cash position equal to 100% of futures contract value maintained in an account earning the weekly 3-month T-bill rate with zero duration.

A futures investment with these characteristics has three components to its total return:

Spot return - Represents the basic up and down movements in the price of the underlying commodities. For example, if crude oil prices rise from $15 to $18 over the course of a year, that represents an annual spot return of 20% for crude oil. The spot return of the GSCI-TR is the production-weighted spot return of the 26 underlying commodity futures.

Roll return - Represents the cost or benefit of rolling the futures positions forward each month. Whether this is positive or negative for an individual commodity depends on whether the price for the contract being rolled into is lower (backwardation) or higher (contango) than the contract being rolled out of. For example, if the GSCI rolls from January crude oil at $15.00 to February crude oil at $14.75, that represents a roll return of +1.67% ($0.25/$15.00) for crude oil for that month . The annual roll return of the GSCI-TR is the production weighted sum of the roll returns of the 26 underlying commodity futures for each month each commodity rolls. It should be noted that roll returns may be offset by spot returns, and thus not completely realized. In the above example, if February crude oil remained at $14.75, the +1.67% roll return would be offset by a -1.67% spot return, for a zero net excess return (spot return + roll return). If however, February crude oil rose in price to $15.00, then the spot return would be zero for that month, the roll return +1.67%, and the excess return +1.67%.

Collateral return - Represents the interest earned on a cash position equal to 100% of the dollar face value of the underlying futures contracts comprising the GSCI-TR. The GSCI-TR imputes a 3-month T-bill return to this cash position. The T-bill rate is updated weekly and the return calculation assumes a zero duration for the cash position . Note also that the GSCI-TR assumes that all margin accounts earn this T-bill rate.

Taken together, these three components comprise the return in the GSCI-TR. We will next look at the characteristics of the GSCI futures on CME and how they can be used to replicate the GSCI-TR.

GSCI Futures on CME
The GSCI futures on CME can be thought of as a production-weighted average of the 26 underlying commodity futures contracts. Therefore, any property of the GSCI futures (spot price, forward price, volatility) will be essentially an average of the properties of the underlying contracts, with the contracts with the largest production weights having the greatest impact on the average. This is a useful point to remember in understanding the behavior of GSCI futures. This property of the GSCI futures makes it extremely easy to replicate the GSCI-TR, because all the underlying components are present with the appropriate weights. Essentially, instead of rolling 26 individual commodity contracts forward, only one contract is needed.

The GSCI futures have the following important properties:

Monthly contracts - Each month's GSCI contract has the appropriate individual commodity nearby contracts underlying it;

Eleventh business day expiration - The contracts expire two days after the GSCI-TR's roll period is finished;

Cash settlement - If held to expiration, the GSCI futures settle against a production-weighted average of the underlying commodity contracts; and

Contract size - $250 x index value.

Pricing GSCI Futures
It is a relatively simple matter to determine the fair market value of GSCI futures. The theoretical price of a given GSCI futures contract month is simply the production-weighted sum of the component contracts divided by the normalizing constant. Details necessary for pricing the futures (components, weights, normalizing constants) are in the CME GSCI Futures & Options 2001 Information Guide and the GSCI Manual, 2001 Edition.

It is possible to price the futures on a real-time basis with a futures data source that feeds directly into a spreadsheet. In fact, a real-time fair-value calculator is present in the GSCI pit at CME and most brokers can report the fair-value to their clients.

There are several reasons that the actual market price may differ from the theoretical fair-value price:

Stale prices - Because the various markets in the GSCI are not all open at the same time during the day [see CME GSCI Futures & Options Information Guide] , the prices that are automatically fed to the fair-value calculator may be stale for those markets that are not yet open.

Last Price - the price computed by the fair value calculator is based on the "last price" traded in the underlying futures contracts. The last price traded may not necessarily be the next price traded, and therefore may not be the best price to use for estimating the fair value of GSCI futures. The next price may depend on the liquidity of the underlying markets and the volume being traded.

Closed markets - GSCI futures trade after all the underlying markets have closed for the day. For this reason bid/ask spreads in the market prices may widen considerably after the constituent markets begin to close.

London Metals Exchange (LME) prices - There are no real-time price feeds available for the LME prices used in the GSCI end-of-day calculation. Therefore, for a portion of the trading day, yesterday's LME prices may be used in the fair-value calculation until today's prices become available from London. In addition, LME markets may have holidays that U.S. markets do not.

Limit moves - If a component of the GSCI is limit up or down, the market price can trade away from the fair-value computed using the limit price.

For these reasons most market makers have developed means of estimating the futures prices that have the problems described above to determine a fair market price that is more relevant than the naïve fair-value calculated using only exchange-supplied prices.

Institutional GSCI futures users may wish to construct their own fair-value calculators to be able to determine when the futures are trading cheaply or richly, and thus have the ability to minimize transaction costs.

Replicating the GSCI-TR With CME GSCI Futures
Replicating the GSCI-TR using CME GSCI futures is a relatively straightforward exercise, but care must be taken to minimize tracking errors and transaction costs. We will discuss implementation of a hypothetical $50 million USD investment.

An initial position is established in GSCI futures with a face value of $50 million USD. Depending on the time of month, the position is established in the following GSCI contract months:

Business Day of Month	% Position in First Nearby	% Position in Second Nearby
1 - 4	100%	0%
5	80%	20%
6	60%	40%
7	40%	60%
8	20%	80%
9 - Last	0%	100%

Note: It is important to note the percentage of position shared between the first and second nearby contracts during the GSCI roll period of the fifth through ninth business days should be interpreted as number of contracts, not dollar amounts.

For example suppose a $50 million USD position is to be established on the fifth business day of November 1998 between the Nov98 contract trading at 147.3 and the Dec98 contract trading at 151.2. We know that the total face value of the contracts must be $50 million USD and that 80% of the number of contracts must be in November and 20% must be in the December contract. The calculation is as follows:

Number of Nov Contracts * $250 * 147.3 +
Number of Dec Contracts * $250 * 151.2 = $50 million USD

Number of Nov Contracts = 4 * Number of Dec Contracts

Substituting and solving:

Number of Nov Contracts	=	1080
Number of Dec Contracts	=	270
Total Contracts	=	1350
Dollars Nov Contract	=	$39,789,303
Dollars Dec Contract	=	$10,210,697
Total Dollars	=	$50,000,000

Notice that the November position has exactly 80% of the number of total contracts, but only 79.6% of the total dollar value of the position. Depending on the relative price differential between the November and December contracts this discrepancy will be more or less pronounced.

The initial GSCI futures position, and in fact all GSCI futures trading is most efficient, in the time window during the day when all the underlying markets are open [see CME GSCI Futures & Options Information Guide].

An initial $50 million USD cash position is established in short-term, low-duration instruments. This position is split between a margin account for the futures and another cash account for the remainder of the collateral. The instruments used should be of very low duration, as the GSCI collateral return calculation assumes zero duration and 3-month T-bill yields updated weekly.

The GSCI futures position is rolled forward every month during the fifth through ninth business days. The position is rolled forward so that the total dollar face amount remains constant during the roll and the relative numbers of contracts held between the first and second GSCI nearbys follows the schedule in Table 1.

The calculation used to determine the relative number of contracts to hold during the roll is identical to the calculation shown above to determine the initial GSCI position.

Because the GSCI-TR is calculated based on the assumption that the rolls occur at the settlement prices of the individual contracts, the GSCI futures should be rolled as late in the trading day as possible provided that a sufficient number of the underlying markets are open.

Outperforming the GSCI-TR Using CME GSCI Futures
GSCI futures have enough flexibility to enable an investor to attempt to outperform the GSCI-TR in several ways.

Adjusting net exposure - A bullish or bearish investor can simply increase or decrease the number of GSCI contracts held to express his view relative to the GSCI-TR. It is to be noted that this type of market timing approach has a somewhat dubious track record for most investors across most asset classes.

Tilting individual commodity exposure - By using individual commodity futures contracts overlaid on top of a GSCI futures position, the exposure to an individual commodity or commodity sector may be increased or decreased. For example, an investor can trade crude oil on top of the GSCI to add value while only needing to trade 2 contracts instead of 26.

Rolling early and/or late - An investor who believes that the net cost of rolling his position may be more attractive before the fifth business day of the month or after the ninth business day of the month can do a roll before or after the GSCI rolls. Some investors roll a portion of their position a few days earlier and a portion a few days later than the GSCI.

Rolling out on the futures curve - This is a somewhat sophisticated strategy for outperforming the GSCI-TR during periods of time when the deferred contract months are priced at a premium to the nearby months (contango market). Because the typical shape of the forward curve is convex and non-linear during periods of contango [see Chart 1], the annualized cost of rolling may be reduced by rolling into a GSCI contract a month or two further out than would normally be appropriate.

For example, in the market conditions shown in Chart 1, the costs of rolling from the Nov98 contract:

To Dec98 contract:
151.2 / 147.3 - 1 = 2.6% for one month or 31.8% annualized.

To Jan99 contract:
151.8 / 147.3 - 1 = 3.1% for two months or 18.3% annualized.

To Feb99 contract:
152.5 / 147.3 - 1 = 3.5% for three months or 14.1% annualized.

Although it appears that rolling out on the curve in periods of contango should be an automatic free lunch, there are at least two reasons why it may not be so:

1. The reduced carry cost must be weighed against increased bid/ask spreads in the GSCI futures contract in the outlying months.

2. Care must be taken to volatility match the position taken in a GSCI contract that is mismatched in maturity. Typically, the volatility of the front month GSCI contract is much higher than that of the second or third month’s and it is not perfectly correlated [see Charts 2 and 3]. If an investor rolls out on the GSCI curve he needs to over-hedge by the ratio of the contract volatilities multiplied by their correlation to minimize the basis risk of the position:
Hedge Ratio = correlation * volatility contract one / volatility contract two.

This over-hedge increases the cost of carry in direct proportion to its size. It is also not a perfect hedge, as the volatility and correlation parameters must be forecast somehow from market conditions and historical data. Therefore, there will be residual basis risk in the position depending on the accuracy of the forecasts. This basis risk may be considerable in the case of a large price change in the front month. An estimate of the hedge ratios for the Nov98/Dec98 and Dec98/Jan99 contract pairs is shown in Chart 4. This chart demonstrates that being mismatched in maturity with GSCI contract pairs may frequently require an increased position in the longer dated contract because of its reduced volatility. The estimate in Chart 4 was done using the 20 day historical correlations and volatilities from Charts 2 and 3. A better estimate might include forward-looking implied volatilities from the GSCI or individual commodity futures options markets.

Writing covered calls - Although they are currently thinly traded, options on GSCI futures trade on CME. This enables an investor who is neutral to bearish to write calls on his underlying position. The investor will earn the call premium as long as the GSCI does not rise to a level above the strike at which the calls were written. An investor can limit his under-performance in the case of large, unanticipated upward moves in the GSCI by writing call spreads instead of outright calls. This limits his under-performance to the spread between the strikes of the written and purchased calls.

Agressive cash management - Because the GSCI-TR only assumes a three month T-bill yield in its cash calulation, it should be relatively easy for most investors to outperform this portion of the benchmark. It is to be emphasized that the GSCI T-bill calculation assumes a zero duration position so that any duration exposure that is taken in cash is a pure risk position on the part of the investor. A cash position that earns 3-month LIBOR is a good match to the GSCI-TR and should outperform by the short term TED spread [see Chart 5].

There are of course a wide variety of more aggressive cash stragegies that are pursued by index out performance managers. Any of these may be considered for a GSCI program.

Conclusion
The GSCI futures contracts traded on CME are a flexible tool for both replicating and outperforming the GSCI Total Return Index. However, managers must take care to understand the unique pricing and trading characteristics of GSCI futures to ensure optimal results. There are several basic steps managers should take to improve their performance:

1. Be aware of the GSCI futures fair-value calculator in the CME pit and its limitations.

2. If possible, construct an in-house real-time fair-value calculator.

3. Understand why the futures may trade away from fair-value during certain times of the day and under certain market conditions.

4.Use the flexibility of rolling GSCI futures to roll anywhere between the first and 11th business days of the month.

More experienced managers may want to consider the following proposals:

1. Constantly examine the GSCI futures curve for opportunities to roll further out, while understanding the trade-off between roll cost, trading spreads and basis risk.

2. Consider using covered calls in neutral-to-bearish environments.

3. Consider trading one or two underlying commodities as overlays on the GSCI futures position. Crude oil is a natural place to start.

4. Manage the collateral as aggressively as possible, while understanding that the GSCI has a zero duration cash return calculation.

The management of GSCI Total Return accounts is still a relatively new business area for most organizations, and aggressive managers should be able to find numerous ways to add value.