Is Value at Risk a Good Risk Measure?

Value at Risk (VaR) is an important risk measure that large financial institutions use for managing the risks and allocating capital. Wikipedia defines VaR as follows:

Value at Risk (VaR) is a measure of the risk of investments. It estimates how much a set of investments might lose, given normal market conditions, in a set time period such as a day. VaR is typically used by firms and regulators in the financial industry to gauge the amount of assets needed to cover possible losses.

For a given portfolio, time horizon, and probability p, the p VaR can be defined informally as the maximum possible loss during the time if we exclude worse outcomes whose probability is less than p. This assumes mark-to-market pricing, and no trading in the portfolio.

Bloomberg recently reported that the combined VaR of the six largest US banks has decreased from $1 billion in 2009 to $279 million. Does this mean that we have much less risk now than before?

Not so if we adjust for the decreasing trend in volatility

What if we strip it out to get a sense of whether risk-taking has really declined, independent of the broader market? The result won’t be perfect, 3 but it should give us a rough idea.

It indicates that, relative to the broader market, the banks’ trading operations are only about 25 percent less risky than they were in 2009 -- and have actually become a bit riskier over the past year. Read more

In a similar context, Peter Guy pointed out that, generally speaking, risk models are vulnerable because they were developed and tested in a market environment that can change in the future

... risk models are vulnerable because a decade of zero interest rates have never occurred before in financial and economic history. No one possesses accurate historical data to predict the future. And quantitative models and algorithms heavily depend on historical data for forecasting risk.

“There are no models that are able to accurately capture the effect of rising interest rates. You need to reach back to the period before quantitative easing began,” Read more

So what are the solutions?

One solution is to develop stress scenarios, then use them to calculate probability-weighted, forward-looking risk measures. Additionally, we can implement other VaR variants that better account for the tail risks.

Originally Published Here: Is Value at Risk a Good Risk Measure?

Are Short Out-of-the-Money Put Options Risky? Part 2: Dynamic Case

This post is the continuation of the previous one on the riskiness of OTM vs. ATM short put options and the effect of leverage on the risk measures. In this installment we’re going to perform similar studies with the only exception that from inception until maturity the short options are dynamically hedged. The simulation methodology and parameters are the same as in the previous study.

As a reference, results for the static case are replicated here:

		ATM  (K=100)			OTM (K=90)
Margin	Return	Variance	VaR	Return	Variance	VaR
100%	0.0171	0.0075	0.1940	0.0118	0.0031	0.1303
50%	0.0370	0.0292	0.3844	0.0206	0.0133	0.2783
15%	0.1317	0.3155	1.2589	0.0679	0.1502	0.9339

 

Table below summarizes the results for the dynamically hedged case

		ATM  (K=100)			OTM (K=90)
Margin	Return	Variance	VaR	Return	Variance	VaR
100%	-0.0100	1.9171E-05	0.0073	-0.0059	1.4510E-05	0.0062
50%	-0.0199	7.6201E-05	0.0145	-0.0118	5.8016E-05	0.0121
15%	-0.0660	8.7943E-04	0.0480	-0.0400	6.5201E-04	0.0424

 

From the Table above, we observe that:

• Similar to the static case, delta-hedged OTM put options are less risky than the ATM counterparts. However, the reduction in risk is less significant. This is probably due to the fact that delta hedging itself already reduces the risks considerably (see below).
• Leverage also increases risks.

It is important to note that given the same notional amount, a delta-hedged position is less risky than a static position. For example, the VaR of a static, cash-secured (m=100%) short put position is 0.194, while the VaR of the corresponding dynamically-hedged position is only 0.0073. This explains why proprietary trading firms and hedge funds often engage in the practice of dynamic hedging.

Finally, we note that while Value at Risk takes into account the tail risks to some degree, it’s probably not the best measure of tail risks. Using other risk measures that better incorporate the tail risks can alter the results and lead to different conclusions.

 

Article Source Here: Are Short Out-of-the-Money Put Options Risky? Part 2: Dynamic Case

Lessons From an Option Seller

Victor Niederhoffer is a famous option seller. According to Wikipedia:

Niederhoffer studied statistics and economics at Harvard University (B.A. 1964) and the University of Chicago (Ph.D. 1969). He was a finance professor at the University of California, Berkeley (1967–1972). In 1965, while still at college, he co-founded with Frank Cross a company called Niederhoffer, Cross and Zeckhauser, Inc., an investment bank which sold privately held firms to public companies. This firm is now called Niederhoffer Henkel, and was run by Lee Henkel (who died May 30, 2008), the former general counsel to the IRS. Niederhoffer pioneered a mass marketing approach in investment banking and did a large volume of small deals at this firm. He also bought many privately held firms with Dan Grossman, his partner during this period.

As a college professor in the 1960s and 1970s, Niederhoffer wrote academic articles about market inefficiencies, which led to the founding in 1980 of a trading firm, NCZ Commodities, Inc. (aka Niederhoffer Investments, Inc.). The success of this firm attracted the attention of George Soros. Niederhoffer became a partner of Soros and managed all of the fixed income and foreign exchange from 1982 to 1990.[15] Soros said in The Alchemy of Finance that Niederhoffer was the only one of his managers who retired voluntarily from trading for him while still ahead. Soros held Niederhoffer in such high esteem that he sent his son to work for him to learn how to trade. Read more

His trading strategy provided high returns for more than 20 years. However, he suffered a huge loss in 1997.

…reward comes with risk, and Niederhoffer embraced risk in ways that would eventually become costly. He got caught leaning the wrong way when the Asian financial crisis hit in 1997, all but completely wiping his fund out. But he slowly rebuilt, and once again amassed another fortune, only to see this capital pool destroyed by the financial crisis of 2007-09.

Bloomberg recently interviewed Niederhoffer.

Niederhoffer is a brilliant and fascinating character, a study of rich contrasts. He is a nationally ranked squash champion, and former Berkeley professor of finance and statistics. He is an undeniably talented trader, except for that small issue of occasionally blowing up and getting wiped out.

I am not sure that he fully accepts responsibility for his various disasters. His trading record is akin to setting the track record on the straightaways, only to crash into the wall on the curves. Still, he teaches an important lesson for any trader. As revealed in his first book, “The Education of a Speculator,” the risk-embracing style that created his first fortune comes with some caveats. Read more

Click here to listen to the interview.

Is shorting volatility a dangerous game?

ByMarketNews

What Do Creators of the VIX Think of Volatility?

The volatility index was created more than 30 years ago. Since then it has become a favorite tool for both speculation and risk management.  There is now strong evidence that VIX futures and related exchange-traded products are changing the market dynamics. Specifically, in the early days of the VIX, the cash market led the futures. But since 2012, VIX futures leads cash 75% of the time.

[caption id="attachment_413" align="aligncenter" width="794"] VIX Contango as at Sep 15, 2017. Source: vixcentral.com[/caption]

Business Insider recently interviewed two of the creators of the volatility index, Robert Whaley and Dan Galai. Here are the key takeaways from R. Whaley interview,

• Where VIX is the volatility over the next 30 days, VIX futures is the expectation of the volatility 30 days from now. Those two series don't behave like one another, in fact quite differently.
• If you look at VXX and go to 13F filings, you'll see it's largely an instrument used by retail customers, not institutions. If you go over to the ownership of XIV, it's largely institution.
• Retail customers do not look at the prospectus because those things are 300 pages long. Institutional investors do read them and they know exactly what’s going on.
• His investment strategy is to own long term VXX put options and it has worked out well for him. Read more

Regarding bullet point #1, we have repeatedly said that VIX futures are (risk-neutral) expectation values of forward volatilities, and not spot VIX. Furthermore, since they are expection values in the risk-neutral world, they do not represent the future expected value of the spot VIX in the physical measure.

Here are the key takeaways from Dan Galai interview

• It's hard to say the market is biased one way or another. The VIX is actually reflecting market expectations in the sense that people pay for the options, it's traded, and anybody can be on any side of the fence. It's doing its job of reflecting the market consensus going forward.
• The market always has its own dynamics, and the effect is marginal. I don't think they change the market. Volatility is low, and it's been low. If the market was expected to change abruptly, we'd see it in options prices.
• When interest rates start moving up, so will volatility.
• There's no doubt that passive investment and ETFs changed the nature of correlations in the marketplace among different securities. Once you create baskets, you create artificially high correlations between the members of those baskets. Whether it changes the environment in the long term, he’s not sure. We don't have enough history to make any strong conclusions about it.
• You can find what's happening in the US on a global basis. You have the same phenomenon of low volatility. Maybe the US is the dominant force, but it's happening everywhere. Read more

Post Source Here: What Do Creators of the VIX Think of Volatility?

Interview with a Co-creator of the Volatility Index

Dan Galai was a co-creator (along with M. Brenner and R. Whaley) of VIX, the volatility index.  According to Wikipedia:

The formulation of a volatility index, and financial instruments based on such an index, were developed by Menachem Brenner and Dan Galai in 1986 and described in academic papers.The authors stated the “volatility index, to be named Sigma Index, would be updated frequently and used as the underlying asset for futures and options. … A volatility index would play the same role as the market index play for options and futures on the index.”

In 1986, Brenner and Galai proposed to the American Stock Exchange the creation of a series of volatility indices, beginning with an index on stock market volatility, and moving to interest rate and foreign exchange rate volatility. In 1987, Brenner and Galai met with Joseph Levine and Deborah Clayworth at the Chicago Board of Options Exchange to propose various structures for a tradeable index on volatility; those discussions continued until 1991.

The current VIX concept formulates a theoretical expectation of stock market volatility in the near future. The current VIX index value quotes the expected annualized change in the S&P 500 index over the next 30 days, as computed from the options-based theory and current options-market data.

The CBOE retained consultant Robert Whaley in 1992 to develop a tradable volatility instrument based on index option prices. Since 1993, CBOE has published VIX real-time data. Based on historical index option prices, Whaley has computed a data series of retrospective daily VIX levels from January 1986 onward. Read more

He recently gave an interview to Business Insider. Here are the key takeaways

• It’s hard to say the market is biased one way or another. The VIX is actually reflecting market expectations in the sense that people pay for the options, it’s traded, and anybody can be on any side of the fence. It’s doing its job of reflecting the market consensus going forward.
• The market always has its own dynamics, and the effect is marginal. I don’t think they change the market. Volatility is low, and it’s been low. If the market was expected to change abruptly, we’d see it in options prices.
• When interest rates start moving up, so will volatility.
• There’s no doubt that passive investment and ETFs changed the nature of correlations in the marketplace among different securities. Once you create baskets, you create artificially high correlations between the members of those baskets. Whether it changes the environment in the long term, he’s not sure. We don’t have enough history to make any strong conclusions about it.
• You can find what’s happening in the US on a global basis. You have the same phenomenon of low volatility. Maybe the US is the dominant force, but it’s happening everywhere.

Click here to read the full interview.

ByMarketNews

Credit Derivatives-Is This Time Different?

Credit derivatives, the types of complex financial instruments that were responsible for the 2008-09 Global Financial Crisis, are back to the news.

Two months ago, Frances Schwartzkopff of Bloomberg reported,

A complex credit product that regulators are still trying to get their heads around is proving popular with some big institutional investors in Europe.

The product is a synthetic securitization, in which a bank pays an investor to take on the credit risk of a portfolio while keeping the actual loans on its balance sheet. The Basel Committee on Banking Supervision has warned such deals can hide a bank’s true risk, while Sweden’s regulator has said it’s planning new rules to keep up with the innovation behind the product.

ATP (Denmark’s biggest pension fund) aims to have 20-25 percent of its credit investments in synthetic securitizations. It now holds around 15-20 percent, according to Lorenzen. He wouldn’t say whether the fund was among investors that bought Nordea’s risk. Read more

More recently, Joe Rennison of Financial Times confirmed the growing popularity of credit derivatives,

The market for “bespoke tranches” — bundles of credit default swaps that are tied to the risk of corporate defaults — has more than doubled in the first seven months of 2017.

Traders in this opaque, over-the-counter market estimate there has been issuance of $20bn to $30bn this year, compared to $15bn in the whole of 2016 and $10bn in 2015. Read more

The growing popularity of credit derivatives can be attributed to the fact that under the current low-yield environment, hedge funds and pension funds are looking for ways to earn higher returns. However, higher returns come with higher risks. And some experts fear that the use of complex credit derivatives will lead to another financial crisis. There are, however, other experts who are more optimistic, as pointed out by the Financial Times article:

Banks structuring the deals say that they are more cautious this time regarding the risks of being caught with exposure on their own balance sheets.

 ... Investors are using less leverage than was case before the financial crisis, traders say. Leverage up to 20 times is now typical, pushing returns above 5 per cent.

In the same context, Rick Jones argued that the current regulatory environment has made investments in securitized instruments safer than before:

Lessons were learned; hard lessons. The scales have been removed from the eyes of market participants and they are remarkably clear-eyed today. Ratings models are conservative, the regulatory state’s intrusion into capital formation for all its real, and sometimes ridiculous negative externalities, has heightened appreciation of risk and new rules such as risk retention and enhanced capital requirements have made capital formation safer. Read more

Certainly, we have learned hard lessons.  But is this time really different?

Post Source Here: Credit Derivatives-Is This Time Different?

Are Short Out-of-the-Money Put Options Risky?

Traders often debate whether short out-of-the-money (OTM) or at-the-money (ATM) puts are riskier. The argument for OTM put options being riskier is that their Speeds (or dGamma/dspot) are higher than the ATMs’ ones, thus the Gamma, which is negative, can increase (in absolute value) substantially during a market downturn.

In this post, we will quantify and compare the risks of short OTM and ATM put options. We do so by performing Monte Carlo simulations and calculating the Value at Risk (VaR at 95% confidence interval) and variance of the return distribution.  This strategy involves shorting unhedged puts. The return is determined as follows,

where P_t0 and P_T denote the put prices at time zero and expiration respectively

K is the strike price; K=90, 100 for OTM and ATM options, respectively

m is a factor for margin.   m=100% means that we sell a cash-secured put.

Note that the above equation takes into account the margin requirement in an approximate way. The exact formula for margin calculation depends on brokers, exchanges and countries. But we believe that using a more realistic margin calculation formula will not change the conclusion of this article.

We use the same simulation methodology and parameters as in the previous post. The parameters are as follows,

Parameter	Value
Initial stock price	100
Volatility	20%
Risk-free rate	0.02
Drift	0.07
Days in simulation	252
Time step (day)	1d
Number of paths	10000
Model	GBM

It’s important to note that we focus here on the risks only.  Hence we utilize the same values for the option’s implied volatility and the underlying’s realized volatility. In real life the puts implied volatilities are usually higher than the realized due to volatility and skew risk premia.  This means that the strategy’s real-life expected return is normally higher.  Our simulated return is more conservative.

The table below summarizes the risk characteristics of short put options.

		ATM  (K=100)			OTM (K=90)
Leverage	Return	Variance	VaR	Return	Variance	VaR
100%	0.0171	0.0075	0.1940	0.0118	0.0031	0.1303
50%	0.0370	0.0292	0.3844	0.0206	0.0133	0.2783
15%	0.1317	0.3155	1.2589	0.0679	0.1502	0.9339

We observe that for the same level of leverage, short OTM put positions are actually less risky than the ATM ones. For example, for m=100%, i.e. a cash-secured short put position, the variance and VaR of the OTM position are  0.0031 and 0.1303 respectively; they are smaller than the ATM option’s counterparts which are 0.0075 and 0.1940, respectively.

The risk comes from leverage. Let’s say, for example, a trader wants to sell OTM puts. Since he receives less premium for each put sold, he will likely increase the position size. For example, if he sells 2 OTM puts using leverage (m=50%), then the variance and VaR of his position are 0.0133 and 0.2783 respectively. Compared to selling 1 ATM cash-secured put, the risks increased substantially (VaR went from 0.194 to 0.2783)

In summary, ceteris paribus, a short OTM put option position is less risky than the ATM one. The danger arises when traders use excessive leverage.

Post Source Here: Are Short Out-of-the-Money Put Options Risky?

VIX Futures and Volatility Exchange Traded Notes Drive Volatility

There is now strong evidence that the increased volatility of the spot VIX is due to the growing use of volatility exchange-traded products and futures. About a month ago Alex Rosenberg of CNBC noted:

Interest in the XIV exchange-traded note has surged this year alongside its price. It shouldn’t be too surprising that the XIV exchange-traded note, which is designed to deliver the inverse performance of the well-known CBOE Volatility Index (or the VIX) on a daily basis, is attracting fresh attention after surging as much as 87 percent this year. 

In terms of the dollar value of shares traded, the short-VIX-futures XIV has actually surpassed the long-VIX-futures VXX. “We think it’s especially interesting that there is now more XIV trading than VXX, perhaps pointing to the growing interest in shorting volatility among retail [investors] and others who are not specialists in volatility trading,” Pravit Chintawongvanich, head of derivatives strategy at Macro Risk Advisors, wrote in a Wednesday note to clients. 

As for Schlossberg, his warning about the product is based on his view that volatility is set to rise from its current, ultralow levels. “It’s simply a dangerous trade from a macro point of view,” he said Thursday. “As central banks begin to increase rates, we’re going to see more volatility, and this [product] is going to show some very negative days.” Read more

After the huge volatility spike last week, volumes and open interests in short volatility ETNs kept increasing. Mark Melin of ValueWalk pointed out

The VIX index could drop further after hitting recent highs above 16 on August 11. After the recent up and down behavior of the VIX index, traders have placed short bets on the VIX ETN to the tune of $393 million. These traders are looking for the index to fall near 10.79, the July / August average, Dusaniwski believes.

While most of the VIX pricing comes from the S&P 500 futures, there is also the pressure placed on the market by ETNs and ETFs, which can force market makers to hedge with S&P 500 puts and create a self-reinforcing cycle.

In part, this imbalance mirrors exposure in the ETN that can be tilted in excess of its nominal asset levels. “The VIX ETNs are one of the few securities that at times have short interest which are larger than their AUMs,” Dusaniwski noted, explaining that “it is difficult for asset managers or brokers to create ETN shares on demand because their underlying assets are illiquid or expensive bilateral swaps or futures contracts, and not plain vanilla equities.”

The VIX has been a roller coaster lately, with mean reversion occurring quicker than average in this recent bout of volatility. In the wake of a larger market price adjustment, such as that Gundlach is expecting, the mean reversion might take longer if the past is any guide to the future. Read more

Let’s look closely how VIX futures and ETNs can drive the market volatility.  Kim of CNBC explained

One accomplished options trader said the dramatic one-day VIX surge Thursday likely stemmed from traders being forced to close out losing volatility positions.

“When I see really out sized moves in VIX like yesterday I have to think the reason isn’t just people scrambling for protection as much as some of the so-called smart money being forced to cover their naked shorts,” CNBC contributor Jon Najarian, founder of Investitute.com, wrote in an email.

“If the market moves too quickly to the short strikes, the trader and or his or her clearing firm are forced to buy back the short positions at the worst possible time, when volatility is elevated,” he added. Read more


Market dynamics are changing. The winning traders are those who stay ahead of the curve.


ByMarketNews

VIX Futures Leads Cash Market: Tail Wags Dog

Last Thursday witnessed, again, another dramatic increase in volatility. The volatility index VIX spiked 44 percent to 16.04%, its highest daily close for the year. As shown below, the VIX futures term structure inverted in the short end.

[caption id="attachment_392" align="aligncenter" width="630"] VIX futures term structure as at Aug 10, 2017. Source: vixcentral.com[/caption]

Two days before the event, Helen Bartholomew of Reuters warned that the net short position in the VIX futures had hit a record high.

Net short positioning in the CBOE’s VIX volatility index futures has hit record highs as investors continue to position for a further decline in the index, despite it trading at historic lows.

The latest Commitments of Traders report from the CFTC, released on Friday, showed that speculators including hedge funds and asset managers held a net short of -158,114 contracts – beating the previous record of -143,845, that was hit in mid-June.

The data comes in spite of Wall Street’s “fear gauge” falling back into single-digit territory in recent sessions, defying an array of economic and geopolitical concerns. Two weeks ago the index touched 8.84 in intra-day trading – a record low – after the US Federal Reserve kept interest rates on hold. Read more

So it came to no surprise that when a correction occurred, VIX futures and options volumes for a single day surged to a new record high, as reported by Tae Kim on CNBC,

The CBOE announced VIX options volume hit 2.56 million contracts on Thursday, a record for a single day. In addition, VIX futures volume reached 939,000 contracts, another record.

The high volume coincided with a 44 percent spike in the VIX, to 16.04, its highest daily close for the year. The VIX recently hit a record intraday low of 8.84. On Friday afternoon, it was at 14.54. Read more

With the increase in volume and open interests, a natural question arises:

Does the cash market lead the futures or the futures leads?

Because the volatility market does not follow the cost of carry relation, the answer to this question is not trivial. In other words, since the cost of maintaining the spot VIX is prohibitive, the none-arbitrage principle does not apply here.

In a recent paper in The Journal of Futures Markets, Bollen et al. provided an answer to this question.  They showed that in the early days of the VIX, the cash led the futures. But since 2012, VIX futures leads cash 75% of the time, and by more than 1 minute.

Beginning with VIX futures in 2004, followed by VIX options in 2006 and VIX ETPs in 2009, the daily open interest in volatility contracts is now in the tens of billions of dollars. Given this growth, it is important to develop a better understanding of price discovery and the supply/demand dynamics in each market. Some of the price relations are linked by arbitrage. Others are not. In particular, the relation between the VIX cash index and the VIX futures is not arbitraged, and we show that, where once VIX changes led VIX futures price changes, the VIX futures now leads. Read more

Their finding has important implication for hedgers and speculators who wish to use volatility-linked products to manage the risks.

Post Source Here: VIX Futures Leads Cash Market: Tail Wags Dog

Volatility of Volatility Increasing – The Story Continues

Today’s market action provides another evidence that the volatility of volatility is increasing. At the close, SP500 is down -1.45%, i.e. a normal decline. However, the VIX index shoots up 44% and SVXY, a volatility ETF, is down -13.79%.

So what exactly happened?

VIX as at Aug 10, 2017. Source:stockcharts.com

Business Insider reported,

Geopolitical anxiety has picked up in recent days amid ongoing elevated tensions between the United States and North Korea.

But even though incendiary comments from both US President Donald Trump and North Korea have spooked investors (and everybody else), markets haven’t seen a huge drop.

South Korea’s markets have seen most of the action, with the won trickling down and the benchmark Kospi stock index falling by a “minor” 1.5% this week. Meanwhile, traditionally safe-haven trades like the US dollar, the yen, and gold have picked up a bit, but not significantly. Read more

We agree that the equity indices did not decline too much. But why did the volatility go up disproportionately?

Recall that we said before:
True Volatility Is Created by What is Not Anticipated

But what really is of concern is the risk that is not anticipated. Here Jackson and Vig rely on a volatility trader’s traditional mantra: true volatility is created by what is not anticipated. What the report titled the “unknown unknowns,” a borrowing on former US Defense Secretary Donald Rumsfeld’s famous quote.

However, the tension with North Korea was somewhat anticipated. It was listed as one of the black swans

Kim Jung Un has been shooting off missiles in North Korea without consequence. Given that the North Korean regime appears irrational, who know what could happen. What if they “tried to take out our satellites?

So maybe it was due to the short interest and increased leverage?

ByMarketNews