Financial Time Series

One of the negative reviews of my DIY MFE piece said the following:

Financial markets are nothing more than an infinite time-series

Of course, it was a recent grad saying this. I would like to respond with a parable.

Once upon a time there were two securities analysts, Gemma and Yu Fen. Each was in her office analysing data, making phone calls, and trying to figure out what derivatives she should long and short to get the proper exposure on the same security — XXX — when it made its next big move.

On Friday at work, Gemma received a package with a book she had ordered from Cambridge Press: Nonlinear Filters in the Analysis of Financial Time Series. She had a dinner date, but decided halfway through that the guy was annoying, laid down an embarrasing sum of cash, and bailed to meet up with her friends. It was a great evening out and when she woke up Saturday morning, Gemma started the book.

Yu Fen had plans in Paris for the weekend with her girlfriend (they have an apartment in the Tresiemme). They also went out Friday night and, as often happens at expensive bars, a rich, old guy started buying them both drinks. Since everybody in this story is totally square and corporate, the conversation quickly turned to what they all do for a living, and Richard (the rich guy) seemed fascinated about everything that Yu Fen said about her analysis of the XXX security.

Richard, Yu Fen, and many others got hammered at the expensive bar that night. During the course of their hanging out, Richard let it slip that he ran a hedge fund, and that he was planning to take out a massive short on XXX as soon as it passed 571.91. Richard opined that the fundamentals of XXX weren’t actually sound enough to support a price of more than 400. His analysis is boring so I won’t repeat it but Yu Fen was interested. She understood and agreed with all of his points. Yu Fen is a good enough judge of character (and of drunks) that she knew he wasn’t putting her on; some combination of pretty girl, good conversation, and expensive Scotch had led him to divulge his real position. After that night, the weekend finished pleasantly but without anything else financially relevant occurring.

Back in London, Gemma wrote some code snippets to test some of the most interesting nonlinear filters from her book. She finished two-thirds of the book between Saturday and Sunday reading. The concepts were actually a lot simpler than she had foreseen…but then Gemma has a Ph.D. in a related area.

The next week, Gemma worked her new filters into the existing code infrastructure and started analysing XXX with the new set of tools. She found that a few of the methods from the book, when applied judiciously on the right parts of the past data, transformed the signal in such a way as to shed light on one of the crucial questions she had had about the implied volatility surface.

Yu Fen kept her eye on XXX at the same time and also felt like she had new insight. She had gotten Richard’s business card and called his office, pretending to be a deep-pocketed potential investor and fishing for information about the firm’s position on XXX. She also spent the week making phone calls to check out the fundamental weaknesses in XXX that Richard had delineated. It was difficult to winnow the disinformation out of what she was told, but bullsh*t-detection is one of Yu Fen’s strong suits. Richard’s viewpoint basically checked out — and Yu Fen even found out where the pockets of false support for XXX were and what price they would drop out at. Yu Fen couldn’t convince her desk to give her all of the leverage she wanted, but she loaded up on some disgusting immediate short positions against XXX and even liquidated some of her other positions early to get more attack power on the XXX.

Meanwhile, trading volumes in XXX were growing. Its unflagging ascent had heretofore embarrassed sharp analysts and confounded great traders. Increasing numbers of news articles called a “bubble” in XXX, but for over three years now the bubble had not popped. Gemma, of course, wasn’t naive enough to merely take positions on whether a security would go up or down. She mainly modelled probability distributions of several Greeks parameters. Gemma would update probability distribution of her estimates as new data came in. Her signals were then based on estimates of higher moments of these distributions (the robustness of which had been improved by her weekend reading). Gemma made some important tweaks to her portfolio to reflect the statistical picture she had gained from answering some questions with the new nonlinear filters, in particular saving money by pulling out of a few hedges that she had over-secured herself with.

The next week — on Tuesday, at around 1pm, XXX started testing 572. It had been climbing at a rate of roughly 8 points/month with a weekly standard deviation of 15 — and on Tuesday, it displayed slightly unusual behavior, lagging to 550 at the market’s close. But over the next two days, XXX’s vertiginous drop to 508 surprised nearly everyone who cared about XXX.

Those who traded security XXX, or who had invested a significant chunk of their portfolios in XXX, were generally shocked and panicked. At 530, news wires warned of a speculative attack, or tried to point out causal factors, or took analyst quotes on the situation. Investors missed their kids’ soccer games, came home late, and ran their fingers through their hair as they sought frantically to figure out whether to flee, hedge, hold fast, or double down on XXX.

Yu Fen, Richard, and a few others were among the few who knew where XXX’s final equilibrium price should be: somewhere in the 380-420 range.

Yu Fen had to adjust the timing of her shorts as XXX went down — since it was never clear how much selling pressure it would take to kill the synthetic rallies that each of the players she had investigated tried to mount. Along with the money pumping up XXX’s price at each of the moves was a small flurry of news stories questioning which way XXX would move next. Some were penned or prompted by those fighting XXX’s decline. But Yu Fen trusted her original analysis, trimmed her sails, and rode XXX all the way to 365 before yanking off her shorts.

Gemma, meanwhile, had her positions ravaged. Richard’s firm’s attack on security XXX fundamentally altered the market participants’ perceptions and analysis of XXX. All of Gemma’s higher moments had been estimated using data from the old regime. When the regime shifted, she kept feeding the new data into her prior—but the model took too long to shift its recommendations.

At year’s end, Yu Fen only took home four times the bonus that the rest of her desk did, and Gemma didn’t get in much trouble because the move in XX had been so unprecedented that nobody could have seen it coming. Nevertheless Yu Fen got a big head out of it and started being resented by her coworkers, while Gemma felt discouraged because of the XXX blunder and a number of other issues, and the next year started floating her resume to business schools looking to expand their quant staff.

Moral: Financial data does come as a time series, but future moves can’t necessarily be predicted by time series analysis.

Price(APL, pre-iPod) is drawn from a different distribution than Price(APL, post-iPod), and so on.

And also: A given market isn’t a 1-D time series (price). It’s two (bid & ask) 2-D time serieses (price & volume), … and if you count different types of orders (stops and limits), it’s more like six or eight 2-D time serieses that are all interconnected.

So there.


About isomorphismes

Argonaut: someone engaged in a dangerous but potentially rewarding adventure.
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