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 effects, 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.

Another important property of levered and inverse ETFs is that they are designed to track the daily returns of their underlying index which does not mean that over the long term they will faithfully track the returns of their index.  Cheng and Madhaven illustrate that this can be viewed as an embedded path-dependent option within the product.  This is graphically illustrated with two charts of DIG and DUG over a shorter and longer period.  Over a short period, they track each other admirably, mirror-like, as one would expect.  But over a longer period they diverge quite spectacularly.  In fact, in the example below, one would have lost money betting on either over the same period!

"Heads I win, tails you lose" - ProShares

Another interesting result of Cheng & Madhaven’s research is that the “[hedging] demand as a fraction of closing volume is a non-linear function of return…”.  Thus, the greater the move in the underlying index, the hedging activities of these ETFs will have a (non-linearly!) greater market impact on the close.

There are other gems in here as well including hints at pricing options on these ETFs, and techniques for quantifying the market impact of hedging activities.  But don’t take my word for it.  Go read the original!

Competition has forever been fierce and at times may not be entirely fair.  Thus, a student of the market must be ever aware of the trends around them so they can promptly identify growing areas of opportunity which haven’t yet been revealed to the majority.  Mr Madoff made a very good living (while it lasted) offering clients a steady ~10% return on their investment.  Bush league stuff, it turns out.  The real maestros of money are doing rather better.

Accounting and legal researchers at the University of Kansas have identified a bull market in influence-peddling: returns on the order of 22,000% for firms who “invested” in lobbying efforts to favorably modify the tax code.  These people obviously learned that it’s important to play by the rules.

I’ve written some decent strategies and have been blessed with moments of great luck, but I’m ashamed to note that I’ve never gotten remotely close to these kinds of returns.  Can you imagine the sharpe ratio these guys can claim?  And it’s a repeatable process.  Although the Kansas researchers don’t mention it, there are many other cases of such legal arbitrage as pointed out in an AP piece on the subject:

The nonpartisan group recently released a study comparing the amount spent by bailed-out banks on political contributions and lobbying with the amount of money they got from the Wall Street rescue fund, known as the Troubled Asset Relief Program. The results produced eye-popping rates of return, an overall 258,449 percent for the $114 million they spent on campaign donations and lobbying.

Now this number - ~260,000% ROI - is clearly a bit inflated as $114M barely covers what Citi paid out to Mr Rubin for his services over the relevant period, but we’re probably in the ballpark.  Perhaps the banks only made 100,000% on their investment, but we can still see why they’re “the pros.”

I’m wracking my brains trying to figure out how to shoe-horn this marvelous alpha-generator into my trading algorithms.  I confess that I haven’t yet figured it out.  But I take solace in the knowledge that, as an American, I have the best government money can buy!

A reader of this blog (hey - I’m as surprised as you are!) sent me an email recently detailing a strategy they’d developed.  While the details of that strategy aren’t relevant here, they sounded good and they got me to thinking about the process of selling a trading strategy.  This is an activity that I’ve spent some time on and have decided just isn’t for me.

There are a lot of difficulties with selling a trading strategy.  One of them is a consequence of the foundational problem of back-testing about which I first started posting on this blog.  For any given period of time (that has already elapsed!), it’s not difficult to generate a good number of pretty impressive strategies.  All you have to do is try a good enough number of random strategies and some of them will prove to be too good to be true.

Presumably, any credible person who might be listening to your pitch will be at least intuitively aware of this fact and will thus be highly suspicious of any back-tested results you might present.  For this reason, it’s impossible to sell a strategy on the basis of back-tested results.  Only auditable, real-world returns will be considered valid by any serious person.  Of course, you might find someone who’s less particular, but then you’re flirting with fraud rather than a legitimate sale.

So let’s say you have impressive, verifiable results.  You still have to answer the question:

If this strategy is so good, why are you selling it?  Why not just trade it yourself?

I suppose one answer might be that you have insufficient capital, but I just don’t think it’s a very satisfying answer.  It’s hard not to think that everyone can borrow money somewhere or run up credit cards or somesuch.  Another, possibly better, answer might be that the strategy requires more favorable commissions than you can obtain, thus you’re looking for an organization that’s either an exchange member or just trades in sufficient volume to have significantly lower costs than you can muster.  Again, not totally satisfying, particularly given that you really need a track-record to have gotten to this point.

Another impediment to selling a trading strategy is that it’s just an idea and ideas can be stolen.  You have to somehow give enough information to make your story credible, without giving away the strategy itself.  This can be harder than it sounds as the person listening to you presumably knows something about the relevant markets and might have some good understanding about the kinds of strategies that can be effectively deployed.  As a minimum, you have to convey the relevant performance characteristics of the system in good detail.  Even this can be revealing as the returns will often tell a tale about the strategy that generated them.  Additionally, most will want to hear a compelling “story” about how/why the strategy works.  What inefficiencies are the strategy capitalizing on?  This can be even more revealing as it will be in the form of a free-form discussion followed up with questions etc.  In the end, you might find that you’ve told a number of people revealing characteristics about your strategy - enough at least for them to do some digging of their own - without getting any closer to your aim.

But let’s say that you’ve managed to find someone who is interested.  Now the real difficulties begin!  How do you structure the deal?  I suppose you could sell the signals if the system trades sufficiently infrequently, but this obviates the entire class of higher frequency strategies.  It’s also a bit of an asymmetric deal in the sense that you presumably sell the signals on some kind of a fixed subscription basis whereas the purchaser can use an arbitrary amount of capital on the strategy.  In spite of these difficulties, this seems the cleanest kind of deal and I’ve seen it done in institutional contexts, so it’s not beyond the realm of possibility.

Another option, particularly for high-frequency systems or in cases where commission structures or trading infrastructure are a key element of the viability of the deal, is to partner in some concrete way through a partnership or a formalized joint venture.  This, too, is something that I’ve seen and have even engaged in, so it’s not too fanciful, but at the end of the day it ends up being like any other partnership or business: it fundamentally requires a deep level of trust.

(Another possibility, of course, is to wrap the strategy into a hedge fund, etf, structured product or other salable instrument and market it in a normal way.  But that’s another discussion as it requires significant capital upfront which means you could, if you chose, monetize your strategy directly by trading it.  So, it’s really a different issue entirely…)

Thus, if one can overcome the myriad difficulties, it is possible to sell a trading strategy.

That said, I wouldn’t recommend doing it and it’s not something that I’m interested in as a business model.  Why not?  Ultimately, it’s about what interests you and how you want to spend your time. Do you want to be a salesperson and spend your time preparing and smoothly delivering presentations, networking and glad-handing &tc?

Or do you want to research, develop and trade your algorithms?

ultimately, it's about what you want to do...

rebranding opportunity?

A friend of mine pointed out an article he came across on his bloomberg terminal today which reminded him of a strategy I’d described to him sometime back and which we’ve been trading over the past year or so with good results.

To the great chagrin of some of my partners, I even wrote a few posts about the phenomenon underlying our strategy and its evolution as we capitalized on it.  Eventually, they persuaded me to shut up already, but the outline was there for all - including Goldman! - to see.

My first post on the topic, “unsung virtues of a dynamic hedge” published June 4th of last year, was pretty coy and didn’t mention the source of alpha itself but talked about enhancing it with a dynamic hedge.

My next post on the topic, “to dream” was published July 14th of last year and laid out the exploitable discrepancy of the market’s behavior.  Interestingly, the data I provided in that posting went back the same amount of time as in Goldman’s piece.

I explicitly wrote one last time about the strategy in “evolution of a strategy” wherein I detailed the process by which we’d been evolving the strategy.

Now, one of the more entertaining things about having a blog is that you get to see who is viewing your content.  I’m happy to note that all of the major IBs are represented including a variety of distinct IPs within Goldman.

Now, I’m not accusing them of stealing my ideas or anything untoward like that… but I’ll admit that I am wondering how long it’s going to take them to make similar observations across markets beyond US Equities…

Read on for the Bloomberg article…

From the Bloomberg article:

By Alexis Xydias

March 12 (Bloomberg) — Investors should take advantage of others’ “fear” of the night, according to a study by Goldman Sachs Group Inc. that shows holding U.S. stocks overnight since 1993 would have quadrupled an investment.

Buying futures on the Standard & Poor’s 500 Index, or a fund that replicates the benchmark for U.S. equities, just as the trading session ends and selling them when the market opens the next day has yielded 309 percent since 1993, New York-based analyst Peter Berezin wrote in a report sent to clients today. The inverse strategy lost 58 percent.

Investors and traders may have become more reluctant to hold securities overnight, when they’re unable to react to market declines abroad, Berezin wrote. The S&P 500 has plummeted 54 percent since reaching a record in October 2007 as the crisis in credit markets and the collapse of banks including Lehman Brothers Holdings Inc. hammered equities, while the Chicago Board Options Exchange Volatility Index, the so-called gauge of fear, has more than doubled.

“A large number of market participants are averse to holding overnight positions, which causes them to sell at the close (thereby depressing intraday returns) and buy at the open (thereby inflating overnight returns),” Berezin wrote. “Such aversion to overnight risk is likely to be higher during bear markets.”

Overnight Spread

The difference between market-close and market-open prices has widened to 9 basis points since October 2008, the study said, from a “long-term” average of 5 basis points. A basis point is 0.01 percentage point.

The best way to benefit is to hold the S&P 500 at night, while short-selling it during the day, Berezin wrote. The strategy would have returned 507 percent in the period, the analyst said, while acknowledging the increased costs of such a trading-intensive strategy. Short-sellers sell borrowed securities on expectations they will be able to repurchase them at a cheaper price before their loan is due.

The S&P 500 reached 666.79 on March 6, the lowest intraday level in more than 12 years. The benchmark index for American equities has fallen 20 percent this year.

“Even when one is pondering less trading intensive strategies, the analysis above suggests that there is a cost to be paid for avoiding overnight risk,” Berezin wrote.

During some recent travels, I read William Poundstone’s ramblingly entertaining Fortune’s Formula.  It had been sitting on my shelf after I’d originally gotten it, perused it and offhandedly discarded it as yet another of these science-is-fun-and-full-of-wacky-characters books for the butch humanities student.  My initial impression was a bit harsh as the book proved entertaining and covered a lot of ground including significant coverage of Ed Thorp and his stat arb alchemy (see here for his own papers on the topic).

One of the more compelling segments of the book relates Claude Shannon’s demon which is a nice thought-experiment / trading-strategy which illustrates the tractability of the problem of trading on a random walk market with fixed properties.  I wrote the above applet to explore the impacts of applying friction and otherwise modifying the behaviors of the market and the demon.

The original demon posited a world with no friction in which the market contains one instrument which doubled or halved in value each day.  Shannon’s demon looks to take advantage of this volatility by maintaining a portfolio which was rebalanced each day to ensure a 50/50 split between cash and the market.  The applet implements a very simple monte-carlo test-bed for Shannon’s Demon.  You can configure the demon and the marketplace along a variety of parameters, and then run many instances of the demon, each on its own self-contained random-walk market.

Although Shannon’s demon is a highly “stylized” case in the sense that it operates on a very synthetic, unrealistic and favorable formulation of a random-walk marketplace, it has spawned a great deal of interest and serious research.

Most of all, it’s a revealing illustration of the kind of reasoning one must embrace in order to address stat arb strategy development.  Enjoy.

—
Updated: March 4th - made price axis logarithmic to better reveal mc paths.

one view on the important stuff

There seem to be two kinds of economists in today’s world.

Keynesians and Austrians?  Freshwater and saltwater? Macros and micros? Voodoos and uh well-adjusted?

No.  These may be valid distinctions ordinarily, but in today’s debate on how to solve the great self-inflicted wound known as the credit crisis the only two that matter are those who’ve worked for prop trading outfits (or perhaps more broadly, those who would someday like to once their time of public service is up) and those who just practice economics, typically academically.

Among the former, the solution is uniformly, as Mish so memorably put it, “to patch the busted dam with water” and to do it now or the consequences could be incomprehensibly bad.

Among the latter, the views are many and divergent, but they at least agree that throwing trillions of dollars about is a serious bit of work and should be undertaken with deliberation, transparency and a long view.

I’m not qualified to opine on which type of economist has a better chance of saving us from ourselves.  But I can observe that the only kind sitting at the decision-making side of our president, pre- or post- January 20th 2009, is the prop trader.

Reminds me of a song I once knew…

Given the enduring value of return distributions, I found this morning’s post in ft.com/alphaville especially interesting.  They cite a Dresdner study examining the distribution of returns for Goldman Sachs’ prop trading in 2003 and 2008.  Eye opening stuff.

normal

not so much

The above applet re-uses the one I’d written previously in discussing simple stochastic processes.  This time, it illustrates a point & figure chart below the regular line chart.  Point & figure charts expose two characteristics: a “box size” (in ticks) and a “reversal” (in boxes).  The applet allows you to vary both and then generate a day’s worth of random/synthetic data to view it.  One of the nice features of JFreeChart is that you can easily “zoom” into a chart by dragging within the chart.  I’ve disabled this in the line chart but you can try it in the p&f chart.  (Note: you should right-click and “Auto-Range-Both Axes” before you generate new data or you’ll stay in the zoomed segment of the chart.)

Now that I think I understand the basics of point & figure charting, it will be interesting to see what an algo might do with it…

"We've run out of Federal Firearm Licenses"

Yesterday I read this article in the New Yorker: The New Paranoia: Hedge-Funders Are Bullish on Gold, Guns, and Inflatable Lifeboats.

In his book Wealth, War, published last year, former Morgan Stanley chief global strategist Barton Biggs advised people to prepare for the possibility of a total breakdown of civil society. A senior analyst whose reports are read at hedge funds all over the city wrote just before Christmas that some of his clients are “so bearish they’ve purchased firearms and safes and are stocking their pantries with soups and canned foods.”

It reminded me of my experience on 9/11 and my thought that a really handy item for the paranoid Manhattanite in uncertain times might be a conveniently inflatable raft.

Yes, I was a little warped by the experience.  Evidently I’m not the only one, though…

These guys would prefer to be in a high-speed boat or ex-military vehicle, heading off toward their fully provisioned compounds in pursuit of the ultimate goal: to win the chaos.

Then today I came across the above notification from the ATF indicating that we’ve literally run out of firearms licenses.  I guess the optimistic interpretation is that there’s “always a bull market somewhere…”

I was gambling in Havana
I took a little risk
Send lawyers, guns and money
Dad, get me out of this

- Warren Zevon

This is *not* Hank Paulson's Piggy bank...

I came across this Bloomberg story on the state of Hank Paulson’s piggy bank.  As a dutiful steward of our Nation’s interests, he was forced to place his fortune into a blind trust upon accepting his current position as Treasury Secretary.  Now he gets to find out what happened to his money.  Always a charmer, he jokes about it:

“I’ve got to find out where my money has been invested,” Paulson, 62, said today after a speech, drawing laughter from the Washington Economic Club.

“You know the old joke about how you make a small fortune? And that is, give a large fortune to a person in a blind trust,” he said today. “I haven’t even thought about how I’m going to be investing my money.”

Ah what fun.  Of course, given the impact of his visionary stewardship on most Americans’ portfolios, it’s easy to imagine that many will have forgotten that he likely only accepted his position of unfailing public service for the >$100M tax loophole it afforded him.

Before taking the Treasury job, Paulson sold his Goldman Sachs shares and wasn’t required to pay capital gains taxes, according to a June 2006 divestiture notice about a stake that was valued at the time at about $485 million.

In this day and age, no self-respecting citizen so much as blinks at a mere ~$170M looting of the nation’s coffers.  But it does raise the question: which is more ironically piquant?  Our ring-side seats for the hollowing out of the American Republic or our knowledge that we paid through the nose for the privilege?