In constant-mix strategies, how does the relationship between portfolio returns and stock returns appear?

In constant-mix strategies, the investment approach maintains a fixed proportion of a portfolio's value allocated to different asset classes, such as stocks and bonds. This means that as stock prices fluctuate, the portfolio is periodically rebalanced to maintain the predetermined investment ratios. The relationship between changes in the portfolio's returns and stock returns can indeed be described as concave.

This concave relationship arises because, at lower levels of stock returns, the impact of stock fluctuations on the overall portfolio is more pronounced due to the constant rebalancing. As stock prices increase, the portfolio becomes more equity-heavy, and the proportional gains from added stock increments can lead to diminishing marginal returns. Consequently, the return profile shows a concave shape, reflecting this diminishing sensitivity to increases in stock market performance.

In contrast, a linear relationship would suggest that the portfolio returns change in direct proportion to stock returns, which does not accurately capture the rebalancing dynamics of a constant-mix strategy. A convex relationship would imply increasing marginal returns to stock investments, which again does not represent the mechanism of constant rebalancing effectively. Lastly, describing the relationship as variable does not precisely communicate the expected shape derived from the strategies' characteristics. Thus, the usage of "concave" to describe the