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XLeratorDB/financial Documentation

SQL Server systematic risk of asset returns


SystematicRisk

Updated: 31 January 2016


Use the aggregate function SystematicRisk to calculate the Systematic Risk. Systematic Risk is calculated as:

Systematic Risk
Where

Ra
=
asset return
Rb
=
benchmark return
Rf
=
risk-free return
freq
=
periodicity of returns
s
=
sample standard deviation

Syntax
SELECT [wct].[SystematicRisk](
  <@Ra, float,>
 ,<@Rb, float,>
 ,<@Rf, float,>
 ,<@Freq, int,>)
Arguments
@Ra
the asset return for a period; the percentage return in floating point format (i.e. 10% = 0.10). @R is an expression of type float or of a type that can be implicitly converted to float.
@Rb
the benchmark return for a period; the percentage return in floating point format (i.e. 10% = 0.10). @R is an expression of type float or of a type that can be implicitly converted to float.
@Rf
the risk-free return for the period in floating point format (i.e. 10% = 0.10). @Rf is an expression of type float or of a type that can be implicitly converted to float.
@Freq
the period in which @Ra, @Rb, and @Rf are expressed. For example, a @Freq of 1 would indicate that the returns are annual; 4 would be quarterly, 12 would be monthly, and 252 would be business-daily. @Freq must be of a type int or of a type that implicitly converts to int.
Return Type
float
Remarks
·         If @Ra or @Rb IS NULL it is not included in the calculation.
·         If @Rf IS NULL it is set to zero.
·         If there are no non-NULL rows in a GROUP then NULL is returned.
·         @Freq must be greater than zero.
·         If @Freq IS NULL then @Freq is set to 12.
·         Available in XLeratorDB / financial 2008 only
Examples
In this example we have monthly returns for an asset, its benchmark, and risk-free returns for the last three years.
SELECT
   wct.SystematicRisk(Ra,Rb,Rf,12) as SystematicRisk
FROM (VALUES
   ('2012-12-31',0.001378,-0.003929,0.00142)
   ,('2013-01-31',0.028677,-0.001701,0.00075)
   ,('2013-02-28',0.005801,0.003165,0.001579)
   ,('2013-03-31',0.01442,-0.006487,0.00017)
   ,('2013-04-30',0.00229,-0.004653,0.001034)
   ,('2013-05-31',0.014905,0.009577,0.00071)
   ,('2013-06-30',0.008594,0.00588,0.000256)
   ,('2013-07-31',0.011531,0.005089,0.00101)
   ,('2013-08-31',0.008268,0.005233,0.001522)
   ,('2013-09-30',0.013993,-0.004338,0.001119)
   ,('2013-10-31',0.009147,-0.006109,0.001232)
   ,('2013-11-30',-0.00316,-0.002222,0.001374)
   ,('2013-12-31',-0.00595,0.005451,0.001406)
   ,('2014-01-31',0.013398,-0.008099,0.000624)
   ,('2014-02-28',0.002847,-0.000299,0.00164)
   ,('2014-03-31',-0.009544,-0.009809,0.001427)
   ,('2014-04-30',0.002516,0.008875,0.001618)
   ,('2014-05-31',0.004626,-0.002681,0.000937)
   ,('2014-06-30',-0.002141,0.000312,0.0008)
   ,('2014-07-31',0.009247,0.00936,0.001733)
   ,('2014-08-31',-0.01253,0.005434,0.000325)
   ,('2014-09-30',0.00441,0.008157,0.000535)
   ,('2014-10-31',0.01626,-0.006766,0.001325)
   ,('2014-11-30',0.013207,0.005742,0.001152)
   ,('2014-12-31',-0.008561,-0.005063,0.001246)
   ,('2015-01-31',0.012357,0.004357,0.000372)
   ,('2015-02-28',-0.002057,-0.00044,0.001045)
   ,('2015-03-31',0.008217,-0.004866,0.001419)
   ,('2015-04-30',-0.013439,-0.007649,0.001383)
   ,('2015-05-31',0.004391,-0.002073,0.000783)
   ,('2015-06-30',-0.008997,0.00399,0.0007)
   ,('2015-07-31',-0.001878,-0.00613,0.001188)
   ,('2015-08-31',-0.014381,-0.00351,0.000771)
   ,('2015-09-30',-0.001885,0.001172,0.000742)
   ,('2015-10-31',-0.001121,-0.000024,0.001119)
   ,('2015-11-30',0.000816,0.002596,0.001116)
   ,('2015-12-31',-0.003088,-0.009025,0.001332)
   )n(dt,Ra,Rb,Rf)

This produces the following result.


In this example we have the monthly returns for 6 managers plus a benchmark stored in the #managers table which is in 'spreadsheet' format. The minimum acceptable rate is 0.005.
SELECT
   *
INTO
   #managers
FROM (VALUES
   ('2012-12-31',-0.002546,NULL,NULL,0.003006,NULL,0.005007,-0.001839,0.00142)
   ,('2013-01-31',0.00977,NULL,NULL,0.001,NULL,-0.007579,0.008614,0.00075)
   ,('2013-02-28',0.024726,NULL,NULL,0.005703,NULL,0.006496,-0.004624,0.001579)
   ,('2013-03-31',0.000942,NULL,NULL,0.007578,NULL,0.008333,0.005031,0.00017)
   ,('2013-04-30',0.022139,NULL,NULL,0.007118,NULL,-0.007312,-0.005431,0.001034)
   ,('2013-05-31',0.019449,NULL,NULL,0.005659,NULL,-0.003902,-0.001878,0.00071)
   ,('2013-06-30',-0.007964,NULL,NULL,0.003757,NULL,-0.001899,-0.00706,0.000256)
   ,('2013-07-31',-0.008262,-0.002824,NULL,0.003762,NULL,-0.007347,-0.001982,0.00101)
   ,('2013-08-31',0.009617,0.007319,NULL,0.0022,NULL,-0.002116,0.003867,0.001522)
   ,('2013-09-30',-0.004118,0.004128,NULL,0.001394,NULL,0.008333,0.001356,0.001119)
   ,('2013-10-31',0.010754,-0.001578,NULL,0.003483,NULL,-0.004724,-0.001342,0.001232)
   ,('2013-11-30',0.002402,0.020835,NULL,0.001,NULL,0.003954,-0.000306,0.001374)
   ,('2013-12-31',0.004581,0.015689,NULL,0.002146,NULL,0.008333,0.001118,0.001406)
   ,('2014-01-31',-0.00055,-0.001027,-0.008245,0.00732,NULL,0.004025,-0.007227,0.000624)
   ,('2014-02-28',-0.001512,0.001653,-0.009029,0.009919,NULL,-0.008333,-0.003878,0.00164)
   ,('2014-03-31',0.008784,0.004364,-0.011608,0.001,NULL,-0.008333,-0.004822,0.001427)
   ,('2014-04-30',0.008412,-0.012369,-0.004692,0.004536,NULL,-0.006303,0.004306,0.001618)
   ,('2014-05-31',0.003945,0.010651,-0.016833,0.001,NULL,-0.007974,0.005221,0.000937)
   ,('2014-06-30',0.012371,0.01773,-0.010384,0.010593,NULL,-0.004781,-0.000731,0.0008)
   ,('2014-07-31',0.011915,0.004308,-0.012965,0.001,NULL,0.007751,-0.009239,0.001733)
   ,('2014-08-31',-0.013738,0.00039,0.000009,0.005139,0.001,-0.003319,-0.003636,0.000325)
   ,('2014-09-30',-0.004081,0.01968,-0.008214,0.007976,0.001,-0.003799,0.005563,0.000535)
   ,('2014-10-31',0.01608,0.015291,-0.002969,0.01303,0.001,-0.004645,0.001599,0.001325)
   ,('2014-11-30',0.011241,0.012312,0.007088,0.00384,0.000852,0.006783,-0.008487,0.001152)
   ,('2014-12-31',-0.004251,0.008737,-0.013576,0.001,0.001,-0.0034,0.001013,0.001246)
   ,('2015-01-31',-0.004039,0.012938,-0.011891,0.004576,0.001,-0.004195,-0.002653,0.000372)
   ,('2015-02-28',0.026326,0.019695,-0.013178,0.010737,0.001,0.006418,-0.00952,0.001045)
   ,('2015-03-31',-0.000628,0.008029,0.005917,0.017461,0.00048,-0.00501,0.007879,0.001419)
   ,('2015-04-30',0.005688,0.01249,-0.018813,0.001,-0.002104,0.003657,0.009886,0.001383)
   ,('2015-05-31',0.010039,0.008442,-0.01465,0.001,0.001,0.001024,0.001695,0.000783)
   ,('2015-06-30',-0.004267,0.001391,-0.022504,0.003104,0.001,-0.003507,0.009854,0.0007)
   ,('2015-07-31',-0.001672,0.020558,-0.011859,0.001,0.001,NULL,0.008361,0.001188)
   ,('2015-08-31',0.015726,0.017419,-0.004556,0.001,-0.000462,NULL,-0.007253,0.000771)
   ,('2015-09-30',0.001977,0.007301,-0.00811,0.013011,-0.001032,NULL,0.009911,0.000742)
   ,('2015-10-31',0.016201,0.00877,-0.005536,0.014527,-0.000833,NULL,0.009897,0.001119)
   ,('2015-11-30',0.019996,-0.000785,-0.002161,0.001947,0.001,NULL,-0.007307,0.001116)
   ,('2015-12-31',-0.003254,0.009595,-0.013785,0.001,0.001,NULL,0.007196,0.001332)
   )n(dt,man1,man2,man3,man4,man5,man6,bmark,rf)


To calculate the systematic risk for each manager we run the following SQL.
SELECT
       wct.SystematicRisk(man1,bmark,rf,12) as man1
       ,wct.SystematicRisk(man2,bmark,rf,12) as man2
       ,wct.SystematicRisk(man3,bmark,rf,12) as man3  
       ,wct.SystematicRisk(man4,bmark,rf,12) as man4  
       ,wct.SystematicRisk(man5,bmark,rf,12) as man5  
       ,wct.SystematicRisk(man6,bmark,rf,12) as man6
FROM
       #managers

This produces the following result.


Using the same data from the previous example in the #nmanagers table which is in 3rd normal form we perform the same calculation.
SELECT
   *
INTO
   #nmanagers
FROM (VALUES
    ('2012-12-31','man1',-0.002546)
   ,('2012-12-31','man4',0.003006)
   ,('2012-12-31','man6',0.005007)
   ,('2012-12-31','bmark',-0.001839)
   ,('2012-12-31','rf',0.001420)
   ,('2013-01-31','man1',0.009770)
   ,('2013-01-31','man4',0.001000)
   ,('2013-01-31','man6',-0.007579)
   ,('2013-01-31','bmark',0.008614)
   ,('2013-01-31','rf',0.000750)
   ,('2013-02-28','man1',0.024726)
   ,('2013-02-28','man4',0.005703)
   ,('2013-02-28','man6',0.006496)
   ,('2013-02-28','bmark',-0.004624)
   ,('2013-02-28','rf',0.001579)
   ,('2013-03-31','man1',0.000942)
   ,('2013-03-31','man4',0.007578)
   ,('2013-03-31','man6',0.008333)
   ,('2013-03-31','bmark',0.005031)
   ,('2013-03-31','rf',0.000170)
   ,('2013-04-30','man1',0.022139)
   ,('2013-04-30','man4',0.007118)
   ,('2013-04-30','man6',-0.007312)
   ,('2013-04-30','bmark',-0.005431)
   ,('2013-04-30','rf',0.001034)
   ,('2013-05-31','man1',0.019449)
   ,('2013-05-31','man4',0.005659)
   ,('2013-05-31','man6',-0.003902)
   ,('2013-05-31','bmark',-0.001878)
   ,('2013-05-31','rf',0.000710)
   ,('2013-06-30','man1',-0.007964)
   ,('2013-06-30','man4',0.003757)
   ,('2013-06-30','man6',-0.001899)
   ,('2013-06-30','bmark',-0.007060)
   ,('2013-06-30','rf',0.000256)
   ,('2013-07-31','man1',-0.008262)
   ,('2013-07-31','man2',-0.002824)
   ,('2013-07-31','man4',0.003762)
   ,('2013-07-31','man6',-0.007347)
   ,('2013-07-31','bmark',-0.001982)
   ,('2013-07-31','rf',0.001010)
   ,('2013-08-31','man1',0.009617)
   ,('2013-08-31','man2',0.007319)
   ,('2013-08-31','man4',0.002200)
   ,('2013-08-31','man6',-0.002116)
   ,('2013-08-31','bmark',0.003867)
   ,('2013-08-31','rf',0.001522)
   ,('2013-09-30','man1',-0.004118)
   ,('2013-09-30','man2',0.004128)
   ,('2013-09-30','man4',0.001394)
   ,('2013-09-30','man6',0.008333)
   ,('2013-09-30','bmark',0.001356)
   ,('2013-09-30','rf',0.001119)
   ,('2013-10-31','man1',0.010754)
   ,('2013-10-31','man2',-0.001578)
   ,('2013-10-31','man4',0.003483)
   ,('2013-10-31','man6',-0.004724)
   ,('2013-10-31','bmark',-0.001342)
   ,('2013-10-31','rf',0.001232)
   ,('2013-11-30','man1',0.002402)
   ,('2013-11-30','man2',0.020835)
   ,('2013-11-30','man4',0.001000)
   ,('2013-11-30','man6',0.003954)
   ,('2013-11-30','bmark',-0.000306)
   ,('2013-11-30','rf',0.001374)
   ,('2013-12-31','man1',0.004581)
   ,('2013-12-31','man2',0.015689)
   ,('2013-12-31','man4',0.002146)
   ,('2013-12-31','man6',0.008333)
   ,('2013-12-31','bmark',0.001118)
   ,('2013-12-31','rf',0.001406)
   ,('2014-01-31','man1',-0.000550)
   ,('2014-01-31','man2',-0.001027)
   ,('2014-01-31','man3',-0.008245)
   ,('2014-01-31','man4',0.007320)
   ,('2014-01-31','man6',0.004025)
   ,('2014-01-31','bmark',-0.007227)
   ,('2014-01-31','rf',0.000624)
   ,('2014-02-28','man1',-0.001512)
   ,('2014-02-28','man2',0.001653)
   ,('2014-02-28','man3',-0.009029)
   ,('2014-02-28','man4',0.009919)
   ,('2014-02-28','man6',-0.008333)
   ,('2014-02-28','bmark',-0.003878)
   ,('2014-02-28','rf',0.001640)
   ,('2014-03-31','man1',0.008784)
   ,('2014-03-31','man2',0.004364)
   ,('2014-03-31','man3',-0.011608)
   ,('2014-03-31','man4',0.001000)
   ,('2014-03-31','man6',-0.008333)
   ,('2014-03-31','bmark',-0.004822)
   ,('2014-03-31','rf',0.001427)
   ,('2014-04-30','man1',0.008412)
   ,('2014-04-30','man2',-0.012369)
   ,('2014-04-30','man3',-0.004692)
   ,('2014-04-30','man4',0.004536)
   ,('2014-04-30','man6',-0.006303)
   ,('2014-04-30','bmark',0.004306)
   ,('2014-04-30','rf',0.001618)
   ,('2014-05-31','man1',0.003945)
   ,('2014-05-31','man2',0.010651)
   ,('2014-05-31','man3',-0.016833)
   ,('2014-05-31','man4',0.001000)
   ,('2014-05-31','man6',-0.007974)
   ,('2014-05-31','bmark',0.005221)
   ,('2014-05-31','rf',0.000937)
   ,('2014-06-30','man1',0.012371)
   ,('2014-06-30','man2',0.017730)
   ,('2014-06-30','man3',-0.010384)
   ,('2014-06-30','man4',0.010593)
   ,('2014-06-30','man6',-0.004781)
   ,('2014-06-30','bmark',-0.000731)
   ,('2014-06-30','rf',0.000800)
   ,('2014-07-31','man1',0.011915)
   ,('2014-07-31','man2',0.004308)
   ,('2014-07-31','man3',-0.012965)
   ,('2014-07-31','man4',0.001000)
   ,('2014-07-31','man6',0.007751)
   ,('2014-07-31','bmark',-0.009239)
   ,('2014-07-31','rf',0.001733)
   ,('2014-08-31','man1',-0.013738)
   ,('2014-08-31','man2',0.000390)
   ,('2014-08-31','man3',0.000009)
   ,('2014-08-31','man4',0.005139)
   ,('2014-08-31','man5',0.001000)
   ,('2014-08-31','man6',-0.003319)
   ,('2014-08-31','bmark',-0.003636)
   ,('2014-08-31','rf',0.000325)
   ,('2014-09-30','man1',-0.004081)
   ,('2014-09-30','man2',0.019680)
   ,('2014-09-30','man3',-0.008214)
   ,('2014-09-30','man4',0.007976)
   ,('2014-09-30','man5',0.001000)
   ,('2014-09-30','man6',-0.003799)
   ,('2014-09-30','bmark',0.005563)
   ,('2014-09-30','rf',0.000535)
   ,('2014-10-31','man1',0.016080)
   ,('2014-10-31','man2',0.015291)
   ,('2014-10-31','man3',-0.002969)
   ,('2014-10-31','man4',0.013030)
   ,('2014-10-31','man5',0.001000)
   ,('2014-10-31','man6',-0.004645)
   ,('2014-10-31','bmark',0.001599)
   ,('2014-10-31','rf',0.001325)
   ,('2014-11-30','man1',0.011241)
   ,('2014-11-30','man2',0.012312)
   ,('2014-11-30','man3',0.007088)
   ,('2014-11-30','man4',0.003840)
   ,('2014-11-30','man5',0.000852)
   ,('2014-11-30','man6',0.006783)
   ,('2014-11-30','bmark',-0.008487)
   ,('2014-11-30','rf',0.001152)
   ,('2014-12-31','man1',-0.004251)
   ,('2014-12-31','man2',0.008737)
   ,('2014-12-31','man3',-0.013576)
   ,('2014-12-31','man4',0.001000)
   ,('2014-12-31','man5',0.001000)
   ,('2014-12-31','man6',-0.003400)
   ,('2014-12-31','bmark',0.001013)
   ,('2014-12-31','rf',0.001246)
   ,('2015-01-31','man1',-0.004039)
   ,('2015-01-31','man2',0.012938)
   ,('2015-01-31','man3',-0.011891)
   ,('2015-01-31','man4',0.004576)
   ,('2015-01-31','man5',0.001000)
   ,('2015-01-31','man6',-0.004195)
   ,('2015-01-31','bmark',-0.002653)
   ,('2015-01-31','rf',0.000372)
   ,('2015-02-28','man1',0.026326)
   ,('2015-02-28','man2',0.019695)
   ,('2015-02-28','man3',-0.013178)
   ,('2015-02-28','man4',0.010737)
   ,('2015-02-28','man5',0.001000)
   ,('2015-02-28','man6',0.006418)
   ,('2015-02-28','bmark',-0.009520)
   ,('2015-02-28','rf',0.001045)
   ,('2015-03-31','man1',-0.000628)
   ,('2015-03-31','man2',0.008029)
   ,('2015-03-31','man3',0.005917)
   ,('2015-03-31','man4',0.017461)
   ,('2015-03-31','man5',0.000480)
   ,('2015-03-31','man6',-0.005010)
   ,('2015-03-31','bmark',0.007879)
   ,('2015-03-31','rf',0.001419)
   ,('2015-04-30','man1',0.005688)
   ,('2015-04-30','man2',0.012490)
   ,('2015-04-30','man3',-0.018813)
   ,('2015-04-30','man4',0.001000)
   ,('2015-04-30','man5',-0.002104)
   ,('2015-04-30','man6',0.003657)
   ,('2015-04-30','bmark',0.009886)
   ,('2015-04-30','rf',0.001383)
   ,('2015-05-31','man1',0.010039)
   ,('2015-05-31','man2',0.008442)
   ,('2015-05-31','man3',-0.014650)
   ,('2015-05-31','man4',0.001000)
   ,('2015-05-31','man5',0.001000)
   ,('2015-05-31','man6',0.001024)
   ,('2015-05-31','bmark',0.001695)
   ,('2015-05-31','rf',0.000783)
   ,('2015-06-30','man1',-0.004267)
   ,('2015-06-30','man2',0.001391)
   ,('2015-06-30','man3',-0.022504)
   ,('2015-06-30','man4',0.003104)
   ,('2015-06-30','man5',0.001000)
   ,('2015-06-30','man6',-0.003507)
   ,('2015-06-30','bmark',0.009854)
   ,('2015-06-30','rf',0.000700)
   ,('2015-07-31','man1',-0.001672)
   ,('2015-07-31','man2',0.020558)
   ,('2015-07-31','man3',-0.011859)
   ,('2015-07-31','man4',0.001000)
   ,('2015-07-31','man5',0.001000)
   ,('2015-07-31','bmark',0.008361)
   ,('2015-07-31','rf',0.001188)
   ,('2015-08-31','man1',0.015726)
   ,('2015-08-31','man2',0.017419)
   ,('2015-08-31','man3',-0.004556)
   ,('2015-08-31','man4',0.001000)
   ,('2015-08-31','man5',-0.000462)
   ,('2015-08-31','bmark',-0.007253)
   ,('2015-08-31','rf',0.000771)
   ,('2015-09-30','man1',0.001977)
   ,('2015-09-30','man2',0.007301)
   ,('2015-09-30','man3',-0.008110)
   ,('2015-09-30','man4',0.013011)
   ,('2015-09-30','man5',-0.001032)
   ,('2015-09-30','bmark',0.009911)
   ,('2015-09-30','rf',0.000742)
   ,('2015-10-31','man1',0.016201)
   ,('2015-10-31','man2',0.008770)
   ,('2015-10-31','man3',-0.005536)
   ,('2015-10-31','man4',0.014527)
   ,('2015-10-31','man5',-0.000833)
   ,('2015-10-31','bmark',0.009897)
   ,('2015-10-31','rf',0.001119)
   ,('2015-11-30','man1',0.019996)
   ,('2015-11-30','man2',-0.000785)
   ,('2015-11-30','man3',-0.002161)
   ,('2015-11-30','man4',0.001947)
   ,('2015-11-30','man5',0.001000)
   ,('2015-11-30','bmark',-0.007307)
   ,('2015-11-30','rf',0.001116)
   ,('2015-12-31','man1',-0.003254)
   ,('2015-12-31','man2',0.009595)
   ,('2015-12-31','man3',-0.013785)
   ,('2015-12-31','man4',0.001000)
   ,('2015-12-31','man5',0.001000)
   ,('2015-12-31','bmark',0.007196)
   ,('2015-12-31','rf',0.001332)
)n(dt,man,R)
SELECT
    m.man as manager
   ,wct.SystematicRisk(m.r, b.r,rf.r,12) as SystematicRisk
FROM
   #nmanagers m
INNER JOIN
   #nmanagers b
ON
   m.dt = b.dt
INNER JOIN
   #nmanagers rf
ON
   m.dt = rf.dt
WHERE
   m.man <> 'bmark' AND m.man <> 'rf'
   AND b.man = 'bmark'
   AND rf.man = 'rf'
GROUP BY
   m.man
 
This produces the following result.

 

See Also

 



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