Returns the Jensen's alpha measure in annual percentage rate (APR).
Syntax
NxJensen($R^i$,$R^b$, $R_f$, Freq)
 $R^i$
 is the portfolio simple rate of returns data series (a onedimensional array of cells (e.g., rows or columns)).
 $R^b$
 is the index/benchmark simple returns data (a onedimensional array of cells (e.g., rows or columns)).
 $R_f$
 is the riskfree simple returns data (a single value or a onedimensional array of cells (e.g., rows or columns)). If missing, a zero (0) riskfree 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.
Status
The NxJensen function is available starting with NumXL version 1.68 CAMEL.
Remarks
 In finance, Jensen's alpha (or Jensen's Performance Index, expost alpha) determines the abnormal return of a security or portfolio of securities over the theoretical expected return.
 The Capital Asset Pricing Model (CAPM) describes the relationship between systematic risk and expected return for assets.
 Per the CAPM, the formula for calculating the expected return of an asset is:
$$E[R^i] = R_f + \beta \times (E[R^b]  R_f) $$
Where: $E[R^i]$ is the expected return on investment.
 $R_f$ is the riskfree rate of return.
 $E[R^b]$ is the expected return on the overall market.
 $\beta$ is the CAPM beta of the investment.
 Jensen's alpha is a riskadjusted performance measure representing the average return on a portfolio or investment, above or below that predicted by the CAPM, given the portfolio's or investment's beta and the average market return.
 Jensen's alpha accounts for the riskfree rate of return.
 By definition, all values in the input data set (i.e., X) must be greater than 1.
 The input data series may include missing values (e.g., #N/A, #VALUE!, #NUM!, empty cell) but will not be included in the calculations.
 The sample data ($R^i$, $R^b$, or $R_f$) may include missing values.
 The number of rows of the response variable ($R^i$) must equal the number of rows of the explanatory variable ($R^b$ or $R_f$).
 Observations (i.e., rows) with missing values in $R^i$, $R^b$, or $R_f$ are removed.
 If the riskfree rate of return ($R_f$) argument contains one value, it is assumed the value is the riskfree annual rate of return.
 If the riskfree rate or return argument ($R_f$) contains multiple values (i.e., array), its size must be equal to the size of the portfolio return ($R^i$).
Examples
Example 1:


Formula  Description (Result) 

=NxJensen(\$B\$2:\$B\$14,\$C\$2:\$C\$14,\$D\$2:\$D\$14,12)  Jensen Alpha (0.129528) 
Files Examples
Related Links
References
 Hamilton, J .D.; Time Series Analysis, Princeton University Press (1994), ISBN 0691042896
 Tsay, Ruey S.; Analysis of Financial Time Series John Wiley & SONS. (2005), ISBN 0471690740
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