An asset allocation is considered optimal when which condition holds?

An asset allocation is considered optimal when the condition that the ratio of the expected excess return of an asset over the risk-free rate to its marginal contribution to risk (MCTR) is the same for all assets holds true. This condition is derived from the principles of mean-variance optimization, which is central to portfolio theory.

When this ratio, often referred to as the "Sharpe ratio" in a more general context, is identical across all assets in the portfolio, it indicates that investors are getting the best possible trade-off between risk and return. It allows for the most efficient allocation of resources, as no other asset provides a higher risk-adjusted return than the others.

In practical terms, if all assets had different ratios, reallocating the portfolio could enhance the expected return for the same level of risk or reduce risk for the same expected return. By keeping this ratio equal across all investments, an investor can ensure that they are not leaving potential returns unrealized or exposing themselves to excess risk unnecessarily.

Therefore, achieving this equality across assets signals that the portfolio is efficiently structured, maximizing returns per unit of risk taken, which is essential for an optimal asset allocation.