ACCY 511 Notes -Day 3

8/13/2019 ACCY 511 Notes -Day 3

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ACCY 511

Class Notes – Day 3

Concepts of Risk and Uncertainty

Measurement of Risk

Risk: The possibility of suffering a loss. It derives from the uncertainty in

predicting future outcomes.

Cance of an outcome !"ain or loss# occurrin": The relative frequency of

the outcome occurring. Thus, the chance of, say, loss is the ratio of the

number of losses likely to occur compared to the larger number of possible

losses in a given group.

Example: 1, cars in a to!n are susceptible to the risk of collision. If past

experience indicates that " of these cars are likely to be in a collision

during a given time period #year$, then the chance of loss due to a collision

is "%1&." #"'$. Objective measurement

De"ree of Risk: The amount of objective risk present in a situation. The

degree of risk tells us ho! far from our target our relative frequency numbercan be. (e calculate the degree of risk as the ratio of the range of ho! many

observations !e actually get to ho! many !e expect to get.

)egree of risk & #maximum * minimum$%expected

or in general the ratio:

#+robable variation of actual from expected losses$ % #Expected losses$

Variability of possible outcomes

Example: There are 1, buildings in each city, rbana and -hampaign

and, on average, each city has 1 fires per year. ut closer look at the past

data suggests that in rbana the actual number of fires !ill range from /0 to

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Re&ie' some statistical concepts

5 +robability: the long5term frequency of occurrence of an event.

- +robability distribution: a mutually exclusive and collectively exhaustivelist of all events that can result from a chance process and contains the

probability associated !ith each event. 8 probability distribution isuseful for evaluating the expected frequency of an event.

Take t!o coins and toss them into the air. Table 1 sho!s all possibleoutcomes and that the probability of each outcome is "0'. The probability

of heads is 0' and the probability that !e get one head and one tail is also0'. 9ur expectation is !rong 0' of the time.

Table 1 * +robability distribution of a t!o coin toss

eads, eads "0'

eads, Tails "0'

Tails, eads "0'

Tails, Tails "0'

Table " * +robability distribution of a t!o dice thro!

Total +rob

" 1%=

= "%=6 =%=

0 6%=

0%=

> %=

=

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2 0%=

/ 6%=

1 =%=

11 "%=1" 1%=

The probability distributions in Tables 1 and " are theoretical. (e calculatethem because !e kno! ho! a pair of unbiased coins or dice is supposed to!ork. If the probability distribution is equal to anything else then the coinsor the dice are crooked and the game is invalid.

(e could toss the dice =, times and observe the outcome. This is calleda ?onte -arlo simulation and can be done easily #if slo!ly$ !ith excel.Table = sho!s that the observations are close, but not exactly equal, to thetheoretical distribution in Table ".

Table = * ?onte -arlo simulation of a t!o dice thro!

Total 9bs +rob

" 1,/ 1%=

= ", "%=6 =,111 =%=

0 =,2>2 6%=

0,1> 0%=

> 0,/6= %=

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2 6,//0 0%=

/ 6,60 6%=

1 ",/06 =%=

11 1,//0 "%=1" 1,0= 1%=

=,

T!o types of probability distributions are used: empirical and theoretical.9ne forms an empirical probability distribution by observing the events thatactually occur as in table =.(hen !e have some basis for understanding the nature of a distribution, thetoss of a coin, the thro! of the dice, the pull of a single card for a deck of 0"

cards, then !e can use a theoretical distribution. 3or more complexrelationships !e use more complex theoretical distributions based onmathematical formulas. The inomial, the @ormal and Aog@ormal, and the+oison are theoretical probability distributions !idely used in riskmanagement. They are also fairly easy to model and are built into mostspreadsheet programs.

ut Bust as !e need to assume that the coin is fair, the dice evenly !eighted,and the deck of cards contains only one 8ce of Cpades, !e must also be ableto assume that events are random and independent. 9ther!ise the

distribution !ill be misleading.

Every financial statements has a probability distribution. There are differentobservations for different accounts. Draph the observations to get thedistribution, analye the mean

1. Take revenues for 2 quarters.F1: G"F": G"."HH

F2: G0". 3ind the mean=. -alculate the variability around the mean: standard deviation

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Random: the probability that any one event !ill occur is equal to the probability that any other event !ill occur. Co !hen I thro! adie the probability of a 1 equals the probability of a " equals the

probability of a = etc.

(ndependent: !hen one event occurs the probability that a secondevent !ill occur is not changed. If I thro! a then this does notalter the probability of a on the next thro!.

Independence is often a difficult concept to internalie. If I thro! 1" tails ina ro! then I believe the universe !ould not be so cruel as to give me a 1=th tail. I anticipate a 1=th tail as though the probability of thro!ing it is the sameas the probability of getting 1= tails #1%2,1/"$ rather than the probability ofgetting the 1=th tail after I have already thro!n the first 1" tails. #1%"$

If the events against !hich !e manage are not random and not independentthen the risk manager is in the same position as the gambler playing !ithloaded dice: theres no !ay you can !in. To effectively use theoreticaldistributions, the risk manager must be reasonably confident that thedistribution of the firmJs events is similar to the theoretical distributionchosen.

- ?easures of central tendency of a probability distribution: ?ean, median,

and mode.- ?easures of variation of a probability distribution: Ctandard deviation,

variance, coefficient of variation.

$%pected )alues and Risk *remiums

The Expected Kalue, ELKM, of a risky prospect is the value of each possibleoutcome !eighted by its probability. Cince the ans!er comes out in dollars

and cents this is a convenient !ay to measure risk aversion.

$%ample: Nou are faced !ith the choice bet!een a certainty ofG0, and a risky opportunity under !hich you !ill get G",0

plus some probability x' of an extra G1,.

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8t first x is only 1' #//' of G",0 and 1' of G1,$ so you decline the

risk and take the G0,. If you do not take the risk then it is offered to

someone else. If no one takes the risk at 1' then x is increased to "', =',

6', etc. In general, x depends on someones attitude to!ards risk #risk

preference or subBective risk$.

Nou take the risk !hen x is 60'

Nou have demonstrated that you are indifferent bet!een G0, !ithcertainty and a risk of G",0 !ith 00' probability and G1, !ith 60'

probability. (e calculate this decision #potential proBect$ as

$%pected )alue: ELKM & .00 O ",0 P .60 O 1, & G0,2>0

Certainty $+ui&alent: -E & G0, #keep the money in the bank$

Risk *remium: 4+ & ELKM 5 -E & G0,2>0 5 G0, & G2>0

Qohn takes the risk !hen x is 0'. e is more risk averse than you are. 3orQohn, the expected value of the risk is G,"0, and his risk premium G1,"0.Qohn is !illing to forego G1,"0 to avoid this risk !hereas you are !illing toforego only G2>0 to avoid the risk.

8ndre! is unacquainted !ith the concept of risk aversion. e calculates thathe should take the risk !hen x is == '. e thus takes the gamble !ith a riskof G",0 !ith ' probability and G1, !ith ==' probability.

$%pected )alue: ELKM & . O ",0 P .=== O 1, & G0,

Certainty $+ui&alent: -E & G0,

Risk *remium: 4+ & ELKM 5 -E & G0, 5 G0, & G

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e is risk neutral in that he !ill not sacrifice Expected value in order to gaincertainty at all.

The risk premium is the amount of money you are !illing to give up to

avoid the risk of loss or alternatively the amount you are !illing to earn to

assume the risk.

+eople !ith positive risk premiums are called risk averse.+eople !ith negative risk premiums are called risk lovers.

+eople !ith ero risk premiums are called risk neutral .

Conservative managers forgo good projects

Aggressive managers take on riskier projects.

The utility function is a construct economists use to represent dollar amountsin terms of their utility to the individual, using the individuals o!nsubBective risk preference. In other !ords, the utility function is a constructthat reflects someones subBective risk preferences.

The utility function is -oncave for a risk averse person.

The utility function is -onvex for a risk loving person.

The utility function is a straight line for a risk neutral person.

The utility function is C5shaped for a person !ho is a risk lover for lo!

!ealth levels and risk averse for high !ealth levels.

Decreasin" Risk A&ersion: (ith a larger !ealth base an individual can takemore risk and thus !ould pay or give up less to avoid risk #risk premiumsdecrease$. Implication: cash rich firms can become more aggressive #morerisk$. 8uditors, be a!are. ig firms are !illing to take on more risks.?anagers tend to be empire building.

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,y do 'e mana"e risk- ecause of the asymmetry bet!een losses andgains, i.e. the utility lost from G1 loss is larger than the utility gained from G1gain #risk aversion$. ?ore later !ith finance reasons.

Measurement of Risk: The variance of the future outcome distribution.

Modern (n&estment .eory #arry ?arko!it$: Investors are R Mean-

variance optimizersS i.e. they form a RportfolioS #a combination ofinvestments$ !ith the lo!est possible return variance for any given level ofmean #expected$ return. This suggests that the variance of an investmentreturn is the appropriate measure of risk.Graph of efficient portfolio frontier

Mean/&ariance analysis: ?athematical description of ho! the risk ofindividual assets contributes to the risk and return of portfolios.

• seful in asset allocation decisions #ho! much in stocks, bonds, etc$.

• seful to corporate managers in selecting among investment proBects #a firm is a portfolio of real and financial assets$.?anagers !ant to kno! ho! the risk of individual investmentsaffects the overall risk of the firm #expected earnings and theirvariability$.

• 3oundation of the -apital 8sset +ricing ?odel #-8+?$ !hichis the theory that relates risk to return.

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Market Risk and )alue/at/Risk !)AR#

Market Risk is the risk of loss arising from adverse can"es in market ratesand prices, such as interest rates, foreign currency exchange rates,

commodity prices, and similar market rate or price changes #e.g. equity prices$. 8lternatively, market risk is the uncertainty resulting from changesin market prices.

istory• Explosion in financial innovation in the 1/2s

o ?any 3inancial instruments discovered and used in the market place

• Cignificant changes in market !ide factorso E.g. interest rateso E.g. exchange rateso E.g. stock priceso E.g. commodity prices

• The changes imply turmoil in the macro environment, the changes areunexpected !hich implies increased uncertainty !hich in turn implieshigher cost of capital and potential for negative earnings.

• Cignificant losses for many firms, e.g. +roctor and Damble, DibsonDreetings, Qapan 8irlines, arings ank

o The need for a statement of R+robable lossS became apparent

o Q+ ?organ chairman )ennis (eatherstone demanded a simplereport at the end of each day on ho! the firms position couldchange due to market risk: the 6.10 report

o Q+ ?organ analysts came up !ith Kalue at 4isk #K84$

o Droup of = largest banks in 1//= recommended K84 as ameasure #internal$ of a firms overall market risk

o Q+ ?organ further developed !hat is kno!n as 4isk ?etricsno! used around the !orld and disclosed in financial reports

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• In 1//6 the 38C issued C38C 11/R Disclosures about derivative financial instruments and fair valueof financial instrumentsS

• )isclosea$ )etails about current positions and activity during the reporting

period

b$ The hypothetical effects on equity, or on annual income, ofseveral possible changes in market prices, e.g. interest rates

c$ 8 D8+ analysis of interest rate repricing D8+ is the difference bet!een dollar amounts of interest rate sensitive assets andinterest rate sensitive liabilities. D8+ & change in net interestincome due to a percent change in interest rates. D8+ is forgroups of instruments.

d$ The duration of financial instruments #ho! sensitive eachfinancial instrument is to changes in interest rates$ If you kno!the sensitivity and kno! the direction of interest rates you cancalculate the potential loss and take action for that instrument.)uration is the interest rate sensitivity of each instrument # per

instrument$ different from D8+ #group of instruments$

e$ The firms K84 from financial instruments and from other positions at the end of the period and the average value over the period.

• CE- #1//>$o -ommon frame!ork to enhance the comparability #important

obBective of financial information$ of market risk disclosures

across firms and types of market risk exposures.o It required three disclosure alternatives

Tabular * #a$ #c$ of C38C 11/ Censitivity analysis * #b$ #d$ of C38C 11/ K84 * #e$ of C38C 11/

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0*M RiskMetrics

)etermine the )aily Earnings at 4isk #)E84$ for your trading portfolio

)E84 is defined as the estimated potential loss of a portfolioJs value over aone5day period as a result of adverse moves in market conditions, such aschanges in interest rates, foreign exchange rates, commodity prices, andmarket volatility.

D$AR is comprised of

#a$ The dollar value of the position,

#b$ The price sensitivity of the assets to changes in the risk factor, and#c$ The adverse move in the return #yield$.

D$AR !a# % !2# % !c#

*rice &olatility & #b$ x #c$, i.e. the product of the price sensitivity ofthe asset and the adverse move in the yield.

D$AR Dollar &alue of te position % price &olatility

o If !e assume that changes in the yield are normally distributed,!e can construct confidence intervals around the proBected)E84. #9ther distributions can be accommodated$.

o 8ssuming normality, /' of the time the disturbance !ill be!ithin 1.0 standard deviations of the mean.

#0' of the extreme values greater than P1.0 standarddeviations and 0' of the extreme values less than 51.0standard deviations$

$%ample 1:

Cuppose that !e are long in >5year ero5coupon bonds, !ith market value ofG1,,, face value of G1,=1,62= and current yield of >."6=' per year.(e define RbadS yield changes such that there is only 0' chance of theyield change being exceeded in either direction. 8ssuming normality, /'of the time yield changes !ill be !ithin 1.0 standard deviations of themean. If the standard deviation is 1 basis points, this corresponds to 1.0

1=

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basis points #1x1.0$. -oncern is that yields !ill rise. +robability of yieldincreases greater than 1.0 basis points is 0'.

+rice volatility & ?odified )uration #?)$ × +otential adverse change in

yield & #.0">$ × #.10$ & 1.>>'

?) & )uration%1P4 & >%1.>"6= & .0">)E84 & ?arket value of position × #+rice volatility$

& #G1,,$ × #.1>>$ & G1,>>

(nterpretation: The potential daily loss in earnings on the G1,, position is G1,>> if the 1 bad day in " #0'$ occurs tomorro!.

To calculate the potential loss for more than one day:?arket value at risk #K84$ & )E84 U V@

$%ample:

3or a five5day period,K84 0 & G1,>> U V0 & G"6,2"

@ote: 3ive5day variance & one5day variance x 0Taking squared roots of both sides !e get:

3ive5day standard deviation &one5day standard deviation x V0, i.e. W0 & W1 x V0

.e case of orei"n $%can"e

)E84 & dollar value of position U 3oreign Exchange #3X$ rate volatility

3X rate volatility is taken as 1.0 x W3X

$%ample 4:ank of Couthern Kermont has determined that its inventory of " millioneuros#Y$ and "0 million ritish pounds #Z$ is subBect to market risk. Thespot exchange rates are G.6%Y and G1."2%Z, respectively. The σs ofthe spot exchange rates of the Y and Z, based on the daily changes ofspot rates over the past six months, are 0 bp and 60 bp, respectively.

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)etermine the banks 15day K84 for both currencies. se adverse ratechanges in the /0th percentile.

3X position of Y & "m x .6 & G2 million3X position of Z & "0m x 1."2 & G=" million

3X volatility Y & 1.0 x 0bp & 1>."0bp, or 1.>"0'3X volatility Z & 1.0 x 60bp & >6."0bp, or .>6"0'

)E84 & #G Kalue of position$ x #+rice volatility$

)E84 of Y & G2m x .1>"0 & G20,2)E84 of Z & G="m x .>6"0 & G"=>,

K84 of Y & G20,2 x √1 & G20,2 x =.1"= & G">1,="=K84 of Z & G"=>, x √1 & G"=>, x =.1"= & G>01,=0>

.e case of e+uities

Total risk & Cystematic risk P nsystematic risk

If the portfolio is !ell diversified then)E84 & dollar value of position U stock market return volatilityCtock market return volatility is taken as 1.0 x W?.

$%ample 3:

ank of 8laskas stock portfolio has a market value of G1 million. The betaof the portfolio approximates the market portfolio, !hose standarddeviation #σm$ has been estimated at 1.0 percent. (hat is the 05dayK84 of this portfolio, using adverse rate changes in the //th percentile7

)E84& #)ollar Kalue of portfolio$ x #".== x σm $ & G1m x #".== x .10$& G1m x .=6/0 & G=6/,0

K84 & G=6/,0 x √0 & G=6/,0 x "."=1 & G>21,0

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A""re"atin" D$AR estimates:

-annot simply sum up individual )E84s.In order to aggregate the )E84s from individual exposures !e requirethe correlation matrix.

T!o5asset case:)E84 portfolio & L#)E84 a$" P #)E84 b$" P "[ab U )E84 a U )E84 bM1%"

$%ample : (e have a t!o5asset portfolio. 9ne asset has an expected return

of "', the other has 1"'. The variance of the first assets return is 6' andthe variance of the second assets return is ='. The covariance of the t!oassets is "'. The t!o assets are equally !eighted in the portfolio.

Expected portfolio return&.0O."P.0O.1"&.1

Kariance of the portfolio return&#.0$" O.6P#.0$" O.=P"O#.0$O#.0$O."&.">0

Ctandard deviation of the portfolio return&.">01%" &.102

The 0' tail on the left of the returns distribution is:1.0 O .102 & .">= a!ay from the mean.

The /0' confidence level of K84 is.1 * .">= & 5.11= i.e. there is a 0' chance the portfolio !ill

lose more than 11.='.

The 1' tail on the left of the returns distribution is:".== O .102 & .=2= a!ay from the mean.

The //' confidence level of K84 is.1 * .=2= & 5.""= i.e. there is a 1' chance the portfolio !ill

lose more than "".='.

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)erify tis solution usin" te D$AR portfolio formula a2o&e6

.ree/asset case:

)E84 portfolio & L#)E84 a$" P #)E84 b$" P #)E84 c$" P #"[ab U )E84 a U)E84 b$ P "[ac U )E84 a U )E84 c P "[ bc U )E84 b U )E84 cM1%"

$%ample 5:

The -39 of -hoice ank is estimating the aggregate )E84 of the banks portfolio of assets consisting of loans #A$, foreign currencies #3X$, andcommon stock #EF$. The individual )E84s are G=,>, G">6,, and

G1",> respectively. If the correlation coefficients ρiB bet!een A and 3X,A and EF, and 3X and EF are .=, .>, and ., respectively, !hat is the)E84 of the aggregate portfolio7

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[ ] "1/,0==G,:":,="","26G

$>,1":$#G,">6$#G.#"$>,1":$#G>,=$#G>.#"

$,">6$#G>,=$#G=.#">,1":G,">6G>,=G

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$#$#$#

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EQ ! EQ !

EQ " EQ "

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#EA$ % #EA$ %

#EA$ % #EA$ %

#EA$ % #EA$ %

#EA$ #EA$ #EA$

portfolio #EA$

ρ

ρ

ρ

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)alue at Risk !)AR# is a summary statistical measure of market risk: the!orst loss possible under Rnormal market conditionsS for a given time

period. It is constructed so that losses greater than the value at risk aresuffered only !ith a specified small probability. Thus, using a probability ofx percent and a holding period of t days, a firms value at risk is the loss thatis expected to be exceeded !ith a probability of only x percent during thenext t5day holding period. Example of a K84 statement: Rthere is a 0'chance the firm !ill lose more than G0 million over the next trading !eek.S

K84 is also called a measure of RnormalS market risk, and the probability xis the cutoff that defines Ran abnormalS #!orst$ loss. Typical values for the

probability x are 1', ".0' and 0' !hile common t periods are 1, ", and 1 business days and 1 month.

-onstructing K84 using normal distribution

a$ -alculate current market value of portfolioi$ ased on todays trading pricesii$ ased on todays discount rates

b$ ?easure variability of risk factorsi$ )iscount rates * bondsii$ Ctock prices * optionsiii$-ommodity prices * futures contracts

c$ Cet time horioni$ 1 dayii$ = daysiii$1 days

d$ Cet confidence leveli$ //'

ii$ //.0'

e$ -alculate )E84 and then K84 using the above formulas

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Anoter $%ample: suppose !e have G1 million invested in a stock thathas a =' standard deviation for a year and !e !ant the //.0'confidence K84 over 1 day.

i$ (hat is the volatility over 1 day assuming independence7#1$(hat percentage of the year is 1 trading day7#"$(hat is the variance over 1 year7#=$(hat is the variance over 1 day7#6$(hat is the standard deviation over one day7

ii$ G1 millioniii$=' O #1%"0"$1%"

iv$K84 1 & 1,,O#='O#1%"0"$1%" $O ".02 & G62,>0>

7istorical 8imulation

se historical changes in market rates and prices to construct a distributionof potential future portfolio profits and losses. 4ank the profits and lossesand choose a confidence level for the estimate. The value at that percentilein the distribution represents the K84 for the portfolio. E.g. Ka4 0',1day is theloss that is exceeded only 0' of the time over 1 dayse current portfolio and subBect it to actual changes in market factorsexperienced in each of the last @ periods, i.e. revalue the portfolio for thechange that !ould occur if history repeated itself. y subtracting the future

portfolio value from the current value you find the amount that !ould be lostdue to market risk if these conditions occurred again.

Monte Carlo 8imulation

Identify market factors, i.e. change in stock price or change in discount rates.8ssume a distribution for the change in these factors, e.g. the @ormaldistributionDenerate hypothetical values for the changes

8s !ith the istorical simulation method calculate the G change in portfoliovalues4ank the hypothetical profits and losses-alculate the loss that is equaled or exceeded 0' of the time.

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,ic metod is 2est-

-apturing risks of options5like instrumentsCimulations methods !ork !ell even !hen !e have options.4isk?etrics * normal approach assumptions need to be made to makethe math tractable. (hen there are a lot of options it doesnt !ork as!ell as the other methods

Ease of implementationistorical simulation is easy to implement if !e have the dataavailable.4isk?etrics * normal method is available in soft!are so if the

portfolio only contains interments and factors that are covered in thesoft!are it is easy to implement?onte -arlo simulation soft!are is also available

Ease of communicationistorical simulation is easy to understand4isk?etrics * normal and ?onte -arlo methods are difficult for non5technical people to understand.

4eliability of resultsistorical simulation may rely on data that is not representative.?onte -arlo and 4isk?etrics * normal methods use historical data toget the parameters so there is also some risk that this data is notrepresentative. o!ever the problem is less severe than for historicalsimulation.o!ever, ?onte -arlo and 4isk?etrics * normal methods assumedistributions that may not be representative.

3lexibility of assumptions(hat5if analysis does not !ork !ell !ith historical simulation.

8lternatives to K84 Censitivity 8nalysis

Imagine hypothetical changes in the value of each market factor.se pricing models to compute value of portfolio given the ne! valueof the market factor.

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)etermine the change in portfolio value resulting from the change inmarket factor.(hen combined !ith kno!ledge of magnitude s of likely changes infactors these computations provide a good picture of the risks of

portfolios. If there are many relevant factors, this !ill beover!helming.

Cas lo' at Risk !CAR#

-84 is similar to K84 but it differs in quantifying the potential loss in -ashflo!s rather than market values.

sed by non5financial companies8ll cash flo!s are considered not only those associated !ith marketablesecurities3actors !ill include changes in customer demand, 4) success etc.sed for internal planning4equires a great deal of kno!ledge and Budgment.

$arnin"s at Risk

Earnings at risk is similar to K84Fuantifying the potential loss in earnings rather than in market values.

9imitations of )AR

K84 is a single summary statistical measure of market risk.It uses historical data and assumes that future !ill be like the past.istorical simulation directly uses past data?onte -arlo and 4isk?etrics * @ormal method use the past to

determine the appropriate distribution, mean and varianceCometimes the past isnt very good for predicting the futureCystematic shift * internet bubbleo!ever the alternatives are unappealing.

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Disclosure re+uirements

Fualitative disclosuresIdentify primary market risk exposures)iscuss obBectives and general strategies used to manage exposures)iscuss significant changes in exposures or risk managementstrategies

Fuantitative )isclosuresCE- regulation C5\

uantitati&e information a2out market risk6

#a$ 4egistrants shall provide, in their reporting currency,quantitative information about market risk as of the end ofthe latest fiscal year, in accordance !ith one of the follo!ingthree disclosure alternatives.

#b$ In preparing this quantitative information, registrants shallcategorie market risk sensitive instruments into instrumentsentered into for trading purposes and instruments entered

into for purposes other than trading purposes.

#c$ (ithin both the trading and other than trading portfolios,separate quantitative information shall be presented, to theextent material, for each market risk exposure category #i.e.,interest rate risk, foreign currency exchange rate risk,commodity price risk, and other relevant market risks, suchas equity price risk$.

"=

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16 .a2ular *resentation

Information related to market risk sensitive instruments

3air values of the market risk sensitive instruments and contract terms

sufficient to determine future cash flo!s from those instruments, categoried by expected maturity dates

Information relating to contract terms shall allo! readers of the tableto determine expected cash flo!s from the market risk sensitive instrumentsfor each of the next five years.

-omparable tabular information for any remaining years shall bedisplayed as an aggregate amount

Instruments shall be grouped based on common characteristics.

46 8ensiti&ity analysis

)isclosures that express the potential loss in future

#i$ earnings#ii$ fair values#iii$ cash flo!s

?arket risk sensitive instruments resulting from one or more selectedhypothetical changes in

interest rates

foreign currency exchange rates

commodity prices,

and other relevant market rates or prices over a selected period of time.

4egistrants shall provide a description of the model, assumptions, and parameters, !hich are necessary to understand the disclosure.

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36 )alue at risk disclosures

Express the potential loss in future earnings, fair values, or cash flo!sof market risk sensitive instruments over a selected period of time !ith aselected likelihood of occurrence, from changes in interest rates, foreigncurrency exchange rates, commodity prices, and other relevant market ratesor prices.

(hy three quantitative market risk disclosure alternatives7 The CE- arguedthat Rdisclosure requirements about market risk should be flexible enough toaccommodate different types of registrants, different degrees of market riskexposure, and alternative !ays of measuring market risk.S

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8/13/2019 ACCY 511 Notes -Day 3


ualitati&e information a2out market risk

To the extent material, describe:

1. The registrantJs primary market risk exposures

". o! those exposures are managed. Cuch descriptions shall include, butnot be limited to, a discussion of the obBectives, general strategies, andinstruments, if any, used to manage those exposures

=. -hanges in either the registrantJs primary market risk exposures or ho!

those exposures are managed, !hen compared to !hat !as in effect duringthe most recently completed fiscal year and !hat is kno!n or expected to bein effect in future reporting periods.

Fualitative information about market risk shall be presented separately formarket risk sensitive instruments entered into for trading purposes and thoseentered into for purposes other than trading.

8tress .estin"

4ecall that the main purpose of K84 is to measure potential losses underRnormalS market conditions. The problem is that K84 measures based onrecent historical data can fail to identify extreme unusual situations thatcould cause severe losses. This is !hy K84 methods should besupplemented by a regular program of stress testing.

Ctress testing can be described as a process to identify and manage situationsthat could cause extraordinary losses. This can be made !ith #a$ scenarioanalysis, #b$ stressing models, volatilities, and correlations, and #c$ policy

responses.Ccenario analysis consists of evaluating the portfolio under various states ofthe !orld, mainly large movements in key variables.

ACCY 511 Notes -Day 3

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