a)

Your mother is worried that she will make a huge loss in March 2022 by investing in one of the HSI, 0008 and IBM. Using historical returns (but without assuming that they come a normal distribution), comfort her by estimating a monthly return x% so that she will make at least x% with a 95% chance (i.e., only with 5% chance she will make less than x%; x could be negative). The following are the averages & standard deviations:

amr_HSI	gmr_HSI	amr_0008	gmr_0008	amr_IBM	gmr_IBM
0.2729%	0.0882%	0.9283%	0.6318%	0.6396%	0.4508%
	s_r_HSI		s_r_0008		s_r_IBM
	0.060477		0.076160		0.061047

b)

Your mother is risk-averse and is thinking which index or security she should invest in. If she can only pick one from HSI, 0008.HK, and IBM, can we advise her which one to pick?