It seems like many of my posts lately have been critical of others lately (#1: POMO, #2: Dollar / Gold, #3: Twitter ).  On the downside, everybody wants to get along and nobody makes friends on the attack.  On the upside, it’s good for plenty of site hits and provides two sides to a discussion.

So what the hell, here it goes – here’s why I think the ZeroHedge submitted/accepted ratio post gets it wrong. (Note that all of the analysis, both here and by John Lohman, suffers from an in-sample issue.  None of this is really a strategy that could be implemented without information about the submitted-to-accepted ratio in advance.  This may still be profitable if you took the positions at 11am instead of 9:30am, but none of the data we’re providing proves it.  I will be performing real intraday analysis with out-of-sample backtesting in the  paper I’m working on right now).

First of all, I think John Lohman’s logic is mostly right in the hypothesis.  If the “conspiracy theory” is really true, then the ratio of submitted-to-accepted should be proportional to the market’s return.  However, there are a few points I’d like to make for rigor’s sake here.

  • First, why can’t PDs go short too?  Maybe it makes more sense to put the absolute value of the market’s return on the LHS, dropping the sign. (Hint: See below if you want the answer!)
  • Second, there are a number of alternate hypotheses that are not conspiracy-like that could also result in this proportional relationship.  Maybe market participants just take some days of the week off, and the Fed chose to schedule POMO on days that would have higher liquidity anyway.  If you were Brian Sack, wouldn’t you want to schedule these operations on days where the most PDs would participate or they would be best staffed?
  • Third, just to emphasize it again, neither John nor I are actually presenting these analyses as something you can take to the market.  The submitted-accepted ratio comes out after the operation begins, which is never before 9:30am, which means you could never realize the returns we’re showing precisely.  For a strategy you can actually execute, see yesterday’s post (but don’t assume it’s profitably stable).
  • Fourth, I’ve switched from submitted-to-accepted to accepted-to-submitted.  This makes everything easier to see and interpret.

OK, so again, John’s logic is decent enough.  If I had to guess, Tyler at ZH likely added his own emphasis to the post “for effect,” which might have masked some of John’s real tone.  So down to the brass tacks and the data.  First of all, I’m using the SPY for the S&P 500 and my POMO dataset for information on the submitted-to-accepted ratio.  I’m also publishing the Matlab code here, just for full disclosure sake.

Now, if you run this code, you’ll see the following two scatter plots pop up.  The red are the bottom third of the POMO operations by accepted-to-submitted ratio, the blue are the middle third, and the green are the top third.

OK, so it looks like there’s definitely something going on for the dollar volume.  However, the story for the return is a little bit more fuzzy.  It appears that the spread increases as the accepted-to-submitted ratio increases, but not necessarily that there is a strong direction to the sign.  Maybe, as I mentioned above, the magnitude of the return is what’s  proportional, not just the value.  As you can see in the Matlab code, I fit a simple GLM for each of these and get the following:

  • log(close) – log(open) ~ accepted/submitted ratio: The coefficient on the ratio is slightly positive (0.0066, +-0.0047) but the t-stat is 1.4.  No go.
  • log(dollar volume) ~ accepted/submitted ratio: The coefficient is on the ratio is definitely positive (1.75, +-0.18) and the t-stat is 9.6.  This conclusion is definitely supported – the ratio of accepted-to-submitted is proportional to the total dollars traded on SPY.
  • abs(log(close) – log(open)) ~ accepted/submitted ratio: In this case, the coefficient is definitely positive (0.0159, +-0.0032) and the t-stat 5.0.  This conclusion is also supported – the ratio of accepted-to-submitted is proportional to the magnitude of SPY’s return, but not necessarily the direction.

So there you have it – the dollar volume and magnitude of the change are statistically significantly related to the POMO accepted-to-submitted ratio, but the direction is not really guaranteed.  Much more of this to come in a research paper I’m currently working on.

I noticed that there’s been some analysis of the performance of the market on days with and without POMO from Pragmatic Capitalism.  I’ve been running some preliminary calculations for a short research paper on the topic and noticed that my numbers didn’t match up.  I’ve decided to publish some of these results.

First of all, I’m using the dataset that I published yesterday on all Permanent Open Market Operations.  There have now been 230 POMO operations, including both Treasury and agency transactions and purchases and sales.  I’m also using the performance of SPY from August 2005 to October 25th, 2010.

Furthermore, my numbers diverge from the Pragmatic Capitalism on returns.  Returns are a bit of a fuzzy concept, however, so I’ve tried quite a few options.

Option 1: Log(close) – Log(open) on the day of POMO.  In this case, POMO returns 13.9% with a daily std. dev. of 1.18%, whereas no POMO returns -34.7% and a daily std. dev. of 1.26%.  52.68% of POMO intraday returns are positive, whereas 51.49% of no POMO returns are positive.

Option 2: Log(tomorrow close) – Log(close).  In other words, buy at the end of a POMO day and market-on-close tomorrow.  In this case, POMO returns 8.30% with a daily std. dev. of 1.46%, whereas no POMO returns -11.4% with a daily std. dev. of 1.56%.

Option 3: Log(close) – Log(yesterday close).  This means buy market-on-close the day before POMO and sell market-on-close the day of POMO.  This strategy returns 29.5% with a daily std. dev. of 0.57%.  The alternative returns -32.7% with a daily std. dev. of 1.44%.  Clearly frontrunning POMO on SPY is profitable, but we should all be clear about what we’re calculating when we talk about strategies here.

N.B.: As I mentioned, this will be part of a short research paper in the next week or so.  I’ll address whether or not these returns are stable, especially in the past few weeks, in the paper.

I’m glad the FT Alphaville team is on GMT, because it makes waking up in EST so much more entertaining. Read this morning’s article on the NZDUSD bounce, or, as it’s been dubbed, the “Hobbit bounce.”

What does the trailing monthly correlation between the S&P 500 (SPY) and its constituent sectors (SPDR sector ETFs) look like over the past few years? The figure below shows this moving correlation for the intraday return (log close/open), regular return (log adjusted close), and total dollar volume (using open/close midpoint).  It looks like we’re sitting just under the high set last week.  I’ll let you decide how you think this factors into the ongoing discussion on correlation, but correlation periodicity may be more of an intraday than monthly thing.

P.S. This uses the Matlab code I posted for calculating moving correlations here.

In the next day or two, I’m hoping to produce some comprehensive research (at least comparatively in the blogosphere) on the relationship between the S&P 500 and the Federal Reserve’s permanent open market operations. Historical data for these operations is available back to August 2005.

In order to do this, I needed to get the Fed’s POMO data into a much more reasonable format.  The spreadsheet below is the result of my work.  You can download the spreadsheet here.

As an added bonus, I’ve decided to release the Python code I used to process the NYFRB’s XML data (you’ll need lxml, too). Here it is below:

Here’s another new paper on q-FIN that I thought might be worth mentioning.  Having skimmed it, I have a few questions.  First, if the paper’s title includes the phrase “different time-scales,” you should include more than 15-minute interval sampling.  I’d like to see whether their conclusions are robust on two-minute or 60-minute intervals as well (like this).  Second, there is a large body of literature on the leading eigenvalues of the correlation matrix.  This path of inquiry is twenty years old and has already produced a number of the conclusions that are in the paper.  I guess I’m curious as to why they chose to use sum-of-signs instead of something like the proportion of the leading eigenvalue to the sum of eigenvalues (it works well here).   Anyway, even if there are some methodological issues, the paper’s conclusions are interesting and it’s always nice to see fresh work on intra-day dynamics and market “panic.”

Cross-sectional signatures of market panic were recently discussed on daily time scales in [1], extended here to a study of cross-sectional properties of stocks on intra-day time scales. We confirm specific intra-day patterns of dispersion and kurtosis, and find that the correlation across stocks increases in times of panic yielding a bimodal distribution for the sum of signs of returns. We also find that there is memory in correlations, decaying as a power law with exponent 0.05. During the Flash-Crash of May 6 2010, we find a drastic increase in dispersion in conjunction with increased correlations. However, the kurtosis decreases only slightly in contrast to findings on daily time-scales where kurtosis drops drastically in times of panic. Our study indicates that this difference in behavior is result of the origin of the panic-inducing volatility shock: the more correlated across stocks the shock is, the more the kurtosis will decrease; the more idiosyncratic the shock, the lesser this effect and kurtosis is positively correlated with dispersion. We also find that there is a leverage effect for correlations: negative returns tend to precede an increase in correlations. A stock price feed-back model with skew in conjunction with a correlation dynamics that follows market volatility explains our observations nicely.

L. Borland, Y. Hassid. Market panic on different time-scales. arXiv:1010.4917

Here’s a nasty looking headline from FT’s 6am cut this morning (which is now paywalled, btw)  - European bank bail-ins will cost +87 basis points.  The article summarizes the results of a JP Morgan survey on the effect of various “bail-in” options.  Here’s JPM’s summary:

Survey responses indicated that the implementation of bail-in frameworks is likely to have a material impact on the pricing of senior debt. Firstly, respondents indicated that the greater loss outcomes associated with bail-in regimes are not being priced in, despite the existence of special resolution regimes which already may imply similar loss outcomes for senior bondholders. Secondly, the average risk premium that investors would demand for a single ‘A’ bank under a bail-in regime would be 87bp. Thirdly, investors clearly expect that the implementation of a bail-in framework will lead to an increase in price differentials across issuers of differing credit quality. In our opinion, the sum total of the implementation bail-in regimes together with the current extensive regulatory capital reform process could be a major driver of M&A activity amongst the European banking sector, as smaller and lower ratings issuers may struggle to access capital markets at levels which allows their business models to remain intact.

Yikes.

Heatmaps have been all the rage this week. I was driving down US-23 to Ann Arbor last Monday and heard Jim Cramer introduce the thing to Erin Burnett.  My first instinct was that we’d see something like this, followed by a rant from Mark Haines.  However, the real thing turned out to be much more tame and reasonable.

Now that heatmaps are en vogue, I figured I’d take my own shot at one.  I’ve always been a fan and use them in publications, but there’s a very fine line between conveying large amounts of information intuitively and just overloading the viewer.  The figure below shows two pieces of information simultaneously:

  1. The diagonal cells show the cumulative log-return time series of each asset over the past month.  The upper left hand corner of the diagonal cell displays the past month’s return.
  2. Off-diagonal cells show the color-coded correlation between assets.  For example, reading across the first row shows the correlation of each asset with the S&P 500.  Reading the figure indicates that the S&P 500 (SPY) has a correlation coefficient of 75.9% with the Nasdaq (QQQQ) and 92.6% with the Russell 2000 (IWM).  The upper left hand corner of these off-diagonal cells displays the correlation coefficient.

Please let me know what you think of the figure, pro or con.  If you’ve got any other suggestions, also feel free to leave a comment.  Note that there are a still a few “degrees of visualization freedom,” e.g., thickness of cell borders, opacity of cells, plenty of free pixels in the interior of cells.   For instance, how would you suggest I convey information about the volatility of each fund over the week?