Final answer:
The statement is false as the Treynor Index measures excess returns per unit of market risk and is not equivalent to the slope of the portfolio possibility line.
Step-by-step explanation:
The statement "The Treynor Index is equal to the slope of the portfolio possibility line" is false. The Treynor Index actually measures the returns earned in excess of that which could have been earned on a riskless investment per each unit of market risk. The slope of the portfolio possibility line, often represented in capital market theory, refers to the capital market line (CML), which shows the risk-return trade-off for efficient portfolios, and is distinctly different from the Treynor Index.