NxSharpe - Calculates the Sharpe Ratio

Returns the Sharpe ratio.

Syntax

NxSharpe(X,Freq, $R_f$)

X

is the portfolio's rate of returns data series (a one-dimensional array of cells (e.g., rows or columns)).

Freq

is the data sampling frequency per year (i.e., number of data points in one year) (e.g., 12 = monthly, 4 = quarterly, etc.). If missing, a monthly frequency is assumed.

$R_f$

is the risk-free simple returns data (a single value or a one-dimensional array of cells (e.g., rows or columns)). If missing, a zero (0) risk-free return is assumed.

Remarks

1. The shape ratio is the average return earned over the risk-free rate per volatility or total risk unit.
2. The Sharpe ratio is expressed as follows: $$\textrm{Sharpe Ratio} = \frac{R_p-R_f}{\sigma}$$ Where:
   • $R_p$ is the return of a given portfolio or strategy.
   • $R_f$ is the risk-free return.
   • $\sigma$ is the standard deviation or volatility of the portfolio excess return.
3. The risk-free rate of return is the return of an investment with zero risks, meaning it's the return investors could expect for taking no risk. The risk-free rate could be a U.S. Treasury rate or Yield, such as a one-month T-bill or T-note.
4. The Sharpe ratio can evaluate a portfolio’s past performance (ex-post) where actual returns are used in the formula and help explain whether a portfolio's excess returns are due to smart investment decisions or a result of too much risk.
5. By definition, all values in the input data set (i.e., X) must be greater than -1.0.
6. The input data series may include missing values (e.g., #N/A, #VALUE!, #NUM!, empty cell), but they will not be included in the calculations.
7. If the risk-free rate of return argument contains one value, it is assumed the value is the annual percentage risk-free rate of returns.
8. If the risk-free rate of return argument contains multiple values, their size must be equal to the size of X.

Examples

Example 1:

Related Links

• Wikipedia - Sharpe ratio
• Investopedia - Sharpe Ratio

References

• Hamilton, J .D.; Time Series Analysis, Princeton University Press (1994), ISBN 0-691-04289-6
• Tsay, Ruey S.; Analysis of Financial Time Series John Wiley & SONS. (2005), ISBN 0-471-690740