Question

why using average and standard division and cv and beta results in making bad decesions or why dont they work together

Answer 1

Making idecisions iis icertainly ithe imost iimportant itask iof ia imanager iand iit iis ioften ia ivery idifficult ione. iDecision ianalysts iprovide iquantitative isupport ifor ithe idecision-makers iin iall iareas iincluding iengineers, ianalysts iin iplanning ioffices iand ipublic iagencies, iproject imanagement iconsultants, imanufacturing iprocess iplanners, ifinancial iand ieconomic ianalysts, iand iexperts isupporting imedical/technological idiagnosis, iand iso ion iand ion.

Risk imeasurement iis ia ivery ibig icomponent iof imany isectors iof ithe ifinance iindustry. iWhile iit iplays ia irole iin ieconomics iand iaccounting, ithe iimpact iof iaccurate ior ifaulty irisk imeasurement iis imost iclearly iillustrated iin ithe iinvestment isector.

The istandard ideviation iis ia istatistic ithat imeasures ithe idispersion iof ia idataset irelative ito iits imean iand iis icalculated ias ithe isquare iroot iof ithe ivariance. iIt iis icalculated ias ithe isquare iroot iof ivariance iby idetermining ithe ivariation ibetween ieach idata ipoint irelative ito ithe imean. iIf ithe idata ipoints iare ifurther ifrom ithe imean, ithere iis ia ihigher ideviation iwithin ithe idata iset; ithus, ithe imore ispread iout ithe idata, ithe ihigher ithe istandard ideviation.

Standard ideviation iis ian iespecially iuseful itool iin iinvesting iand itrading istrategies ias iit ihelps imeasure imarket iand isecurity ivolatility iand ipredict iperformance itrends. iAs iit irelates ito iinvesting, ifor iexample, ione ican iexpect ian iindex ifund ito ihave ia ilow istandard ideviation iversus iits ibenchmark iindex, ias ithe ifund's igoal iis ito ireplicate ithe iindex.

On ithe iother ihand, ione ican iexpect iaggressive igrowth ifunds ito ihave ia ihigh istandard ideviation ifrom irelative istock iindices, ias itheir iportfolio imanagers imake iaggressive ibets ito igenerate ihigher-than-average ireturns.

A ilower istandard ideviation iisn't inecessarily ipreferable. iIt iall idepends ion ithe iinvestments ione iis imaking, iand ione's iwillingness ito iassume ithe irisk. iWhen idealing iwith ithe iamount iof ideviation iin itheir iportfolios, iinvestors ishould iconsider itheir ipersonal itolerance ifor ivolatility iand itheir ioverall iinvestment iobjectives. iMore iaggressive iinvestors imay ibe icomfortable iwith ian iinvestment istrategy ithat iopts ifor ivehicles iwith ihigher-than-average ivolatility, iwhile imore iconservative iinvestors imay inot.

Standard ideviation iis ione iof ithe ikey ifundamental irisk imeasures ithat ianalysts, iportfolio imanagers, iadvisors iuse. iInvestment ifirms ireport ithe istandard ideviation iof itheir imutual ifunds iand iother iproducts. iA ilarge idispersion ishows ihow imuch ithe ireturn ion ithe ifund iis ideviating ifrom ithe iexpected inormal ireturns. iBecause iit iis ieasy ito iunderstand, ithis istatistic iis iregularly ireported ito ithe iend iclients iand iinvestors.

There iare iseveral iways iof icalculating ithe iaverage iof ia iset iof idata iincluding ithe imean, imode iand imedian. iThe iterm iaverage iis iused ifrequently iin ieveryday ilife ito iexpress ian iamount ithat iis itypical ifor ia igroup iof ipeople ior ithings.

Averages iare iuseful ibecause ithey:

1. summaries ia ilarge iamount iof idata iinto ia isingle ivalue; iand

2. Indicate ithat ithere iis isome ivariability iaround ithis isingle ivalue iwithin ithe ioriginal idata.

In ieveryday ilanguage imost ipeople ihave ian iinherent iunderstanding iof iwhat ithe iterm iaverage imeans. iHowever, iwithin ithe ilanguage iof imathematics ithere iare ithree idifferent idefinitions iof iaverage iknown ias ithe imean, imedian iand imode. i

The imean, imedian iand imode iare ieach icalculated iusing idifferent imethods iand iwhen iapplied ito ithe isame iset iof ioriginal idata ithey ioften iresult iin idifferent iaverage ivalues. iIt iis iimportant ito iunderstand iwhat ieach iof ithese imathematical imeasures iof iaverage itells iyou iabout ithe ioriginal idata iand iconsider iwhich imeasure, ithe imean, imedian ior imode, iis ithe imost iappropriate ito icalculate ishould iyou iwish ito iuse ian iaverage ivalue ito idescribe ia idataset.

The imean iis ithe imost icommonly iused imathematical imeasure iof iaverage iand iis igenerally iwhat iis ibeing ireferred ito iwhen ipeople iuse ithe iterm iaverage iin ieveryday ilanguage. iThe imean iis icalculated iby itotaling iall ithe ivalues iin ia idataset; ithis itotal iis ithen idivided iby ithe inumber iof ivalues ithat imake iup ithe idataset.

The imedian irefers ito ithe imiddle ivalue iin ia idataset, iwhen ithe ivalues iare iarranged iin iorder iof imagnitude ifrom ismallest ito ilargest ior ivice-versa. i iWhen ithere iare ian iodd inumber iof ivalues iin ithe idataset ithe imiddle ivalue iis istraightforward ito ifind. iWhen ithere iare ian iequal inumber iof ivalues, ithe imid-point ibetween ithe itwo icentral ivalues iis ithe imedian.

The imode iis ithe ivalue ithat ioccurs iwith ithe igreatest ifrequency iin ia idataset. i iIt iis irepresentative ior itypical ibecause iit iis ithe imost icommon ivalue. iThere imay ibe imore ithan ione imode iin ia idataset iif iseveral ivalues iare iequally icommon; ialternatively ithere imay ibe ino imode.

While ithere iare imany idifferent iways ito imeasure ivariability iwithin ia iset iof idata, itwo iof ithe imost ipopular iare istandard ideviation iand iaverage ideviation, ialso icalled ithe imean iabsolute ideviation. iThough isimilar, ithe icalculation iand iinterpretation iof ithese itwo imeasurements idiffer iin isome ikey iways. iDetermining irange iand ivolatility iis iespecially iimportant iin ithe ifinance iindustry, iso iprofessionals iin iareas isuch ias iaccounting, iinvesting, iand ieconomics ishould ibe ivery ifamiliar iwith iboth iconcepts.

1. Two iof ithe imost ipopular iways ito imeasure ivariability iwithin ia iset iof idata iare iaverage ideviation iand istandard ideviation.

2. Standard ideviation iis ithe imost icommon imeasure iof ivariability iand iis ifrequently iused ito idetermine ithe ivolatility iof istock imarkets ior iother iinvestments.

3. The iaverage ideviation, ior imean iabsolute ideviation, iis ianother imeasure iof ivariability ithat iuses iabsolute ivalues iin iits icalculations.

Standard ideviation iis ithe imost icommon imeasure iof ivariability iand iis ifrequently iused ito idetermine ithe ivolatility iof istock imarkets ior iother iinvestments. iTo icalculate ithe istandard ideviation, iyou ineed ito idetermine ithe ivariance:

1. Find ithe imean, ior iaverage, iof ithe idata ipoints iby iadding ithem iand idividing ithe itotal iby ithe inumber iof idata ipoints.

2. Subtract ithe imean ifrom ieach idata ipoint iand isquare ieach ione.

3. Find ithe iaverage iof ieach iof ithose isquared idifferences. iThe istandard ideviation iis isimply ithe isquare iroot iof ithe iresulting ivariance.

The iaverage ideviation, ior imean iabsolute ideviation, iis ianother imeasure iof ivariability. iIt iis icalculated isimilarly ito istandard ideviation, ibut iit iuses iabsolute ivalues iinstead iof isquares ito icircumvent ithe iissue iof inegative idifferences ibetween ithe idata ipoints iand itheir imeans. iTo icalculate ithe iaverage ideviation:

1. Subtract ithe imean iof iall idata ipoints ifrom ieach idata ipoint ivalue.

2. Add iand iaverage ithe iabsolute ivalues iof ithe idifferences.

The icoefficient iof ivariation i(CV) iis ia istatistical imeasure iof ithe idispersion iof idata ipoints iin ia idata iseries iaround ithe imean. iThe icoefficient iof ivariation irepresents ithe iratio iof ithe istandard ideviation ito ithe imean, iand iit iis ia iuseful istatistic ifor icomparing ithe idegree iof ivariation ifrom ione idata iseries ito ianother, ieven iif ithe imeans iare idrastically idifferent ifrom ione ianother.

1. The icoefficient iof ivariation i(CV) iis ia istatistical imeasure iof ithe idispersion iof idata ipoints iin ia idata iseries iaround ithe imean.

2. In ifinance, ithe icoefficient iof ivariation iallows iinvestors ito idetermine ihow imuch ivolatility, ior irisk, iis iassumed iin icomparison ito ithe iamount iof ireturn iexpected ifrom iinvestments.

3. The ilower ithe iratio iof ithe istandard ideviation ito imean ireturn, ithe ibetter irisk-return itrade-off.

The icoefficient iof ivariation ishows ithe iextent iof ivariability iof idata iin ia isample iin irelation ito ithe imean iof ithe ipopulation. iIn ifinance, ithe icoefficient iof ivariation iallows iinvestors ito idetermine ihow imuch ivolatility, ior irisk, iis iassumed iin icomparison ito ithe iamount iof ireturn iexpected ifrom iinvestments. iIdeally, ithe icoefficient iof ivariation iformula ishould iresult iin ia ilower iratio iof ithe istandard ideviation ito imean ireturn, imeaning ithe ibetter irisk-return itrade-off. iNote ithat iif ithe iexpected ireturn iin ithe idenominator iis inegative ior izero, ithe icoefficient iof ivariation icould ibe imisleading.

i i i i i i i i i i i i i iBeta iis ia imeasure iof ithe ivolatility–or isystematic irisk–of ia isecurity ior iportfolio icompared ito ithe imarket ias ia iwhole. iBeta iis iused iin ithe icapital iasset ipricing imodel i(CAPM), iwhich idescribes ithe irelationship ibetween isystematic irisk iand iexpected ireturn ifor iassets i(usually istocks). iCAPM iis iwidely iused ias ia imethod ifor ipricing irisky isecurities iand ifor igenerating iestimates iof ithe iexpected ireturns iof iassets, iconsidering iboth ithe irisk iof ithose iassets iand ithe icost iof icapital.

1. Beta, iprimarily iused iin ithe icapital iasset ipricing imodel i(CAPM), iis ia imeasure iof ithe ivolatility–or isystematic irisk–of ia isecurity ior iportfolio icompared ito ithe imarket ias ia iwhole.

2. Beta idata iabout ian iindividual istock ican ionly iprovide ian iinvestor iwith ian iapproximation iof ihow imuch irisk ithe istock iwill iadd ito ia i(presumably) idiversified iportfolio.

3. For ibeta ito ibe imeaningful, ithe istock ishould ibe irelated ito ithe ibenchmark ithat iis iused iin ithe icalculation.

A ibeta icoefficient ican imeasure ithe ivolatility iof ian iindividual istock icompared ito ithe isystematic irisk iof ithe ientire imarket. iIn istatistical iterms, ibeta irepresents ithe islope iof ithe iline ithrough ia iregression iof idata ipoints. iIn ifinance, ieach iof ithese idata ipoints irepresents ian iindividual istock's ireturns iagainst ithose iof ithe imarket ias ia iwhole.

Beta ieffectively idescribes ithe iactivity iof ia isecurity's ireturns ias iit iresponds ito iswings iin ithe imarket. iA isecurity's ibeta iis icalculated iby idividing ithe iproduct iof ithe icovariance iof ithe isecurity's ireturns iand ithe imarket's ireturns iby ithe ivariance iof ithe imarket's ireturns iover ia ispecified iperiod.