This post is about copulas and heavy tails. In a previous post we discussed the concept of correlation structure. The aim is to characterize the correlation across the distribution. Prior to the global financial crisis many investors were under the impression that they were diversified, and they were, for how things looked there and then. Alas, when things went south, correlation in the new southern regions turned out to be different\stronger than that in normal times. The hard-won diversification benefits evaporated exactly when you needed them the most. This adversity has to do with fat-tail in the joint distribution, leading to great conceptual and practical difficulties. Investors and bankers chose to swallow the blue pill, and believe they are in the nice Gaussian world, where the math is magical and elegant. Investors now take the red pill, where the math is ugly and problems abound.
Tag: volatility
Multivariate volatility forecasting, part 2 – equicorrelation
Last time we showed how to estimate a CCC and DCC volatility model. Here I describe an advancement labored by Engle and Kelly (2012) bearing the name: Dynamic equicorrelation. The idea is nice and the paper is well written.
Departing where the previous post ended, once we have (say) the DCC estimates, instead of letting the variance-covariance matrix be, we force some structure by way of averaging correlation across assets. Generally speaking, correlation estimates are greasy even without any breaks in dynamics, so I think forcing some structure is for the better.
Correlation and correlation structure (1); quantile regression
Given a constant speed, time and distance are fully correlated. Provide me with the one, and I’ll give you the other. When two variables have nothing to do with each other, we say that they are not correlated.
You wish that would be the end of it. But it is not so. As it is, things are perilously more complicated. By far the most familiar correlation concept is the Pearson’s correlation. Pearson’s correlation coefficient checks for linear dependence. Because of it, we say it is a parametric measure. It can return an actual zero even when the two variables are fully dependent on each other (link to cool chart).
Live volatility monitor
In April this year, Rstudio notified early users of shiny that Glimmer and Spark servers which host interactive-applications would be decommissioned. Basically, the company is moving forward to generate revenues from this great interactive application service. For us aspirants who use the service strictly as a hobby, that means, in a word: pay.
Basic subscription now costs around 40$ per month. Keeping your applications free of charge is possible BUT, as long as it is not used for more than 25 hours per month. So if your site generate some traffic, most users would simply not be able to access the app. Apart from that, you are subject to some built-in Rstudio’s logo which can’t be removed without having a paid subscription. That is a shame, but a company’s gotta eat right? I am using Rstudio’s services from their very beginning, and the company definitely deserve to eat! only I wish there would be another step between the monthly 0$ option which provides too slim capabilities, and the monthly 40$ option which is, in my admittedly biased opinion, too pricey for a ‘sometimes’ hobby.
Multivariate volatility forecasting (1)
Introduction
When hopping from univariate volatility forecasts to multivariate volatility forecast, we need to understand that now we have to forecast not only the univariate volatility element, which we already know how to do, but also the covariance elements, which we do not know how to do, yet. Say you have two series, then this covariance element is the off-diagonal of the 2 by 2 variance-covariance matrix. The precise term we should use is “variance-covariance matrix”, since the matrix consists of the variance elements on the diagonal and the covariance elements on the off-diagonal. But since it is very tiring to read\write “variance-covariance matrix”, it is commonly referred to as the covariance matrix, or sometimes less formally as var-covar matrix.
A Simple Model for Realized Volatility
The post has two goals:
(1) Explain how to forecast volatility using a simple Heterogeneous Auto-Regressive (HAR) model. (Corsi, 2002)
(2) Check if higher moments like Skewness and Kurtosis add forecast value to this model.
Volatility forecast evaluation in R
In portfolio management, risk management and derivative pricing, volatility plays an important role. So important in fact that you can find more volatility models than you can handle (Wikipedia link). What follows is to check how well each model performs, in and out of sample. Here are three simple things you can do:
Intraday volatility measures
In the last few decades there has been tremendous progress in the realm of volatility estimation. A major step is the additional use of intraday price path. It has been shown that estimates which consider intraday information are more accurate. Which is to say they converge faster to the real unobserved value of the true volatility.
Reducing Portfolio Fluctuation
THIS IS NOT INVESTMENT ADVICE. ACTING BASED ON THIS POST MAY, AND IN ALL PROBABILITY WILL, CAUSE MONETARY LOSS.
Most of us are risk averse, so in our portfolio, we prefer to have stocks that will protect us to some extent from market deterioration. Simply put, when things go sour we want to own solid companies. This will reduce return fluctuation and will help our ulcer index against large downwards market swings. Large caps are such stocks. But which large caps should we chose? The squared returns are often taken as a proxy for the volatility so, keeping simplicity in mind, I use those.