Forums > Pricing & Modelling > covariance matrix of unequally spaced returns?

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 Strange Total Posts: 1540 Joined: Jun 2004
 Posted: 2019-02-19 16:29 I have return snapshots for a few securities that are unequally spaced and need to calculate a covariance matrix for the basket. Do I want to rescale the returns to the constant time basis to avoid domination by the longer periods? I don't interest myself in 'why?'. I think more often in terms of 'when?'...sometimes 'where?'. And always how much?'
 ronin Total Posts: 443 Joined: May 2006
 Posted: 2019-02-19 17:07 > Do I want to rescale the returns to the constant time basis to avoid domination by the longer periods? I don't think the diagonal will be a big problem. It's the correlations that are the problem.I did something like that a few times in the past. Trying to do interpolate the time series and do correlations by hand is a dead end. Garbage in, garbage out. You might have better luck with likelihood optimization. But depending on how sparse the data is, the confidence intervals could be very wide. "There is a SIX am?" -- Arthur
 nikol Total Posts: 676 Joined: Jun 2005
 Posted: 2019-02-19 17:39 Try to google for "covariance structure of asynchronous time series". It is rich subject. For example, you should find "Epps effect".Also, I would suggest to think about "why people use copulas".
 Strange Total Posts: 1540 Joined: Jun 2004
 Posted: 2019-02-19 18:31 @ronin, @nikolRight, actually trying to figure out what happens in a missing time period is next to impossible.The problem I am trying to solve is much simpler and I think I was unclear what my series look like. The price series are synchronized, but the time intervals are uneven. A simple example would be prices that are snapped every hour with an overnight break. I don't interest myself in 'why?'. I think more often in terms of 'when?'...sometimes 'where?'. And always how much?'
 ronin Total Posts: 443 Joined: May 2006
 Posted: 2019-02-19 19:21 That is not very different from weekends in daily data. You can use the same adjustment. The laziest adjustment in the world."Shall we do something?""Nope.""OK."In all seriousness, the concept of hourly returns isn't particularly meaningful. There are hours and there are hours. And then there are hours. You'd normalize, but not to time. Think VWAP, or what ever is applicable to your market. Which should solve the problem with overnight returns. "There is a SIX am?" -- Arthur
 Strange Total Posts: 1540 Joined: Jun 2004
 Posted: 2019-02-19 20:01 Ha, yeah, normalizing to stdevs in volume (e.g. % of adv) would be nice if I had an idea what the volume is :P these are OTC quotes. But yes, I hear you. PS. come to think of it, nothing prevents me from running the covariances raw and then rescaling using some method and seeing which produces more stable results. I don't interest myself in 'why?'. I think more often in terms of 'when?'...sometimes 'where?'. And always how much?'
 nikol Total Posts: 676 Joined: Jun 2005
 Posted: 2019-02-19 22:17 > these are OTC quotes.I am sorry, you cannot analyse OTC quotes, "just like that". 1. OTC quotes of what derivatives with what underlying assets.2. Who is counterpart? what is his balance sheet? what is his funding? etc etc.Even when it is Markit, still there are things to consider.PS. I remember one of heads of IR trading desk I was working with saying - "I can tell position of the counterpart by looking his collateral settlements with us".
 Strange Total Posts: 1540 Joined: Jun 2004
 Posted: 2019-02-19 22:39 ** I am sorry, you cannot analyse OTC quotes, "just like that". **Of course I can, as long as I understand the limitations (trust me, I traded these products for many years). The funding, balance sheet and many other things would only really matter when the size gets meaningful. In any case, the stuff I am looking at is a bunch of semi-standardized layoff structures traded in the IDB and it's not from a provider but rather actual quotes/trades via a friendly IDB broker. These things trade by appointment, so sometimes I get 10-20 quotes/prints a day and sometimes there is nothing going through for a few days. I don't interest myself in 'why?'. I think more often in terms of 'when?'...sometimes 'where?'. And always how much?'
 nikol Total Posts: 676 Joined: Jun 2005
 Posted: 2019-02-19 23:22 > trust me, I traded these products for many yearsI bless you then ))
 Strange Total Posts: 1540 Joined: Jun 2004
 Posted: 2019-02-20 01:47 > I bless you then ))Amen! ) I don't interest myself in 'why?'. I think more often in terms of 'when?'...sometimes 'where?'. And always how much?'
 mtsm Total Posts: 235 Joined: Dec 2010
 Posted: 2019-02-20 02:25 I agree "asynchronous time series" is the right search term. I also think that these timing issues may or may not be important, and it's worth thinking about it. I came across a related problem a few years ago. In my case it was a European single names universe issue. I remember collecting a couple of references on this. I can send that to you if you like.
 ronin Total Posts: 443 Joined: May 2006
 Posted: 2019-02-20 09:42 Got it. Ultimately, it's just about intraday seasonality of variance. VWAP is only useful if you have it. If you don't, look for seasonality in variance directly. "There is a SIX am?" -- Arthur
 NeroTulip Total Posts: 1022 Joined: May 2004
 Posted: 2019-02-20 15:04 "These things trade by appointment, so sometimes I get 10-20 quotes/prints a day and sometimes there is nothing going through for a few days."Interesting problem. Before thinking about covariance, I would think about how to even estimate *volatility* from such data. Normalising returns by sqrt(t) is the simplest way to get an answer that is not totally absurd, but there's gotta be better ways to do it. "Earth: some bacteria and basic life forms, no sign of intelligent life" (Message from a type III civilization probe sent to the solar system circa 2016)
 fomisha Total Posts: 34 Joined: Jul 2007
 Posted: 2019-02-20 16:31 Bergomi had a nice talk on the subj:http://www.cmap.polytechnique.fr/financialrisks/conference2011/talks/lorenzo_bergomi.pdf
 ronin Total Posts: 443 Joined: May 2006
 Posted: 2019-02-21 10:37 Yes, that's the "garbage in, garbage out" approach. Correlation is an unstable measure at the best of times, and correlation of interpolated time series is just nonsense. Google "correlation likelihood estimation" or something like that. It's been done in credit, where you have similar issues with sparsity and timing. But you are very likely to end up doing a lot of work, only to end up with "correlation = 0 +/- 100%". "There is a SIX am?" -- Arthur
 rickyvic Total Posts: 180 Joined: Jul 2013
 Posted: 2019-03-05 18:13 I would add one thing that hasnt been mentioned I think.Interpolating in missing data problems (mixed frequency data is just that) has the issue of a collapsing variance, especially if you use the "forward filling" interpolation. There are ways to correct that (mixed frequency models can give you an idea, or dynamic factor models for mixed frequency) but you need to ask yourself what you are really doing with these data.I hope I added something to the conversation... "amicus Plato sed magis amica Veritas"
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