What should the standard deviation of an account's returns be relative to a good benchmark?

The standard deviation of an account's returns should ideally be less than the volatility of a good benchmark, such as a market index. A lower standard deviation relative to the benchmark indicates that the account is achieving a level of return with less risk compared to the market. This relationship is often desirable for investors, as it demonstrates the manager's skill in generating returns while managing risk effectively.

In practical terms, a fund or account that can maintain returns with less volatility than the market index suggests a more stable investment. This becomes particularly important in the context of risk-adjusted performance measures such as the Sharpe ratio, where lower risk (as measured by standard deviation) with maintained or higher returns results in a favorable risk-return profile.

If the standard deviation were greater than that of the market index, it would signal that the account has higher volatility and hence is taking on more risk for the same or potentially lesser return, which could be unattractive to risk-averse investors. Furthermore, being equal to the average market returns does not capture the risk associated, as volatility needs to be considered alongside returns for a complete assessment of an investment's performance. Lastly, the idea that the standard deviation of returns is unrelated to market conditions is a mischaracterization, as market conditions typically