Assets 1 and 2 have same return r1=r2 < rf , and sharpe ratios are SR1 > SR2 which has higher risk?
The Sharpe Ratio measures the excess return of an asset per unit of risk, where risk is typically defined as the volatility of returns. Since Asset 1 has a higher Sharpe Ratio, it means that it has a higher excess return per unit of risk compared to Asset 2, even though both assets have the same expected return. This implies that Asset 1 has a more efficient risk-return trade-off than Asset 2, and therefore, is considered less risky than Asset 2.
What is the Sharpe ratio?
SR:
Measures the risk-adjusted return of an investment
Calculates the excess return per unit of total risk (both systematic and unsystematic risk)
Considers both the expected return and the volatility of returns
A higher Sharpe Ratio indicates better risk-adjusted performance
Useful for evaluating investments with similar risk levels
What is the treynor ratio?
Calculates the excess return per unit of systematic risk (beta)
Considers only the expected return and the beta of the investment
A higher Treynor Ratio indicates better risk-adjusted performance
Useful for evaluating investments with different levels of systematic risk
Does the risk favoring effect of Sharpe/ Traynor ratio also apply to Differential return?
The risk-favoring effect of the Sharpe ratio and the Treynor ratio may not apply to differential return, as these metrics are designed to evaluate the risk-adjusted performance of a single investment, not the performance difference between two investments.
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