Modeling Natural Disaster Effects on Stock Returns with GARCH

# Measure the effect of a natural disaster on a stock market index


# Measure the effect of a natural disaster on a stock market index












I am very new to using stata and very new to using Garch models. I am currently doing my final dissertation for my MSc in Finance studies and regarding my topic I understood that i had to use garch to find answers to my questions.

So, I am trying to find if natural disaster events have any effect on a daily data of composite index (time series variable). I have my two data sets. one of the composite index and I have created a few dummy variables, each one for the date that every event took place (within my time range). Moreover, I want to include one control variable that affects the dependent variable (composite index) and I want to include it to remove any noise on my examination.

So, my questions are: 1) how to include these variables, meaning where should i put the control variables and where my independents ( I am using the menu of ARCH/GARCH testing, I'm not writing code)

2) I would like to examine the persistence of each event (each dummy variable) on my dependent variable. meaning that I want to check if the shock is still affecting the dependent variable up to 5 days after of its occurrence. how can I do that? give my dummy variable the value of 1 not only on the day of the occurrence of the event but on the 5 following days as well?

3) finally, do you think that it is correct to create one dummy variable for each catastrophic event or one dummy variable for each type of shock (i.e. 1 for floods, 1 for storms, 1 for earthquakes etc..)

Thanks a lot in advance, Evangelos

EDIT: my work is based on this paper. (Lin Wang 2013 - The Impact of Japanese Natural Disasters on Stock Market) http://artsci.wustl.edu/~gradconf/LinWang.pdf

## Answer by Quantopik (score 1)

https://quant.stackexchange.com/a/18716

As regards the point (1), you do not have to include the exogenous variables in the garch model, but, as described in the paper (IV. Methodology, p. 7), you must estimate the following models and steps:

- Get residuals vector $\epsilon_t$ by running:

$RetJP_t$ $=$ $\alpha_0$$+$$\alpha_1$$RetUS_{t-1}$$+$$\alpha_2$$ChgIR_{t-1}$$+$$\alpha_3$$RetEXR_{t}$$+$$\epsilon_t$;

To run the previous linear regression model, type the `regress` command in stata followed by all the dependent variables ($RetJP_t$ $RetUS_{t-1}$ ...) with the variable name you gave them.

To get the residuals, type `predict epsilon, resid` in stata and you'll find a new variable in the stata variable manager called `epsilon` and corresponding to the model residuals.

- Get the mean equation by running:

$RetJP_t$ $=$ $\alpha_0$$+$$\alpha_1$$RetUS_{t-1}$$+$$\alpha_2$$ChgIR_{t-1}$$+$$\alpha_3$$RetEXR_{t}$$+$$+$$\alpha_4$$RetJP_{t-1}$$+$$\alpha_5$$\epsilon_{t-1}$$+$$w_t$;

- Get the conditional variance estimate by running the following model in stata:

$ln(h_i)$ $=$ $\beta_0$ $+$ $\beta_1$*$\left|\frac{\epsilon_{t-1}}{\sqrt[2]{h_{t-1}}}\right|$ $+$ $\beta_2$$\frac{\epsilon_{t-1}}{\sqrt[2]{h_{t-1}}}$$+$$v_t$

where $h_i$ is the variance of $RetJP_t$ and $\epsilon_t$ is he residuals vector you got at the previous step; to get the estimate of the conditional variance, type the `predict` command after you run the previous model at this step.

- Estimate the GARCH-in-mean equation, by running the following model:

$RetJP_t$ $=$ $\alpha_0$$+$$\alpha_1$$RetUS_{t-1}$$+$$\alpha_2$$ChgIR_{t-1}$$+$$\alpha_3$$RetEXR_{t}$$+$$+$$\alpha_4$$RetJP_{t-1}$$+$$\alpha_5$$\epsilon_{t-1}$$+$$\alpha_6$$\sqrt[]{\hat{ln(h_i)}}$$+$$z_t$

where $\hat{ln(h_i)}$ is estimated conditional variance got in the previous step by using the command `predict`.

You cannot do this procedure by the menus in stata, but only by command line.

As regards the point (2), you need to use the event study methodology; to this purpose, I suggest you to follow:

> Kothari, S. P., and Jerold B. Warner. "The econometrics of event studies." Available at SSRN 608601 (2004).

that explains how to conduct this kind of study.

As regards the point (3), it is not convenient to create a dummy variable for each event. This mainly is because a natural disaster is a rare event and you will have too little observation in your dummies, such that the model will not be able to measure fully the effect of the event on your dependent variable; so, I suggest to collect all the event and create a unique dummy variable to measure the effect of such event. Moreover, the effect of a natural disaster is supposed to be negative in all cases, so, it is reasonable to think collecting all events together and assuming the weight of the different effects is similar.

Hope this helps.