Sharpe and Treynor Ratios on Treasury Bonds

Sharpe (1966) introduces the reward-to-variability ratio, more commonly referred to as the Sharpe index, Sharpe measure, or Sharpe ratio. For consistency of usage, we use the term Sharpe ratio in this paper. For any risky asset or portfolio of assets, the Sharpe ratio is defined as the ratio of the excess return to the standard deviation of that return. Treynor (1965) provides an alternative reward-to-risk ratio. The Treynor ratio is the ratio of the excess return to the systematic risk of that return. Both the Sharpe and Treynor ratios can be based on either ex ante or ex post excess returns and standard deviations (see Sharpe 1994). Ex post ratios are most useful for evaluating past investment performance. To the extent that historical results have predictive ability, ex post ratios are also useful for making decisions about future portfolio allocations. However, for decision-making purposes ex ante ratios are preferred.