Volatility Perspective

Transcription

1 September 7, 2010 Volatility Perspective Strategic Rules for Better Put Option Protection SCOTT JACOBSON, CFA, CPA EQUITY DERIVATIVE STRATEGY Sanford C. Bernstein & Co., LLC 1345 Avenue of the Americas New York, NY Continuous put protection is prohibitively expensive, so we search for active strategies to provide some level of portfolio protection at lower cost. We developed an intuitive set of timing rules and tested preferable periods to hold puts vs. running a portfolio un-hedged. We also varied the initial delta exposure and tested put strategies. The hypothetical results show that timing and strategies were superior to continuous put protection. Moreover, the active timing strategies outperformed the un-hedged market, with less volatility. Objective The objective of this note is to explore whether using rules to time put option purchases, or using put option s, can produce superior returns when hedging a portfolio. Intuitively, active deviation from a continuous hedging strategy should afford some level of portfolio protection with lower cost. But can you achieve enough protection to make the exercise worthwhile? Exhibit 1 Performance of continuous hedging vs. active management of put strategies (1997 to April 2010) 10% 5% 0% -5% -10% -15% Average annual excess return over S&P 500 for various deltastrike put strategies M ACRO S TRATEGY -20% delta 30 delta x2 Always hedged Timing rule Introduction The price of options, implied volatility, started to rise measurably in July 2007 when the Bear Stearns mortgage funds collapsed. That event pushed the market into a high volatility regime. Then, in the wake of the market crash of , investor demand for portfolio protection increased substantially. We observe increased demand for put options in S&P index volatility and option skew. The information provided herein was prepared by Sanford C. Bernstein & Co., LLC ("Bernstein") but is not a product of Bernstein s Equity Research Department.

2 Skew steepened during the crash and remains relatively steep today. Even after the decline from panic levels in , implied volatility remains above long-run averages. The ongoing high-volatility and steep-skew environment is evidence that heavy demand for option protection persists. High implied volatility and steep skew create a high, if not insurmountable, hurdle for the total return manager trying to hedge her portfolio. In an environment with 20% implied volatility and moderate skew, it could cost from 500 to 900 bps to protect a portfolio at strikes of 90% to 95% (approximate annual cost of rolling quarterly puts at those strikes). However, in a flat to rising market, the cost of such protection cannot be fully recovered and the performance drag is too substantial to be effective over long periods of time. In this note, we search for active hedging strategies with favorable return characteristics using historical data since The period encompasses asset bubbles, significant market rallies and declines, and both high and low volatility regimes. This search for more cost-effective put protection strategies focused on two primary tactics: 1. Developing timing rules to identify preferable periods to hold puts vs. running un-hedged; and 2. Varying the initial delta exposure of the put strikes and using put s instead of outright puts. The hypothetical results show that timing and strategies were superior to continuous put protection. The strategies also significantly outperformed the market over the studied periods. Data and Methodology Data We used daily S&P 500 index price & return data from Bloomberg to produce hypothetical results for the period from January 1997 to April For simplicity, we computed theoretical prices for put options using daily implied volatility surfaces (delta strikes) for the S&P 500 index from OptionMetrics. Methodology We formed simple portfolios consisting of the S&P 500 index and, when the timing rules dictate, hypothetical one-month put options held to expiration. We rolled options at expiration if the timing signal remained active. When buying puts, we reduced the S&P component of the portfolio by the cost of the puts. To compensate for potential errors in the volatility data, we bought puts over a three-day window when the timing signal was active. We priced the options and computed total returns each day. Results presented are an average of 21 different starting dates in the first month to partially compensate for sampling bias. We realize that after the model reaches the first or second exit point, all subsequent samples are likely the same for each run. However, since our objective was to find these historically preferable times to hedge, this is the expected result. The data should be adequate for an indication of success since the period studied covers a wide range of volatility paths and we limit ourselves to one-month tenors. Timing Trigger We developed simple timing rule triggers to start and stop hedging based upon trailing index prices and spot implied volatility. We consider volatility to be inherently mean-reverting, so we took a somewhat contrarian view: the timing rule tests avoid volatility spikes when buying put options. In contrast, stock returns are not necessarily mean reverting, especially over longer runs. For stock index returns, we assume three broad classes of stock market prices: 1) strongly advancing, 2) oscillating, or 3) strongly declining. Ideally, we don t buy unnecessary puts in an advancing market, so our trigger rule tests look for oscillating or declining markets. An oscillating market consists of shorter term cycles of rallies and corrections. In this case, Page 2 of 10

3 a timing rule based on mean reversion of the market might work to signal appropriate times to buy downside protection. To create this timing trigger, we computed the ratio of near-term returns to medium-term returns. Such a ratio will be high when the market is rising from a recent bottom and the ratio will be low after the market has fallen substantially. We avoid those areas and focus on a medium range for the ratio to catch turning points. For this study, we established a range for this ratio while looking at in-sample data, so it is subject to question. However the resulting +/- 5% range we used is not unreasonable and the selection method was intuitive. Exhibit 2 is a conceptual drawing of how such a medium-range ratio signal becomes active in an oscillating market. The vertical bars represent times when the signal is activated. In our return testing, we bought put options at these times and rolled them at maturity until we reached an exit rule signal. Exhibit 2 Artist's depiction of timing trigger rule in action Return ratio timing signal activated Mediumterm (6 months) Exit signal Exit signal Near-term (1 month) To test timing rules for efficacy, we computed simple t-statistics as shown in Exhibit 3. This analysis did not drive our rule selection, but it exemplifies a process that could be used to narrow a set of possible timing rules. In this example, for each day in the testing period, we assigned a '1' if the subsequent trailing one-month return was less than -2.5%, or '0' otherwise. The incidence rate for such "down months" for each period is noted in the first data column of Exhibit 3. Then, in the third column, we computed the incidence rate using only the days when the timing signal was on. In this example, the difference between incidence rates was significant for the entire sample period and most sub-periods (t-stat column). Exhibit 3 Efficacy of timing signal for oscillating markets Severe down months (return less than -2.5%) from any given day during sample periods Always hedged Downmonth incidence rate SE of estimate Downmonth incidence rate SE of estimate t-stat A. Entire testing period Jan-97 to Apr % 0.8% 36.1% 1.4% 7.84 B. High volatility tech bubble and collapse Jan-97 to Dec % 1.1% 36.5% 1.8% 5.02 C. High volatility housing crash Jul-07 to Apr % 1.9% 37.6% 2.3% 0.21 D. Tech Bubble Jan-97 to Jun % 1.4% 32.1% 6.2% 1.79 E. Low volatility period Jan-04 to Dec % 1.2% 29.6% 4.4% 2.92 Timing rule active Page 3 of 10

4 Also in Exhibit 3, we note that the housing crash (period C) did not show a statistical difference in down months when the timing rule was active. This effect is due to the third kind of stock market mentioned above: strongly declining. To ensure hedging during such periods, we added a simple rule to provide hedging during secularly declining markets. Rule Set The sample rule set combines the oscillating and secularly declining market rules with exit rules designed to stop hedging after some period of positive hedging performance. Entry Criteria - The decision to activate the hedging strategy in an oscillating market occurs when the stock market is up but not trending, and when volatility is not at a high. Specifically, the trigger to start hedging begins 1) When the trailing 6-month index return is greater than 2% (stocks up), and 2) When the ratio of the 1 month/6 month annualized returns is between the 45th and 55th percentiles of the ratio over the entire sample period (i.e. market is not trending higher), and 3) When the current ATM implied volatility is less than 95% of the trailing 10-day average implied volatility. This rule prevents buying the options at the peak of a spike in volatility. OR 1) When the trailing 12-month index return is negative (12-month rule). This simple momentum-based rule looks for longer-term (secular) market declines that would not be caught by the contrarian rule for oscillating markets described above, and it is not volatility sensitive. Exit Criteria When we decide to exit the hedging strategy, we reduce or eliminate the window for reinvesting in the put strategy after the options expire. In other words, we simply hold existing options to maturity and do not roll maturing options. The exit occurs 1) If the 12-month rule above is NOT in effect, when the trailing one-month S&P return is negative (i.e. a correction occurred), 2) If the 12-month rule IS in effect, when the trailing 12-month index return becomes positive (secular market rebound). Option Spread Selection For each period and timing signal test run, we ran six different portfolios with distinct put or put strikes: 40 delta puts, 30 delta puts, delta put s, delta put s, delta put s, and delta 1x2 put s (selling two 20-delta puts for each 50-delta put purchased). Exhibit 4 is a table showing the one-month theoretical costs for the option strategies in this note under various volatility assumptions. These costs are in essence the hurdle or break-even corrections required after buying one-month put options. The skew assumption used in the table is a change of 20% for implied volatility between 50-delta and 25-delta puts. This is slightly steeper than current market skew. Note that strategies would be more (less) expensive in a flatter (steeper) skew environment. For example, using 25% implied volatility in a 10% skew environment, the delta put would cost approximately 2.1% vs. the 2.0% shown in the table. Page 4 of 10

5 Exhibit 4 Hedging costs for given levels of implied volatility One-month cost of hedging strategies (hurdle for market decline to break even) Using 20% skew between 50 and 25 delta strikes ATM Implied vol 10% 15% 20% 25% 30% 35% 40% 45% put 0.8% 1.2% 1.6% 2.0% 2.4% 2.8% 3.2% 3.7% put 0.5% 0.8% 1.1% 1.3% 1.6% 1.9% 2.2% 2.5% put 0.5% 0.7% 1.0% 1.3% 1.5% 1.8% 2.1% 2.4% 40 delta put 0.9% 1.4% 1.8% 2.3% 2.8% 3.3% 3.8% 4.3% 30 delta put 0.6% 1.0% 1.3% 1.7% 2.0% 2.4% 2.7% 3.1% x2 put 0.4% 0.5% 0.7% 0.9% 1.1% 1.3% 1.5% 1.7% Investor preference will dictate ultimate strategy. However, we note particularly good results when buying or delta s. These strategies are appealing to us because they provide protection in the getting fired zone where professional managers are most at risk and where individual investor losses are most painful. Greater losses are less frequent, typically subsidized by government intervention, and shared in collective grief. Return Results The chart on page 1, Exhibit 1, summarizes the results of using the timing rules vs. full-time hedging for each of the delta strategies over the entire testing period. Note the extreme cost of full-time hedging with high-delta put options. Using put s reduces the cost of overpaying, and makes the hedging hurdle much more attainable. It appears the timing strategy provides a significant advantage over full-time hedging. Exhibit 5 Continuous hedging reduces volatility but outperforms only in down markets Excess Returns Hedged 100% of the time (Strategy less S&P) Period Delta put strategies delta 30 delta x2 A. Entire testing period Jan '97 - Apr ' % 0.5% -19.4% -93.7% -92.7% 97.9% Annual Avg -1.8% 0.0% -1.6% -18.8% -17.9% 5.3% B. High volatiltiy tech bubble and collapse Jan '97 - Dec ' % -0.5% -10.3% -53.1% -52.0% 47.0% Annual Avg -1.6% -0.1% -1.6% -10.4% -10.1% 5.7% C. High volatility housing crash Jul '07 - Apr '10 4.9% 5.1% 2.8% -1.9% -4.0% 8.4% Annual Avg 1.7% 1.8% 1.0% -0.7% -1.5% 3.0% D. Tech bubble Jan '97 - Jun ' % -13.7% -24.4% -64.5% -58.9% 19.7% Annual Avg -10.0% -4.2% -7.9% -26.1% -22.9% 5.4% E. Lower volatility period Jan '04 - Dec '07-9.8% -4.7% -7.4% -28.6% -26.7% 14.9% Annual Avg -2.6% -1.2% -2.0% -8.2% -7.6% 3.6% Exhibit 5 presents tabular results of full-time hedging strategies for the entire period and also for selected subperiods representing different return and volatility environments. We show cumulative excess returns (strategy less S&P) for the entire period and the annual average excess return. Panel A represents the data for the entire Page 5 of 10

6 period (same data as in Exhibit 1). Note that even in the high-volatility housing crash (Panel C), the 40 and 30 delta strategies struggled to just break even, while they cost dearly in other environments. Spread strategies fared better, but suffer in up markets (Panel D) and low volatility environments (Panel E). Exhibit 6 shows the results for the same periods when we use an active hedging strategy with the timing rules discussed above. The percentage of time spent with a hedging position is shown in parentheses. Most of the periods have significantly better results and positive signs for excess returns when using the timing rules. In particular, the 50-20, 50-30, and delta put strategies performed 6.0%, 3.6%, and 4.3% better than full-time hedging, respectively, on an annualized basis, over the entire period. Exhibit 6 Simple timing rule creates better performance vs. continuous hedging Excess Returns Using Timing Rules (Strategy less S&P) Period Delta put strategies delta 30 delta x2 A. Entire testing period (hedging 62% of the time) Jan '97 - Apr ' % 60.2% 43.2% 12.1% -12.4% 97.3% Annual Avg 4.2% 3.6% 2.7% 0.9% -1.0% 5.3% B. High volatiltiy tech bubble and collapse (hedging 67% of the time) Jan '97 - Dec ' % 20.7% 9.7% -13.2% -20.9% 45.3% Annual Avg 2.7% 2.8% 1.4% -2.0% -3.3% 5.5% C. High volatility housing crash (hedging 83% of the time) Jul '07 - Apr '10 9.1% 7.2% 6.0% 8.9% 5.6% 2.7% Annual Avg 3.2% 2.6% 2.2% 3.1% 2.0% 1.0% D. Tech bubble (hedging 44% of the time) Jan '97 - Jun '00-1.9% 4.4% -6.0% -22.8% -22.9% 16.8% Annual Avg -0.6% 1.3% -1.8% -7.3% -7.3% 4.7% E. Lower volatility period (hedging 34% of the time) Jan '04 - Dec ' % 11.7% 11.1% 6.6% 0.5% 21.6% Annual Avg 4.0% 2.9% 2.7% 1.7% 0.1% 5.1% The one-by-two put strategy, that fared well return-wise in the fully-hedged mode, did not see any improvement with these timing rules. The positive returns for this strategy come at the expense of additional risk. It is interesting to note that this strategy maintained positive excess returns during sub-period C, the highvolatility housing crash. Risk Results To assess risk or volatility in the timing strategies, we first examine graphical returns of hedged and un-hedged portfolios in Exhibit 7. This chart plots cumulative returns for the S&P 500, a continuously hedged portfolio, and a hedged portfolio using the timing rules. The hedge strategies use delta put s. The shaded regions indicate the periods when we actively hedged pursuant to the timing rules. The continuously-hedged strategy is clearly less volatile, but at the expense of significant underperformance at times. Using the timing rules kept the portfolio un-hedged enough to capture more positive returns, but volatility appears closer to the index. It appears that the timing rules may have helped to keep good tracking error and hedged away bad tracking error. Page 6 of 10

7 Exhibit 7 Cumulative performance of delta put strategies vs. S&P 500 (Jan = 100) '97 '98 '99 '00 '01 '02 '03 '04 '05 '06 '07 '08 '09 '10 Hedging active Un-hedged Always hedged Timing Exhibit 8 details realized volatility for each strategy and time period. Constant hedging significantly reduces portfolio volatility. When we use timing rules, volatility is higher than under full-time hedging, but the results still show less volatility than an un-hedged market return. Note that the 1x2 strategy has equal or greater volatility than the index whether hedging full-time or timing the strategy. That is consistent with the outperformance noted in Exhibit 5 and Exhibit 6. Exhibit 8 Realized volatility comparison for hedging strategies Period Delta put strategies using the combined rules delta 30 delta x2 A. Entire testing period Jan '97 - Apr '10 -- S&P Vol = 21.4% Always hedged 14.7% 16.9% 16.7% 12.9% 14.8% 21.2% Timing rules engaged 16.5% 18.0% 17.9% 15.0% 16.3% 21.9% B. High volatiltiy tech bubble and collapse Jan '97 - Dec '03 -- S&P Vol = 20.7% Always hedged 14.2% 16.4% 16.0% 12.5% 14.3% 19.4% Timing rules engaged 16.7% 17.9% 17.8% 15.9% 16.9% 19.8% C. High volatility housing crash Jul '07 - Apr '10 -- S&P Vol = 30.9% Always hedged 21.3% 24.3% 24.2% 17.6% 20.5% 33.6% Timing rules engaged 22.0% 24.8% 24.6% 18.4% 21.1% 33.8% D. Tech bubble Jan '97 - Jun '00 -- S&P Vol = 19.8% Always hedged 14.1% 15.9% 15.8% 12.7% 14.3% 18.6% Timing rules engaged 17.8% 18.4% 18.4% 17.4% 17.9% 19.3% E. Lower volatility period Jan '04 - Dec '07 -- S&P Vol = 12.1% Always hedged 8.2% 9.4% 9.4% 7.7% 8.9% 10.3% Timing rules engaged 10.6% 11.2% 11.0% 10.2% 10.5% 12.0% Page 7 of 10

8 Exhibit 9 displays return dispersion using a histogram of daily returns for the un-hedged S&P 500 and the continuously hedged 40-delta portfolio. The hedging effectively reduces volatility and the number of left-tail returns. The hedging strategy nearly matches the index for occurrence of positive return days between zero and +2.5%. However, many of those returns are in the 0% to +0.5% bucket. The extreme cost of continuous hedging is revealed in the gaps for the +0.5% to +2.5% daily return buckets where the count of un-hedged days outnumbers hedged days by 953 to 633. That is significant opportunity cost. Exhibit 9 Distribution of daily returns for entire period: fully hedged 40-delta vs. un-hedged S&P 500 Observations -2.5% to 0% daily: S&P unhedged 1458 Hedged 1678 Observations 0% to +2.5% daily: S&P unhedged 1692 Hedged % -4% -3% -2% -1% 0% 1% 2% 3% 4% 5% S&P 500 Always hedged with 40 delta puts Exhibit 10 is a similar histogram for the delta and timing strategy. We observe a hedging effect, but also greater dispersion for the hedging strategy returns compared to Exhibit 9. Importantly, we do not forfeit excessive upside when returns are positive. The timing strategy for delta put s had 816 daily results in the +0.5% to 2.5% daily return buckets. Exhibit 10 Distribution of daily returns for entire period: timing rule delta put vs. un-hedged Observations -2.5% to 0% daily: S&P unhedged 1458 Hedged 1525 Observations 0% to +2.5% daily: S&P unhedged 1692 Hedged % -4% -3% -2% -1% 0% 1% 2% 3% 4% 5% S&P 500 Timing (50-20 delta put ) Page 8 of 10

9 Conclusion The prohibitive cost of continuous put protection drives us to look for timing and strategies that might be superior to constant put protection. Using the data in this study, a timing strategy with put s appears to be a better form of portfolio protection than continuously hedging with straight puts. Moreover, the active timing strategies outperformed the un-hedged market, with less volatility, over the entire time period and most sub-periods. A quick read of the 40 and 30 delta bars in Exhibit 1 tells us that simply avoiding puts at certain times dramatically improves performance. This is why the market's desire for portfolio protection is cyclical. In essence, market participants want to time their pursuit of hedging strategies. Actual portfolio management must address current and future environments and expectations. The result of this empirical work may be some tools or concepts to help with human judgment and the management of portfolio hedging strategies. For example, when the timing signal indicators favor hedging, that may be a time to consider it more carefully. Our objective was not to posit the perfect hedging rule, but rather to seek some evidence that actively managing a hedging strategy could add value to a portfolio. We stipulate that the study was a back-test of a model developed in-sample using hypothetical tenors and option prices. However, a little intuition went a long way in these tests, and the period studied contained a wide variety of market conditions, volatility levels, and price paths. Thank you to Abhay Subramanian (Stanford) and Cabral Tondji (NYU) for your patience and tireless efforts to build and run models and pull this project together. Page 9 of 10

10 SCOTT JACOBSON, CFA, CPA EQUITY DERIVATIVE STRATEGY Sanford C. Bernstein & Co., LLC 1345 Avenue of the Americas New York, NY SALES Steve Miller John Karl Walter Lamerton TRADING Ralph Edwards Stephen Thurer Matthew Tym William Looney DISCLOSURES This communication is issued by Sanford C. Bernstein & Co., LLC ( Bernstein ) Options Sales and Trading Department to institutional investors only and is not intended to be and should not be construed as research. This communication does not constitute a recommendation or an offer to sell or a solicitation to buy any financial product. The information presented herein is obtained from sources believed to be reliable, and Bernstein believes that, as of the date of this publication, it is accurate. Bernstein makes no representation, however, that the information is accurate, complete or current, or that it reflects the current opinion or all information known to Bernstein or its affiliates. The views and information expressed in market commentary and strategy ideas from Bernstein s Options Sales and Trading Department may change or cease being operative at any time without reason or notice. If information provided herein includes extracts or summary material derived from research reports published by Bernstein s Research Department, you are directed to the original piece of research to see the Research Analyst s full analysis and disclosures. Options involve risk and may not be suitable for all investors. Investors who buy options may lose their entire premium, and investors who sell uncovered options have unlimited risk. Prior to buying or selling options, an institutional investor must receive a copy of Characteristics and Risks of Standardized Options, which may be obtained at Bernstein disclaims all liability for any loss that may arise (whether direct or consequential) from any use of the information contained in this communication. This material is furnished on the understanding that Bernstein is not managing and does not have investment powers over any of your accounts and that Bernstein services do not serve as a primary basis for any investment decisions made. Hypothetical performance results have many inherent limitations. Bernstein makes no representation that you will or are likely to achieve profits or losses similar to those shown. In fact, there are frequently material differences between hypothetical performance results and actual results achieved by any particular trading program. Numerous factors related to markets in general or to the implementation of any specific trading program cannot be fully accounted for in the preparation of hypothetical performance results, all of which can adversely affect actual trading results. Moreover, hypothetical performance results cannot completely account for the impact of the financial risk associated with actual trading, including your ability to withstand losses. Past performance is not necessarily indicative of future results. All stocks and options shown are included for demonstrative purposes only. These are not recommendations to buy or sell any security and they do not represent in any way a positive or negative outlook for any security. Potential returns do not take into account your trade size, brokerage commissions, taxes or interest charges that will affect actual investment returns. They assume options positions will be maintained until expiration. Supporting documentation for any claims (including any claims made on behalf of options programs or the options expertise of sales persons), comparisons, recommendations, statistics or other technical data, is available upon request. Page 10 of 10