The concept of indexation long has been accepted by both institutional investors and, increasingly, retail mutual fund buyers. The premise behind indexation is simple: over time, an actively managed portfolio is expected to underperform an unmanaged index by the cumulative costs of active management.
Implicit in the acceptance of indexation, however, is the full acceptance of market risk. While common stocks have outperformed other asset classes over time, the history of equity markets is replete with both long periods of both underperformance relative to other asset classes and absolute loss.
However, there is a methodology that can produce, over time, returns greater than or equal to those of an unmanaged index in a favorable price environment, but with less market risk in an adverse price environment.
Concept and methodology
Sophisticated investors quickly realize the non-linear profit profiles described above can be achieved only through the use of options. Yet a fairly priced option position cannot be expected to outperform an unmanaged index because of the effects of time decay.
Superior performance from an option-based index can be derived from structuring of the position and management of the position over the life of the trade.
Structuring of the position is achieved through the use of proprietary methodology designed to provide maximum return at minimal risk and cost. The system is expected to produce positions with superior stochastic properties at a lower cost than a simple option purchase.
By substituting an enhanced position for a normal index alternative, such as the Standard & Poor's Depository Receipts or customized baskets, several benefits are realized. First and foremost is downside protection. Second, because an option position requires only a fraction of the funds required by a risky equity position, the remaining capital can now be devoted to money market instruments. Third, these positions can be managed according to the discipline described below.
Management of the position over the life of the trade is accomplished through the disciplined application of a few simple trading rules. The most important is the disposition of excess position delta, which is the expected change in the option price given a change in the underlying index price. Delta management is achieved by matching the total delta of a position against a target exposure.
For example, with the S&P 100 index (OEX) trading at 423.62, it would take a total delta of 1,180 to match the price behavior of $50 million of the index. A position placed to match this exposure would become overhedged if the OEX rose from its original level. The excess call option delta could then be sold back to the market to both defray the original cost of the position and to reduce the overall risk of the holdings. This automatic "scale-up" selling feature allows the structured position to outperform the unmanaged index in favorable markets.
In addition to delta management, the gamma, or rate of change of position delta with respect to price, must be managed as well. In practice, this involves selling existing option position after favorable market moves and replacing them with delta-equivalent positions at another strike; this tactic both maximizes the return from subsequent favorable market moves and protects existing profits from subsequent adverse market moves.
The fundamental principle of position management is that the net delta of the position must be less than or equal to the target exposure of the position (1,180 in the reference above), with maximal gamma. Should the market decline, and the position delta falls below the target, additional calls are not purchased to maintain full exposure. This is how structured option positions can be expected to outperform the unmanaged index in adverse markets as well. Since there are no "free lunches" in the markets, zones of underperformance should occur as well, and will in fact occur at both trend turning points and periods of quiescence.
A case study
In order to test whether the assertions above perform as stated, a simulated portfolio test was launched at the end of July 1994 for two hypothetical $50 million portfolios indexed to the OEX. One of these portfolios had an inverse relationship to the OEX; it was designed to profit if the OEX declined. The following constraints were imposed.
Purchases and sales would be "filled" at the offer and bid prices at the close, respectively.
No intraday position management would be allowed.
Commission costs would be $9 per round turn.
The positions would be placed in the second nearby option month and would be rolled forward each month as the spot options expire.
Both these portfolios and the base-case unmanaged OEX portfolios were normalized to a $10 per share net asset value at initiation. The incremental percentage gain path of the two portfolios are shown in the accompanying graphs.
The performance history seems to confirm the predictions. The long enhanced portfolio outperformed the unmanaged index up until the mid-September market top. Excess position delta was sold from the position throughout this period. As the market fell rapidly from mid-September, the downside protection inherent in the option structure made its presence felt, and the enhanced portfolio rapidly recovered it relative performance to the unmanaged index.
Another drop occurred with the mid-October rally, and, once again, the enhanced portfolio rapidly recovered its performance advantage to the unmanaged index. A final, more protracted period of underperformance occurred in fall following the November election and the subsequent choppy recovery; overperformance was restored after mid-December.
The short enhanced portfolio underperformed the unmanaged index up until the mid-September top by virtue of being consistently underhedged. As the market fell, the enhanced portfolio sharply underperformed the index for several days, and then recovered its relative performance rapidly. The sharp market drop of mid-November propelled the short enhanced portfolio to substantial overperformance, which has been retained through the end of December.
These relative performance profiles are not mirror images of one another for two main reasons. First, the option structures determined for each portfolio were quite different; the long enhanced portfolio generally consisted of "calendar call spread" - buying a call in a near month and selling an out-of-the-money call in a later month - or in "calendar bull put spreads" - buying an at-the-money put in the near month and selling a deep-in-the-money put in a later month.
The short enhanced portfolio generally employed either simple put positions or "calendar straddles" - buying an out-of-the-money call in a near month and an in-the-money put in a later month.
Second, the path of the market determines what position management is required.
The sharp rise in the market in August allowed the long portfolio to seize a greater advantage, while the sharp drops in early October and mid-November allowed the short portfolio to achieve greater outperformance.
Enhanced index portfolios can be constructed for any common index for which liquid options are available, including fixed-income portfolios, commodity-linked portfolios and international equity portfolios, or any combination thereof.
The trading history of the OEX portfolios underscore the ability of properly structured option positions to both retain outperformance in favorable markets and to achieve downside protection at a reasonable cost.
A family of such index funds - long/short equity, long/short fixed income, global long/short fixed income and cash - could be constructed with frequent but not unlimited portfolio switching allowed.