Wednesday, January 31, 2018

Correlation Between SPX and VIX

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"]volatility arbitrage trading strategies 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"]volatility trading strategies based on correlation 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.

Post Source Here: Correlation Between SPX and VIX

Sunday, January 28, 2018

Correlation Breakdown

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"]volatility trading strategies SPX VIX SPX and VIX correlation as at Jan 26 2018. Source:[/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"]statistical arbitrage equity currency correlation Nikkei 225 and USDJPY as at Jan 26 2018. Source:[/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.

Article Source Here: Correlation Breakdown

Saturday, January 13, 2018

Goldman Sachs Expressed Concerns About the Growth of Volatility Exchange Traded Products

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.


Sunday, December 31, 2017

Most Important Investment Lessons of 2017

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:

  • No security price is too high (or low) that it cannot go higher (or lower)
  • Turns in markets are impossible to time
  • Big changes in market prices frequently occur far in advance of when the reasons for the changes become apparent, and by then it is too late to incorporate the new information into one’s trading at the old prices Read more

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.


Friday, December 29, 2017

Mean Reverting and Trending Properties of SPX and VIX

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).

Lag (days) SPX VIX VXX
5-20 0.45 0.37 0.46
200-250 0.51 0.28 0.46

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.


[1] T. Di Matteo et al. Physica A 324 (2003) 183-188

Post Source Here: Mean Reverting and Trending Properties of SPX and VIX

Friday, December 22, 2017

Liquidity Risk and Exchange Traded Funds

The sell-off in the high yield bond Exchange Traded Funds space last month reminds us of an important risk factor: liquidity.

But what exactly is liquidity risk? According to Aleksander Kocic, derivatives strategist at Deutsche Bank AG,

Liquidity transforms the risk of default (the ability that the debtor may not be able to pay back his debt) into the risk that the securities representing the debt find no purchasers ... today’s era of booming bond sales has an eerie parallel to the subprime crisis of the mid-2000s. Back then, low interest rates spurred an intense search for yield that culminated in investors purchasing risky home loans in the form of securitized and salable bonds. Such securitizations had the benefit of convenience as investors could buy and sell specific exposures comprising hundreds of thousands of individual home loans.

The forced unwind of leverage was responsible for the transformation of conditional insolvency to unconditional illiquidity. Read more

[caption id="attachment_436" align="aligncenter" width="561"]High Yield Bond exchange traded fund HYG High Yield Bond ETF as at Dec 22, 2017. Source: Interactivebrokers[/caption]

With the recent proliferation of Exchange Traded Funds, there is no surprise that there exist ETFs that are supposedly designed to offer “liquidity transformation”, i.e. they would allow investors to buy and sell illiquid debt instantaneously. However, liquidity risk is still there, and those ETFs can actually exacerbate the risk.

As for now, an important question to ask is: was the liquidity risk priced in? According to John Davi on Valuewalk, it is not, and 2018 can see an increase in liquidity risk.

The markets, however, trade on the margin and 2018 will begin to see liquidity decline in the US. The Fed has started to raise rates, wants to hike more, and quantitative tightening will further reduce liquidity.  The repercussions are quite significant – especially on the margin.

It is not surprising that liquidity sensitive asset classes such as US high yield credit, US Small Caps, and Japan corrected in October/November. Historically, liquidity in capital markets starts to decline in Q4 as banks begin to wind down their balance sheet ahead of year end.  Plus, we have the potential for another Fed rate hike in December.  The “liquidity based correction” was likely in anticipation of both events. Read more

If liquidity deteriorates, portfolio managers can use liquid credit and/or volatility derivatives to hedge the risks.

Originally Published Here: Liquidity Risk and Exchange Traded Funds

Saturday, December 2, 2017

Interview with Robert Shiller, 2017 Truman Medal Recipient

Robert James Shiller  is an American Nobel Laureate, economist, academic, and best-selling author. He currently serves as a Sterling Professor of Economics at Yale University and is a fellow at the Yale School of Management's International Center for Finance. Shiller has been a research associate of the National Bureau of Economic Research (NBER) since 1980, was vice president of the American Economic Association in 2005, and president of the Eastern Economic Association for 2006–2007. He is also the cofounder and chief economist of the investment management firm MacroMarkets LLC. Read more

Tommy Atlee '20 sits down with Economics Professor Robert Shiller, 2017 Truman Medal recipient and 2013 Nobel Prize in Economics Laureate, to talk about his background in economics and his thoughts for the future.

Click here to watch the interview

Click here for more interviews.


Thursday, November 30, 2017

Statistical Distributions of the Volatility Index

VIX related products (ETNs, futures and options) are becoming popular financial instruments, for both hedging and speculation, these days.  The volatility index VIX was developed in the early 90’s. In its early days, it led the derivative markets. Today the dynamics has changed.  Now there is strong evidence that the VIX futures market leads the cash index.

In this post we are going to look at some statistical properties of the spot VIX index. We used data from January 1990 to May 2017. Graph below shows the kernel distribution of spot VIX.

[caption id="attachment_313" align="aligncenter" width="564"]volatility trading strategies: VIX distribution is not normal Kernel distribution of the spot VIX index[/caption]

It can be seen that the distribution of spot VIX is not normal, and it possesses a right tail.

We next look at the Q-Q plot of spot VIX. Graph below shows the Q-Q plot. It’s apparent that the distribution of spot VIX is not normal. The right-tail behavior can also be seen clearly. Intuitively, it makes sense since the VIX index often experiences very sharp, upward spikes.

[caption id="attachment_314" align="aligncenter" width="564"]volatility arbitrage: Q-Q plot of spot volatility index Q-Q plot of spot VIX vs. standard normal[/caption]

It is interesting to observe that there exists a natural floor around 9% on the left side, i.e. historically speaking, 9% has been a minimum for spot VIX.

We now look at the distribution of VIX returns. Graph below shows the Q-Q plot of VIX returns. We observe that the return distribution is closer to normal than the spot VIX distribution. However, it still exhibits the right tail behavior.

[caption id="attachment_315" align="aligncenter" width="564"]Relative value arbitrage: distribution of VIX returns Q-Q plot of VIX returns vs. standard normal[/caption]

It’s interesting to see that in the return space, the VIX distribution has a left tail similar to the equity indices. This is probably due to large decreases in the spot VIX after sharp volatility spikes.

The natural floor of the spot VIX index and its left tail in the return space can lead to construction of good risk/reward trading strategies.

Post Source Here: Statistical Distributions of the Volatility Index

Sunday, November 19, 2017

Volatility, Skew, and Smile Trading

Peter Carr recently gave a talk on volatility trading at the Fields institute.


In general, an option’s fair value depends crucially on the volatility of its underlying asset. In a stochastic volatility (SV) setting, an at-the-money straddle can be dynamically traded to profit on average from the difference between its underlying’s instantaneous variance rate and its Black Merton Scholes (BMS) implied variance rate. In SV models, an option’s fair value also depends on the covariation rate between returns and volatility. We show that a pair of out-of-the-money options can be dynamically traded to profit on average from the difference between this instantaneous covariation rate and half the slope of a BMS implied variance curve. Finally, in SV models, an option’s fair value also depends on the variance rate of volatility. We show that an option triple can be dynamically traded to profit on average from the difference between this instantaneous variance rate and a convexity measure of the BMS implied variance curve. Our results yield precise financial interpretations of particular measures of the level, slope, and curvature of a BMS implied variance curve. These interpretations help explain standard quotation conventions found in the over-the counter market for options written on precious metals and on foreign exchange.

In this talk, Carr discussed which options you should trade when

  • You know the realized volatility will exceed 10% and yet the ATM volatility is currently below 10%
  • You know that the correlation of every IV with the underlying will realize positive and yet an OTM call’s IV is currently below an equally OTM put’s IV
  • You know that IVs are themselves volatile and yet 3 IVs currently plot linearly

Click here to watch

Post Source Here: Volatility, Skew, and Smile Trading

Saturday, October 7, 2017

Arbitrage Pricing Theory and Factor Investing

Factor investing is becoming popular these days. It has its roots in Arbitrage Pricing Theory. According to Wikipedia
Arbitrage pricing theory (APT) is a general theory of asset pricing that holds that the expected return of a financial asset can be modeled as a linear function of various macro-economic factors or theoretical market indices, where sensitivity to changes in each factor is represented by a factor-specific beta coefficient. The model-derived rate of return will then be used to price the asset correctly—the asset price should equal the expected end of period price discounted at the rate implied by the model. If the price diverges, arbitrage should bring it back into line.

S. Ross is the Father of Arbitrage Pricing Theory. D. Musto of Wharton recently summarized the key points of Arbitrage Pricing Theory in this podcast
  • … the risk that faces the investor, the risk that ultimately is going to deliver the payoff to his bank account, is going to be the risk of this portfolio. And once you think of it that way, you realize that the correct measure of risk is not a stock’s risk by itself, but instead, the risk that it’s going to add to a diversified portfolio.
  • … stock returns follow what you could call a factor structure … All of the systematic portion of their stock returns is captured by those five factors. Everything that’s not captured by them is idiosyncratic.
  • …the risk of a stock that’s going to matter to investors is its exposure to those factors. And every factor is going to have associated with it what you would call a risk premium
  • …the idiosyncratic component of the stock’s return is not going to give you any additional expected return. It shouldn’t, because to an intelligent investor putting together an optimal portfolio, that’s just going to wash out. It’s the factor-driven part of the return that’s going to matter. And so that’s going to be driving expected returns
  • [factors] could be things like changes in expected inflation. They could be developments to GNP. They could be things having to do with interest rates — and what kind of risk premium you would need to be compensated for exposure to that factor.
Another significant contribution of S. Ross is the binomial option pricing model.

This is a very elegant way to price the whole range of derivative securities out there. So Steve, building on the work of [Fisher] Black and [Myron] Scholes, showed how you could take what they did and think about it as a binomial framework that would help you price a wide range of securities, and show you how you go about replicating the payoff of any derivative security you might be interested in, with this binomial trading technique.