Indexed Portfolios and Options

April 01, 1999

The author reviews the major pluses and minuses of using futures contracts to track an index in a passive portfolio and concludes the balance is heavily in favor of the pluses. He goes beyond futures to describe a strategy for outperforming the benchmark index using options.

Why not pay low fees to an index-fund manager who can deliver consistent index results, which happen to beat 60% or more of all active managers?

Unfortunately, the plan sponsor finds that simply reconstructing a portfolio to match the S&P 500 does not necessarily guarantee exact results. On the contrary, the issue of tracking error comes into play, which also introduces the notion of isolating a source of alpha and combining it with a passive indexed portfolio to better control tracking error. Additionally, we demonstrate how to turn negative tracking error into positive tracking error.


Before addressing the issue of tracking error, consider the role of futures contracts in the indexing process. Futures offer many advantages over the traditional cash-based index portfolio. Whereas cash-based index portfolios can be cumbersome to maintain due to size constraints, liquidity and rebalancing factors, a derivatives-based indexing approach can help overcome some of these difficulties, despite some costs of its own.

The dynamics of a derivatives-based portfolio are fairly simple. Instead of buying physical securities to replicate the index, futures contracts are purchased with cash invested to yield some short-term interest rate. Due to the arbitrage relationship between the futures contract and the underlying asset, the combination of futures price movement and the interest earned on the invested cash should, over time, closely track, and hopefully slightly exceed (see Indexes, Issue 1) the total return of the index. This relationship is explained below.

It is because of this relationship between cash securities and futures contracts, and the related 'ease of management' benefits, that derivatives-based indexing has become the popular choice in the investment community. When expanded to markets outside the U.S., using futures can offer a tremendous advantage:

• Asset Class Trading - As in the U.S., global equity futures are based on recognizable indexes, and allow the investor the ability to gain desired exposures without having to accumulate a 'basket' of individual stocks. Even on an individual country basis, we find that the futures contracts offer better tracking to the local index than undiversified stock baskets.

• Reduced Transaction Costs - Derivatives offer dramatic costs savings over cash securities. This is even more evident in global markets where the savings can equal up to 95% of cash securities transactions (execution, clearing and market impact) costs.

• Ample Liquidity/Rapid Execution - In many countries, futures volume will exceed cash volume (on a dollar-equivalent per day basis). Futures also allow instantaneous exposure with one execution rather than the accumulation of several individual issues. With this huge liquidity it is often possible to complete a trade entirely at the open or closing price, which can be tremendously helpful when markets are turbulent or there exists a need to benchmark a trade off the day's closing price.

• Simultaneous One Day Settlement - Futures 'settle' the next day, whereas cash securities can settle from 2 to 14 days or more after trade date. Instantaneous settlement eases the managers' ability to manage the underlying cash assets and control portfolio allocations. This benefit is especially valuable when shifting exposure between various global indexes. If one were to want to simply move money out of a European index fund, an investor in the physical securities must wait upwards of one week to receive the cash proceeds to deploy them into another index such as the S&P500. If the same investor uses futures the trade can be accomplished simultaneously on the same day and with the exposure being shifted between the markets at virtually the same time.

• Tax Advantages - Futures do not carry transfer taxes or dividend withholding taxes as certain foreign cash markets do. The average global investor pays 40 basis points in withholding taxes on their physical holdings.

• Cash Management - With the advent of single currency margining it has become much easier to generate a higher rate of return for the investor in their own home currency by concentrating the pool of margin funds into one single currency. By using currency margining, the investor can manage a true global futures program yet still post initial margin and meet or receive daily margin calls in the home currency.

Futures contracts are not without disadvantages, however, as the issue of tracking error - or the futures contract's ability to properly replicate the underlying index - is introduced.


By definition, the performance of a futures contract should closely approximate the performance of the underlying asset. If bought at fair value and held to expiration (when futures converge to a cash settlement), a futures contract should have a return equal to the cash instrument - assuming that the cash component was invested at the same rate used to calculate fair value. Unfortunately, life is not that simple. There are a variety of factors that can affect how a futures-based portfolio performs relative to the index:

• Futures Mispricing - Futures contracts will trade rich or cheap for periods based on supply/demand factors prevalent in the market at any given time. Buying futures when they trade 'rich' would lead to underperformance whereas buying cheap futures would lead to outperfor-mance. Currently, there are a number of software packages available to the institutional investor which aid in determining the 'richness' or 'cheapness' of a futures contract.

• Futures Roll - All futures have a finite life, with contracts usually expiring every 3 months. The selling of one contract (closing out the near-term) and the purchase of another (opening the next serial contract) is called the futures roll. Just as futures can trade rich or cheap, so can the quarterly roll. Whether the roll trades rich or cheap is determined by supply/demand factors in the market and the net hedging bias of 'the Street' as a whole. Periods of extended upward price movement generally lead to a rich roll period due to the demand for long futures positions. On the other hand, when there is a large short bias in the investment community, the futures roll can trade cheap as these positions are rolled as well.

• Fees - Although commission rates on futures contracts are relatively low compared to other instruments (well under one basis point per round-turn), any fee structure will result in a performance drag compared to an index free of transaction costs.

• Cash Yield - Yield differences between the actual rate earned on the total portfolio and the rate the market uses to calculate fair value will also affect the tracking of the futures contract. Libor or the 3 month U.S. Treasury Bill rate are the common choices in calculating futures' fair value. The more important factor is the managers' ability to keep 100% of the portfolio (all cash) invested in these short-term instruments. Any underinvestment will lead to a performance drag. Conversely, any cash management strategy which earns a higher yield than Libor or T-Bills will boost performance. Many index fund managers use this strategy to offset the first two costs of a derivatives-based program.

• Trading Hours - Assuming you have been successful in managing all the factors listed above, you are still faced with the performance differential which can occur due to the fact that futures trading ends 15 minutes after the cash markets close. For example, a futures price movement of just 1 point (after the close of the cash market) will equal about 10 bps difference in performance. These differentials tend to be offset when the markets reopen, but they can nevertheless affect month-end performance comparisons.

  S&P Total Return Interest Return Futures Return Futures+ Interest Return Difference Tracking Error*
1992 7.67% 3.97% 3.96% 7.93% 0.26% 0.94%
1993 9.97% 3.27% 5.62% 8.89% -1.08% 0.59%
1994 1.31% 4.46% -3.75% 0.71% -0.59% 0.57%
1995 37.47% 6.17% 30.40% 36.57% -0.89% 0.59%
1996 22.92% 5.59% 17.11% 22.70% -0.22% 1.38%
1997 33.34% 5.79% 27.75% 33.54% 0.20% 1.46%
1998 28.60% 5.51% 23.69% 29.20% 0.60% 1.25%
Total 19.48% 4.87% 13.17% 19.21% -0.27% 1.01%
Annual Risk 12.31% 2.73% 12.34% 12.41%    
* This is the monthly tracking error, annualized (i.e. multiplying by Ö12 to give us the annualized tracking error.


Comparing the year-to-year performance of the S&P500 futures contract (plus interest) and the total return of the cash index shows very similar returns over the past 7 years (1992-1998). Although annual returns compare favorably, differences can occur on a monthly basis, as evidenced by the large tracking error between the two. These monthly differences tend to cancel: If futures trade 25 basis points 'rich' (above fair value) at the end of this month, then this month's return is inflated by 25 basis points and next month's performance is reduced by a like margin.

Tracking error of the futures contract to the cash index has steadily increased over the past few years as the markets have become more volatile (although they are still nowhere near the levels of 1982-84 or 1987-88). The differences in trading hours and consistent 'richness' of the futures contract and calendar roll has led directly to increased dispersion in monthly return figures. The tracking error of futures tends to reverse from one month to the next: if futures finish this month above fair value, that typically leads to positive tracking error this month and negative tracking error next month. So this measure substantially overstates the tracking error that we can expect over the course of a full year. The graph below shows how the swings in the performance differential have grown over the past few years.

Should a plan's sponsors care about tracking error measured in a few tens of basis points when annual returns compare favorably? Of course they should! The timing of cash flows becomes critical to long term success when tracking error is introduced. At issue is the relative pricing of futures contracts when contributions and withdrawals are factored in. Contributions which are timed when futures trade 'rich' vs. withdrawals which are timed when the futures trade 'cheap' can lead to overall fund underperformance, which over time can be dramatic.


The most logical 'next step' in our exercise is to explore how to enhance this process.

The traditional approach to indexing has been to accept the indexing process for what it is - a systematic investment method to provide the portfolio with a desired 'benchmark' or target return. For one reason or another, actual results fall short of the desired result. One way to make up this difference is to employ an actively managed portfolio enhancement strategy. Portfolio enhancement can be a valuable addition to the indexing process. If structured within the context of rigidly designed objectives and risk parameters, an enhancement strategy can provide the portfolio with total returns that exceed the benchmark, without significantly increasing the portfolio's tracking error.

 It is important when assessing the benefits of any enhancement strategy that two main objectives be kept in mind: 1) The enhancement strategy should provide stable and consistent value added during all phases of an investment cycle, and 2) The enhancement strategy should not offset the ability of the base investment program to provide index returns.


Combining options with a futures-based indexing strategy can provide favorable opportunities to enhance overall returns. Using options as an enhancement tool is nothing new; investment managers have been using them since the inception of the first exchange traded options in 1974. Typically, options are sold in the portfolio with returns generated as these options decay in value over time. There are a variety of option-based strategies that can be employed to enhance portfolio returns. Each of them carries their own set of risk parameters and profitability profiles. At First Quadrant, we designed the Tactical Option Program with this mandate in mind, specifically the creation of an option-based strategy that can be used as an enhancement to any portfolio.

This strategy incorporates the simultaneous purchase and sale of put and call options over a variety of financial markets, either domestic or global. In the program, a portfolio of options is created to maintain a 'market neutral' exposure over a wide range of market price movements. The combination of long and short positions allows for specific management of the risks inherent in option-based strategies, namely the delta (market exposure) and gamma (change in market exposure) of each option position. The strategy profits from the difference in decay rates of the options sold and the decay of the options bought:

The ability of this strategy to provide stable and consistent returns while mitigating losses during volatile market periods we feel is best suited to an enhancement program. When combined with 'direction-based' strategies (such as an index program), we find that it consistently adds value, and at the same time, reduces the volatility of portfolio returns.

The combination of our Tactical Option Program with a base futures equitization strategy has proven to be quite successful. The following table provides a performance recap on this approach.

  Futures S&P 500 Return F.Q.'s +T.O.P. Return Total T.O.P. Alpha Program Alpha
1992 7.67% 12.36% 4.14% 4.69%
1993 9.97% 9.06% 0.15% -0.91%
1994 1.31% 2.41% 1.68% 1.10%
1995 37.47% 33.66% -2.21% -3.81%
1996 22.92% 23.42% 0.49% 0.50%
1997 33.34% 41.18% 5.67% 7.85%
1998 28.60% 34.09% 3.88% 5.49%
Annual 19.48% 21.55% 1.99% 2.07%
Standard Deviation 12.32% 12.21% 1.98% 2.42%

A few observations concerning the table:

• The inclusion of the T.O.P. in a futures-based index strategy led to a total alpha of 207 bps. per annum, while the standard deviation of portfolio returns actually decreased by 11 bps.

• Along with an alpha of 207 bps, the tracking error of the portfolio increased to 242 bps, in effect, creating positive tracking error.

• FQ's 'enhanced index' strategy was profitable 6 out of 7 years, compared to only 3 out of 7 for a futures-only replication.


We believe there are long term benefits to be gained by introducing an enhancement element to a core indexation strategy. The key to a successful enhancement program is, as it is with all successful investment programs, based on the objectives and guidelines as defined by the investment committee or plan sponsor.

Important to this concept are the two objectives of an enhancement program as outlined earlier, and which bear repeating:

1.The enhancement strategy should provide stable and consistent value added during all phases of an investment cycle, and

2.The enhancement strategy should not offset the ability of the base investment program to provide index returns.

Ultimately, the viability of any enhancement program will rest on the program's ability to generate alpha. Whereas a core investment strategy is designed to provide 'exposure-based' returns, second tier strategies (enhancement, overlay, etc.) are designed to add value. Without the ability to consistently add value, the enhancement program offers the portfolio no value at all.

Even within the most passive approach to indexing, we would recommend the inclusion of such an enhancement strategy. When managed within a set of well-defined objectives and guidelines, we feel that the benefits of an enhancement program can provide an important addition to any portfolio. S


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