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Sharpe Ratio, Sortino Ratio, and Treynor Ratio
Sharpe Ratio
The Sharpe ratio measures how good an investment’s return is relative to the risk taken. It shows whether returns are earned because of smart investing or simply by taking excessive risk. The calculation removes the return of a risk-free investment (such as a UK Treasury bill) from the portfolio’s return and divides the result by the portfolio’s standard deviation.
Simple Example (Sharpe Ratio)
Sharpe ratio = (10% − 2%) ÷ 4% = 2
A higher Sharpe ratio means the investment is giving better returns for each unit of risk. A lower Sharpe ratio means the investor is taking more risk without sufficient compensation.
Sortino Ratio
The Sortino ratio is a modified version of the Sharpe ratio. It focuses only on downside risk and ignores positive volatility. Instead of using total standard deviation, it considers only returns that fall below a required or target return. This makes it more suitable for investors who are concerned only about losses.
Simple Example (Sortino Ratio)
Sortino ratio = (10% − 5%) ÷ 3% = 1.67
This ratio is useful when an investor wants to be rewarded for avoiding losses rather than penalised for positive price movements.
Treynor Ratio
The Treynor ratio measures return relative to systematic (market) risk, using beta instead of standard deviation. It evaluates whether an investor is being compensated for taking risk beyond the overall market risk.
Simple Example (Treynor Ratio)
Treynor ratio = (12% − 3%) ÷ 1.5 = 6
A higher Treynor ratio indicates better returns for the level of market risk taken.
Key Differences to Remember
Key Takeaway
Higher ratios are generally better, as they indicate more efficient risk-adjusted performance.
Sharpe Ratio, Sortino Ratio, and Treynor Ratio
Sharpe Ratio
The Sharpe ratio measures how good an investment’s return is relative to the risk taken. It shows whether returns are earned because of smart investing or simply by taking excessive risk. The calculation removes the return of a risk-free investment (such as a UK Treasury bill) from the portfolio’s return and divides the result by the portfolio’s standard deviation.
Simple Example (Sharpe Ratio)
- Portfolio return = 10%
- Risk-free return = 2%
- Standard deviation = 4%
Sharpe ratio = (10% − 2%) ÷ 4% = 2
A higher Sharpe ratio means the investment is giving better returns for each unit of risk. A lower Sharpe ratio means the investor is taking more risk without sufficient compensation.
Sortino Ratio
The Sortino ratio is a modified version of the Sharpe ratio. It focuses only on downside risk and ignores positive volatility. Instead of using total standard deviation, it considers only returns that fall below a required or target return. This makes it more suitable for investors who are concerned only about losses.
Simple Example (Sortino Ratio)
- Portfolio return = 10%
- Required return = 5%
- Downside deviation = 3%
Sortino ratio = (10% − 5%) ÷ 3% = 1.67
This ratio is useful when an investor wants to be rewarded for avoiding losses rather than penalised for positive price movements.
Treynor Ratio
The Treynor ratio measures return relative to systematic (market) risk, using beta instead of standard deviation. It evaluates whether an investor is being compensated for taking risk beyond the overall market risk.
Simple Example (Treynor Ratio)
- Portfolio return = 12%
- Risk-free return = 3%
- Portfolio beta = 1.5
Treynor ratio = (12% − 3%) ÷ 1.5 = 6
A higher Treynor ratio indicates better returns for the level of market risk taken.
Key Differences to Remember
- Sharpe ratio measures return per unit of total risk
- Sortino ratio measures return per unit of downside risk only
- Treynor ratio measures return per unit of market (systematic) risk
Key Takeaway
Higher ratios are generally better, as they indicate more efficient risk-adjusted performance.
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