Derivative Valuation, Risk Management, Volatility Trading
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In a previous post, we showed that the spot volatility index, VIX, has a strong mean reverting tendency. In this follow-up installment we’re going to further investigate the mean reverting properties of the VIX. Our primary goal is to use this study in order to aid options traders in positioning and/or hedging their portfolios. To do so, we first calculate the returns of the VIX index. We then determine the quantiles of the return distribution. The table below summarizes the results.
We next calculate the returns of the VIX after a significant volatility spike. We choose round-number spikes of 3% and 6%, which roughly correspond to the 75% and 85% quantiles, respectively. Finally, we count the numbers of occurrences of negative VIX returns, i.e. instances where it decreases to below its initial value before the spike. Tables below present the numbers of occurrences 1, 5, 10 and 20 days out. As in a previous study, we divide the volatility environment into 2 regimes: low (VIX<=20) and high (VIX>20). We used data from January 1990 to December 2017.
We observe the followings,
The implication of this study is that
Learn More Here: VIX Mean Reversion After a Volatility Spike
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The violent sell off in the equity markets during the last 2 months reminds us of the importance of risk management. Some traders, investors wanted to eliminate the risks completely. However, we note that risks cannot be eliminated, only managed.
In this video, Anthony Carfang of Treasury Strategies testifies before the U.S. House Committee on Financial Services. The Subcommittee on Capital Markets and Government-Sponsored Enterprises conducted the hearing on February 24, 2016. First five minutes are Carfang's opening statement. That is followed by questions to him from members of the committee.
He stated that risk can only be transferred, but cannot be suppressed.
Similarly, Perry Kaufman made the same statement in this video. This is an interview conducted by Alex Gerchik for his Russian audience.
Click here for more interviews.
ByMarketNews
Published via http://harbourfronttechnologies.blogspot.com/ In this post, we are going to examine a trading system with the goal of using it as a hedge for long equity exposure. To this end, we test a simple, short-only momentum system. The rules are as follows, Short at the close when Close of today < lowest Close of the last 10 days Cover at the close when Close of today > lowest Close of the last 10 days The Table below presents results for SPY from 1993 to the present. We performed the tests for 2 different volatility regimes: low (VIX<=20) and high (VIX>20). Note that we have tested other lookback periods and VIX filters, but obtained qualitatively the same results.
It can be seen that the average PnL for all trades is -0.3%, so overall shorting SPY is a losing trade. This is not surprising, since in the short term the SP500 exhibits a strong mean reverting behavior, and in a long term it has a positive drift. We still expected that when volatility is high, the SP500 would exhibit some momentum characteristics and short selling would be profitable. The result indicates the opposite. When VIX>20, the average trade PnL is -0.37%, which is higher (in absolute value) than the average trade PnL for the lower volatility regime and all trades combined (-0.23% and -0.3% respectively). This result implies that the mean reversion of the SP500 is even stronger when the VIX is high. The average trade PnL, however, does not tell the whole story. We next look at the maximum favorable excursion (MFE). Table below summarizes the results
Despite the fact that the short SPY trade has a negative expectancy, both the average and median MFEs are positive. This means that the short SPY trades often have large unrealized gains before they are exited at the close. Also, as volatility increases, the average, median and largest MFEs all increase. This is consistent with the fact that higher volatility means higher risks. The above result implies that during a sell-off, a long equity portfolio can suffer a huge drawdown before the market stabilizes and reverts. Therefore, it’s prudent to hedge long equity exposure, especially when volatility is high. An interesting, related question arises: should we use options or futures to hedge, which one is cheaper? Based on the average trade PnL of -0.37% and gamma rent derived from the lower bound of the VIX, a back of the envelope calculation indicated that hedging using futures appears to be cheaper. See More Here: A Simple System For Hedging Long Portfolios We have written many blog posts about the increase in volatility of volatility. See, for example Is Volatility of Volatility Increasing? What Caused the Increase in Volatility of Volatility? Similarly, last week Bloomberg reported, The sudden rise in volatility in February and March showed that even with strong growth fundamentals, financial markets remain vulnerable. Since 2008, there have been seven flash crashes followed by sudden recoveries. Volatility has become binary, with markets swinging between periods of shock and calm. The VIX index traded at a median of 16 after the start of QE and at 18 before, but the spikes in volatility have become twice as frequent. It is the equivalent of swapping a stable drizzle rain with many days of scorching sun, at the price of occasional natural disasters. Read more [caption id="attachment_454" align="aligncenter" width="628"] The rise of the volatility of volatility increases the chance of a Black Swan event happening. Recently, we presented a study showing that a down day of 4% during a bull market is a very rare event. It happened on February 5, and before that the last time this occurred, it was 18 years ago. We next counted the number of days when the SP500 dropped 4% or more during a bull market. We defined the bull market as price > 200-Day simple moving average. Since 1970 there have been 5 occurrences, i.e. on average once every 10 years. We don’t know whether this qualifies as a black swan event, but a drop of more than 4% during a bull market is indeed very rare. Read more Similarly, AQR looked at the February 5 event from the implied/realized volatility perspective. ... As of now (no predictions going forward!) this recent wild period is not super crazy when we look just at volatility itself (it’s high, but not super high vs. history). But, when we look at it as a surprise (by comparing the realized 5-day volatility to the starting VIX) it’s a considerably more shocking event, though still not unprecedented. Similar events have occurred five or so times in the 1990 - present history (again, see the above figure). Finally, when just using the simple method of targeting constant volatility that we employ here, this recent surprise swoon was, as we’d expect, pretty bad for volatility targeters. But, over the longer term, volatility targeting, even the super simple volatility targeting our toy risk-model employs, may, on average, deliver more downside stability than not volatility targeting and implicitly letting the market dictate the volatility of your investment. Read more Again, from the implied/realized volatility point of view, the recent event was a rare occurrence, though not unprecedented. In times like this, risk management is more important than ever. Post Source Here: Black Swan and Volatility of Volatility On February 5, the SP500 experienced a drop of 4% in a day. We ask ourselves the question: is a one-day 4% drop a common occurrence? The table below shows the number of 4% (or more) down days since 1970.
On average, a 4% down day occurred each 1.2 years, which is probably not a rare occurrence. We next counted the number of days when the SP500 dropped 4% or more during a bull market. We defined the bull market as price > 200-Day simple moving average. Since 1970 there have been 5 occurrences, i.e. on average once every 10 years. We don’t know whether this qualifies as a black swan event, but a drop of more than 4% during a bull market is indeed very rare. The table below shows the dates of such occurrences. It’s interesting to note that before the February 5 event, the last two 4% drops when price> 200-day SMA occurred around the dot-com period.
Source Here: Is a 4% Down Day a Black Swan? Last week, many traders noticed that there was a divergence between SPX and VIX. It’s true if we look at the price series. Graph below shows the 20-day rolling correlation between SPX and VIX prices for the last year. We can see that the correlation has been positive lately. [caption id="attachment_327" align="aligncenter" width="564"] However, if we look at the correlation between SPX daily returns and VIX changes, it’s more or less in line with the long term average of -0.79. So the divergence was not significant. [caption id="attachment_328" align="aligncenter" width="564"] The implied volatility (VIX) actually tracked the realized volatility (not shown) quite well. The latter happened to increase when the market has moved to the upside since the beginning of the year. Originally Published Here: Correlation Between SPX and VIX The US equity market just reached new highs, and it broke many records. For example, Bloomberg reported that the US market had not been overbought like this in 21 years. The S&P 500 Index’s superlative start to 2018 is making a contrarian technical indicator look silly. The benchmark gauge is poised to end trading Thursday with a 16th straight day in overbought territory, as judged by the Relative Strength Index. That would be the longest such run in more than two decades. A close above 70 on Thursday passes the 15-session string seen in October. From Nov. 6 through Dec. 2, 1996, the gauge’s overbought streak reached 18 sessions. Read more The rare behavior of the equity index not only manifested itself in the overbought level, but also in the breakdown of correlation. The chart below shows the 20-day rolling correlation (upper panel) between the SPX and the volatility index, VIX. Usually, the correlation is negative, in the order of -0.79. However, it has been in the positive territory for more than a week now. [caption id="attachment_449" align="aligncenter" width="628"] We notice that there has been a breakdown in the Nikkei stock market and USDJPY correlation as well. The chart below shows the USDJPY (upper panel) and the Nikkei 225 equity index (lower panel). The relationship was usually positive. But since November of last year, it broke down: a stronger Japanese Yen did not lead to a weaker equity market and vice versa.
[caption id="attachment_450" align="aligncenter" width="628"] For the moment, we are not going to delve deeper into the reasons behind these correlation breakdowns. We note, however, that if correlations don’t revert back to normal within a reasonable time frame, then there might be a shift in the market fundamentals. Post Source Here: Correlation Breakdown
We have written about how the increase in popularity of VIX-related Exchange Traded Products could impact the financial market:
Is Volatility of Volatility Increasing? What Caused the Increase in Volatility of Volatility? Recently, Goldman Sachs derivatives analyst Rocky Fishman expressed concerns regarding the impact of VIX ETPs positions on the markets. Fishman wrote to clients early Thursday morning that he has no concerns about the net number of shorts but is concerned about the impact a sudden rise in the VIX futures would have on derivative products. He notes that over the past few weeks net positioning in VIX ETPs has gone short for only the second time in their eight year history. The analyst believes “the potential for short and levered ETPs to start buying VIX futures quickly on a sudden vol spike has grown” which in turn makes short-date VIX-based hedges timely. Therefore, his biggest concern is a one-day, end-of-day vol spike should the SPX selloff near the end of the trading day which would push issuers to replace positions quickly to avoid being exposed to unhedged overnight risk or excessive tracking error. Fishman also notes that Asset Managers and Institutions appear most at risk as they have recently started reporting short VIX futures positions. Perhaps we should just hope that there won’t be a negative market headline in the final minutes of any trading day anytime soon but should any of our readers wish to know the derivatives analyst would prepare for something jarring in the short term, Fishman suggests that client buy February 18-strike VIX call versus selling April 18-strike VIX calls with an intention to close the trade before the February 14 expiry. Read more At the same time, Bloomberg also reported that the 50-cent VIX player started buying short-dated options This entailed buying back 262,500 January VIX puts with a strike price of 12, selling 262,500 15 calls, and buying back 525,000 25 calls in order to close out the existing position. Then, the new position was established by selling 262,500 12 February puts, buying 262,500 15 calls, and selling 525,000 25 calls. While the ‘Elephant’ originally traded three-month options, rolling after two months, they appear to have switched to a one-month cycle More generally, the ‘Elephant’ trades reflect a trend towards low premium outlay hedges with minimal convexity,” the strategist concludes. “Clients we talk to have been more interested in VIX call flies or S&P put flies that carry well and have a fairly low initial cost, but may not mark up as much as an outright option in a risk-off scenario. Read more You can invest in volatility ETPs, but be prudent and hedge the risks accordingly. ByMarketNews Published via http://harbourfronttechnologies.blogspot.com/
On this last day of 2017, we are going to list some of the most important lessons of the year.
In May, Paul Singer of Elliott Management laid out some of his major investment lessons in his letter to investors. In our opinion, the followings are the most important:
Click here to watch Paul Singer’s Strategy for Successful Investing Elliott Management Founder and Co-CEO Paul Singer discusses his investment technique as trying to “make money as close as possible to all the time.” He also talks about why his strategy for holding Argentina bonds paid off so well. He speaks to David Rubenstein on “The David Rubenstein Show: Peer-to-Peer Conversations.” Click here for more interviews. ByMarketNews Published via http://harbourfronttechnologies.blogspot.com/ In the previous post, we looked at some statistical properties of the empirical distributions of spot SPX and VIX. In this post, we are going to investigate the mean reverting and trending properties of these indices. To do so, we are going to calculate their Hurst exponents. There exist a variety of techniques for calculating the Hurst exponent, see e.g. the Wikipedia page. We prefer the method presented in reference [1] as it could be related to the variance of a Weiner process which plays an important role in the options pricing theory. When H=0.5, the underlying is said to be following a random walk (GBM) process. When H<0.5, the underlying is considered mean reverting, and when H>0.5 it is considered trending. Table below presents the Hurst exponents for SPX, VIX and VXX. The data used for SPX and VIX is the same as in the previous post. The data for VXX is from Feb 2009 to the present. We display Hurst exponents for 2 different ranges of lags: short term (5-20 days) and long term (200-250 days).
We observe that SPX is mean reverting in a short term (average H=0.45) while trending in a long term (average H=0.51). This is consistent with our experience. The result for spot VIX (non tradable) is interesting. It’s mean reverting in a short term (H=0.37) and strongly mean reverting in a long term (H=0.28). As for VXX, the result is a little bit surprising. We had thought that VXX should exhibit some trendiness in a certain timeframe. However, VXX is mean reverting in both short- and long-term timeframes (H=0.46). Knowing whether the underlying is mean reverting or trending can improve the efficiency of the hedging process. References [1] T. Di Matteo et al. Physica A 324 (2003) 183-188 Post Source Here: Mean Reverting and Trending Properties of SPX and VIX |
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VVIX (volatility of volatility index) as at March 23 2018. Source: stockcharts.com[/caption]
20-day rolling correlation SPX-VIX prices, ending Jan 26 2018[/caption]
20-day rolling correlation SPX return -VIX changes ending Jan 26 2018[/caption]
SPX and VIX correlation as at Jan 26 2018. Source: Stockcharts.com[/caption]
Nikkei 225 and USDJPY as at Jan 26 2018. Source: Stockcharts.com[/caption]
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