The risk of a stock when it is added to a portfolio is the stock's standard deviation of returns; the risk of a stock when it is your only investment is the stock's beta.

When forming a well-diversified large company portfolio like the S&P 500, the standard deviation (of returns) of the portfolio can be reduced to 0.

If risk aversion increases in the stock market, stock prices will increase.

Diversification allows you to reduce your risk without lowering your return.

Diversification allows you to reduce your risk without lowering your return.

Step-by-step explanation

Diversification refers to a strategy used in risk management which mixes different types of investment within a portfolio. When a portfolio is diversified, it means that it contains a mix of different asset types and investment vehicles in a to attempt to reduce exposure to a particular single risk. The rationale behind this strategy is that when a portfolio is made up of various kinds of assets, it will on average yield higher returns in the long-term and lower risk of any particular security or holding.

Therefore, diversification allows one to reduce risk of his or her portfolio without lowering the potential returns of the portfolios/investments. This is possible because diversification reduces volatility of one's portfolio over time in that all portfolios do not perform the same way in different times.