SQL Server RunningSHARPE Function

Updated 2024-03-14 15:26:45.167000

Description

Use the scalar function RunningSHARPE to calculate the Sharpe ratio from column values in an ordered resultant table without the need to a self-join. The Sharpe ratio is calculated over all the values from the first value to the last value in the ordered group or partition. If the column values are presented to the function out of order, an error message will be generated.

The Sharpe ratio is calculated using Sharpe's 1994 revision of his original formula and is calculated as the mean difference of the returns and risk-free rate divided by the standard deviation of the differences multiplied by the square root of a scaling factor. For daily returns the scale factor might be 252; for weekly returns 52; for monthly returns 12. For the sake of consistency, the risk-free rate should be in the same units as the scaling factor. The standard deviation is the sample standard deviation.

SHARPE=\ \frac{\bar{R}-\ \bar{R_f}}{\sigma_{R-R_f}}\ast\ \sqrt{scale}

Syntax

SELECT [westclintech].[wct].[RunningSHARPE](
  <@R, float,>
 ,<@Rf, float,>
 ,<@Scale, float,>
 ,<@Prices, bit,>
 ,<@RowNum, int,>
 ,<@Id, tinyint,>)

Arguments

@R

the return or price value; if return values are being supplied, it should the percentage return in floating point format (i.e. 10% = 0.1). @R is an expression of type float or of a type that can be implicitly converted to float.

@Rf

the risk-free rate. @Rf is an expression of type float or of a type that can be implicitly converted to float.

@Scale

the scaling factor used in the calculation. @Scale is an expression of type float or of a type that can be implicitly converted to float.

@Prices

a bit value identifying whether the supplied @R values are prices (or portfolio values) or returns. If @Prices is true, then the return is calculated. @Prices is an expression of type bit or of a type that can be implicitly converted to bit.

@RowNum

the number of the row within the group for which the Sharpe ratio is being calculated. If @RowNum for the current row in a set is less than or equal to the previous @RowNum and @RowNum is not equal to 1, an error message will be generated. @RowNum is an expression of type int or of a type that can be implicitly converted to int.

@Id

a unique identifier for the RunningSHARPE calculation. @Id allows you to specify multiple Sharpe ratios within a resultant table. @Id is an expression of type tinyint or of a type that can be implicitly converted to tinyint.

Return Type

float

Remarks

If @Scale IS NULL then @Scale is set to 12.

If @Prices IS NULL then @Prices is set to 'False'.

Examples

In this example we have 12 months' worth of return data for and we want to calculate the SHARPE ratio.

SELECT CAST(eom as date) as eom,
       cast(r as float) as r,
       Cast(rf as float) as rf
into #s
FROM
(
    VALUES
        ('2012-01-31', -0.0123631941629511, 0.010733),
        ('2012-02-29', 0.021547301457008, 0.008281),
        ('2012-03-31', 0.109883487344315, 0.009401),
        ('2012-04-30', -0.135203619909502, 0.009261),
        ('2012-05-31', 0.053578903306823, 0.007886),
        ('2012-06-30', -0.0701231624950338, 0.008206),
        ('2012-07-31', 0.100833155308695, 0.009777),
        ('2012-08-31', 0.0118377644090821, 0.011936),
        ('2012-09-30', -0.0176448024549291, 0.009263),
        ('2012-10-31', -0.0300663803201874, 0.008798),
        ('2012-11-30', -0.0853462157809984, 0.013932),
        ('2012-12-31', 0.143485915492958, 0.008757)
) n (eom, r, rf);
SELECT EOM,
       r,
       rf,
       wct.RunningSHARPE(   r,                                    --@R
                            rf / 12,                              --@Rf
                            12,                                   --@Scale
                            'False',                              --@Prices
                            ROW_NUMBER() OVER (ORDER BY eom ASC), --@RowNum
                            NULL                                  --@Id
                        ) as SHARPE
FROM #s;
DROP TABLE #s;

This produces the following result.

In this example we have 13 months' worth of price data for and we want to calculate the SHARPE ratio.

SELECT CAST(eom as date) as eom,
       cast(pr as float) as pr,
       cast(rf as float) as rf
into #s
FROM
(
    VALUES
        ('2011-12-31', 49.34, 0.011124),
        ('2012-01-31', 48.73, 0.010733),
        ('2012-02-29', 49.78, 0.008281),
        ('2012-03-31', 55.25, 0.009401),
        ('2012-04-30', 47.78, 0.009261),
        ('2012-05-31', 50.34, 0.007886),
        ('2012-06-30', 46.81, 0.008206),
        ('2012-07-31', 51.53, 0.009777),
        ('2012-08-31', 52.14, 0.011936),
        ('2012-09-30', 51.22, 0.009263),
        ('2012-10-31', 49.68, 0.008798),
        ('2012-11-30', 45.44, 0.013932),
        ('2012-12-31', 51.96, 0.008757)
) n (eom, pr, rf);
SELECT EOM,
       pr,
       rf,
       wct.RunningSHARPE(   pr,                                   --@R
                            rf / 12,                              --@Rf
                            12,                                   --@Scale
                            'True',                               --@Prices
                            ROW_NUMBER() OVER (ORDER BY eom ASC), --@RowNum
                            1                                     --@Id
                        ) as SHARPE
FROM #s;
DROP TABLE #s;

This produces the following result.

In this example we have 13 months' worth of price data for three different portfolios and we want to calculate the SHARPE ratio.

SELECT CAST(eom as date) as eom,
       aaa,
       bbb,
       ccc,
       rf
into #s
FROM
(
    VALUES
        ('2011-12-31', 74.58, 49.34, 54.97, 0.011124),
        ('2012-01-31', 75.17, 48.73, 56.07, 0.010733),
        ('2012-02-29', 74.61, 49.78, 54.66, 0.008281),
        ('2012-03-31', 74.69, 55.25, 55.39, 0.009401),
        ('2012-04-30', 75.6, 47.78, 57.4, 0.009261),
        ('2012-05-31', 75.53, 50.34, 54.92, 0.007886),
        ('2012-06-30', 75.41, 46.81, 55.12, 0.008206),
        ('2012-07-31', 75.83, 51.53, 55.56, 0.009777),
        ('2012-08-31', 74.58, 52.14, 54.24, 0.011936),
        ('2012-09-30', 74.77, 51.22, 57.41, 0.009263),
        ('2012-10-31', 74.33, 49.68, 55.76, 0.008798),
        ('2012-11-30', 75.06, 45.44, 56.28, 0.013932),
        ('2012-12-31', 75.25, 51.96, 53.19, 0.008757)
) n (eom, aaa, bbb, ccc, rf);
SELECT EOM,
       wct.RunningSHARPE(AAA, rf / 12, 12, 'True', ROW_NUMBER() OVER (ORDER BY eom 
                 ASC), 1) as AAA,
       wct.RunningSHARPE(BBB, rf / 12, 12, 'True', ROW_NUMBER() OVER (ORDER BY eom 
                 ASC), 2) as BBB,
       wct.RunningSHARPE(CCC, rf / 12, 12, 'True', ROW_NUMBER() OVER (ORDER BY eom 
                 ASC), 3) as CCC
FROM #s;
DROP TABLE #s;

This produces the following result.

In this example, we have the same data as in the previous example, except that is stored in 3^rd normal form rather than in the de-normalized form. The risk-free rate is included in the table with using the symbol RF. We use the PARTITION clause in order to generate the correct row number within a symbol.

SELECT CAST(eom as date) as eom,
       sym,
       CAST(pr as float) as pr
INTO #s
FROM
(
    VALUES
        ('2011-12-31', 'AAA', 74.58),
        ('2012-01-31', 'AAA', 75.17),
        ('2012-02-29', 'AAA', 74.61),
        ('2012-03-31', 'AAA', 74.69),
        ('2012-04-30', 'AAA', 75.6),
        ('2012-05-31', 'AAA', 75.53),
        ('2012-06-30', 'AAA', 75.41),
        ('2012-07-31', 'AAA', 75.83),
        ('2012-08-31', 'AAA', 74.58),
        ('2012-09-30', 'AAA', 74.77),
        ('2012-10-31', 'AAA', 74.33),
        ('2012-11-30', 'AAA', 75.06),
        ('2012-12-31', 'AAA', 75.25),
        ('2011-12-31', 'BBB', 49.34),
        ('2012-01-31', 'BBB', 48.73),
        ('2012-02-29', 'BBB', 49.78),
        ('2012-03-31', 'BBB', 55.25),
        ('2012-04-30', 'BBB', 47.78),
        ('2012-05-31', 'BBB', 50.34),
        ('2012-06-30', 'BBB', 46.81),
        ('2012-07-31', 'BBB', 51.53),
        ('2012-08-31', 'BBB', 52.14),
        ('2012-09-30', 'BBB', 51.22),
        ('2012-10-31', 'BBB', 49.68),
        ('2012-11-30', 'BBB', 45.44),
        ('2012-12-31', 'BBB', 51.96),
        ('2011-12-31', 'CCC', 54.97),
        ('2012-01-31', 'CCC', 56.07),
        ('2012-02-29', 'CCC', 54.66),
        ('2012-03-31', 'CCC', 55.39),
        ('2012-04-30', 'CCC', 57.4),
        ('2012-05-31', 'CCC', 54.92),
        ('2012-06-30', 'CCC', 55.12),
        ('2012-07-31', 'CCC', 55.56),
        ('2012-08-31', 'CCC', 54.24),
        ('2012-09-30', 'CCC', 57.41),
        ('2012-10-31', 'CCC', 55.76),
        ('2012-11-30', 'CCC', 56.28),
        ('2012-12-31', 'CCC', 53.19),
        ('2011-12-31', 'RF', 0.011124),
        ('2012-01-31', 'RF', 0.010733),
        ('2012-02-29', 'RF', 0.008281),
        ('2012-03-31', 'RF', 0.009401),
        ('2012-04-30', 'RF', 0.009261),
        ('2012-05-31', 'RF', 0.007886),
        ('2012-06-30', 'RF', 0.008206),
        ('2012-07-31', 'RF', 0.009777),
        ('2012-08-31', 'RF', 0.011936),
        ('2012-09-30', 'RF', 0.009263),
        ('2012-10-31', 'RF', 0.008798),
        ('2012-11-30', 'RF', 0.013932),
        ('2012-12-31', 'RF', 0.008757)
) n (eom, sym, pr);
SELECT s1.EOM,
       s1.sym,
       wct.RunningSHARPE(
                            s1.pr,
                            s2.pr / 12,
                            12,
                            'True',
                            ROW_NUMBER() OVER (PARTITION BY s1.SYM ORDER BY s1.sym,
                                      s1.eom ASC),
                            1
                        ) as SHARPE
FROM #s s1
    JOIN #s s2
        ON s1.eom = s2.eom
WHERE s1.sym <> 'RF'
      AND s2.sym = 'RF';
DROP TABLE #s;

This produces the following result.

Using the same data, we could PIVOT the results into a tabular format.

SELECT EOM,
       AAA,
       BBB,
       CCC
FROM
(
    SELECT s1.EOM,
           s1.sym,
           wct.RunningSHARPE(
                                s1.pr,
                                s2.pr / 12,
                                12,
                                'True',
                                ROW_NUMBER() OVER (PARTITION BY s1.SYM ORDER BY 
                                          s1.sym, s1.eom ASC),
                                1
                            ) as SHARPE
    FROM #s s1
        JOIN #s s2
            ON s1.eom = s2.eom
    WHERE s1.sym <> 'RF'
          AND s2.sym = 'RF'
) d
PIVOT
(
    sum(SHARPE)
    for sym in (AAA, BBB, CCC)
) as P;

This produces the following result.