I recently posted a paper, “Transforming Stock Market Forecasts with Variable Expected Returns,” on the SSRN online repository. This paper resolves an issue that has been bugging me for years. The link is: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=495384 This paper is not about making

The Cboe’s VIX®, VIX3Msm (93-day), and VIX6Msm (184-day) indexes enable us to quantify volatility term structures but until now, historical analyses between VIX style indexes have been limited to dates after December 2001 in the case of VIX3M and January 2008 for VIX6M. This post introduces the

The Cboe’s VIX® (30-day) and VIX3M (93-day) indexes enable us to quantify volatility term structures but until now, historical analyses between VIX style indexes have been limited to dates after December 2001. This post introduces the results of VIX3M style calculations back to 1990, and reviews

Sometimes an online option calculator isn’t enough and you’d like to implement the Black & Scholes (B&S) option pricing equations in Excel. If you’re just playing around it doesn’t matter how you structure the calculation. In fact, for clarity’s sake, it’s probably a good idea to

Hardly a month goes by without some pundit trumpeting that the VIX is broken. But before you worry too much, consider some of the non-obvious characteristics of the Cboe’s Fear Gauge. First a Summary These charts list possible explanations for perceived VIX “brokenness” Complaint Market in Low

In the afternoon of February 5th, 2018, what looked like a bad day for a group of high flying volatility-based products turned into a devastating decline. Four factors combined to ruin their day: A Flawed Architecture Relying on the Past to Predict the Future Billions Under Management A

Using a tool like Bollinger Bands® to forecast future price ranges is a time-honored technique but its calculations are simplified and in some situations flawed. Incorporating the log-normal nature of stock prices into the calculations gives better answers. One greed inducing aspect of volatility

Below I’ve collected links to some of my favorite white papers and presentations on volatility. I’ve organized them in the following categories: Volatility Concepts & Volatility Trading Probability Distributions—Normal and Otherwise The VIX and VIX Futures Volatility Contagion—Will Short

Just about anyone who’s looked at a multi-year chart for a long volatility fund like Barclays’ VXX has thought about taking the short side side of that trade. VelocityShares’ ZIV is an Exchange Traded Product (ETP) that allows you to hold a short volatility position while avoiding some of the

Finding quotes and historical data for Bitcoin and Bitcoin futures can be an adventure. Below I’ve assembled links to the online resources that I’ve been able to find. In many cases, data is available from multiple sources. I did not attempt to list all of them. BTC Quotes Yahoo Finance

Models are useful. They help us understand the world around us and aid us in predicting what will happen next. But it’s important to remember that models don’t necessarily reflect the underlying reality of the thing we’re modeling. The Ptolemaic model of the solar system assumed the Earth was

It’s well known that long volatility Exchange Traded Products (ETPs) like VXX, UVXY, and TVIX often experience devastating losses during market quiet spells—even when the value of the VIX is staying relatively stable. These heavy losses occur when the VIX futures that underlie these funds are in

I have generated simulated end-of-day close indicative share values (4:15 PM ET) for VelocityShares' BSWN, LSVX, and XIVH Exchange Traded Notes (ETNs) from March 31st, 2004 through July 14th, 2016. BSWN VelocityShares VIX Tail Risk ETN LSVX VelocityShares VIX Variable Long/Short ETN XIVH

The indexes that power VelocityShares new BSWN, LSVX, and XIVH funds have been live since 2011, but they haven’t been directly accessible via exchange traded products until July 2016. The goals of these new funds are pretty straightforward, on the long side BSWN & LSVX track upside volatility

After every crash or major geopolitical event that roils the market we are exposed to graphics like this one containing sigma numbers: Black Swan The message associated with these charts is usually, "We should be very worried because the events that just occurred were really unlikely." The

While it’s certain that short-term volatility exchange traded products (ETPs) like VXX, TVIX, and UVXY are doomed to march towards zero, their decay rates are not consistent. Things like bear markets and big corrections can cause big upward swings. On the downside, the term structure of VIX

Everyone agrees the normal distribution isn’t a great statistical model for stock market returns, but no generally accepted alternative has emerged. A bottom-up simulation points to the Laplace distribution as a much better choice. A well-known problem in financial risk assessment is the failure

Serious volatility watchers are always attending a three ring circus. The left ring holds the general market. Center ring has options on the S&P 500 and the various CBOE VIX® style indexes and to the right are VIX futures, Volatility Exchange Traded Products like VXX, UVXY, TVIX, and XIV plus