The positive value of $c_p$ in the regression equation indicates that the fund manager has successfully timed the market. This is because the term $c_p(r_m - r_f)^2$ in the regression equation is introduced to assess the impact of market timing on portfolio return. In this case, the positive $c_p$ signifies that the fund manager's attempts to time the market have resulted in a positive impact on the portfolio's return. This means that the changes in the composition of the fund and the timing of these changes have been beneficial, leading to excess returns. Therefore, a positive $c_p$ is an indication of successful market timing by the fund manager.

Choice B is incorrect. A positive $c_p$ does not indicate that the fund manager was unsuccessful in timing the market. Rather, it suggests that the manager has been able to generate excess returns by adjusting the portfolio's composition between the market index and Treasury bills based on market conditions.

Choice C is incorrect. The beta of a portfolio being constant would imply that there is no change in risk relative to the market, regardless of changes in market conditions. However, a positive $c_p$ indicates that there has been an adjustment in risk exposure based on changing market conditions, which contradicts with the concept of a constant beta.

Choice D is incorrect. As explained above, a positive $c_p$ does suggest successful timing of the market by altering portfolio composition according to changing market conditions.