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## Abstract

A wide range of research has suggested that informed trading in options markets may effectively signal subsequent changes in equity prices. In this article, the authors analyze the performance of long/short strategies based on a number of signals from options markets. In addition, they create an easily implemented long-only strategy based on a subset of the signals (volatility risk premium, option/stock volume ratio, implied volatility skew, and realized volatility). In order to minimize transaction costs and liquidity issues, they restrict their analysis to S&P 500 constituents, rebalance the portfolio monthly, and limit the holdings to 50 individual stocks. The analysis of the period from 1996 through mid-2015 shows significant outperformance of a long-only, equal-weighted portfolio of 50 stocks (and found similar results when considering 10-stock portfolios), relative to the S&P 500 and the equal-weighted S&P 500. A return attribution analysis confirms that the outperformance is provided by individual stock selection rather than sector selection.

Extant literature suggests that insiders and informed traders may favor option markets due to the potential for increased leverage, the ease of short directional exposure, and the wide variety of available strategies. To the extent that informed traders favor option markets to the underlying equity markets, price discovery may occur in option markets and informational inefficiencies may result in equity trading opportunities based on information from options markets. In this analysis, we explore the characteristics of a variety of hypothetical portfolios constructed based on information from options markets. While much of the extant literature in this area applies various signals to a very large universe of a broad range of stocks, we restrict our analysis to S&P 500 constituents to limit issues related to liquidity in the stock and options markets.

In addition to considering a number of 50-stock long portfolios each constructed using individual option-based signals that have been found to predict high returns, we also construct long/short portfolios based on individual bullish and bearish signals and a long- only portfolio based on a combination of four bullish signals. Portfolios that attempt to take advantage of the information available in the options markets may generate high transaction costs due to frequent trading of a large number of stocks. We control turnover by restricting the portfolios to 50 stocks and rebalancing only once per month. In order to test the effectiveness of these signals in an even lower turnover framework, we also construct 10-stock portfolios using similar methodology.

While the performance of the resulting portfolios varies significantly both cross-sectionally and over time, we find general outperformance relative to an equal-weighted portfolio both for the 10-stock and 50-stock long-only portfolios.

## LITERATURE REVIEW

The option-based signals used in our analysis are based on a wide range of literature. The extant literature uses a variety of stock market and option market data including but not limited to option volume, stock volume, realized volatility, and implied volatility (see Exhibit 1 for a subset of these signals). A selection of the extant literature is briefly described below.

Johnson and So (2012) consider a few measures based on the relative size of option volume versus corresponding stock volume. They find that a low option volume to stock volume ratio predicts high returns. They use only short-term, 5-day to 35-day options. They also consider two measures that capture the change in the volume ratio.

Han and Zhou (2013) consider the spread between implied volatility and realized volatility, often referred to as the ‘realized volatility risk premium.’ They find that stocks that exhibit high volatility risk premiums outperform those with low volatility risk premiums for up to 12 months. Goyal and Saretto (2009) compare the implied volatility of at-the-money (ATM), one-month call and put options versus the prior one-year realized volatility using daily data. They consider the performance of straddle trades and find that historical volatility is more effective than implied volatility as a predictor of future volatility. An et al. (2014) consider the month-to-month change in call and put implied volatility. Using implied volatility of 30-day, 50 delta calls and −50 delta puts they find that an increase in call implied volatility predicts high stock returns, while an increase in put implied volatility predicts low returns. The best performing strategies are long/short high call volatility change minus low call volatility change, or low put volatility change minus low call volatility change. Furthermore, performance is enhanced when a high change in call volatility occurs in combination with a high change in stock volume.

A number of studies consider the predictive power of implied volatility skew. Xing, Zhang, and Zhao (2010) find that stocks with large put skews underperform. Similarly, Cremers and Weinbaum (2010) consider ATM implied volatility skew and find that stocks with higher call ATM implied volatility than put ATM implied volatility exhibit higher subsequent returns. Bali and Hovakimian (2009) use both implied volatility for near the money one- to three-month options and realized volatility in their analysis. The find that low realized volatility predicts high returns. A low realized volatility minus implied volatility spread predicts high returns. In addition, they find that a high call implied volatility minus put implied volatility predicts high returns. They also find that implied volatility on its own did not predict returns. Baltussen et al. (2011) also consider the realized volatility versus implied volatility spread (negative of the volatility risk premium). Similar to other studies, they find that a low volatility risk premium predicts underperformance.

There are a wide variety of option-based signals utilized in the literature that we do not consider in our analysis. These include but are not limited to those discussed in Bali, Scherbina, and Tang (2009) and Pan and Poteshman (2006). Bali, Scherbina, and Tang (2009) consider idiosyncratic volatility rather than total realized volatility. They find that high idiosyncratic volatility shocks predict high returns in the first month, but the effect is reversed in two to six months. Pan and Poteshman (2006) use a non-public dataset to allow them to identify option purchases that result in the opening of new positions. They use this data to calculate an open buy put-call ratio. Low open buy put-call ratios are found to outperforms high ratios by 40 basic points the next day and 1% over the following week.

## DATA AND METHODOLOGY

Option and stock data is provided by Optionmetrics and covers the period from January 1996 through March 2016. In order to restrict the analysis to liquid, large cap U.S. stocks, only S&P 500 constituents as of October 2016 are considered. For the sake of parsimony and to avoid any impacts associated with new inclusions into the index, we do not change the list of stocks considered over the period of study. Any survivorship bias resulting from this practice is obviated by benchmarking performance of the resulting stock portfolios to an equal-weighted index of the stocks under consideration rather than using the S&P 500 as a point of comparison.

In order to assess the predictive power of the option market-based measures under consideration, we construct indexes that represent the total return streams generated by forming portfolios based on ranking on these measures. The portfolios represent returns to passive algorithmic strategies that follow a fixed set of stock selection rules.

In order to construct these portfolios, at the market close on each month end all stocks under consideration are ranked based on the measure under consideration and the 50 stocks with the most bullish signals are selected for inclusion in the long-only portfolio for the following month, while the stocks with the most bearish signals are selected for the short portfolio. To calculate the option signal portfolio returns, equal-weighted portfolios are constructed from the chosen stocks and total returns are calculated for the following month. In the case of long/short portfolios, the monthly return is calculated as the net of the long-only portfolio and the short portfolio. This methodology introduces some slight inaccuracy since, in practice, the market would be closed once the signals are calculated. Thus, in practice the signals would have to be calculated prior to the close, or the trades would have to occur at the market open on the first trading day of the next month, leaving the portfolio un-invested from the close to the next market opening.

To minimize transaction costs and to maximize the spread between the long signals and short signals, portfolios are constructed using only 50 stocks. In addition, to further investigate the performance of low transaction cost portfolios we later construct 10-stock portfolios following the same methodology.

As presented in Exhibit 2, we consider a total of eight measures based on extant literature in this analysis.

### ATM and OTM Implied Volatility Skew

Cremers and Weinbaum (2010) find that higher 30-day ATM call implied volatility than 30-day ATM put implied volatility predicts higher returns. We create two signals based on skew. First we rank on the spread between the implied volatilities of the 50 delta call and the −50 delta put for each stock. The higher this number is (call implied volatility above put implied volatility), the more bullish is the signal. We also calculate a similar 30-day OTM signal using the 40 delta call and the −40 delta put and rank in a similar manner.

### Realized Volatility Risk Premium

Bali and Hovakimian (2009) find that a low realized volatility minus implied volatility spread predicts high returns. We subtract the previous 30-day historical volatility from the average of the current 30-day 50 delta call and −50 delta put implied volatilities at month-end and rank stocks on the size of this spread, with the highest spread indicating the most bullish signal for the stock.

### Realized Volatility

Bali and Hovakimian (2009) also find that realized volatility is an effective predictor of returns as a stand-alone measure. We rank stocks on their historical 30-day volatility with the lowest realized volatility providing the most bullish signal for the stock.

### Call and Put Implied Volatility Change

An et al. (2014) find that the month-to-month change in the implied volatility of calls and puts can predict returns. We rank stocks on the month-end-to-month-end change in implied volatility for 30-day 50 delta calls and −50 delta puts. The greater the increase in implied volatility for the calls, the more bullish the call signal is. The opposite is true of the put signal. The greater the increase in implied volatility for the puts, the more bearish the put signal is.

### Option Volume to Stock Volume Ratio

Johnson and So (2012) find that the ratio of total near-term option volume to stock volume is an effective predictor of returns. Low option volume relative to stock volume predicts high returns. We calculate the ratio of total option volume (across puts and calls, all strikes and all maturities) to stock volume. We rank stocks on this ratio with a lower ratio providing a more bullish signal.

### Option Volume to Stock Volume Ratio Change

Johnson and So (2012) also find that the change in the ratio of total near-term option volume to stock volume is an effective predictor of returns. We rank on the month-end-to-month-end change in this ratio with a larger decrease in the ratio providing a more bullish signal.

### Long Score

Finally, we create long-only portfolios based on a subset of the signals described above (volatility risk premium, option/stock volume ratio, implied volatility skew, and realized volatility). We assign a score from 1 to 50 (10 for the 10-stock portfolio) to each stock that ranked in the bullish portfolio for each signal with the most bullish being 50 (10 for the 10-stock portfolio). All stocks that did not rank in the top 50 (10) for a particular measure are assigned a score of zero for that measure. We then sum up the bullish scores for the volatility risk premium, option/stock volume ratio, implied volatility skew, and realized volatility measures and rank based on the total bullish score. The higher the score, the more bullish the rank. Only those stocks that fall in the top 50 (10) of this long score are included in the long score portfolio. Thus, a stock that scores well in one of the four measures may be excluded or included in the long score portfolio.

### Benchmark

We also construct an equal-weighted portfolio of all stocks in the universe from which we calculate our option-based measures and potentially include in the 50-stock and 10-stock portfolios. As mentioned earlier, we use the S&P 500 constituents as of October 2016. We do not alter the universe of stocks under consideration historically to track the makeup of the S&P 500 back to 1996. This could induce a survivorship bias impact if we were to compare the performance of the option-based signal portfolios to the market cap-weighted or equal-weighted S&P 500 index. One would expect that stocks that are added to the S&P 500 index may have performed well historically prior to inclusion and stocks that are dropped from the index may have performed poorly historically prior to being dropped from the index. Using the equal-weighted index of stocks in the universe under consideration as a benchmark both mitigates the issue of survivorship bias and any positive impacts of a stock being newly included in the index.

## EMPIRICAL RESULTS

Summary statistics for the eight 50-stock long/short portfolios based on the individual bullish and bearish signals are presented in Exhibit 3. The summary statistics represent performance for the portfolios from March 1996 through April 2016, based on signals starting in January 1996. In addition, results are presented for the benchmark portfolio (equal-weighted portfolio of all the stocks in the universe under consideration) for comparison purposes as well as the S&P 500 for general informational purposes. It is worth noting again, that the equal-weighted portfolio is the relevant benchmark portfolio since the historical constituents of the S&P 500 do not correspond to the stocks considered in the analysis. For each long/short portfolio we calculate the equal-weighted return of the 50 stocks selected at the end of the previous month by the long signal and subtract the equal-weighted return of the 50 stocks selected by the short signal.

The results in Exhibit 3 indicate that the 50 stock long/short option signal-based portfolios significantly underperform the equal-weighted portfolio on an absolute return basis. However, all of the 50 stock long/short portfolios outperform the equal-weighted index on a risk-adjusted basis as measured by alpha, based on a single factor model using the equal-weighted portfolio as the factor, although some of these alphas are not significant at the 95% confidence level. The alphas range from a low of 1.3% for the put implied volatility portfolio to 11.9% for the volatility risk premium portfolio. It is worth noting the low and often negative betas of the long/short portfolios, ranging from −1.21 (for the realized volatility portfolio) to 0.13 (for the call implied volatility change portfolio). Many of the long/short portfolios also exhibit greater maximum drawdown than the equal-weighted portfolio. Five of the eight long/short portfolios provided statistically significant positive alphas, while all but one of them had reduced standard deviations relative to the equal-weighted portfolios. Thus the performance of the long/short portfolios is generally superior to that of the equal-weighted portfolio.

Exhibit 4 provides a graphical presentation of the performance of the long/short portfolios from February 1996 through April 2016. The exhibit indicates that the cumulative growth is significantly lower for the long/short portfolios than for the equal-weighted portfolio. This is not surprising, due to their significantly reduced and often negative exposure to the market.

We next consider long-only 50-stock portfolios based on the eight bullish signals. The results in Exhibit 5 indicate that the majority of the long-only option signal-based portfolios significantly outperform the equal-weighted portfolio on an absolute return basis, with the exception of the put implied volatility change and realized volatility signals. With the exception of the put implied volatility change portfolio, all of the eight portfolios outperform the equal-weight portfolio on a risk-adjusted basis as measured by alpha, based on a single factor model using the equal-weighted portfolio as the factor. The annualized alphas range from a low of −1.1% for the put implied volatility change portfolio to 6.6% for the OTM skew portfolio, with all the presented alphas significant at the 99% confidence level. Most of the portfolios have higher standard deviation than the equal-weighted portfolio. In contrast, most of the portfolios exhibit smaller maximum drawdowns than the equal-weighted portfolio. So while the signal-based portfolios outperform the equal-weighted portfolio, they may exhibit somewhat higher risk. This is not surprising, since they are likely less diversified than the equal-weighted portfolio.

Exhibit 6 provides a graphical presentation of the performance of the portfolios from February 1996 through April 2016. The exhibit indicates that the cumulative growth varies significantly across the portfolios and over time. The significant outperformance of a number of the long portfolios is quite evident.

Over the period of study, the long-only portfolios generally outperformed the long/short portfolios and the equal-weighted portfolio. We now consider a simplified long-only scoring model based on a sub-section of the long signals. Here we consider only four signals: High ATM 30-day Volatility Risk Premium, Low Option/Stock Volume Ratio Change, Low OTM 30-day Put/Call Skew, and Low OTM 30-day Realized Volatility. As previously mentioned, this portfolio is constructed by summing up the rank derived scores of each of the four signals. Exhibit 7 provides summary statistics for the long score portfolio as well as the equal-weighted portfolio.

The long score portfolio generated significantly higher absolute return (20.3% versus 17.5%) and alpha (3.6%, significant at 99% confidence level) versus the equal-weighted portfolio. The beta (with respect to the S&P 500) of the long score portfolio is somewhat lower than that of the equal-weighted portfolio (0.92 versus 1.02). From a risk perspective, the long score portfolio exhibited lower risk with a slightly lower standard deviation and a smaller drawdown. Exhibit 8 provides a clear graphic presentation of the long-only portfolio’s outperformance.

Exhibits 9 and 10 provide the rolling 36-month annualized returns and standard deviations, respectively, of the long score portfolio. The largest outperformance of the long score portfolio in absolute terms occurred in the period covered by the extant literature that identified the predictive power of these measures. In particular, the rolling returns from about 2002 to 2005 (covering returns from 1999 through 2005) exhibited wider spreads above the equal-weighted portfolio returns than much of the remainder of the period. However, the performance spread remains positive throughout the period of study. The rolling standard deviations of the long score portfolio tended to be quite similar to those of the equal-weighted portfolio over the entire period although the long score portfolio tended to have a slightly lower standard deviation than the equal-weighted portfolio in the second half of the period.

Exhibit 11 provides the rolling betas of the long score portfolio and the equal-weighted portfolio relative to the S&P 500. While the betas of the two portfolios follow similar time series patterns, the long score portfolio tended to have a slightly lower beta over time.

The 36-month rolling annualized alphas of the long score portfolio relative to the equal-weighted portfolio are provided in Exhibit 12. With the exception of two short periods in early 2000 and mid-2006, the rolling alpha is positive, although it varies significantly over time.

## PERFORMANCE ATTRIBUTION

Since the long-only portfolio is always fully invested, any outperformance relative to the equal-weighted portfolio is not due to market timing, but rather due to sector rotation or stock selection. In this section we attempt to identify which of these is the primary driver of outperformance.

To this means, we construct two additional portfolios—a portfolio that equally weights each of the sectors and a portfolio that weights the sectors with the same sector weights as the long score portfolio. In order to construct these portfolios, we first create equal-weighted portfolios for each sector as identified by their SIC industry provided by Optionmetrics. We then weight each of these sectors equally to create the equal-weighted sector portfolio. This portfolio differs somewhat from the equal-weighted portfolio since each sector contains a different number of stocks. To determine the sector loading of the long score portfolio each month we simply count the number of stocks in the portfolio that belong to each of the sectors. We use this count to weight each of the equal-weighted sectors to calculate the returns to the loaded sector portfolio. This portfolio represents the returns to the sector rotation component of the long score portfolio. Thus, any performance difference between the loaded sector portfolio and the equal-weighted sector portfolio we attribute to sector rotation and any performance difference between the long score portfolio and the loaded sector portfolio we attribute to stock selection.

Exhibit 7 provides summary statistics for the equal-weighted sector portfolio, the loaded sector portfolio, and the long score portfolio. The results do not suggest that sector rotation is the source of the outperformance. In fact, the loaded sector portfolio provides a lower return than the equal-weighted sector portfolio, albeit at a lower standard deviation. More telling is that the loaded sector portfolio’s alpha is only 0.2%, versus the 0.9% alpha of the equal-weighted sector portfolio and the 3.6% alpha of the equal-weighted portfolio. The long score portfolio clearly provided a higher return and alpha than the signal loaded portfolio.

## STOCK SELECTION ANALYSIS

To further consider the source of outperformance and turnover of the long score portfolio over the period of study we look at the stocks included in the portfolio over time. Exhibit 13 provides an analysis of the number of times any particular stock was included in the long score portfolio. This histogram allows us to determine whether the performance is due to a single superior performing stock, or a few strong stocks being included in the portfolio throughout the period of study. It is clear that no single stock is included in the portfolio for the whole period of study. In fact, few of the stocks are included more than 55 of the 242 months of returns in the period. The most common occurrence is for a stock to be included 15 out of the 242 months. Exhibit 14 provides additional detail. The histogram provides the frequency of month-to-month position repeats in which a stock is included in the long score portfolio for two consecutive months. The exhibit indicates that the most frequent occurrence is for 10 stocks out of the 50 in the portfolio being a holdover from the previous month. Of the 242 months, almost 100 included 10 stocks that had been in the portfolio in the previous month.

### Ten-Stock Long-Score Portfolio

Since transaction costs play an important part in assessing the performance of such strategies and we do not implicitly adjust for transaction costs in our analysis, we further analyze the long score portfolio performance under the restriction of only including 10 stocks.

We next consider long-only 10-stock portfolios based on the eight bullish signals. The results in Exhibit 15 indicate that the majority of the long-only option signal-based portfolios significantly outperform the equal-weighted portfolio on an absolute return basis, with the exception of the option/stock ratio change and realized volatility signals. All of the eight portfolios outperform the equal-weighted portfolio on a risk-adjusted basis as measured by alpha, based on a single factor model using the equal-weighted portfolio as the factor. The annualized alphas range from a low of 0.3% for the option/stock ratio change portfolio to 15.1% for the OTM skew portfolio, with all the presented alphas significant at the 99% confidence level. It is worth noting the wide range of standard deviation of the portfolios, ranging from 11.3% (about 2/3 of the standard deviation of the equal-weighted portfolio) to 33.5% (about twice the standard deviation of the equal-weighted portfolio). A number of the portfolios also exhibit greater maximum drawdown. So while the signal-based portfolios outperform the equal-weighted portfolio, they do so at a higher level of risk. This is not surprising, since they are likely far less diversified than the equal-weighted portfolio.

Exhibit 16 provides a graphical presentation of the performance of the 10-stock long signal portfolios from February 1996 through April 2016. The exhibit indicates that the cumulative growth varies significantly across the portfolios and over time. The significant outperformance of the ATM skew signal is evident.

We now present results for the 10-stock long-only scoring model. As with the 50-stock long-only scoring model, we consider four signals: High ATM 30-day Volatility Risk Premium, Low Option/Stock Volume Ratio Change, Low OTM 30-day Put/Call Skew, and Low OTM 30-day Realized Volatility. Exhibit 17 provides summary statistics for the long score portfolio as well as the equal-weighted portfolio.

The 10-stock long score portfolio exhibited slightly higher risk than the 50-stock long score portfolio both in terms of standard deviation and maximum drawdown. However, it generated significantly higher absolute return (25.2% versus 20.3% and 17.5%) and alpha (7.1%, significant at 99% confidence level versus 3.6%) versus the 50-stock long-only portfolio and the equal-weighted portfolio. The S&P 500 betas (with respect to the S&P 500) of the 10-stock long score portfolio is slightly higher than that of the 50-stock portfolio (0.96 versus 0.92) and almost identical to the beta of the equal-weighted portfolios (0.96 versus 1.02). From a risk perspective, the 10-stock long score portfolio had a slightly higher standard deviation, but a slightly smaller drawdown than the equal-weighted portfolio. Exhibit 18 provides a clear graphic presentation of the 10-stock long-only portfolio’s outperformance.

Exhibits 19 and 20 provide the rolling 36-month annualized returns and standard deviations, respectively, of the 10-stock long score portfolio. As with the 50-stock portfolio, the largest outperformance of the long score portfolio in absolute terms occurred in the period covered by the extant literature that identified the predictive power of these measures. In particular, the rolling returns from about 2002 to 2005 (covering returns from 1999 through 2005) exhibited wider spreads above the equal-weighted portfolio returns than much of the remainder of the period. However, the performance spread remains positive throughout almost all of the period of study. Interestingly, the rolling standard deviations of the long score portfolio tended to be significantly higher than those of the equal-weighted portfolio over the same 2002 to 2005 period and quite similar to those of the equal-weighted portfolio the remainder of the period.

Exhibit 21 provides the rolling betas of the 10-stock long score portfolio and the equal-weighted portfolio relative to the S&P 500. While the betas of the two portfolios follow similar time series patterns, it is clear that the long score portfolio has a more stable beta over time, ranging from about 0.8 to 1.2 versus about 0.6 to 1.7 for the equal-weighted portfolio.

The 36-month rolling annualized alphas of the long score portfolio relative to the equal-weighted portfolio are provided in Exhibit 22. With the exception of a short period in mid-2006, the rolling alpha is positive, although it varies significantly over time. Once again, we see the largest outperformance in the pre-2005 period. In addition, the rolling alpha trended downward since 2012, although it remained around 5% at the end of the period.

## CONCLUSIONS

In this article we examine the performance of a range of long and long/short portfolios based on individual signals from options markets that have been found in the extant literature to have predictive power for future returns. In order to limit issues related to liquidity in the stock and options markets, we restrict our analysis to S&P 500 constituent stocks.

While the results for individual signals is somewhat mixed, our analysis of the period from 1996 through mid-2015 shows significant outperformance relative to the S&P 500 and the equal-weighted S&P 500 of a long-only equal-weighted portfolio of 50 stocks. Similar results were found when considering smaller 10-stock portfolios. The return attribution analysis confirms that the outperformance is provided by individual stock selection rather than sector selection.

While the results of the analysis suggest that the option-based signals were generally predictive of future stock returns over the period of study, such analysis is particularly period dependent and thus might not be indicative of any predictive power in the future. The results of the analysis, however, certainly suggest that more research in this area may be warranted.

## Disclaimer

Any references to securities in this article should not be construed as an endorsement or indication of the current or future value of any product, security, fund, or investment strategy. The authors make no representation regarding the advisability of investing in any products. An investor should consider their investment objectives, all risks, fees, and expenses carefully before investing. Before investing in any fund or security, please closely read the applicable prospectus and other pertinent information.

Options involve risk and are not suitable for all investors. Prior to buying or selling an option, a person must receive a copy of Characteristics and Risks of Standardized Options. Copies are available from your broker, by calling 1-888-OPTIONS, or from The Options Clearing Corporation at www.theocc.com.

The information presented herein is provided for general education and information purposes only. No statement within this article should be construed as a recommendation to buy or sell a security or to provide investment advice. Investors should consult their tax advisor as to how taxes affect the outcome of contemplated options transactions.

Past performance does not guarantee future results. This document contains index performance data based on back-testing. Back-tested performance information is purely hypothetical and is provided in this paper solely for informational purposes. Back-tested performance does not represent actual performance and should not be interpreted as an indication of actual performance.

Financial products based on S&P indices are not sponsored, endorsed, sold, or promoted by Standard & Poor’s, and Standard & Poor’s makes no representation regarding the advisability of investing in such products. All other trademarks and service marks are the property of their respective owners. All information provided by the authors are presented “as is” and without representations or warranties of any kind. The Parties shall not be liable for loss or damage, direct, indirect or consequential, arising from any use of the data or action taken in reliance upon the data. Redistribution, reproduction, and/or photocopying in whole or in part are prohibited without the written permission of the authors.

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