Rich people become rich day by day, I think it was because of their mentality. A rich people are not afraid of losses. They always learn from it so that they won't fail next time. So they became sucessful each day.
One can always look back into the history of rich people and if they are critical enough - they will be able to understand how a rich person actually became "rich". Not everyone is born rich, many people become rich because of their actions. Hence it is wrong to assume that they are not afraid of losses. Rather the truth is that they have learnt from being poor at one time and now they are not spending their money in things they dont need.
Risk taking attitude can be present in any person be it rich or poor. When someone has earned their money from hard work, be it rich or poor, they will have more attachment to their wealth and will not waste it. But someone who got that money from illegal methods will always want to spend it away and take more risks with it.
Again rich does not equal financially stable. Rich or poor is a relative term. Financially stable is theoretical term which depends on how you manage your earning and expenditure.