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Showing posts from 2017

Selecting an Index Option Expiration

A few weeks ago, I wrote about  what option strikes were best to sell when harvesting the variance premium. This is part of an ongoing project to find optimal option strategies for volatility trading, hedging and directional trading. As the next step, today I’m going to look at what expiration to trade when selling index volatility.
First, let’s look at the theoretical arguments in the Black-Scholes-Merton world. On average the total PL for an option sold at si when the realized volatility is (the lower) sr is


But it is the way that this comes about that is important to us here. This is actually the sum of gamma profits which occur continuously. In one time step


(Traders usually think in terms of the first equation but this second equation is probably more fundamental as it comes straight from the first term in the BSM differential equation). So instantaneous PL is directly proportional to gamma. And short term (ATM) options have more gamma than long term (ATM) options. So you can ex…

The Crowded Short Vol Trade

It is commonly accepted that shorting the volatility ETNs is a crowded trade. Is this true and what, if anything, does it mean?

First, we need to note that these ETNs are backed by VIX futures which are cash settled and, as futures have no fixed issuance, a traditional short-squeeze can't happen. As the demand increases, the authorized participants can just create new shares. There is no limited supply as there would be with a stock or a physically settled future.

It is also important to notice that all of these volatility products are derivative based. For every short there is a long so we could also say there is a crowded trade on the long side. While current short interest in VXX is about 85% of shares outstanding (compared to a heavily shorted stock like TSLA where the short ratio is only 27%), I can't see this as the root of any problem. If we take into account the futures, variance swaps and options the total short ratio of the volatility market has to be 100%.

The long…

"The Strangest Thing..."

A few weeks ago I wrote an entry about the historical context of current equity volatilities. The conclusion was that volatility is low (startling I know), but if we compare it to the years from the pre-VIX era it isn't quite the extreme outlier it appears. Since 1950, two years have had lower volatilities (1964, 1965) and four others (1952, 1963, 1972, 1995)  are about the same.

But 2017 is unusual in a couple of other ways. First, the ratio of absolute value of return to the realized volatility is very high. Volatility is low but we have actually moved a fair distance. As of mid-October, the S&P 500 annualized return to average 20-day volatility ratio was 3.07 (return of 21.5% and a volatility of 7%). The average ratio since 1950 has been only 1.29. Only 1954, 1958 and 1995 have had higher ratios.

Even more extreme is the ratio of maximum draw-down to realized volatility. The average value has been 0.99. So far this year the number is 0.4. The biggest draw-down has been onl…

Straddles and Strangles Part 1

This is essentially a re-post of an entry from the (now dead) FactorWave blog. It is relevant again because it is the first part of what will be a series on strike and strategy selection.
One of the things that make options great is that there are many ways to express an opinion. But this is also one of the things that make options tricky. Just because there are many ways to express an opinion doesn't mean they will all be equally good. Some will be a lot worse than others.
Let's assume implied volatility is too high. While there are many ways to trade this, the two simplest are to sell either a straddle or a strangle. Here we are going to compare there two strategies. It is easy to work out the expected profit of an option position. It is just the position value at the volatility we sold at, minus the position value evaluated at the realized volatility. But obviously this doesn't tell the whole story. When selling options our upside is capped by the collected premium, but…

Equity Volatility is at All Time Lows

Well Maybe…


The author, explaining volatility to the kids of today.
There is no doubt that equity implied volatility is very low. As of October 13th, 2017, the VIX has closed below 10 on 41 occasions. 32 of those days have been this year. As the VIX is popularly known as a “fear index” this situation been labelled a “bubble of complacency” (which sounds like it should be located close to the sea of tranquility). This can be read as putting the blame for low volatility squarely on the shoulders of options’ traders, who actions create the VIX. But this is exactly backward. Implied volatility is low because of realized volatility being a lot lower.
But is realized volatility actually at an all-time low?
Generally, traders don’t have long careers. Bad ones lose their money or get fired. Competent ones see their specialty disappear. Successful ones end up in management. Few traders have any long term perspective. Their idea of history might be as short as five years.
I looked at 20 day …

The Kelly Criterion and Option Trading

(This is based on/cut-and-pasted from a paper that I co-wrote with Reuben Brooks.)
The Kelly criterion can be used to calculate the optimal size of a trade. Specifically, it gives the size that increases the trader's account at the fastest possible rate. It is possible that a given trader might not actually want this. She might want some sort of volatility or draw down constraint as well, but traders should still understand the ideas and implications of Kelly sizing. And misunderstanding abounds.
Generally, traders use an approximate form of the Kelly fraction that only takes into account the first two moments of the return distribution. While in many cases this can be a useful heuristic, when returns are highly skewed the approximation breaks down. In particular, for trades with identical expected returns, the presence of skew can drastically impact the relative sizing of long and short option positions.
Long option positions have unlimited profit potential and limited loss pote…

If I Knew Then What I Know Now

I love cars (actually I find engineering in general fascinating). When I was about eight I was watching a Formula One race and the commentators mentioned that the current car was a big improvement over that of the year before. I remember vividly that this struck me as odd. If the same people made the improved car, why didn’t they just make that version first? Whether this thought was unusually astute or just stupid isn’t the point here. The point is that we can’t improve until we have something to improve on. We don’t just learn from mistakes, we also improve on our successes.
The first issue of “Volatility Trading” came out in 2008 and the much expanded second edition was released in 2013. I still firmly believe in the process I wrote about: find an edge, size appropriately, execute, evaluate, repeat. I also (typos aside) believe in the individual theories about volatility measurement, forecasting, hedging and sizing. But I have drastically changed my mind about the relative importa…

Night Terrors

Following on from my recent posts about trading volatility over weekends, I’m now going to briefly look at trading options overnight.
Option traders have always complained when they were too long options overnight, expecting to usually lose money on overnight longs. This doesn’t make sense in a pure Black-Scholes-Merton world. In that world the time decay (theta) will be balanced by the expected change in the underlying (gamma). But we have already seen that this doesn’t hold over weekends.  So while option traders might be the whiniest group of trading professionals and are more than willing to complain about anything (I’ve heard such classics as, “I hate summer” and “Christmas is literally the worst thing ever”), it is worth examining whether they were right about this particular thing.
Dmitriy Muravyev and Xuechuan Nia wrote a paper that studies this.  While it is very well known that returns to index options are negative (about -0.7% a day in terms of actual premium decay for the…

I Don't Like Mondays

Actually I don’t dislike Mondays more than any other day, but that is a title that I can get a funny picture to go with.
In the last few blog posts I wrote about how equity options don’t fully account for the weekend and that there is edge in selling on Friday. In this post I’m going to briefly look at how we can exploit the same effect in the VIX.

It is well known that the VIX tends to be up on Mondays. This effect has been consistent, and highly statistically significant, since 1990. The average return by day of the week is shown in Figure One.

Figure One: The average (log) VIX returns by weekday.
There is a structural reason for this. The VIX is based on calendar time. It uses actual days to expiration to calculate the variance swap it is based on. So if an option is priced at 5 on Friday afternoon, and opens at 5 on Monday, the VIX calculation thinks that implied volatility has to have increased because no time decay has occurred even though time has passed.
But the options’ mar…

Theta and Weekends Again

Last week we stated that market makers don't fully account for weekend decay in equity options. Today we show specific results.
Christopher Jones and Joshua Shemesh studied this issue and presented the findings in a paper that they presented to the 2010 American Finance Association meeting. They looked at the returns of long option portfolios on U.S. equities from 1996 to 2007 and found the average return over the weekend was negative (0.62% of the portfolio value) while the returns for all other days were slightly positive (0.18% a day). It is important to be clear what these numbers mean. The 0.62% number means the average option (averaged over puts, calls, and all strikes and maturities) declines in value by this amount over the weekend. This is not the return on equity of a trader holding a short position. This position would need to be secured by an amount of margin that is appreciably greater than the option premium.
Having established that weekend returns are significantl…

Theta and Weekends

A number of traders, some of whom are even successful, claim you don’t need to understand the “Greeks” to trade options. They might have a point. Although the Greeks exist whether or not we keep track of them or understand them, in the final reckoning the option price is what matters. If we buy some options for $1,000 and later sell them for $2,000, we will have made $1,000 no matter why the price change happened. However, understanding the Black-Scholes-Merton paradigm and the associated Greeks is like knowing a new language. Sometimes it is simply easier to express a certain idea in a different language, and sometimes a certain trading idea can be most easily visualized with the help of the Greeks.
Here we will talk about one such trade, based on one Greek: theta. Theta is the change in the option price over a certain time interval if nothing else changes, particularly the underlying price. But over the same time interval we expect the underlying price will change. The amount the …

War and the Markets

I was going to write about the weekend effect in options and the VIX, but this seemed more appropriate. It is a blog post from the now retired (to a Caribbean island) FactorWave blog.

This post is based on an article I wrote for Active Trader Magazine.
"Buy to the sound of cannons, sell to the sound of trumpets." -Lord Nathan Rothschild, 1810

The Rothschilds were one of the world’s richest families and formed a modern financial dynasty. In 1815 they were rumored to have made a fortune when they used a carrier pigeon to send the result of the Battle of Waterloo (which was “a damn close-run thing-the nearest run thing you ever saw in your life” according to the victorious general, the Duke of Wellington) from Belgium to London. Having the news before his rivals gave Nathan an edge over his competitors on the floor of the Stock Exchange.
This is a good story. It isn’t true, but it is a good story. It is true that the Rothschilds were known to use pigeons to communicate (an 18thcentu…