According to Marketwatch, Goldman Sachs strategists just issued a warning regarding the volatility index, VIX,
Goldman analysts Rocky Fishman and John Marshall said that the VIX, which uses options bets on the S&P 500 to reflect expected volatility over the coming 30 days, has been hovering at or below 13, marking its lowest level since around January (though it is tipping up in Monday trade). Its current level takes the gauge of implied volatility, which tends to rise when stocks fall and vice versa, well below its historic average at about 19.5 since the fear index ripped higher in February.
Goldman argues that the 5-day intraday swings of the S&P 500 have been out of whack with the price of the cost of a one-month straddle on the index. A straddle is an options bet that allows an investor to profit from a sharp move in an asset, but without wagering on the specific direction of that expected move. In other words, it is an inherent bet on volatility. A straddle can be structured by buying a put option, which confers the owner the right but not the obligation to sell an asset at a given time and price, and a call option, which offers the comparable right to buy an underlying asset, at the same expiration date and strike price. Read more
But is the volatility index predictable? How about VIX futures and ETFs?
A recent research article raised some interesting questions,
The VIX index is not traded on the spot market. Hence, in contrast to other futures markets, the VIX futures contract and spot index are not linked by a no-arbitrage condition. We examine (a) whether predictability in the VIX index carries over to the futures market, and (b) whether there is independent time series predictability in VIX futures prices.
The answer is no.
The answer to both questions is no. Samuelson (1965) was right: VIX futures prices properly anticipate predictability in volatility, and are themselves unpredictable. Read more
But then why do we trade VIX futures and ETFs?
We think that the reasons might be:
Published via http://harbourfronttechnologies.blogspot.com/
The overnight index swap (OIS) has come into the spotlight recently, due to the widening of the Libor-OIS spread. For example, the Economist recently reported:
WATCHING financial markets can be like watching a horror film. A character walks into the darkness alone. A floorboard creaks. The latest spooky sign is the spread between the three-month dollar London interbank offered rate (LIBOR) and the overnight index swap (OIS) rate. It usually hovers at around 0.1%, but has recently climbed to 0.6% (see chart). As it widens, bankers are bracing for a jump scare.
To see why, consider what each rate represents. LIBOR is the rate that banks charge other banks for unsecured loans. The OIS rate measures expectations for the federal funds rate, which is set by the central bank. As LIBOR rises above the OIS rate, that suggests banks fear it is getting riskier to lend to each other. (The gap was 3.65 percentage points in the depths of the crisis, after Lehman Brothers filed for bankruptcy.) Read more
[caption id="attachment_459" align="aligncenter" width="628"] Libor-OIS spread as at May 2, 2018. Source: Bloomberg[/caption]
What exactly is an overnight index swap?
An overnight index swap is a fixed/floating interest rate swap that involves the exchange of the overnight rate compounded over a specified term and a fixed rate. The floating leg of the swap is related to an index of an overnight reference rate, for example Canadian Overnight Repo Rate Average (CORRA) in Canada or Fed Funds rate in the US.
Usually, for swaps with maturities of 1 year or less there is only one payment. Beyond the tenor of 1 year, there are multiple payments at regular intervals. At the inception of the swap, the par swap rate makes the value of swap zero. That is, the net present value (NPV) of the fixed leg equals the NPV of the floating leg,
where N denotes the notional amount of the swap,
Ri-1,i is the forward OIS rate,
Zi is the discount factor at time ti
is the daily accrual factor, and
sK is the par swap rate of a swap with maturity tK.
The OIS discount factors (DF) are often used to value interest rate derivatives that require a posting of collateral. The OIS discount factor curve is built by bootstrapping from the short maturity and long maturity overnight index swap rates in order of increasing maturity. The processes for backing out the discount factors from the short and long maturity swap rates are, however, different.
In the short end of the curve, given that there is only 1 payment, the discount factor is calculated based on the spot rates. At the long end of the curve, the DF curve is determined as follows,
This is just an introduction to OIS discounting. The process for building an OIS discount curve involves many technical details. We are happy to answer your questions.
Article Source Here: Overnight Index Swap Discounting
Bill Benter is one of the most profitable professional gamblers in the world. According to Wikipedia
William Benter was born and raised in Pittsburgh, Pennsylvania. As he grew up, he wanted to use his mathematical talents to make a profit so immediately after finishing a university physics degree in 1977, he went to the blackjack tables in Las Vegas and used his skills to count cards. He came across the book, Beat the Dealer, by Edward O. Thorp, which helped him improve his methods. Seven years later, he was banned from most of Vegas’ strip’s casinos.
Benter then met with Alan Woods, a like-minded gambler whose expertise in horse racing complemented his own in computers. The two became racing partners and in 1984, moved to Hong Kong. Starting with a mere US$150,000 (equivalent to US$353,331 in 2017), the pair relied on their mathematical skill to create a formula for choosing race winners.
Using his statistical model, Benter identified factors that could lead to successful race predictions. He found that some came out as more important than others. Benter later worked with Robert Moore.
Benter is a visiting professor at the Southampton Management School as part of the Centre for Risk Research and a fellow of the Royal Statistical Society.
Bloomberg recently published an interesting story about his career,
Benter grew up in a Pittsburgh idyll called Pleasant Hills. He was a diligent student and an Eagle Scout, and he began to study physics in college. His parents had always given him freedom—on vacations, he’d hitchhiked across Europe to Egypt and driven through Russia—and in 1979, at age 22, he put their faith to the test. He left school, boarded a Greyhound bus, and went to play cards in Las Vegas.
Benter had been enraptured by Beat the Dealer, a 1962 book by math professor Edward Thorp that describes how to overcome the house’s advantage in blackjack. Thorp is credited with inventing the system known as card counting: Keep track of the number of high cards dealt, then bet big when it’s likely that high cards are about to fall. It takes concentration, and lots of hands, to turn a tiny advantage into a profit, but it works.
Thorp’s book was a beacon for shy young men with a gift for mathematics and a yearning for a more interesting life. When Benter got to Las Vegas, he worked at a 7-Eleven for $3 an hour and took his wages to budget casinos. The Western—with its dollar cocktails and shabby patrons getting drunk at 10 a.m.—and the faded El Cortez were his turf. He didn’t mind the scruff. It thrilled him to see scientific principles play out in real life, and he liked the hedonistic city’s eccentric characters. It was the era of peak disco, with Donna Summer and Chic’s Le Freak all over the radio. On a good day, Benter might win only about $40, but he’d found his métier—and some new friends. Fellow Thorp acolytes were easy to spot on casino floors, tending to be conspicuously focused and sober. Like them, Benter was a complete nerd. He had a small beard, wore tweedy jackets, and talked a lot about probability theory. Read more
But can a winning horse racing system be applied to the stock markets? Benter himself provided an answer in this video
Published via http://harbourfronttechnologies.blogspot.com/
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
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.
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
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"] VVIX (volatility of volatility index) as at March 23 2018. Source: stockcharts.com[/caption]
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"] 20-day rolling correlation SPX-VIX prices, ending Jan 26 2018[/caption]
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"] 20-day rolling correlation SPX return -VIX changes ending Jan 26 2018[/caption]
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"] SPX and VIX correlation as at Jan 26 2018. Source: Stockcharts.com[/caption]
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"] Nikkei 225 and USDJPY as at Jan 26 2018. Source: Stockcharts.com[/caption]
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