Analysis of Proctor and Gamble Crash. Not a Fat-Finger Mistake.
The spike in DJI at 2.42pm on 6 May seems to have come from Proctor and Gamble and Accenture. Attached is the intra-day price and volumes from Yahoo Finance showing minute-resolution prices and volume. PG is blue and ACN is red. Volume for P&G is shown at the bottom.
Rumour was that this was a “fat-fingered” trading error with a trader entering the wrong price. That would necessarily imply:
1. No increase in volume before the spike.
2. A clean price drop due to the mistake. There shouldn’t be any visible acceleration before the drop.
This is not born out of the data. Volume in P&G starts rising strongly from 2.00pm onwards. There’s a very big spike of volume at 2.31pm with no visable price-impact. Then in the next ten minutes volume steady rises with increasing price-impact, until the free-fall at 2.42pm.
In ACN, there is less of a volume build up before its price decline. However, there is a stranger effect: the ACN price starts to drop 3-4 minutes before any effect in PG. It shows an accelerating price decline from 2.31pm onwards until a spike at 2.42pm. Both prices are highly correlated through out — notice both share a small uptick at the same moment three minutes before the crash.
Volume does not build up and prices don’t start accelerating minutes before a simple error in entering a quote, as per the fat-finger hypothesis.
What could have caused this? The best predecessor event is the United Airlines / Google News Bankruptcy event in September 2008 where google released an old story from 2002 stamped 2009 that algorithms ripped into until the mistake was uncovered.
Yesterday’s event had far more price impact by bringing down the DJI; and it feels less like a mistake, and more like a highly-strung out market that is fragile due higher financial uncertainty: EU crumbling, rising TED spread, falling equity prices in preceding days.
A good paper idea for a budding PhD would be a paper titled “Liquidity and Fragility” formalizing the trade off between higher average liquidity / lower-spreads andwith higher volatility in levels of that liquidity. Specialists in the old days couldn’t be discretionary in liquidity provision. HFT liquidity providers are now highly discretionary, leading to more fragile markets.
Turner and Astronomy
Left, a photo of a milky-way dust cloud from the Planck satellite.
Right, a Turner painting.
Art follows nature.
High Frequency Trading going Google
Prediction: The next round of hedge fund stars will be ex-Googlers
Google’s business is algorithms. High speed algorithms that datamine, rank, suggest and predict. Lo and behold, that’s also what HFT outfits are doing on their data. HBS MBAs do not make good HFT traders, instead, young and bright computer scientists. The sort google employ.
Case in point: Tradeworx, the six-year old New Jersey high frequency trading, [Reuters write-up here].
{London , Business , School , College , Finance}
Business Eduction in London:
I guess this is one indication of why LBS’s brand-name is weak. On the flip side, the imitation is flattering.
Maybe LBS should go Booth. Any big donors?
The Market Rejects the Efficient Market Hypothesis
If a rational market allocates capital to hedge funds, the market believes in its own inefficiency.
Eugene Fama defended his position market efficiency this week. He put this little gem of a sentence:
Hedge funds, private equity, and other alternative asset classes, which have attracted big fund inflows in recent years, are built on the proposition that markets are inefficient.
What’s strange about Eugene’s defense is that he more or less highlights that the market believes (though capital allocation) in its own inefficiency.
Despite this, he still claims markets are more or less efficient. In particular, he claims market efficiency is a practical belief for individual investors.
The alternative asset industry exists because managers and their investors believe they can make money from market inefficiency. Investors know they pay substantial fees to managers, which only pays off if the manager produces excess returns above fees. The industry is not trivial in size — hedge funds account for between $1 trillion to $2 trillion of assets in 2008-09. For a reference, the total US equity capitalization in 2007 was $15 trillion. Is this $1 trillion dollar industry the result of collectively irrational investors living with efficient markets? I doubt it.
Large allocations to hedge funds does not mix with market efficiency regardless of whether investors are rational or not. Suppose we understand an “efficient market” as one that efficiently allocates capital. Then we have a simple proposition about market efficiency and the alternative asset industry and their investors (“HF investors”).
Proposition
A market cannot both be efficient and rational investors allocate capital to high fee funds managers. Either the market is inefficient, and managers are able to make money off the inefficiency for rational investors to warrent paying fees; or investors are irrational, and there is an inefficient allocation of capital to hedge funds.
Proof
There are three possible joint hypotheses to consider: 1. {efficient markets, rational HF investors}; 2. {inefficient markets, rational HF investors}; and 3. {efficient markets, irrational HF investors}.
1. In an efficient market with rational HF investors, hedge fund managers will not be able to earn their fees – their “alpha” will be close to zero before fees, and after fees investors receive negative alpha. Rational investors will therefore not allocate capital to these high fee managers. Instead, they will put their assets in lower fee investments, such as ETFs. Therefore efficiency and rationality does not support large hedge fund allocations.
2. In an inefficient market with rational HF investors, some hedge fund managers will be able to earn their fees — their “alpha” will be positive both before and after fees. Rational investors will allocate capital to these managers In doing so, investors are pushing the market towards a more efficient capital allocation. Therefore, inefficiency and rationality supports large hedge fund allocations.
3. In an efficient market with irrational HF investors, hedge funds cannot earn their fees. Investors are inefficiently alocating capital to hedge funds; and this contradicts the premise of allocative efficiency. Therefore, efficiency and irrationality cannot support hedge fund allocations, whithout the markets ceasing to be efficient.
QED
Of these possible hypotheses, the only one that supports a large hedge fund allocation is {inefficient markets, rational HF investors}. This is the world we live in. Large allocations to hedge funds is a sign that the market recognizes its own inefficiency.
Financial markets aggregate the beliefs of thousands of intelligent and highly incentivized participants. It is a gigantic system that no individual or group of individuals can match in processing power or efficiency. Contrast this to the efficient market hypothesis, which developed and tested by individuals (econometricians), who look at data and cannot find arbitrage opportunities to refute the hypothesis. The combined intellegence of a financial market is far greater than an individual academics. This means the best place to look for whether the EMH holds is in the market’s capital allocations, and not in journal articles.
The EMH predicts that rational investors hold low fee investments (ETFs) and do not persue active trading strategies. In reality, investors willingly give huge fees to managers who’s mandate is to make money off market inefficiency, and this rejects the EMH.
The very fact that the market rejects EMH proves EMH wrong.
How Efficient are Markets? Not, Are Markets Efficient?
No engine is perfectly efficient — there’s always friction. The first and second laws of thermodynamics prevent perfectly efficient engines from existing. . Asking if a machine is “efficient” is preposterous; what matters is how efficient it is.
So why do economists insist on asking “Are markets informationally efficient”? As posed as an absolute, the answer is certainly no. Any engine for aggregating information (for example, a market) cannot be informationally efficient: there is always friction. There are well defined versions of thermodynamic laws for information [here], and the laws basically state that any efficient market violates either the first and/or second laws. As the French fondly say, it is impossible.
Its not the case that the financial economics literature is aloof to the impossibility of perfect efficiency. Grossman and Stiglitz’s article on “The Impossibility of Efficient Markets” argues as such, although doesn’t directly appeal to laws of informational thermodynamics (they could have). Fischer Black’s seminal “Noise” article identified one major source of friction: “noise traders”, or people who traded on what they presume as information, but instead is noise. Another contribution is Kyle’s (1985) famous model of insider trading, which demonstrates the problems of entropy increasing — insider trading leaks information out, and consequently insiders don’t reveal all their information.
Those who ask: “Are Markets Efficient” imply a ”yes/no” response; and this is the wrong question. The right question is: how efficient are our present markets? And, while knowing perfect efficiency is unreachable, what can we do to improve current levels of efficiency.
There is a maximum efficiency in any thermal system, which is achieved only by the theoretical Carnot heat engine. The equation looks like:
where eta_max is the maximum thermal efficiency, T_c is the cold side of the engine and T_h is the hot side of the engine. It’s very likely an analogous result for informational efficiency already exists (and a statistical physicist could probably give me the reference). Likewise, the efficiency of an engine can be easily measured and compared to others — all modern washing machines carry efficiency ratings.
Heat is easy to measure. But unfortunately, there’s no such thing as information meters — information is largely invisible. The best we can do is get proxies for information. A very crude one is trading volume — the higher the volume, the more disagreement there is about prices, and therefore more likely to be new information traded upon. Higher trading volume is probably a sign of more efficient markets. Taken the other way, a market with zero trading volume cannot be highly efficient; during the credit crisis, some markets (e.g. CDOs) froze completely.
I think its quite feasible to measure market efficiency. Bid-Ask spreads, market liquidity and volume are all proxies for the level of information out there.
- Bid-ask spread is probably a good proxy for the asymmetry of information. Market makers keep big spreads to insure against informed traders(see Kyle 1985; or Bollen, Smith and Whaley’s “Modelling the bid-ask spread”)
- Market impact is the sensitivity of the price to large trades, and so is probably a good proxy for the depth of information flowing around.
- Volume is a proxy for both the level of disagreement on that information and the amount of information being released.
Put together, lower bid-ask spreads, low market impact and high volume are a sign of more efficient markets, over less efficient markets.
Bottom line is: no machine is theromynamically efficient. Why should we hold markets to higher standards? We shouldn’t, and they’re not. How efficient is the real question.
Do Hedge Funds Misreport Returns?
Yes, certainly looks like it.
Nick Bollen and Veronika Pool have a nice paper forthcoming in JF showing that the histogram of all hedge fund returns has a mysterious “kink” or discontinuity around zero. They look at returns in the CISDM database.
Here is a histogram I made of 390,622 observed monthly returns from the TASS Database where the same phenomenon occurs. The sample includes 6173 hedge funds, of which 55% are alive and 45% dead.
The “Kink” in TASS Monthly Hedge Fund Returns.
Bollen and Pool show that the kink is more likely to occur in months the hedge fund is not audited, and also in more illiquid hedge funds where assets are harder to price. The kink does not occur in portfolios replicating hedge fund returns and is not just a simple rounding artefact.
Hedge fund managers have fairly strong incentives to report positive returns. Money churns around quickly in the hedge fund world — a small negative return may cause outflows and thus lower fees for the manager. The Bollen & Pool paper suggests that managers are, in aggregate, rounding up realized small negative fees in hope of avoiding reporting losses.
What is very interesting is how significant the kink is — the above plot shows just the raw monthly returns across the entire database. That this is a visible feature across all funds suggests this sort of misreporting is a fairly common practice.
Play “Name your Hedge Fund” Game
The following amusing hedge fund names are now copyright of rmetrisk blog:
“Split Strike Conversion Capital”
“Death Star Capital”
“Fat-Boy Fund”
“OPM Holdings”
“LHC Capital”
“Steamroller Trading”
“JWM Partners LLC II III”
“Latency Trading Capital Management”
“Coca Capital LLC”
“Four Nineteen Limited”
“Front-Running Futures Fund”
“K-Meson-Alpha Trading”
“Stable Distribution Capital”
“Skewed Strategies Limited”
“Harvford Management Company”
“Booty Trading LLC”
Unfortunately “Pirate Capital LLC” is already taken; see
http://www.piratecapitalllc.com/
Academic Journals in the PageRank Age
Why has there been no innovation in academic journals? A proposal for a better system for publications.
The internet is creating tremendous innovation in communicating ideas. Case in point is the rise of the professional bloggers, particularly in economics: Felix Salmon, Paul Kedrosky, Tyler Cowen among many others. The discussions are fresh, in depth and highly niche. RSS and google reader is my newspaper now, not The Economist or NY Times.
Economic academics are now also joining blogging in a big way: Eugene Fama and Ken French (Fama/French forum), Simon Johnson (Baseline Senario) ; Garry Becker and Richard Posner (Becker-Posner Blog); NYU Stern professors (Stern on Finance).
Blogs are an example of the creative destruction the internet is causing. Old media incumbants, such as the music industry or news-papers, had their day in the sun and are now struggling to survive. In both industries, incumbents have actively fought to stem technological change (Peer-to-Peer litigation; Google Books / News / Youtube litigation) as part of their death rattles. Bad for them, but good for everyone else: the old technology is replaced with better and/or cheaper; and old rent-extractors are replaced with new rent-extractors: Spotify, Youtube, Hulu, Google Books, RSS and Blogs.
Academic journals are relics of the past and are ripe for innovation. They currently do not offer much other than rent-seeking and prervayers of presigue. In the pre-internet ages, they provided the service of physical distribution.
When an academic paper is published, the journal obtains its copyright. Technically the author cannot post it elsewhere; instead, the Journal becomes the gatekeeper of content.
Proposal:
SSRN type repositories
Page Ranking of authors: #downloads of paper; citations weighted by rank of those who download it; rank equals the equilibrium distribution on connected grid
Eigenfactor.org applies the idea to whole journals. Here is the pagerank of Economics journals.
Distribution of My Consumption in Beijing, Chicago, Florence and London
I get research support from a scholarship. This allows me to travel to many conferences. Expenses from this travel are reimbursed, so I have records for many thousands of items I’ve bought; all either for accommodation, food or transportation.
This last six months, I’ve lived in Beijing (Peking University), been to conferences in Chicago and Italy (twice) and am now living in London (London Business School).
How do these countries compare according to consumption? In particular, what does the distribution of consumption look like?
Italian mathematician Vilfredo Pareto discovered that incomes different countries all seem to follow the same distribution; he titled this the Pareto distribution. While the average level of income differs across countries, the relative difference across richest to poorest follows what is now termed a power law.
Similarly, linguist George Zipf and mathematician Boit Mandlebrot discovered that the frequency of words in languages also follows an approximate power law. If we listed all the words in a long text and sorted the list starting with the most frequent word, then the distribution of frequency against rank follows a power law. Specifically, the probability function for frequency of the kth ranked word, f(k), follows a Zeta distribution.
where ζ(s) is the Riemann zeta function, and s is the shape parameter.
Power law distribution functions often arise from complex systems, such as stock markets, earthquakes, and even the popularity of webpages. Why these laws appear in complex systems is still not very well understood, but in physics they arise from phase transitions.
Most distributions in nature are not power laws; they are exponential laws The normal distribution function is an important example — the tails of the distribution decay exponentially, which leads to thinner tails and “nicer” statistical properties. By the central limit theorem, many processes generate distributions with exponential tails. The distribution function looks like:
Peoples’ height follows an exponential-tail distribution, so do levels of radioactivity over time and the rate of metabolising drugs in humans.
So, all this is very interesting; but lets get to the point:
What distribution does my consumption follow: Power or Exponential?
Here are the figures. The first and second rows plot respectively:
1. log(consumption) ~ rank
2. log(consumption) ~ log (rank)
With a power law, the distribution is linear when plotted with both x and y axes as logarithms. So in the second row, the red dots should be linear if it follows a power law. Conversely, if consumption follows an exponential decay, the lines should follow a reflected log curve.
I’ve got excel to draw both power and exponential fits. Clearly, the linear fit (=> power law) does poorly; the curved fit (=> exponential law) does much better.
So: my consumption follows an exponential law.
Surprisingly, the fits across different cities all very similar. The decay parameters (λ) are all within 50% of each other; my consumption distribution in both Beijing and London are very similar after removing a few hotel outliers.
Why would we ever care about this? In a power law decay, lots of little expenses summed will dominate the larger expenses. In an exponential decay, a few large expenses dominate the sum of the little expenses. This is what “The Long Tail” by Chris Anderson was about: if interests followed power-law, the Amazon model of supplying every niche dominates the retail model of supplying block-busters.
If my consumption followed an exponential, it means I can ignore the little items and only need to focus on the big price tag items — hotel costs mainly, but also cars and houses. If its a power law, all those little expenses balloon out to be a very large amount.
So exponential decay is good news. I can freely buy lots of snacks, Starbucks and short taxi rides without much explosion in my budget. Its London hotels I need to avoid.
M
MP
