Market Sense and Nonsense: How the Markets Really Work (and How They Don't)

Appendix B

Formulas for Risk-Adjusted Return Measures

This appendix provides the formulas for the performance measures described in Chapter 8.

Sharpe Ratio

where:

SR = Sharpe ratio

AR = Average return (used as proxy for expected return)

RF = Risk-free interest rate (e.g., Treasury bill return)

SD = Standard deviation

The standard deviation is calculated as follows:

where:

= Mean

Xi = Individual returns

N = Number of returns

Assuming monthly data is used to calculate the Sharpe ratio, as is most common, the Sharpe ratio would be annualized by multiplying by the square root of 12. Note that the return is an arithmetic average return, not the compounded return.

Sortino Ratio

where:

SR = Sortino ratio

ACR = Annual compounded return

MAR = Minimum acceptable return (e.g., zero, risk-free, average)

DD = Downside deviation

where DD is defined as:

where:

Xi = Individual returns

MAR = Minimum acceptable return (e.g., zero, risk-free, average)

N = Number of data values

For example, if we define ...