The VIX has a daily autocorrelation of −.04, a weekly autocorrelation of −.21, and a monthly autocorrelation of −.12.
Posts tagged with stat arb
Euan Sinclair, Volatility Trading
In this paper an exhaustive characterization of financial markets was given.
- Dependence: Autocorrelation in returns if largely insignificant. (Exceptions being at the tick level and annual returns.)
- Distribution: Approximately symmetric, increasingly positive kurtosis as the time interval decreases and a power-law or Pareto-like tail.
- Heterogeneity: Non-stationary (clustered volatility).
- Non-linearity: Non-linearities in mean and (especially) variance.
- Scaling: Markets exhibit non-trivial scaling properties.
- Volatility: Volatility exhibits autoregressive conditional heteroskedasticity. Long-range dependence of autocorrelation, log-normal distribution, non-stationary, non-linear and scaling.
- Volume: Distribution decays as a power law, also calendar effects.
- Calendar effects: Intraday effects exist, the weekend effect seems to have all but disappeared, intramonth effects were found in most countries, the January effect has halved, holiday effects exist in some countries.
from Characterization of Financial Time Series by Martin Sewell.via maxdama
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The point of statistical arbitrage is to make markets consistent. For example, if
- GBP trades against USD at 2:1, and
- USD trades against JPY at 10 000:1, then
- GBP had better be trading against JPY at 20 000:1 !!
! Anything else wouldn’t make sense. Wouldn’t be fair either. The Japanese shouldn’t get a better or worse deal vis-à-vis the British than anybody else.
So stat arbs look for inconsistencies across markets — across currencies, products, different issues of the same stock — and trade against them.
(Source: matlab.com)
The point of high-frequency trading is to smooth markets over time.
Imagine that you know a big block order is coming in. Some huge pension fund needs to send 70,000 checks out next week so they’re selling some asset.
The asset’s price doesn’t really deserve to go down. The fund just wants to cash out. So you buy the huge block order and dole it out in smaller pieces as regular buy orders ebb in over the next few weeks. Or, you know, minutes.
You just smoothed the asset’s price, as well you should.
That’s not ultra-high-frequency trading — which is more about having the fastest technology — making it possible to liquidate a position RIGHT, RIGHT, RIGHT now.
A series of short “What’s the point?” pieces about high frequency trading, leverage, stat arb, shorts, value investing, animal spirits and all that forthcometh.
Warning: this is all stuff that an economist would say, not stuff that a trader would say (unless the trader was doing PR).
μ dt + σ dWt, my #$$
The simplest model of a stock price movement is that the log of the price moves in a direction, plus some noisy drift (like adding a Gaussian W𝓽 at every timestep).
Agustin Silvani gives a counterexample: Federal Open Market Committee meetings precede a volatile market episode, meaning long-term changes in μ and short-term spikes in σ come after an FOMC announcement.
“Stop hunting” by dealers and other smart-money players can sometimes shake up the price pattern ONLY during a super-short period. This occurs most in the least regulated market, FX, because dealers will pull the rug out from under their retail clients’ feet. The dealers can see their clients’ stops and will just blatantly cheat the retail clients (according to Silvani), because they only need to retain a big client’s business. (Hence it’s more profitable to cheat the small fry — there will always be more.)
Efficient markets, my #$$
Not only does this violate the Black-Scholes model (a freak σ^7 comes in and then disappears), it also violates the Strongly Efficient Market Hypothesis, which says that market price—at any instant—reflects all available information and are the best measure of the “true” value of an asset. You would obviously get a more accurate valuation from taking a one-hour average than from relying on any instantaneous price, in the above graph.
According to Silvani’s story, the dealers are very efficient at bilking worse-informed or less-experienced participants, but don’t use this as a Prediction Market!
This really puts my mind at ease as far as whether it’s an economically doomed strategy to pursue quantitative finance:
The Efficient Markets Hypothesis is neither necessary nor sufficient for the Random Walk Hypothesis.
Apparently the Cowles Commission was the first to discover a Gaussian pattern in stock market returns—and its members thought it was proof that financial markets are irrational. Later on, Paul Samuelson established the connection between EMH, greed, arbitrageurs, and random walks of the price of a publicly traded stock. (Benoit Mandelbrot figures into this story too.)
Anyway, Eugene Fama eventually coined the phrase “Prices fully reflect all available information” which is the story I got in Economics 101. But like most bite-sized wisdom, apparently it’s more complicated than that. (Phew, said the hedge fund investor.)
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No-arbitrage conditions are so often assumed in economics papers that they’ve come to seem magical. As I read more books by arbitrageurs, the obvious has become apparent: real people have the job of making financial markets equilibrate.
Given that companies are trying to raise funds for their projects by offering shares of the profits on public exchanges — which is the state of things* — it’s not at all obvious that various mathematical balancing conditions should come about. It takes hedge funds and stat arbs spending their days looking for profit opportunities to smooth these markets out.
For example, take high-frequency traders. They learn the nitty-gritty trading rules (aka market microstructure) and look for tiny opportunities to hold a security for just a little longer (intraday) and then sell it for more than transaction cost a wee bit later. Effectively they act as a short-term warehouse holding the security in between the person who wanted to dump it and the person looking to pick it up.
Knightridge Capital and Jesse Livingston both advised traders not to fight the market, but to go where it wants to go.
As with most ways of making money, to extract it over the long term you have to make the world more like people want it. (So I believe.)
* but not necessarily the way things would have to be done. For example I could just call people up and ask them if they wanted a share of my company; or I could auction shares on eBay; or I could post a message on Craigslist to get local people to meet up and talk together about various people buying various proportions of the company.
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![“The advantage scientists bring into the [investing] game is less their mathematical and technical ability than their ability to think scientifically.”—James Simons, founder of Renaissance Technologies
[Q]uants are forced to think deeply about many aspects of their strategy that are taken for granted by nonquant investors. Why does this happen? Computers are obviously powerful tools, but without absolutely precise instruction, they can achieve nothing…. You can’t tell a computer to “find cheap stocks”. You have to specify what “find” means, what “cheap” means, and what “stocks” are.
—Rishi K Narang](http://www.tumblr.com/photo/1280/isomorphismes/1049141228/1/tumblr_l7de1cJsDQ1qc38e9)
“The advantage scientists bring into the [investing] game is less their mathematical and technical ability than their ability to think scientifically.”
—James Simons, founder of Renaissance Technologies
[Q]uants are forced to think deeply about many aspects of their strategy that are taken for granted by nonquant investors. Why does this happen? Computers are obviously powerful tools, but without absolutely precise instruction, they can achieve nothing…. You can’t tell a computer to “find cheap stocks”. You have to specify what “find” means, what “cheap” means, and what “stocks” are.
—Rishi K Narang
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“This has become something of a ‘me-too’ trade lately,” said Mark Spitznagel, a former Taleb trading partner at Empirica.
The upside of everyone piling onto these catastrophe protection funds is that — guess what — all those people hedging against a catastrophe will reduce its likelihood of happening.
Which of these pictures come from a random normal distribution and which come from a mixed distribution?
plot(rnorm,-3,3);
mix <- function(x) {
rnorm(x)+rnorm(x-3)
}
plot(mix(x), -3,3);
I’m deeply skeptical about this. Why is Ernie Chan telling me how I can make millions? Is he just trying to increase the pool of suckers for him and his like to take money from? If so, how does he know other firms wouldn’t profit from the suckers instead of his?
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