What it is:
Risk averse is an oft-cited assumption in finance that an investoralways choose the least risky alternative, all things being equal.
How it works/Example:
Modern portfolio theory (MPT), which is the theory behind why diversification works, relies on the assumption that investors are risk averse.
There is evidence to support the idea that investors are basically risk averse. People buy insurance on valuable assets. People expect a higher yield on bonds that are lower in priority when it comes to repayment. The assumption of risk aversion leads to the conclusion that in order to entice someone to take a larger risk, he must be compensated with a higher expected rate of return, or else he won't do it.
Why it matters:
In finance and, it is almost universally recognized that the relationship among all of the assets and liabilities in an investor's portfolio should be considered in order to build an "optimum portfolio" for that investor's particular level of risk -- and this phenomenon is called modern portfolio theory.
In other words, modern portfolio theory is the formula that explains both why and how a portfolio should be diversified, and -- as mentioned above -- the assumption that investors are risk averse is an underpinning of modern portfolio theory.