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- 1. March 6, 2006 Volatility Monthly: Low Volatility Marches On Ryan Renicker, CFA Complacency in the Options Market? Most of the risk indicators we follow suggest we are 1.212.526.9425 living in a period of market complacency. However, we believe equity risk expectations areryan.renicker@lehman.com unreasonably low, particularly in light of a host of possible market-moving catalysts that could Devapriya Mallick increase investor uncertainty. 1.212.526.5429 dmallik@lehman.com Options on the VIX. Open interest has increased steadily since VIX options began trading slightly more than a week ago. Although implied volatility data and the information content inferred from the various strike levels and expiration terms in VIX options are likely to become more reliable as liquidity in these contracts increases, we believe the current shape of the curve provides insights into the extent of complacency in the marketplace. Mean Reversion in Implied Volatility Skews. We find that implied volatility skew displays a tendency to revert to its longer term mean. Higher levels of skew, measured by percentile ranking relative to their 1-year history, tend to be followed by lower skew levels in the future with increasing probability. This is found to be true for put skews as well as call skews. Sector Volatility Snapshots. Our Sector Volatility Snapshots allow investors to quickly assess aggregate volatility information for each S&P 500 GICS sector. The snapshots include implied and realized volatility for each sector and sector-based ETF, along with other useful metrics such as sector put-call skews, sector term structure trends, and notable volatility increases and decreases for stocks within each of the 10 GICS sectors.Lehman Brothers does and seeks to do business with companies covered in its research reports. As a result, investors should be aware that the firm may have a conflict ofinterest that could affect the objectivity of this report.Customers of Lehman Brothers in the United States can receive independent, third-party research on the company or companies covered in this report, at no cost to them,where such research is available. Customers can access this independent research at www.lehmanlive.com or can call 1-800-2LEHMAN to request a copy of this research.Investors should consider this report as only a single factor in making their investment decision.PLEASE SEE ANALYST(S) CERTIFICATION AND IMPORTANT DISCLOSURES BEGINNING ON PAGE 22.
- 2. Equity Derivatives Strategy | Volatility Monthly: Low Volatility Marches On Table of Contents Equity Volatility Overview ...........................................................................................3 Complacency Unwarranted?............................................................................................. 3 Volatility Trading Environment ......................................................................................5 VIX Options ................................................................................................................... 5 Mean Reversion in Implied Volatility Skews.....................................................................6 Introduction.................................................................................................................... 6 Volatility Skew as a Measure of Market “Fear” ..................................................................... 6 Mean Reversion in Volatility Skew ...................................................................................... 7 Put Skews vs Call Skews .................................................................................................. 8 Conclusion .................................................................................................................... 9 Appendix I: Sector Volatility Snapshots ........................................................................10 Sector Highlights........................................................................................................... 11 March 6, 2006 2
- 3. Equity Derivatives Strategy | Volatility Monthly: Low Volatility Marches On Equity Volatility Overview Most of the risk indicators we follow suggest we are living in a period of market complacency. First, short-term equity risk expectations remain near multi-year lows. In fact, as Figure 1 illustrates, S&P 500 3-month implied and 66-day realized volatility are again approaching levels not observed since the end of 1996. Second, longer-term risk expectations (3-month forward volatility in 9 months’ time) are hovering near multi-year lows, and have continued to decline this year, as the S&P 500 rallied since Q4 2005 and is approaching 5-year highs (Figure 2). In addition, the 3-month S&P 500 skew continues its decline, suggesting investors continue to place incrementally smaller bids for downside protection against market downturns. This measure is closely related to the level of implied volatility itself, and we explore index volatility skew more closely later in this report. Credit spreads also continue to trade near historically low levels and the high-yield spread relative to the spread on investment grade debt is also near its all-time lows. This might be a signal that investors’ tolerance for risk has increased and expanded across asset classes.Figure 1: SPX Implied Volatility Remains Ominously Low Figure 2: Long Term Risk Expectations Continue to Decline 45% 1,800 1,350 Implied Vol 20% Realized Vol S&P 500 40% S&P 500 1,600 9m-12m Forward Vol 19% 1,300 35% 1,400 18% S&P 500 Volatility 1,200 1,250 Forward Implied Vol 30% S&P 500 Index 17% S&P 500 Index 1,000 25% 1,200 16% 800 20% 15% 600 1,150 15% 14% 400 1,100 10% 200 13% 5% - 1,050 12% 4 5 7 04 05 06 4 5 6 96 02 4 5 4 5 5 06 4 5 6 9 0 1 3 4 8 -0 -0 -0 -0 -0 -0 -0 -9 -0 -0 l-0 -0 l-0 -9 -0 -0 -0 l-0 -9 -9 n- n- n- n- n- b- ov ov ov ar ar ar ec ar ep ep ay ay ep ug ay pr ct Ju Ju Ju Ja Ja Ja Ja Ju Fe M M M M O A N N N M M M D S S S ASource: Lehman Brothers, OptionMetrics, Bloomberg Source: Lehman Brothers, OptionMetrics, Bloomberg Complacency Unwarranted? We believe equity risk expectations are unreasonably low, particularly in light of a host of possible market-moving catalysts that could be forthcoming and are likely to spill over into a more volatile equity market. For example, there still remains uncertainty regarding when the Fed is likely to stop raising rates (Lehman’s forecast is continued hiking until the August or September FOMC meeting, with the Fed Funds rate peaking at 5.5%). If the Fed continues to raise rates, there runs the risk that the consumer will begin to cut back on spending and the housing market could weaken, thereby reducing home equity extraction. Moreover, since the Fed is expected to become more dependent on economic data releases, we expect the market to become more “unsettled” prior to such releases. For instance, the average absolute daily return of the S&P 500 in response to releases of non-farm payrolls decreased over the “measured” rate hike period and was the lowest in 2005 (Figure 3). The market’s reaction has been larger thus far in 2006; if this persists going forward, option market participants could begin to price in larger moves as well, resulting in elevated levels of implied volatility. March 6, 2006 3
- 4. Equity Derivatives Strategy | Volatility Monthly: Low Volatility Marches On Figure 3: Lowest Average Reaction to Non-Farm Payrolls in 2005 2.0% 2.0 Reaction to Non Farm Payrolls Absolute Change in VIX Higher Absolute Reaction Avg. Absolute Reaction to Payrolls Expected in 2006 Change in VIX after Payrolls 1.5% 1.5 1.0% 1.0 0.5% 0.5 0.0% 0.0 96 97 98 99 00 01 02 03 04 05 06 19 19 19 19 20 20 20 20 20 20 20 Source: Lehman Brothers, Bloomberg. In addition, we believe concern over rising energy prices (potential geopolitical risks in key oil- producing nations, active hurricane season, rising demand during summer months, etc.) and this year’s mid-term congressional elections could contribute to higher market anxiety. Event risks such as an avian flu outbreak could also be a catalyst for greater uncertainty. March 6, 2006 4
- 5. Equity Derivatives Strategy | Volatility Monthly: Low Volatility Marches On Volatility Trading Environment VIX Options Options on the VIX index have been widely awaited by investors and commenced trading on February 24. In a little more than a week since these options started trading, open interest has increased steadily (Figure 4) and the popularity of VIX options can be expected to rise as a larger proportion of long-only fund managers begin using them as a “catastrophe hedge”.Figure 4: Increasing Interest VIX Options Figure 5: VIX Implied Volatility Surface (as of March 3) 180 45,000 160 40,000 VIX Option Volume 140 35,000 VIX Option Open Interest 120 Implied Volatility 30,000 100 25,000 80 20,000 60 Mar-06 15,000 Apr-06 40 10,000 May-06 20 5,000 0 0 10 12.5 15 17.5 20 24-Feb 27-Feb 28-Feb 01-Mar 02-Mar 03-Mar StrikeSource: Lehman Brothers, Bloomberg Source: Lehman Brothers, Bloomberg The implied volatility surface of VIX options exhibits the expected premium for writing out-of-the-money calls (Figure 5). While implied volatility data and the information content inferred from the various strike levels and expiration terms are likely to become more reliable as liquidity in these contracts increases, we believe the current shape of the curve provides insights into the extent of complacency in the marketplace. Thus, one might expect the higher strikes for the April and May maturities to trade at a significant premium to the at-the-money strike, yet the skew is essentially flat at present. Although there are currently not enough data points to draw statistically meaningful conclusions, we believe a persistence of this pattern could indicate unreasonably low levels of “fear” in the market. March 6, 2006 5
- 6. Equity Derivatives Strategy | Volatility Monthly: Low Volatility Marches On Mean Reversion in Implied Volatility Skews Introduction According to the Black-Scholes option valuation model, implied volatility is assumed to be constant across all strikes and expirations. However, in practice, option contracts trade with different implied volatilities, depending on their maturity as well as the distance of the strike from the underlying stock price. The tendency for lower strikes in index options to trade at higher levels of implied volatility has been observed since the stock market crash of 1987. Since then, writers of out-of-the-money puts have tended to demand a premium to compensate for the insurance they provide. In addition, demand/supply technicals explain the sustained existence of a volatility skew in index options. Equity investors, in aggregate, have a net long exposure to equity markets and are a natural source of demand for purchasing out-of-the-money puts, thus raising the implied volatility for lower strikes. On the other hand, they tend to supply volatility at higher strikes by selling out-of-the-money calls as part of systematic overwriting strategies, thus suppressing implied volatility at higher strikes. Another perspective that helps explain skew in the volatility surface is the return distribution of equities. If the Black-Scholes theoretical assumption of stocks’ lognormal distribution was valid, implied volatility would be expected to be flat across strikes. However, the actual return distribution over an extended period of time indicates that equity returns exhibit negative skewness, with fatter downside tails. This supports the notion that investors bid up protection for options having very low strike prices, resulting in higher implied volatility for contracts at these strikes. Volatility Skew as a Measure of Market “Fear” Implied volatility is frequently used as a risk indicator in the equity market since there is a well established negative correlation between spot prices and implied volatility. We find that SPX skew, as measured by the difference in implied volatility for the 20-delta puts and calls, moves closely with the level of implied volatility, and can be considered an alternate metric of market “fear” (Figure 6). We also find that daily changes in implied volatility are strongly correlated with daily changes in skew levels (Figure 7).Figure 6: Skew a Measure of Market Fear Figure 7: Index Implied Volatility Correlated to Skew 50% 20% 6% 3-month Implied Vol 80 Delta-20 Delta Skew (3-month) 3-month 80-20 Delta Skew 40% 4% ATM Implied Vol (3-month) 15% R2 = 0.3274 Daily Change in Skew 30% 2% 10% 0% 20% -6% -4% -2% 0% 2% 4% 6% 5% -2% 10% -4% 0% 0% -6% 6 7 8 9 0 1 2 3 4 5 6 9 9 9 9 0 0 0 0 0 0 0 n- n- n- n- n- n- n- n- n- n- n- Ja Ja Ja Ja Ja Ja Ja Ja Ja Ja Ja Daily Change in Implied VolSource: Lehman Brothers, OptionMetrics Source: Lehman Brothers, OptionMetrics March 6, 2006 6
- 7. Equity Derivatives Strategy | Volatility Monthly: Low Volatility Marches On However, at the single-stock level, implied volatility changes do not appear to be a strong predictor of changes in skew (Figure 8). Figure 8: Correlations of Single-Stock Skew Changes With Implied Volatility Changes 1-month Vols 3-month Vols 20 Delta 1.7% 3.9% 30 Delta 1.8% 3.9% 40 Delta 1.3% 2.7% Source: Lehman Brothers, OptionMetrics Mean Reversion in Volatility Skew We have found that the spread of implied relative to realized volatility displays a tendency to revert to its longer term mean1. We now test whether a similar reversion exists for volatility skews. We consider the 20 delta put – 20 delta call skew on 3-month S&P 500 options since 1996. We categorize skew as being “rich” if it is trading at a high percentile relative to where it had traded during the prior year. On the other hand, if it stands at a lower percentile relative to its 1-year history, we label it as “cheap”. If volatility skew indeed exhibits mean reversion, we would expect periods of high skew percentiles to be followed by lower skew in 3 months’ time, and vice versa. Figure 9 demonstrates that such mean reversion does tend to occur, as successively higher percentiles of skew tend to precede greater declines in skew. For example, on average, when skew was initially labeled as being very “rich” (skew level at a percentile greater than 95%), the skew stood at a lower value in 3 months in 91% of cases and the median drop in skew in these instances was over 2.7%. On the other hand, when skew was trading at a low percentile relative to its history (“cheap”), its subsequent change tended to be positive, though at a lower degree of magnitude than that of “rich” skew. We believe this reflects the fact that during the sample period of the study, skew on index options has, on average, been in a declining trend. (Thus, the likelihood of “rich” skew being followed by lower skew has been greater than the probability of “cheap” skew being a predictor of elevated skew in future.) 1 Please refer to Identifying Rich and Cheap Implied Volatility, December 20, 2005 for additional details. March 6, 2006 7
- 8. Equity Derivatives Strategy | Volatility Monthly: Low Volatility Marches On Figure 9: More Extreme Values of Skew Tend to Revert With Higher Probability "Rich" Skew Median 3- # With Avg 3-month Std Dev Percentile of Skew Relative % month # Subsequent Change in of Skew to 1yr History Correct Change in Skew Decrease Skew Change Skew 70% 644 498 77% -1.23% -1.55% 2.67% 80% 412 344 83% -1.68% -1.85% 2.48% 90% 241 212 88% -2.23% -2.39% 2.34% 95% 144 131 91% -2.68% -2.74% 2.16% "Cheap" Skew Median 3- # With Avg 3-month Std Dev Percentile of Skew Relative % month # Subsequent Change in of Skew to 1yr History Correct Change in Skew Increase Skew Change Skew 30% 882 473 54% 0.57% 0.29% 2.12% 20% 645 349 54% 0.50% 0.27% 1.83% 10% 382 231 60% 0.73% 0.48% 1.60% 5% 237 156 66% 0.96% 0.85% 1.53% Source: Lehman Brothers, OptionMetrics Put Skews vs Call Skews Having established the mean reverting characteristics of volatility skew, we now examine the components of skew more closely. Specifically, rather than analyzing the total difference in put and call implied volatility, we now analyze mean reversion in the put skew (OTM put implied vol – ATM implied vol) and call skew (ATM implied vol – OTM call implied vol) separately. As Figure 10 and Figure 11 illustrate, put skews and call skews have displayed a tendency to revert to their medium-term averages. The effect is stronger for “rich” skew than for “cheap” skew, similar to the observation for put-call skews.Figure 10: Mean Reversion in Put Skew Figure 11: Mean Reversion in Call Skew 1.0% 0.5% < 10th < 5th < 30th < 20th < 10th < 5th < 30th < 20th Percentile Percentile Percentile Percentile Percentile Percentile Percentile Percentile 0.5% 0.0% 0.0% -0.5% -0.5% > 70th > 70th -1.0% Percentile Percentile > 80th > 80th -1.0% Percentile Percentile -1.5% > 90th > 95th > 90th > 95th Percentile Percentile Percentile Percentile -2.0% -1.5% Avg Change in Put Skew ("Rich") Avg Change in Put Skew ("Cheap") Avg Change in Call Skew ("Rich") Avg Change in Call Skew ("Cheap")Source: Lehman Brothers, OptionMetrics Source: Lehman Brothers, OptionMetrics March 6, 2006 8
- 9. Equity Derivatives Strategy | Volatility Monthly: Low Volatility Marches On Conclusion Possible strategies for taking advantage of the mean reversion characteristics in skew include buying or selling delta-hedged spreads. For example, an investor who believes the put skew is trading at very low levels and expects it to increase, can sell put spreads by buying out-of-the-money puts and writing at-the-money puts. Although hedging the net delta of the spread can theoretically eliminate this position’s exposure to the changes in the underlying index, we note that the position would have some exposure to time decay (theta), which can be partly mitigated by selecting longer term options. Moreover, the success of any strategy attempting to exploit the change in skew would depend on the bid-ask spreads involved. For illiquid out-of-the-money contracts, total transaction costs could overwhelm the profit from the expected movement in skew. March 6, 2006 9
- 10. Equity Derivatives Strategy | Volatility Monthly: Low Volatility Marches On Appendix I: Sector Volatility Snapshots In this section, we show our Sector Volatility Snapshots. These snapshots allow investors to quickly assess aggregate volatility information for each GICS sector in the S&P 500 Index. The average volatility (implied or realized) for a GICS sector is calculated as the weighted- average- volatility of each of their respective index constituents, weighted by market capitalization. The weighted-average volatility for a GICS industry group is obtained similarly. ETFs having options are mapped to one GICS sector each, although the mapping is not perfect since stocks in an ETF could be classified into multiple sectors as per the GICS sector classification methodology. However, they closely reflect the performance and volatility characteristics of the sectors and industries they represent. • We display the weighted-average implied and realized volatility at the sector level for a one year period. For each industry group within the sector and each ETF that closely resembles the respective industry or sector, we provide the number of standard deviations the current level of the implied-realized volatility spread is trading above or below to its one-year historical mean. A highly negative standard deviation could indicate that options are trading cheap, whereas a highly positive standard deviation possibly implies such options are relatively rich. (Note that there usually do not exist actively traded options at the industry group level and the relative richness/cheapness indicators for these industry groupings should only be used only as a starting point for identifying single-stock volatility trades within that industry group. Furthermore, while options on ETFs exist, their liquidity should be taken into account before executing a trade, since many are currently thinly traded as well.) • The “Largest Implied Volatility Increases” and “Largest Implied Volatility Decreases” denote the stocks within the sectors that have experienced the highest and lowest absolute changes in implied volatility, over one-week and one-month periods. • The Put-Call Skew is calculated as the difference between the 3-month put-implied volatility and the 3-month call-implied volatility for 20 delta puts and 20 delta calls, divided by the 3- month at-the-money implied volatility. The weighted-average skew at the sector and industry group level are calculated similarly, except the volatility used is the market-cap weighted- average implied volatility. If the current skew level is trading a relatively high number of standard deviations above its one-year average, this could indicate the option market is pricing in increasing risk expectations for the underlying stock, since the put–call implied volatility differential implies that option traders have been bidding up put protection, rather than upside participation via long call positions. • We show the history of the slope of the volatility term structure as measured by the difference between 12-month and 3-month at-the-money implied volatilities. Since longer term implied volatility tends to be more stable than implied volatility on shorter-dated options, a lower term structure spread relative to its historical pattern could indicate 3-month options are trading richer than they typically have in the past. Alternatively, if the slope of the term structure is relatively steep, one might infer near term options are trading at a relative discount to longer dated options. March 6, 2006 10
- 11. Equity Derivatives Strategy | Volatility Monthly: Low Volatility Marches On Sector Highlights Lehman’s U.S. Equity Strategy team has raised its weighting of the Telecommunication Services sector to Overweight from Market-Weight on the back of improved conditions in end markets, realization of consolidation benefits and strong wireless revenue trends. Implied volatility for the Telecom sector on a market-cap weighted-average basis has lagged realized volatility, and its current 3-month implied-realized spread stands more than one standard deviation below its 1-year average. We observe that the Telecom HOLDRS Trust (TTH) ETF has had increasing interest among investors, with the total number of contracts traded in February increasing more than two-fold relative to that of January. We recommend investors looking to implement a bullish view on the Telecom sector consider purchasing relatively inexpensive calls on TTH (Figure 12) or some of its largest constituents.Figure 12: TTH Implied vs Realized Volatility Figure 13: PPH Implied vs Realized Volatility 22% 18% TTH 3-month Implied Vol PPH 3-month Implied Vol 20% TTH 66-day Realized Vol PPH 66-day Realized Vol 16% 18% 14% 16% 14% 12% 12% 10% 10% 8% 8% 05 5 5 05 06 05 05 06 05 05 5 5 06 05 05 5 5 06 5 5 05 05 05 05 l-0 l-0 -0 -0 -0 -0 -0 -0 p- p- - - n- n- n- n- - b- - b- g- g- r- r- ov ec ov ec ay ay ar ar ct ct Ju Ju Ju Ja Ju Ja Ap Se Fe Ap Se Fe Au Au O O M M N D N D M MSource: Lehman Brothers, OptionMetrics Source: Lehman Brothers, OptionMetrics 3-month implied volatility for the S&P 500 Health Care sector steadily declined through February, and currently trades at a discount to 66-day realized volatility. This has been true for both U.S. Major Pharmaceuticals as well as Health Care Equipment stocks. Lehman Brothers Pharmaceuticals analyst Anthony Butler and Medical Supplies analyst Bob Hopkins currently have positive ratings on their respective sectors. We believe investors wishing to implement a bullish directional view for the Health Care sector should consider purchasing relatively cheap calls on the Pharmaceutical HOLDRS Trust (PPH) ETF (Figure 13). March 6, 2006 11
- 12. Equity Derivatives Strategy | Volatility Monthly: Low Volatility Marches OnFigure 14: Energy Sector Volatility Snapshot (as of March 3, 2006) Implied Volatility vs Realized Volatility Implied-Realized Spread (by Industry Groups/ETF) # of Standard Deviations from 1-year Average 40% XNG 35% IYE 30% Energy XLE 25% XOI 20% OSX 15% OIH 5 5 5 05 05 05 5 06 6 5 5 5 -0 -0 -0 0 r-0 l-0 -0 -0 n- g- p- n- b- -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 ay ov ec ar ct Ju Ap Ju Au Se Ja Fe O M N M D Cheap > > > > > > > > > > > > Rich Wgt Avg Implied Vol Wgt Avg Realized VolNote: We calculate each sectors average implied volatility by weighting the 3-month at-the-money implied volatility of its constituents by market capitalization.Investors should consider liquidity of options of a stock or ETF before entering an options position since, although options on ETFs exist, many are thinly traded. Largest Implied Volatility Increases Largest Implied Volatility Decreases 1-week Increase 1-month Increase 1-week Decrease 1-month Decrease Ticker Implied Vol Change Realized Vol Ticker Implied Vol Change Realized Vol Ticker Implied Vol Change Realized Vol Ticker Implied Vol Change Realized Vol EP 32% 1% 29% NOV 42% 2% 44% WMB 30% -2% 28% WMB 30% -5% 28% SLB 33% 1% 37% EOG 42% 2% 41% NBR 36% -2% 35% HAL 33% -3% 36% NOV 42% 0% 44% NE 38% 1% 40% EOG 42% -2% 41% RIG 36% -3% 39% BR 14% 0% 24% SUN 38% 1% 40% AHC 32% -2% 33% XTO 35% -3% 34% CVX 22% 0% 21% BJS 36% 1% 40% XTO 35% -1% 34% XOM 20% -2% 20% 3-Month Put-Call Skew (20 Delta) Relative Skews (by Industry Groups/ETF) 16% # of Standard Deviations from 1-year Average 14% OIH 12% IYE 10% XNG 8% OSX 6% Energy 4% 2% XOI 0% XLE 5 05 5 05 05 05 5 06 06 5 5 5 -0 -0 r-0 -0 -0 l-0 -1.4 -1.2 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 v- n- g- p- n- b- ay ec ar ct Ju Ap No Ju Ja Fe Au Se O M M D Cheap > > > > > > > > > > > > Rich Wgt Avg 20 Delta Skew (3m) Avg + 1 Stdev Avg - 1 Stdev Note: The put-call skew is calculated by taking the difference between the 20-Delta put-implied volatility and 20-Delta call-implied volatility, divided by the 3-month ATM implied volatility. Sector level volatilities are the market cap weighted implied volatilty for each constituent. A high skew is generally associated with a relatively high demand for downside protection. 12-Month - 3-Month Term Spread Relative Term Spreads (by Industry Groups/ETF) # of Standard Deviations from 1-year Average 2% XOI 1% 0% Energy -1% XNG -2% OIH -3% XLE -4% IYE -5% OSX 5 5 5 05 05 05 5 06 6 5 5 5 -0 -0 -0 0 r-0 l-0 -0 -0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 n- n- g- p- b- ay v ec ar ct Ju Ap No Ju Au Se Ja Fe O M M D Cheap > > > > > > > > > > > > Rich Wgt Avg 12m-3m Term Avg + 1 Stdev Avg - 1 Stdev Note: The term structure spread is calculated by taking the difference between the 12-month ATM implied volatility and the 3-month ATM implied volatility. Sector level term spread is calculated from the market cap weighted implied volatilities of the constituents. A steep term structure indicates shorter-dated implied volatility could be cheap relative to longer-dated implied volatility.Source: Lehman Brothers, OptionMetrics March 6, 2006 12

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