Information Ratio, Tracking Error, and Treynor Ratio formulas

Sharpe (total volatility) vs Information Ratio (benchmark Tracking Error) vs Treynor (Beta)

The information ratio divides arithmetic mean benchmark-relative return by the sample standard deviation of those active returns. Treynor divides portfolio excess return over a risk-free rate by a supplied market beta. These ratios answer different questions.

The five rows are hypothetical annual returns measured on a consistent basis. The risk-free input is a comparable annual rate, and beta must be estimated against an appropriate market benchmark and horizon. Five observations do not establish manager skill; no universal performance ranking is inferred.

Column C makes each active-return observation explicit. For monthly observations, annualization requires additional assumptions; do not label the raw monthly ratio as annual. Active return here is not regression alpha.

Information Ratio (Active Return / Tracking Error) and Treynor Ratio formulas

Column C computes annual Active Return A_row - B_row (Portfolio minus Benchmark) for each year.

=IF(COUNT(C2:C6)<2,"Too few observations",IF(STDEV.S(C2:C6)=0,"Undefined zero tracking error",ROUND(AVERAGE(C2:C6) / STDEV.S(C2:C6), 4)))

Treynor Ratio (excess return over Risk-Free Rate E2 per unit of Beta F2)

The example restricts beta to positive values; zero is undefined and negative beta does not support the usual ranking interpretation. This is not a measure of total volatility.

=IF(OR(NOT(ISNUMBER(F2)),F2<=0),"Use positive beta",ROUND((AVERAGE(A2:A6) - E2) / F2, 4))

Further reading

• Microsoft Support — STDEV.S function
• CFA Institute — Sharpe ratio and information ratio