Android action bar home button

I've set my action bar like so but nothing happens when I click the home up button. The two options below are enabled so shouldn't it go to the home activity automatically?

ab.setHomeButtonEnabled(true);
ab.setDisplayHomeAsUpEnabled(true);

Action Bar

@Override
public boolean onCreateOptionsMenu(Menu menu) {
    MenuInflater inflater = getMenuInflater();
    inflater.inflate(R.menu.menu, menu);

    final String[] activities;
    Resources res = getResources();
    activities =  res.getStringArray(R.array.activities);

    ActionBar ab = getActionBar();
    ab.setHomeButtonEnabled(true);
    ab.setDisplayHomeAsUpEnabled(true);
    ab.setTitle(R.string.app_name);
    ab.setNavigationMode(ActionBar.NAVIGATION_MODE_LIST);
    ab.show();

    /** Create an array adapter to populate dropdownlist */
    ArrayAdapter<String> adapter = new ArrayAdapter<String>(getBaseContext(), android.R.layout.simple_spinner_dropdown_item, activities);

    /** Setting dropdown items and item navigation listener for the actionbar */
    getActionBar().setListNavigationCallbacks(adapter, navigationListener);

    /** Enabling dropdown list navigation for the action bar */
    getActionBar().setNavigationMode(ActionBar.NAVIGATION_MODE_LIST);
    return true;
}