NxTreynor - Calculates the Treynor Ratio

Returns the Treynor ratio.

Syntax

NxTreynor($R_p$, $R_f$, Freq, $\beta$)

$R_p$

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

$R_f$

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.

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. 

$\beta$

is the portfolio's Capital Asset Pricing Model (CAPM) beta.

Remarks

1. The Treynor ratio is a performance metric for determining how much excess return was generated for each unit of risk taken by the portfolio.
2. The Treynor ratio is expressed as follows: $$\textrm{Treynor Ratio} = \frac{R_p-R_f}{\beta}$$ Where:
   • $R_p$ is the return of a given portfolio or strategy.
   • $R_f$ is the risk-free return.
   • $\beta$ is the CAPM Beta of the portfolio.
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.
4. The Treynor ratio measures how successful an investment is in compensating investors for taking on investment risk.
5. By definition, all values in the input data set (i.e., $R_p$) must be greater than -1.0.
6. The input data series may include missing values (e.g., #N/A, #VALUE!, #NUM!, empty cell) but 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.

Examples

Example 1:

Related Links

• Wikipedia - Treynor ratio
• Investopedia - Treynor 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