Java exception rethrowing

package tk.lslayer.temp;

import java.util.ArrayList;
import java.util.List;

public class CustomErrorDemo {

    public String errorThrower() throws IndexOutOfBoundsException, NullPointerException  {
//        List<String> myCoolList = null;
        List<String> myCoolList = new ArrayList<String>();
//        Select one of two lines, and uncomment any

        String string = myCoolList.get(100500); //This makes Exception, depends on selected line on top
        return string;
    }

    public void errorCatcher() throws MyCooleCustomException {
        try {
            this.errorThrower();  //Exception will be here
        } catch (Exception e) {
            //rethrowing, wrapped in our MyCoolecustomException
            throw new MyCooleCustomException("We cought an exception!", e);
        }
    }

    public static void main(String args[]) {
        CustomErrorDemo handler = new CustomErrorDemo();
        try {
            handler.errorCatcher();
        } catch (MyCooleCustomException e) {
            System.out.println(e.getMessage()); //We caught MyCooleCustomException
            //warning, "Information expert" violated
            System.out.println(e.getCause().getClass().toString()); //We show a class of caught exception
        }
    }

}