Curse of dimensionality part 3: Higher-Order Comoments

Higher moments such as Skewness and Kurtosis are not as explored as they should be.

These moments are crucial for managing portfolio risk. At least as important as volatility, if not more. Skewness relates to asymmetry risk and Kurtosis relates to tail risk.

Despite their great importance, those higher moments enjoy only a small portion of attention compared with their lower more friendly moments: the mean and the variance. In my opinion, one reason for this may be the impossibility of estimating those moments, estimating them accurately that is.

It is yet another situation where Curse of Dimensonality rears its enchanting head (and an idea for a post is born..).


Portfolio Construction with R


Constructing a portfolio means allocating your money between few chosen assets. The simplest thing you can do is evenly split your money between few chosen assets. Simple as it is, good research shows it is just fine, and even better than other more sophisticated methods (for example Optimal Versus Naive Diversification: How Inefficient is the 1/N). However, there is also good research that declares the opposite (for example Large Dynamic Covariance Matrices) so go figure.

Anyway, this post shows a few of the most common to build a portfolio. We will discuss portfolios which are optimized for:

  • Equal Risk Contribution
  • Global Minimum Variance
  • Minimum Tail-Dependence
  • Most Diversified
  • Equal weights

We will optimize based on half the sample and see out-of-sample results in the second half. Simply speaking, how those portfolios have performed.


On the 60/40 portfolio mix

Not sure why is that, but traditionally we consider 60% stocks and 40% bonds to be a good portfolio mix. One which strikes decent balance between risk and return. I don’t want to blubber here about the notion of risk. However, I do note that I feel uncomfortable interchanging risk with volatility as we most often do. I am not unhappy with volatility, I am unhappy with realized loss, that is decidedly not the same thing. Not to mention volatility does not have to be to the downside (though I just did).

Let’s take a look at this 60/40 mix more closely.


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.


Linking backtesting with multiple testing

The other day, Harvey Campbell from Duke University gave a talk where I work. The talk- bearing the exciting name “Backtesting” was based on a paper by the same name.

The authors tackle the important problem of data-snooping; we need to account for the fact that we conducted many trials until we found a strategy (or a variable) that ‘works’. Accessible explanations can be found here and here. In this day and age, the ‘story’ behind what you are doing is more important than ever, given the things you can do using your desktop/laptop.


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: