risk metrics 2

8/10/2019 Risk Metrics 2

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RISKMETRICS

Dr Philip Symes


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1. Introduction

RiskMetrics is JP Morgan's risk managementmethodology. It as released in 1!!"

This as to standardise risk analysis in the industry. Scenarios are generated using#

$istorical simulation%

Theoretical modelling%

Stress testing scenarios.

Metholodolgies are discussed in the short term limit Collateral is not modelled.


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&. Contents

This resenation ill (ocus on these toics.

Risk )actors in the RiskMetrics aroach.

Methodologies (or risk management.

Products and ricing (rameorks.

Risk analysis and reorting.


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*. Risk )actors

The main (actors a((ecting ort(olio +alue are modelledin RiskMetrics.

E,uities#

Indi+idual rices -asolute or relati+e to an inde/ -0%

Inde/ le+els2 e.g. )TSE 133%

4((ects e,uities and e,uity (utures5otions. )6 rates#

4((ects cash ositions2 )6 (orards5otions and

currency sas. Commodity rices#

Construct constant maturity cur+es%

4((ects sot and (uture rices.


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". Risk )actors (cont)

Interest rates are the (ourth ma7or (actor. 8ield cur+es are constructed (rom

9ero couon and couon ond rices% interest rate sa rices.

Continuously comounded interest rate is used (orsimlicity other IR ayments must e con+erted


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:. Risk )actors -cont

Couon onds are riced in terms o( 9ero couononds.

E/amle# ;ond maturing in 1 year% Semi


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>. Risk )actors -cont

RiskMetrics also deals ith less ma7or (actors that a((ectrice.

Credit sread#

Construct yield cur+es ith similar ,uality instruments% Calirate# add a sread to each security.

Imlied +olatility#

?sed (or ricing otions%

4ssume constant imlied +olatility i( no historic data.


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@. Emirical Models

Aistriution o( returns is gi+en y ast er(ormance Bo theoretical models are used.

The historical simulation method# ?ses oser+ations o( actual changes in risk (actors% E+ents are scaled ith their (re,uency o( occurrence%

Models these changes to generate scenarios. Past oser+ations must e scaled according to their

+olatility -Hull & White Model. Method includes e/treme returns that occurred during

the historical eriod.


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. Emirical Models (cont.)

Changes in asset rices are con+erted to risk (actors. )ormalise ideas in a matri/ Ro( historical returns using

o( nrisk (actors ith mdaily returns#

So each ro o( Rcorresonds to a seci(ic scenario r.


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!. Emirical Models -cont.

Dtain a T


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13. Theoretical Models

The multi+ariate normal model is used to redict returns# This model assumes lognormal returns% Geometric random alk%

This is standard < see Hullor Wilmott (or more details.

Ari(ts are assumed to e 9ero -+olatility dominates#

Bo accurate redictions a+ailale (or time hori9onselo * months% Hero assumtion as good as any rediction.


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11. Theoretical Models -cont.

The return on the risk (actor ith these assumtions is#

olatility estimated (rom e/onentially eighted mo+inga+erage#


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1&. Theoretical Models -cont.

4n e/onentially eighting mo+ing a+erage scheme isused to determine the decay (actors# The otimal +alue as (ound y (inding the minimum

mean s,uare di((erence eteen the +arianceestimate and the actual s,uared return on each day.

Aecay (actors ere set at# 3.!" -1


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1*. Theoretical Models -cont.

This does not reclude a hea+y tailed unconditionaldistriution E.g. i( +olatilities deendent on the day o( the eek2

then days could e dealt ith searately.

Dne day returns are#

Conditioned on the currentle+el o( +olatility%

Indeendent across time%

Bormally distriuted.

RiskMetrics


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1". Theoretical Models -cont.

Multi+ariate method can e generalised to includemultile risk (actors#

L these are correlated ith a co+ariance matri/.

In this case2 the return (or each asset iis no gi+en y#

4nd the co+ariance eteen iandjy#


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1:. Theoretical Models -cont.

The co+ariance matri/ is most easily ritten as#

here the m/nmatri/ o( eighted returns is#


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1>. Theoretical Models -cont.

Monte Carlo -MC simulation# Generates scenarios (rom o( random numers% See MC in Finance presentation for more details.

Generating random scenarios#

?se Princile Comonent 4nalysis to deri+e (ormula.


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1@. Theoretical Models -cont.

The cijused in the (ormula are not uni,ue#

These coe((icients satis(y certain re,uirements. They uild u a +ector Co( units Nc

ijO.

The co+ariance matri/ can then e ritten as#

4nd the +ector o( returns as#


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1. Theoretical Models -cont.

Indeendent standard normal +ariales -ISB are usedto generate random scenarios# F'Ecuyer method ith &/131eriod% ill take 1313years to reeat scenarios.

Matri/ decomosition y Cholesky or Single aluedecomosition methods# See FI!"resentation (or details on matri/

decomosition% Bote that Cholesky decomosition only orks (or

ositi+e de(inite matrices% ;ut any negati+e terms are redundant anyay.


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1!. Theoretical Models -cont.

The scheme to generate the MC +ariales is#1 Generate a set #o( ISB%& Trans(orm ISB to set o( returns r2 correlated to

each risk (actor using matri/ C(rom cijso

* Dtain the rice o( each risk (actor -as (or historicalsimulation%

" Price each instrument at current rice and 1


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&3. Theoretical Models -cont.

Parametric methods -PM are an alternati+e to MC.

The method uses aro/imate ricing (or e+eryinstrument to get analytic (ormulae# 4ssumes lognormality o( returns.

PM uses a Q


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&1. Theoretical Models -cont.

The resent +alue $is gi+en y a 1storder Taylor

e/ansion#

There is a simle e/ression (or PF here Q are deltae,ui+alents#


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&&. Theoretical Models -cont.

4ssume the lognormality o( returns2 ecause# Fognormal returns aggregate nicely across time-temoral additi+e%

Dne eriod returns are indeendent% This imlies that the +olatility scales ith root o( time

consistent ith MC%4+erage PF (rom this method is 3 since instrument

rices and risk le+els are linear.

The alternati+e is ercentage returns

These aggregate across assets.


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&*. Stress Testing

Stress tests are needed to comlement statistical

models# Stress tests and models redict di((erent tyes o(

scenarios% Stress tests need certain tyes o( credile

scenarios.

Selection o( stress e+ents is imortant2 and can e# $istorical e+ents

E.g. Te,uila crisis in 1!!:%

?ser de(ined simle scenarios E.g. interest rate steeeners%

?ser de(ined redicti+e models These take account o( correlations2 etc.


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&". Stress Testing -cont.

?sing historical e+ents is a use(ul ay o( creatingmeaning(ul scenarios hat ould haen to my ort(olio i( the e+ents that

caused%crash haened again In general2 eteen times tand T2 the historical returns

are gi+en y#

The PF (or the ort(olio ased on this is#


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&>. Stress Testing -cont.

E/amle ith 1 core (actor# 12333 in Indonesian JSE e,uity inde/% Scenario o( 13= currency de+aluation -IAR#

ithU3.&2 JSE inde/ dros y an a+erage &=.


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&@. Pricing )rameork# ;asic Concets

Cash(los are the uilding locks (or descriingositions in RiskMetrics. Cash(los must alays e maed and discounted#

The BP o( a cash(lo is the roduct o( cash(loamount and discount (actor%

Cash(lo maing means that rincial and couonayments are con+erted to their e,ui+alent 9erocouon rates at the ayo(( date.

8ield cur+es are treated in RiskMetrics as ieceiselinear.

Points eteen +ertices are 7oined ith straight lines. RiskMetrics uses continuous comounding -see earlier.


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&. Pricing )rameork E/amles

The (irst e/amle is a (i/ed couon ond# Auration & yr% Par +alue 133% Interest rate := .a.%

semi


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&!. Pricing )rameork E/amles -cont.

E.g. a +anilla interest rate sa#

)i/ed (or (loating2 'ithe/change o( notionals% 1.&: y to maturity.

)loating leg# )irm recei+es >.3=% ?se cash(lo maing (or *2 ! 1: months#

)i/ed leg# )irm ays := semi


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*3. Pricing )rameork E/amles -cont.

Dtions can also e riced in this (rameork2 e.g. a

ond otion. ;lack's Model is an e/tension o( ;lack


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*&. Risk Measures

alue 4t Risk is the industry standard methodology#

It states that2 at a certain con(idence limit -e.g. !!=no more that W%ill e lost in a Tday eriod%

The current +alue o( ort(olio is used (or redictinglosses%

4R is the method seci(ied in ;asel &.

Marginal 4R -M4R is an e/tension to the 4Rrincile# It shos the amount o( risk a articular osition is

adding to ort(olio% It uses the arametric aroach to searate out the

risks and (ind correlations.


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**. Risk Measures -cont.

Incremental 4R -I4Ris similar to M4R# I4R uses M4R to ad7ust ort(olio risk% It shos the sensiti+ity o( 4R to ort(olio changes.

$oe+er2 there are se+eral draacks ith 4R# There is no estimate o( the si9e o( losses once the

4R limit is e/ceeded% 4R is not a coherent measure o( risk.


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*". Risk Measures -cont.

Coherent measures o( risk ha+e these roerties#

Translational in+ariance4dding cash to a ort(olio decreases risk y the

same amount% Suadditi+ity

Risk o( the sum o( ort(olios is smaller than thesum o( their indi+idual risks%

Positi+e homogeneity o( degree 1 I( the si9e o( the ositions doules2 the risk ill

doule%

Monotonicity I( ort(olio 4 has higher losses than ; (or all risk(actors2 then 4 is riskier than ;.


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*:. Risk Measures -cont.

E/ected short(all -ES ro+ides more in(ormation than4R on tail o( the PF distriution#

It gi+es an a+erage measure o( ho hea+y the tail is%

It is a con+e/ (unction o( ort(olio eights

use(ul (or risk otimisation% The ES is alays higher than the 4R.

ES is a coherent risk measure. Comined ith 4R2 ES gi+es a measure o( the cost o(

insuring ort(olio losses These to methods are comlementary.


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*>. Risk Reorting

4t the simlest le+el2 reorting is 7ust a PF histogram

Shos 4R and e/ected short(all

MC shos loest(igures

RiskMetrics

$istorical simulationshos mostconser+ati+e (igures


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*@. Risk Reorting -cont.

D(ten need more detailed analysis to dissect risk andidenti(y risk sources in a ort(olio. Arilldons slice


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*. Risk Reorting -cont.

Arilldon dimensions come in to main grous.

Proer dimensions are grous o( ositions# Position assigned to one ucket so easy to calculate% E.g. region could assign 4R to di((erent regions.

Imroer dimensions are grous o( risk (actors# Position might corresond to more than one ucket% E.g. an )6 sa has IR risk2 )6 risk and to yield

cur+es. Simulation or arametric methods must e used.


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*@. Summary

RiskMetrics is the industry standard risk analysis

methodology# ;ut does not include collateral. e ha+e dealt only ith non

risk metrics 2

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