DCC-GARCH Finance master thesis

Finance
1

Hey everyone!

I sincerely, in advance, thank for any help and/or response I receive on this post.

Disclaimer: I work with RStudio.

Context:
I am currently writing my Master’s thesis, in which I have opted to investigate Bitcoin’s relation to other indices / commodities. The selected few are currently

  • Bitcoin (well duh).
  • A “regular” commodity index
  • A power/energy commodity index
  • A non-energy commodity index
  • S&P 500
  • Gold (mostly for comparison purposes).

I am interested in pairs of Bitcoin + X index/commodity, and I am investigating whether we can find proof of safe haven effects during market turmoil, and whether Bitcoin can be used as a hedge against the various indices or if its merely a diversifier.

I have defined both the univariate and the multivariate GARCH model, and gotten the pairwise DCC plots.

The multivariate output is currently a large table of the parameters: mu, ar1, omega, alpha1 and beta1 - for all the time series, and a DCCA1 and a DCCB1.

However, as I am interested in the pairwise correlations, should i really be doing the multivariate pairwise aswell, or is it irrelevant as long as I am able to extract the pairwise DCC (which I am able to).

At this point the main issue at hand is how to use the DCC further, how do I actually investigate the pairs and their relation & properties? I would assume a regression analysis of some kind, but how do I go about doing this?

Another disclaimer:
I am not interested in the prediction aspect of GARCH, as we I am strictly looking at historical data.

If you made it this far, you have my thanks!

2

Hey mate, welcome to the site.

Good thesis topic, very timely.

So you have a few options when approaching this.
You are throwing GARCH and DCC into the mix, so this is telling me you are interested in correlation of volatility rather than correlation of returns?
Volatility is much more stable than returns, so this is a simpler, more stable model.

You could use DCC for the correlation of returns, but then you don’t have to consider GARCH at all.

For the pairwise, if all you care about is BTC against everything else, there isn’t any point in calculating SPX vs gold for example. But if sometimes is just easier to calculate them all and extract what you need in DCC. The number of assets here is low, so you are not going to hit the limits of what is possible for a covariance matrix.

DCC here is useful to see how much correlation deviates compared to the UNCONDITIONAL correlation. Identify a period of stress (say SPX down 4% in a day/month whatever) and see how the correlations move about. You can also use this DCC matrix to generate simulated, correlated random variables, and start to construct model portfolios with them. This is what I did in my PhD for VaR/CVaR estimation, but there are many possibilities.

I am not sure what you mean around regression.

With all of the above, plot as much as you can. It makes life 100 times easier.

Hope the above is useful.

Cheers,

Tino

3

Thank you!

I really haven’t done much which this kind of statistical models before, which is why I am kind of clueless. I have not given much thought to correlation of returns vs volatility, but rather followed a similar research done by one of the professors at the university I go to. Unfortunately he is on parental leave.

The research is:
Bitcoin for energy commodities before and after the December 2013 crash:
Diversifier, hedge or safe haven?
By: Bouri, Jalkh, Molnár and Roubaud

In their research they state:
" Potential diversifying, hedge, and safe-haven properties of Bitcoin are examined using regression
analyses. Practically, pairwise DCCs are extracted from the ADCC model into separate time series
and then regressed on dummy variables (D) representing extreme downward movements in the lower 10th, 5th, or 1st percentile as well as extreme upward movements in the 90th, 95th, and 99th
percentile of the return distribution."

I tried to do the DCC-GARCH coding for BTC and one of the indices (chosen at random), and all the parameters/ coefficient from GARCH remains the same (being; mu, ar1, omega, alpha1 and beta1), but the DCCA1 and DCCB1 changed considerably, and beta became insignificant.

If we set aside everything I have done, and thought I should do for a minute: How would you go about conducting this research?
Exploring whether Bitcoin has safe-haven, hedge or diversifying properties?

EDIT:
Regarding the regression analysis:
The idea is/was that in order to “prove” characteristics/tendencies(…) of Safe haven, hedging or diversying capabilities a regression analysis was to be conducted. The idea, in its simplest form, is that the return of Bitcoin should be positive or zero during times of market turmoil. Perhaps using dummy variables defined on 1%,5% and 10% quantile of VIX index and/or volatility of the relevant index. However, this sounds too simple, and does not use the DCC at all. Anything you can think of regarding this matter?

4

I mean, if I were to do this analysis for real, I would really consider that the liquidity and depth of the market in 2013 for bitcoin would have been tiny. No way you can hedge anything out like that.

There is a feeling that BTC is just interchangeable for any other financial instrument, but that is simply not true. A kid in his dorm room :beers: might be able to go click click and buy sell as the wind changes, but institutions managing trillions are slow turtles :turtle:, which wouldn’t even have this on their radar.

Anyhow, I would look at the DCC of returns and possibly DCC vol via our friend GARCH too.
Plot the time series and highlight when the market is in ‘stress’ to see if you can identify anything. This is where you regression analysis would come into play. The dummy variable being is_stress = 1
Or alternatively, simply plot SPX (or pick your poison) returns on the x axis against BTC returns on the Y axis and see what that looks like. This will give you an idea of what the “hedge” is truly like.

If you really believe BTC should be part of your portfolio, I would do this:

Take all the stress months and use that as dataset 1. Optimize your portfolio using this. Mean-variance or Risk parity or inverse vol (again, pick your poison) for weighting and see what it looks like.
Then take all the other dates (normal market) as dataset 2 and optimize for that using your preferred optimization method so you get weights.

Then plug the time series of weights against the returns and see what the portfolio looks like against a equally weighted/MV optimized with the whole dataset as input/anything else you want to do. Look at the drawdown, look at the vol, not just the returns.

Trust me on this, but return is not the most important thing when running a portfolio. It’s fine if this is your personal $10k you have in there. But for a professional environment, you have strict vol and drawdown targets to adhere to. You won’t have any clients left if you are up 40% one month and down 50% the next.

Lots of info to digest there, but there are some clear actionable points which I think should get your a solid mark for your project. I would give you a great grade if I was marking it anyway :wink:

Let me know how you go.

Tino

1 Like
5

I will look into all your input!
Hopefully this all falls into place sooner rather than later, I suspect there will be some all nighters comming up!
Regardless, thank you so much for your time and effort, you have been extremely helpful!

1 Like
6

I know the feeling. Lots of overwhelming info. But you being on this forum and asking questions means you are on the right path and have the right mindset.

Good luck with everything