benefits_option-based_strategies

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The Benefits of Index Option-Based Strategies for Institutional Portfolios: Summary Version

Thomas Schneeweis, University of Massachusetts

Richard Spurgin, Clark University

Preliminary Version

March 23, 2000

Abstract

This study reviews the potential benefit of index option-based strategies as well as the unique risk and

return distributions that result from these strategies. The empirical results are based on the replication of

passive option-based strategies using daily option data collected over the past thirteen years. Thesepassive benchmarks are then compared to the performance of a number of active managers. The results

indicate that many passive investment strategies offered risk-adjusted returns that exceeded theunderlying index over the time period studied. Furthermore, the returns to these passive option-based

strategies provide useful benchmarks for the performance of the active managers studied. Results

presented here demonstrate that the source of this additional return can be identified and explained by

combining a passive stock index investment with a passively managed option portfolio. This is important

because it demonstrates that the returns achieved by actively managed strategies are not necessarilydependent on the unique skills of the managers.

Please Address Correspondence to:

Thomas SchneeweisCISDM/SOM

University of Massachusetts

Amherst, Massachusetts 01003

Phone: 413-545-5641

Fax: 413-545-3858

Email: [email protected]

The authors gratefully acknowledge the research support provided by the Chicago Board Options

Exchange, as well as ongoing research support provided by the Center for International Security and

Derivative Markets at the Isenberg School of Management, University of Massachusetts.


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The indexes are constructed by assuming a new equity index option is written at the close of trading each

day. The option is priced using prevailing implied volatility and interest rates. Two strategies are

employed. The first uses options that expire at end of the next day's trading. The payoff to the option is

determined by the change in the underlying stock index. This is clearly not representative of a typical

option strategy. Investors rarely deal in 1-day options, and generally close out positions prior to

expiration. However, as a benchmark, this strategy will be useful for analyzing the returns associated

with trading short-dated options. The second strategy involves buying (selling) a 30-day option each dayand then selling (buying) the option the next day. The payoff to this strategy depends on both on change

in the underlying index and the daily change in implied volatility. Benchmarks derived from this strategy

will be useful for investors who hold longer-dated options.

Returns are reported as annualized average daily returns (without compounding). The annualized

standard deviation of daily returns is also reported, as is the Sharpe ratio for the strategy. The M2of the

strategy is computed. This measure of risk-adjusted return shows what the return of the strategy would

have been if it had been levered up (or down) to the same volatility as the SP500. The final statistic

reported is the correlation of the strategy with the SP500. A strategy with a low correlation with the

SP500 will provide diversification benefits when combined with an equity portfolio.

Historical Returns to Option-Based Strategies

Returns to various option strategies over the 1987-1999 test period are reported below. A number ofcommon strategies are analyzed:

Buy-write: Purchase underlying index and write call options on the index. This strategy is analyzed

for at-the-money call options as well as options 1% above the current index value.

Protective Put: Purchase underlying index and purchase put options on the index. This strategy is

analyzed for at-the-money put options as well as out-of-the money put options.

Short Volatility: Write both put and call options on the index. Strategy is analyzed using at-the-

money options (straddle) as well as out-of-the-money puts and calls (strangle). As this index does notinvolve purchasing the index, remaining cash is assumed invested in T-Bills.

Collar Strategy: Purchase underlying index, write out-of-the-money call options on the index, and

purchase out-of-the-money put options on the index.

Pure Collar: Write out-of-the-money call options on the index, and purchase out-of-the-money put

options on the index. No position in underlying index. Invest collateral in T-Bills.

Exhibit 1 shows that strategies incorporating option writing generally offered higher risk-adjusted returns

than the SP500 over the period studied (1987 1999). The Sharpe ratio of the SP500 over the period was

0.66. Protective put strategies, which involved combining put options with a position in the index had

lower risk-adjusted returns than an unhedged index position. At-the-money protective puts fared theworst, with an annual return of -9.5%. Protecting equity positions with out-of-the-money puts fared

better, with an 8.0% annual return, but this was only marginally better than holding Treasury bills over

the time period.

All other strategies offered risk-adjusted returns that exceeded the SP500. Writing 1-day at-the-money

straddles generated the most attractive returns. This strategy earned 35.4% per year with a lower

volatility than the SP500 and a Sharpe ratio of 2.29. Furthermore, this strategy offered a low correlation

with the index of 0.22, suggesting it will offer good diversification benefits when combined with a long


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Historical Trend in Implied and Realized Volatility and Implication for Option-Based Returns

The results discussed in the previous section show that strategies involving option writing have performed

well in the past decade, and would have improved the risk-adjusted return of an equity portfolio.

However, there has been considerable variation in the annual performance of these strategies. As shown

in the following exhibit, returns to option writing were highest in the 1988-1992 period, and have

generally underperformed the SP500 in recent years.

Exhibit 2

Annual Performance of Short Volatility Strategies

1-DAY 1-DAY 30-DAY 30-DAY SP500 AVG

SP500 STRADDLE STRANGLE STRADDLE STRANGLE VOL IMP VOL

1987 3.3% 10.3% -5.0% 1.5% 1.3% 34% 25%

1988 15.4% 75.8% 40.0% 23.9% 23.0% 17% 22%

1989 27.6% 34.4% 9.3% 13.5% 12.9% 13% 15%1990 -3.2% 41.4% 24.8% 17.8% 17.3% 16% 20%

1991 26.7% 28.1% 10.2% 12.1% 11.5% 14% 16%

1992 7.4% 49.9% 17.0% 14.3% 13.0% 10% 14%

1993 9.6% 29.7% 3.7% 9.2% 8.0% 9% 18%

1994 1.3% 27.5% 4.7% 9.5% 8.8% 10% 12%

1995 32.0% 32.1% 3.2% 10.5% 9.6% 8% 11%

1996 20.7% 29.1% 8.2% 9.0% 8.6% 12% 14%

1997 28.8% 27.2% 17.8% 9.7% 9.3% 18% 20%

1998 26.2% 38.4% 22.6% 8.5% 8.1% 20% 22%

1999 18.7% 33.2% 23.9% 13.7% 13.3% 18% 22%

Peak returns to option writing strategies occurred in the years following the 1987 crash, when concernsabout the stability of the market caused increased hedging demand. This resulted in implied volatility for

options exceeding actual volatility by a fairly wide margin. As shown in the exhibit, implieds exceeded

realized by a sizeable margin in 1988, 1990, and 1992 -- all years with peak option-writing performance.

In recent years the spread between implied and actual has narrowed, resulting in lower returns to writing

options. However, the spike in volatility in 1998 (highest annual volatility since 1987) may again trigger

hedging demand that would generate higher returns to options strategies in coming years.

Modeling the Returns to Active Hedged Equity Strategies.

Two mutual funds that employ hedged equity strategies -- Analytic and Gateway -- were analyzed to

identify the potential benefit of adding these programs to an unhedged equity portfolio. Both programs

employ a strategy that involves a core long position in stocks. The stock returns are augmented withoption strategies that involve writing call options as a source of additional income and purchasing put

options for protection against downside risk. These strategies are similar to the collar benchmarks,

although there are a number of important differences between the active programs and the benchmark.

First, the active programs actively managed their underlying equity holdings, while the benchmark holds

the SP500 index. Second, the programs employ options opportunistically, buying puts and selling callsbased on relative value. The benchmark uses the same option strategy throughout. Third, the active

programs use a combination of index options and options on individual stocks, while the benchmark uses


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only index options. Finally, the active programs do not hedge 100% of their equity positions, while the

benchmark assumes a fully hedged portfolio.

In order to model the underlying strategy of the active programs, a portfolio was formed that consists of

two strategies: an unhedged equity index position and a 2% out-of-the-money collar strategy. The collar

involves writing a 2% out-of-the-money call option and buying a 2% out-of-the-money put option. The

options have a 30-day maturity, but are closed at the end of each day and new 30-day option positionsinitiated. The portfolio allocations to the equity index and the option collar were adjusted to provide the

closest possible fit to the observed returns of the active manager. The resulting allocations for Gateway

are 61% equity, 39% option collar. Analytic employs a less active option strategy, with a model

allocation of 80% equity, 20% option collar2.

Exhibit 3

Analytic Investors: Performance Relative to Model and SP500 Benchmarks

Annual Annual Sharpe Best Worst

Descriptive Statistics: Return StDev Ratio Month Month

Analytic Investors 14.6% 9.5% 1.02 7.8% -13.0%Model Portfolio (80/20) 13.4% 9.0% .93 7.5% -9.9%

SP500 16.8% 13.4% .88 10.8% -15.6%

Alpha StDev Max Min

Benchmark Performance: (Annual) Beta Error Error Error

Model Portfolio Benchmark 1.4% .98 1.66% 5.05% -5.37%

SP500 Benchmark 2.8% .64 1.03% 3.77% -3.05%

Gateway Advisors: Performance Relative to Model and SP500 Benchmarks

Annual Annual Sharpe Best Worst

Return StDev Ratio Month Month

Gateway Advisors 10.1% 5.3% .96 5.8% -5.1%

Model Portfolio (61/39) 10.0% 4.6% 1.09 4.3% -4.3%

SP500 16.8% 13.4% .88 10.8% -15.6%

Alpha StDev Max Min

Benchmark Performance: (Annual) Beta Error Error Error

Model Portfolio Benchmark 0.3% .96 0.83% 3.42% -1.81%

SP500 Benchmark 1.2% .34 2.70% 10.58% -6.56%

Monthly Tracking Error

Monthly Tracking Error

2

Note that these allocations do not necessarily indicate that Gateway or Analytic are allocating these proportions of

their assets to options, because the benchmark strategy simulates an option strategy that is always 2% out of the

money. If the active programs trade options that are more (or less) out of the money, the actual proportion of their

assets allocated to these strategies would differ considerably from these figures.


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The model portfolios for Gateway and Analytic provide very accurate benchmarks for their historical

performance. The following exhibit summarizes the performance of the active programs in relation to

two benchmarks: the model portfolio and the SP500.

This exhibit shows that the performance of the model portfolios over the 1990-1999 period tracked the

active programs very closely. For Analytic, annual returns for the active program (14.6%) and the model

(13.4%) are similar, as are the annual standard deviations (9.5% and 9.0%). The risk-adjusted returns (asmeasured by the Sharpe ratio) are similar. By comparison, the SP500 had considerably higher return and

standard deviation over the same period, and a lower Sharpe ratio of 0.66. Maximum and minimum

returns to the model portfolio are somewhat smaller the active program.3

The data for Gateway show a

similar pattern, with the annual returns of the active program and the model almost identical (10.1% and

10%) and a volatility for the active program a bit larger than the model (5.3% vs. 4.6%). The Sharpe ratio

of the model is somewhat higher (.98 vs. .80), although both are better than the SP500 alone (0.66).

The model portfolios are more suitable benchmarks for the active programs than the SP500. For

Analytic, the model has beta of 0.98 and an annualized alpha of just 1.4%. This compares to a beta of

0.64 when the SP500 is used as a benchmark for Analytic, and an annual alpha of 2.8%. The fact that the

passive benchmark explains a large portion of the strategys alpha is evidence that at least some portion of

Analytics return stems from the unique source of return attributable to the option position. If the optionpositions had the same source of return as the underlying stocks, the strategys alpha would have been the

same for both the option-based benchmark and the SP500 benchmark. An analysis of Gateways returnsyields similar results. The model beta for Gateway is 1.09 and the alpha is essentially zero (0.3% per

year). However, the SP500 shows a beta of 0.34 and an annualized alpha of 1.2%. As was true with

Analytic, incorporating the option strategy into the benchmark provides an explanation for the positive

risk-adjusted returns over the time period.

Evidence of Positive Risk-Adjusted Returns

Exhibit 4 shows that adding an option-based strategy to an equity position would have improved the risk-

adjusted return of an equity portfolio during the 1987-1999 time period. The exhibit shows the annual

return and standard deviation of portfolios with different allocations to the SP500 and the option collarstrategy. Although the collar strategy is not attractive as a stand-alone investment (its annual return is

0.5% -- less than the risk-free rate), in combination with the SP500 the strategy provides risk-adjusted

returns that are higher than the SP500 alone, or strategies that combined the SP500 and cash.

Allocation up to 50% of assets to the option strategy provided a risk premium over the SP500 alone.Both of the programs studied follow this strategy. Based on a 2% out-of-the-money benchmark, Gateway

allocates 39% to options and Analytic 20%. These points are indicated on the figure4, and both are

clearly in the allocation range that offers a premium to portfolios consisting of the SP500 and cash.

3

There are a number of possible explanations for this. The model portfolio constructed to give a beta of 1.00. This

results in a somewhat smaller volatility than the active programs. If the portfolio weights were determined in order

to match the volatility of the active programs, a higher allocations to stocks and lower allocation to options results,which in turn brings the maximum and minimum returns closer into line. It is also possible that the larger max/min

returns experienced by the active programs results from the manager's trading strategy. It may be that the managers

hedge less when implied volatility is high -- as was the case in August, 1998 when the programs experiences their

largest losses. Put options were very expensive during this period, and the managers may have reduced their

hedging even though, in retrospect, it would have been more advantageous to hedge during this period.4

It should be noted that the highlighted data points for Gateway and Analytic represent the model portfolios and not

the actual performance. Also, the time frame for this figure is 1987-1999, while the performance data for these

programs is 1990-1999, so the location of these data points will be slightly different from those in the performance

tables.


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Performance of Option-Based Strategies during Market Extremes

One of the principal reasons cited for utilizing options is protection against significant declines in the

underlying asset. The results reported in Exhibits 1-4 show that risk-adjusted returns to certain option-

based strategies exceed that of an unhedged, passive investment in the SP500 index. However, if

investors are risk-averse, they may choose investments that limit large losses even if these investments

reduce the risk-adjusted return of a portfolio. Examine the performance of a protective put strategy(Exhibit 3). During the past thirteen years, investors willingly purchased put options at prices that resulted

in risk-adjusted returns far below an unhedged equity position. The passive collar strategy, however,

offers protection against a sizeable decline in the underlying asset while still offering risk-adjusted return

higher than an equity position alone. As can be seen in Exhibit 5, during the three worst months for the

SP500 in the past decade, the collar strategy and the two active strategies saw declines that were

considerably lower than the SP500 decline.

Returns in S&P 500 Three Worst Months (1990-1999)

Jan. 90

Aug. 90

Aug. 98

-18%

-16%

-14%

-12%

-10%

-8%

-6%

-4%

-2%

0%

MonthlyReturns

Synthetic Collar -2.2% -1.7% -1.1%

Gateway -5.1% -4.1% -3.5%

Analytic -13.0% -4.6% -3.6%

S&P 500 -15.6% -9.6% -6.8%

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Conclusion

Analysis of the returns of both passively managed and actively managed option-based strategies provides

evidence that certain strategies offer higher risk-adjusted returns than are available with equity investmentalone. These strategies are shown to offer a source of return that is different from the underlying source

of equity returns, and thus provides diversification benefits as well as attractive absolute returns.


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Selected References

Arnott, Robert. "Options and Protective Strategies," Journal of Investing, Summer, 1998, pp.16-22.

Beighley, S. "Return Patterns for Equity Indexes Hedge with Options," Journal of Portfolio

Management, Winer, 1994, pp. 68-73.

Canina, L. and S. Figlweski " The Information Content of Implied Volatility," Review of Financial

Studies. Vol 6 (1993), pp. 659-681.

Christensen, B.J. and N.R. Prabhala. "The Relation Between Implied and Realized Volatility," Journal of

Financial Economics. Vol. 50 (1998), pp. 125-150.

Crowley, P. "Why and How Fundamental Managers Should Use Options: Part 1," Derivatives Quarterly

(Spring, 1996), pp.52-66.

Crowley, P. "Why and How Fundamental Managers Should Use Options: Part 2," Derivatives Quarterly

(Summer, 1996), pp.40-55.

Dumas, B., J. Fleming, and R. Whaley. "Implied Volatility Functions: Empirical Tests," Journal of

Finance, Vol. 53 (1998), pp. 2059-2106.

Ferson, W. and Rudi S. "Measuring Fund Strategy and Performance in Changing Economic Conditions,"

Journal of Finance, (Summer-1996) pp. 425-461.

Figlewski, S. "Forecasting Volatility," in Financial Markets, Institutions and Instruments, 1997.

Francis, J., W. Toy, and J. G. Whittaker, eds. The Handbook of Equity Derivatives. Irwin, 1995.

Hill, J. and T. Mitev. "Increasing Perceptions of Downside Risk," Goldman Sachs: Equity DerivativesResearch (November, 1997).

Goldman Sachs Equity Derivatives Research Group, Considering Your Options An Approach to

Comparing Alternative Strategies, Goldman Sachs: Equity Derivatives Research (January, 2000).

Kapadia, N. "Do Equity Options Price Volatility Risk?" CISDM Working Paper, k5-99 (University of

Massachusetts-Amherst, 1999).

Rendleman, R. "Option Investing from a Risk-Return Perspective," Journal of Portfolio Management

(May, 1999), pp. 109-121.

Tsu, M. "Writing Covered Calls to Enhance Returns on U.S. Stocks," Goldman Sachs: EquityDerivatives Research (April, 1997).

Zurach, M. "The Monetizing Collar," Goldman Sachs: Equity Derivatives Research (January, 1988).

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