Portfolio risk and return are fundamental concepts in investment management, encapsulating the potential rewards from investments and the risks undertaken to achieve these rewards. The relationship between risk and return is central to making informed investment decisions and constructing an optimal portfolio.

Portfolio risk refers to the uncertainty and variability in the returns generated by a portfolio. It is influenced by the volatility of the portfolio's individual assets and how they interact with each other. Higher portfolio risk implies greater potential for significant deviations from expected returns, both positive and negative.

Portfolio return is the gain or loss generated by the portfolio over a specific period. It reflects the combined performance of all the assets within the portfolio, including income from dividends, interest, and capital gains. The return of a portfolio is inherently linked to its risk profile; generally, portfolios with higher risk have the potential for higher returns, while those with lower risk tend to offer more stable but lower returns.

Volatility measures the degree of variation in returns from the expected outcome over a given period. This variation is influenced by factors such as market conditions, economic cycles, and specific events impacting individual assets or sectors. Higher volatility signifies greater uncertainty in returns, leading to increased risk. Typically, higher-risk portfolios are anticipated to provide higher returns to compensate for the heightened uncertainty and potential for substantial losses. On the other hand, lower-risk portfolios usually deliver more stable, though lower, returns with minimal risk of significant losses.