Define Treynor’s Performance Index

Treynor’s Performance Index

To understand the Treynor index, an investor should know the concept of characteristic line. The relationship between a given market return and the fund’s return is given by the characteristic line. market performance. The ideal fund’s return rises at a faster rate than the general market performance when the market is moving upwards and its rate of return declines slowly than the market return, in the decline. The ideal fund may place its fund in the treasury bills or short sell the stock during the decline and earn positive return. The relationship between the ideal fund’s rate of return and the market’s rate of return is given by the figure

The market return is given on the horizontal axis and the fund’s rate of return on the vertical axis. When the market rate of return increases, the fund’s rate of return increases more than proportional and vice-versa. In the figure the fund’s rate of return is 20 per cent when the market’s rate of return is 10 per cent, and when the market return is —10, the fund’s return is 10 per cent. The relationship between the market return and fund’s return is assumed to be linear.

This linear relationship is shown by the characteristic line. Each fund establishes a performance relationship with the market. The characteristic line can be drawn by plotting the fund’s rate of return for a given period against the market’s return for the same period. The slope of the line reflects the volatility of the fund’s return.

A steep slope would indicate that the fund is very sensitive to the market performance.

If the fund is not so sensitive then the slope would be a slope of less inclination.

All the funds have the same slope indicating same level of risk. The investor would prefer A fund, because it offers superior return than funds C and B for the same level of risk exposure. This is shown in (Figure)

With the help of the characteristic line Treynor measures the performance of the fund. The slope of the line is estimated by

Beta co-efficient is treated as a measure of undiversifiable systematic risk

Treynor’s risk premium of the portfolio is the difference between the average return and the riskless rate of return. The risk premium depends on the systematic risk assumed in a portfolio. Let us analyse to hypothetical funds.