You can find the spreadsheets for this video and some additional materials here: drive.google.com/drive/folders/1sP40IW0p0w5IETCgo464uhDFfdyR6rh7 Please consider supporting NEDL on Patreon: www.patreon.com/NEDLeducation
Wow, this was really fascinating. I never would've guessed the output would be so close. I like that little touch you did of demonstrating the formula modification process.
Hi Stephen, and glad you enjoyed the video! Planning to do even more videos on various GARCH modifications and generalisations in the future, couple of them in the pipeline already :)
@@NEDLeducation I am curious as well, especially for recent developments since the 1990s, since most of the models were developedaround that time. I wonder, what has been found out since then, because the GARCH can explain the stylized volatilty facts so well and is a great foundation for a conditional CAPM (with time varying betas) :)
@@workforgreatergood1409Hi, and thanks for the question! One of my most recent videos is on DCC GARCH which is precisely about time varying correlations and betas, and integrating it with GARCH-M can give an extremely rich picture! Check it out if you are interested: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-d1qEHNlpGog.html
Hi, and thanks for the comment! The significance testing of individual variables here can be most naturally implemented using a likelihood ratio test (see here: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-BDAHUdNR7BI.html). For t-stats and standard errors of coefficients you would need a Hessian matrix. This is something that is hard to implement in Excel unfortunately. But as soon as I figure out how to streamline Hessians for Excel demonstration, be most ensured I will make a video on that :)
Can you forecast conditional volatility for MGARCH using an altered version of this formula you have previously provided: omega + alpha*e^2. Would it be omega + Delta*e^2???
Hi, such an amazing work you've been working on, would you able to discuss MMAR (Multifractal Model of Asset Return) on stock market? I think that would be fruitful to discuss! thanks :)
Hi, and thanks for the suggestion! MMAR is quite broad and technical and I have not yet found a way of encapsulating it fully in an Excel implementation. However, I have got several videos on the particular case of MMAR, the Hurst exponent, see for example ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-l08LICz8Ink.html and ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-v0sivj2wGcA.html.
and another question, sorry :) did you use the returns log-returns. I am asking becuase of the distribution assumption as the returns usually are leptokurtic. Thank you ;)
On daily frequency, log returns versus simple returns distinction does not deliver a massive difference so either can be used for such an estimation. As for the kurtosis, generally, GARCH effects do explain a large proportion of why return distributions are apparently non-normal, however if you would like to go an extra mile here, I have got a video on GARCH with the non-normal probability density function for maximum likelihood estimations: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-pwGXftsrWYE.html
Can I also use GARCH-M to model the expected return of a stock rather than of the whole market? I don't see any argument, why it couldn't be used for modelling single stocks as well. Am I correct? I am just asking, because also Bollerslev et al use a market index and you mostly see it modeled like that. Thank you in advance! You have such a great channel ! Really cool!
Hi, and thank you so much for such feedback, means a lot to me! Yes, it definitely can be modelled like that, the framework of the model allows to do so. The reason why research mostly focuses on modelling market returns is not empirical but theoretical: as CAPM suggests idiosyncractic risk (stock volatility not associated with market volatility) is not priced, while if you do a GARCH-M on stock level you would implicitly assume it is. Obviously, DCC GARCH or other multivariate GARCH model extended to include GARCH-M effects could also be used to test this :)
@@NEDLeducation Wow, thank you! So, I know that the idiosyncratic (unsystematic) risk will be negligible small in CAPM by diversification and therefore is not priced. And the mean equation in the GARCH-M is a completely different theoretical setting: we have no market portfolio and only take the idiosyncratic risk, namely the conditional variance into the mean equation in order to model the relationship of expected return and volatility, right? So basically, the GARCH-M regression equation (mean equation) is not comparable to the CAPM regression formula... Would my interpretation be correct? Thank you so much!
and by modeling a market index rather than individual stocks, one can infer better on the "market" risk premia. I wonder, if there is any link to CAPM still^^
@@workforgreatergood1409 The link to CAPM in the DCC GARCH using the GARCH-M logic can be modelled the following way: consider a two-asset case, one (asset X) being the market index (returns at time t denoted xt) and another (asset Y) being some stock you are interested in (returns at time t denoted yt). Let the expected return of the market adhere to the GARCH-M formula: xt = mu + delta*vt (or xt = mu + delta*vt^2, I showed both specifications in the video) where mu is the risk-free return, delta is the market risk premium, and vt is conditional volatility of the market. Then, specify the expected stock return as given by the CAPM equation: yt = mu + beta*(xt - mu), where beta is naturally estimated from DCC as cov(yt, xt)/v(xt). Note that in the CAPM framework mu should be the same for all assets as it is the universal risk-free return. Hope it helps!
@@NEDLeducation Thanks for your answer, but no, no, I really meant this question in the setting of GARCH-M only (not DCC GARCH) - so related to the video above. Anyway, I did a brief "deep dive" into Bollerslev et al (1988) and some other sources. I think the theoretical foundation for their GARCH-M is actually really based on a (conditional) CAPM, I mean, even the title speaks for itself^^. The multivariate version they propose and put into a GARCH-M form is only written differently, but implicitely it includes the CAPM formulas - the Expected excess return of the market divided by the variance of the market portfolio will be the delta taken in the mean equation, so that it is not written in the form of a beta, where the Cov(i,m) is divided by the variane of the market portfolio. So, to me it's only written differently, but theoretically consistent, except for the "b", which is a constant that accounts for all other effects not captured by the CAPM ("consumption innovations" and taxation effects...). Also, I think, they take the market index as the individual "asset" and the "market" is represented by 3 asset classes together (stocks, bonds, t-bills). I hope you have no objections or did I miss something? To me this is really interesting, since the GARCH-M really provides strong theory-based evidence (i know, always competing evidence and no "this-is-it", but still cool :) ).
Please do cover the multivariate BEKK GARCH model at the earliest using two data financial time series as it is a very popular mode now in days academic research
@@NEDLeducation ill be obliged if u can make a video on M-GARCH BEKK GARCH Model soon on e views or any other statistical software if not possible on MS Excel . Will really help to get theoritical clarity . Maybe then u can cover others like DCC, CCC, etc...
Hi NEDL, I'm currently doing a research for my dissertation about R&D expenditures and stock return volatility for the biotech industry. Since this is a highly innovative industry that invest a lot in R&D I predict that: (1) high R&D investments leads to high total risk (volatility) and (2) high R&D investments leads to high firm-specific risk. Besides R&D expenditures as independent variable I have 2 control variables Size and Leverage. For the total volatility I was planning on using Fixed effects - and Random effects model by using the annualized Std. deviation of monthly returns and for the firm specific risk the annualized standard deviation of monthly errors from the CAPM mode. However, my professor told me to look into GARCH model instead since it is more accurate. But I have no idea where to begin. How do I get the annualized volatility and error in the GARCH model? Also, when using your excel sheet, should I incorporate all the companies ‘return under each other in one sheet?
Hi, and many thanks for the interesting question! All the best with your dissertation research, this looks like a promising topic! If you are using higher-frequency returns (like daily), GARCH model can provide a better estimation of volatility. To calculate equilibrium long-run volatility of daily stock returns, you can estimate a GARCH model, and then annualise the daily long-run volatility: sqrt(omega/(1 - alpha - beta))*sqrt(252). It would include lots of estimations though, as every single company-year would require a separate GARCH model estimation (a separate sheet for every single company-year). It would be easier perhaps to code it in a loop in Python. For monthly returns, it is generally fine to use ARCH or even the constant volatility assumption as the frequency is low enough. Another way of precisely estimating annual volatility without resorting to any calculations would be to retrieve option implied volatilities (if options on your companies of interest are being traded). Hope this helps!
@@Iheartmusic301 if you are like me, and can't code but need and efficient way to calculate GARCH and perform error checking on your GARCH models across multiple companies, then you might look into the Hoadley excel add-in. It's like $170 for a permanent license, so not too bad given what you receive
@@Iheartmusic301 Long-run annualised volatility would be sqrt(omega/(1 - alpha - beta)*sqrt(12), if you estimate your GARCH on monthly data. If you do it on daily data, multiply by sqrt(252) instead.
Hi Vaibhav, excellent question! It is due to the fact I have implemented the IFERROR function in log-likelihood, if there is an incompatible combination of parameters, Solver will avoid it naturally without the need to impose the restrictions explicitly. Hope it helps!
Hi Shadrack, and glad you are enjoying the channel! I have got a video implementing simple GARCH in Python (ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-3boMYvIzGQ8.html) but I might do one on advanced models, including GARCH-M, in the future. Hope this helps!
