Treynor Index (Treynor): It uses the systematic risk of fund income as a factor for fund performance adjustment, reflecting the excess return obtained by the fund assuming unit systematic risk. The larger the index value, the higher the excess return obtained from assuming unit system risk.
The formula for calculating the Treynor index
The Treynor index is a measure of excess return per unit of risk. In this index, excess return is defined as the difference between the fund's investment rate of return and the risk-free rate of return for the same period. The index calculation formula is:
T=(Rp-Rf)/βp
Among them: T represents Treynor's performance index, Rp represents the average rate of return during the investment review period of a certain fund, Rf represents the average risk-free interest rate during the review period, and βp represents the systematic risk of a certain fund.
The meaning of Treynor's performance index is the excess return (exceeding the risk-free rate Rf) obtained per unit of systematic risk assets. The greater the Traynor Performance Index, the better the fund's performance; conversely, the worse the fund's performance.
The investment risks faced by the fund's investment portfolio include systematic risks and non-systematic risks. In financial theory, two indicators are generally used to measure the risk of investment returns:
The first is the standard deviation of its historical return δ, which measures the total risk of investment returns;
The second is its historical return standard deviation δ Systemic risk coefficient, that is, the estimated value of β.
Traynor believes that fund managers should eliminate all non-systematic risks through investment portfolios, so Traynor uses the excess return rate obtained by unit systemic risk coefficient to measure the performance of investment funds. A sufficiently diversified portfolio has no unsystematic risk, only systemic risk that differs from market movements. Therefore, he used the βp coefficient of fund investment return as an indicator of risk.