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doubling down with levered ETFs

April 22nd, 2009

This weekend I read Jason Zweig’s “Will leveraged ETFs Put Cracks in Market Close?” which references a paper by Minder Cheng and Ananth Madhaven at Barclay’s.   I tried, but couldn’t find their original paper over the weekend.  As luck would have it from across the internets Paul Kedrosky came to the rescue with a post referencing that paper, “The Dynamics of Leveraged and Inverse Exchange-Traded Funds“.

If you have any interest in ETFs, then you should read this paper carefully as it provides a very nice and accessible mathematical treatment of leveraged and inverse ETFs.

I’ve had success using ETFs in portfolio-oriented strategies to conveniently provide specific exposures, eg, to emerging markets.  I’ve also explored strategies that pit ETFs against futures and similar arbs that take advantage of contract rolls or other anomalous behaviors across the markets.  But I’ve never looked at ETFs the way they really should be understood: as structured products that should have well-defined (if not necessarily obvious) properties.

Like many structured products, some of these characteristics are not obvious and may be quite unintuitive but are always important to understand.  For instance, the hedging required to implement these funds is both non-linear and asymmetric.

Specifically, leveraged ETFs must re-balance their exposures on a daily basis to produce the promised leveraged returns. What may seem counterintuitive is that irrespective of whether the ETFs are leveraged, inverse or leveraged inverse, their re-balancing activity is always in the same direction as the underlying index’s daily performance. The hedging flows from equivalent long and short leveraged ETFs thus do not “offset” each other. [...]

The impact is particularly significant for inverse ETFs. For example, a double-inverse ETF promising -2X the index return requires a hedge equal to 6X the day’s change in the fund’s Net Asset Value (NAV), whereas a double-leveraged ETF requires only 2X the day’s change. This daily re-leveraging has profound microstructure e ffects, exacerbating the volatility of the underlying index and the securities comprising the index.

Hence Mr Zweig’s concern that these ETFs feed the volatility we’ve seen for the last 8 months or so near the market close.  If the day has been up then both “bull” and “bear” levered ETFs will need to buy in order to stay hedged - reinforcing the trend and effectively supporting serial correlation of returns.

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dereferenced, portfolio management, strategy development

NVIDIA’s TESLA and Compute Unified Device Architecture

November 29th, 2008

While the war over the latest+greatest video cards for the current generation of graphics intensive games seems always to ebb and flow between nVidia and its arch-rival ATI, I’ve long preferred nVidia for their better support of Linux.  Thus, all of my machines have some sort of nVidia Graphics Processing Unit (GPU) in them.

For those who spend their workdays in the markets and their weekends pondering derivatives pricing, latency, oceans of market data, portfolio optimization, and how to make every last damn thing faster, a preference for nVidia cards could prove to yield an unexpected benefit.

nVidia has recently unveiled a product line dubbed “TESLA” which leverages their absurdly fast GPUs to provide a supercomputer-like High Performance Computing (HPC) platform at a previously unimaginable price point.  TESLA computers are regular machines that have a set of slightly modified GPUs in them; modified such that they have no video out, but instead become additive processing clusters which the machine can use for compute intensive tasks.  For about $10K you can buy a 1U machine with some 4 teraflops of capacity.  By way of comparison, this is over 20 times faster than the funky Helmer project I’d been drooling over a few months ago in a production-worthy package ready for the server room today.

So, TESLA refers to the machines built with these specialized GPUs.  Making all this power usable is what CUDA is about…

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monte-carlo methods, options pricing, portfolio management, technology

portfolio: atomic element of a trading strategy

September 13th, 2008

A wall st risk manager's favorite pastime? A friend recently asked me what I considered to be the “axioms” of alpha-seeking trading strategies. I think there are a few, but probably the one that seems to me most important is that the atomic element of a trading strategy should always be a portfolio as opposed to a single instrument.

In a scenario of perfect knowledge, this wouldn’t be true. If you somehow *know* with certainty that crude will go up or that Citigroup will go down, then concentrating all of your resources into a position based on that belief might be reasonable. But knowledge seldom comes in such a neat package (and will frequently be illegal to act upon when it does!).

Instead, knowledge will typically come in more conditional and less certain forms: “commodities tend to rise during periods of FUD [Fear-Uncertainty-Doubt]” or “companies who announce stadium naming rights deals tend to under-perform.” In some cases, perhaps the knowledge on which you’ll base your strategy can be quantified probabilistically.

Depending on the nature and quality of the knowledge or hypothesis that forms the basis for a given strategy, one can adapt one’s portfolio construction/optimization based on customized relationships amongst the potential portfolio constituents. But one doesn’t need to be so fancy to see the concrete benefits of our first axiom. Below I detail a simple strategy I’ve put together to explore the forces involved.

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performance analysis, portfolio management, strategy development

evolution of a strategy

July 21st, 2008

(d)evolution

I mentioned several weeks ago that I’ve been developing and trading a strategy that’s proven to be quite interesting and profitable. In that post, I described how I’d tried to improve the strategy through the use of a dynamic hedge. The results of that crude hedge were quite good, but just as no worthwhile software project is ever really complete, trading strategies demand constant iterative development.

Below I describe some of the steps I’ve taken to incrementally improve this strategy, discarding the relatively expensive hedge I’d developed earlier in favor of a complementary strategy. We see that when you combine two positive and uncorrelated results, you end up with a product that is literally better than the sum of its parts.

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performance analysis, portfolio management, strategy development

a stat arb story

July 12th, 2008

Ed ThorpThe always excellent Wilmott Magazine has recently posted a series of articles by Ed Thorp (pictured) in which he describes his experiences developing and evolving a statistical arbitrage product. Part I provides some insights into his current operation, revealing that he maintains a dollar-neutral portfolio as I’d discussed in another post, they trade some 1.5 billion shares / year, and that they limit position sizes to 2.5% on the long side of the portfolio and 1.5% on the short side. In Part II, he explains why a stat arb system is considered an “arbitrage” and how, with the help of a talented team and led by the insights of Gerry Bamberger, they developed the first iteration of a stat arb product. Part III details the evolution of the system from a set of dollar-neutral sector-oriented portfolios to the more general sets of portfolios generated through statistical factor analysis. He concludes with some anecdotes including the emergence of David E Shaw. Very recommended.

dereferenced, hedge funds, portfolio management, strategy development

unsung virtues of a dynamic hedge

June 4th, 2008

unsung virtues of a dynamic hedge

I’ve recently been working-on and trading an equity strategy that has some great characteristics and some interesting challenges. The great characteristics revolve around its profitability, volatility and simplicity. The challenges start with the fact that the strategy generates alpha on the short side - thus, you are intrinsically swimming against the tide and can conceivably be ruined in a hurry. Your broker might also be unable to find inventory to short. Other challenges include the native capacity of the strategy - it’s not fundamentally scalable as a strategy and only a relatively small amount of money could be put against it without incurring increasingly onerous costs and risks. In any case, it’s been a fun strategy to develop as it’s an interesting puzzle and it makes money.

Discussing the strategy recently with a potential client, they observed that such a strategy wouldn’t be acceptable within their environment (apart the capacity issues) as their risk management practices required all strategies to maintain dollar neutrality - for any dollar of x that they used to buy something, they needed to sell a dollar of y. This led to an interesting experiment for me, the results of which I share with you below.

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performance analysis, portfolio management, strategy development

When Hedge Funds Blow

April 26th, 2008
boom I’m very pleased to present our first guest blogger to this space - Scott Johnston. Scott’s an experienced hedge fund exec who’s currently a PM and principal at the Belstar Group, an asset allocator and fund-of-funds. This post has been excerpted, with permission, from his monthly newsletter. Contact him at sjohnston {AT} belstargroup [DOT] com.
The biggest single impediment I see for investors contemplating an investment into hedge funds is “blow up” risk. How can they think otherwise, with all the hype? The media enjoy little more than the self-immolation of a hedge fund - Rich Guys Get Theirs! Blow-ups score a 10 on the CNBC schadenfreude scale. (Note: for institutional investors, blow up risk translates more specifically into “headline risk,” which is basically the risk of losing one’s job if a hedge fund you invested in ends up in the papers for the wrong reason.)
How common are hedge fund blow-ups? How often do they happen? What do they do to returns? These are questions I wanted to get to the bottom of.
Fishing around, I found surprisingly little research on the subject, so I thought it might be useful to conduct a survey of our own. Specifically, we will look at hedge fund blow-ups through the years to see what kind of conclusions we can draw. For the sake of argument, we will call anything greater than a 50% loss a blow-up.

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books, guests, hedge funds, portfolio management

the character of a winner

April 4th, 2008

Rocky Marciano, history's only undefeated heavyweight championHe didn’t look like much, but old Rocky Marciano put his back into every awkward punch he threw. More remarkably, he remains the only heavyweight champion to have ever been smart enough to get out of the game on top. He was that rarest of characters - a winner who knew when to engage and when to step away.

I’ve written a good deal about losers and ideas that might not yield the results one’s looking (hoping) for, but I haven’t written too much about life’s winners. This, of course, is absolutely par for the course amongst traders. People aren’t in the habit of giving away trade secrets, leaving sums of money on the sidewalk or revealing their trading strategies. When they do (or claim to) is likely a good time to keep an especially watchful eye on your possessions…

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back-testing, performance analysis, portfolio management, strategy development

Mao’s formulation seemed more broadly applicable…

March 1st, 2008

Mao's formulation seemed more broadly applicable...

This week I attended another of the excellent quant seminars I’ve written about before. This time the talk was about stochastic modeling of equity markets and was presented by Robert Fernholz of Intech. Intech is evidently a subsidiary of Janus which manages some large amount of money presumably based on some of the portfolio management theory on which Dr. Fernholz is an expert. If you visit their site, you’ll be greeted by a bigger version of their credo which I’ve, um, honored as this post’s banner: “Math is power.”

Right then. While Mao would likely have been capable of convincing me otherwise, it’s probably best for everyone involved that portfolio managers are running around with esoteric mathematical models rather than the sorts of munitions favored by 20th century Chinese revolutionaries…

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events, monte-carlo methods, portfolio management

“prudent and… disastrous”

February 4th, 2008

An early risk management innovator

This past week I had the opportunity to see MIT’s Professor Andrew Lo present his paper “What Happened to the Quants In August 2007?” as part of the seminar series on quantitative finance presented by NYU and Columbia and sponsored by BlackRock and other relevant institutions. If you’re in the NYC area and interested in such things, I recommend attending any lectures which might capture your fancy.

I had read his paper some time back and implemented, within the Puppetmaster environment, the mean-reversion trading strategy he used as a microscope into what transpired last August. I was interested to see him speak as he’s a seminal thinker on hedge funds and quantitative finance, but also because the strategy he described works pretty well and I thought he might hint at various improvements.

I’ve stolen a line from his paper to serve as the title of this post as it captures one of the central dilemmas faced by algorithmic traders.

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events, performance analysis, portfolio management, strategy development