What does a confidence band indicate?

A confidence band is a statistical tool used to indicate the range of values within which a certain percentage of future observations are expected to fall, given the underlying data and assumptions. When applied in the context of investment returns, confidence bands help investors and analysts understand the range of potential future outcomes, specifically where value-added returns are anticipated.

In this context, B accurately describes the function of a confidence band, as it reflects the range of expected performance, allowing investors to gauge the potential for excess returns above a benchmark. It provides a visual representation of uncertainty and helps in the analysis of how much of the investment's returns can be attributed to skill (value-added) versus market movements.

In contrast, other options relate to different concepts. The expected maximum loss in investment refers more closely to risk metrics like Value at Risk (VaR), while potential gains in a portfolio might connect to return profiles or upside potential scenarios. The overall market volatility index, on the other hand, pertains to broader market measures such as the VIX and does not relate to individual performance or returns in the same way as confidence bands do. Thus, option B is the most accurate representation of what a confidence band signifies in investment analysis.