Lecture 2 - Risk Management

8/8/2019 Lecture 2 - Risk Management

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Mohamed Eisa MohamedMohamed Eisa Mohamed Risk ManagementRisk Management 11

LectureLecture --22Project Decision MakingProject Decision Making


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Project Decision MakingProject Decision Making

Someone within the organisation may haveSomeone within the organisation may haveto take the bold decision as to whether:to take the bold decision as to whether:

It is better to build a new factory or extendIt is better to build a new factory or extendthe old one;the old one;

It is wiser to use an empty piece of land forIt is wiser to use an empty piece of land for

a multia multi--story car park or to invest a largestory car park or to invest a largesum and build a shopping centresum and build a shopping centre


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Project Decision MakingProject Decision Making

Whether shareholders would be better off if theWhether shareholders would be better off if thefirm returned their money in the form of dividendsfirm returned their money in the form of dividendsbecause shareholders can obtain a better returnbecause shareholders can obtain a better returnelse where, orelse where, or

The firm should pursue itsThe firm should pursue its plan and invest in newplan and invest in newchain of hotels e.g.chain of hotels e.g.

These sort of decisions require not only braveThese sort of decisions require not only bravepeople, but also informed people especially aboutpeople, but also informed people especially aboutthe risk involved in these projects.the risk involved in these projects.


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Time is MoneyTime is Money

Time : individuals generally prefer to have aTime : individuals generally prefer to have adollar today than one dollar in two yearsdollar today than one dollar in two years

time.time. The rate of exchange between certain futureThe rate of exchange between certain future

consumption and certain currentconsumption and certain currentconsumption is the ( pure rate of interest )consumption is the ( pure rate of interest )


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Time is MoneyTime is Money

This occurs even in a world of no inflationThis occurs even in a world of no inflationand no riskand no risk

If you lived in such a world you might beIf you lived in such a world you might bewilling to sacrifice $willing to sacrifice $100100 of consumption nowof consumption nowif you were compensated with $if you were compensated with $102102..3030 to beto bereceived in one year .received in one year .

This would mean that your pure rate ofThis would mean that your pure rate ofinterest isinterest is 22..33%%


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InflationInflation

The price of time (or the interest rateThe price of time (or the interest rateneeded to compensate for time preference)needed to compensate for time preference)

exist even when there is no inflation.exist even when there is no inflation. If there is inflation then the providers ofIf there is inflation then the providers of

finance will have to be compensated for lossfinance will have to be compensated for lossin purchasing power as well as for time.in purchasing power as well as for time.


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RiskRisk

Risk is commonly defined in terms of the variabilityRisk is commonly defined in terms of the variabilityor dispersion of possible future outcomes from aor dispersion of possible future outcomes from adecision.decision.

A capital investment project is said to be riskA capital investment project is said to be risk--freefreeif the return from the initial investment are knownif the return from the initial investment are knownwith certainty.with certainty.

Example: Shahama bondsExample: Shahama bonds

However, the promise of the receipt of a sum ofHowever, the promise of the receipt of a sum ofmoney some years hence generally carries with itmoney some years hence generally carries with itan element of riskan element of risk


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RiskRisk

Risk simply means that the future return hasRisk simply means that the future return hasa variety of possible values.a variety of possible values.

The issuer of a security, whether it is aThe issuer of a security, whether it is ashare, a bond or bank accounts, must beshare, a bond or bank accounts, must beprepared to compensate the investors forprepared to compensate the investors fortime, inflation & risk involved.time, inflation & risk involved.

Otherwise no one will be willing to buy theOtherwise no one will be willing to buy thesecurity.security.


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Required ReturnRequired Return

Take the case of an investor who is considering aTake the case of an investor who is considering a$$10001000 oneone--year investment and requireyear investment and requirecompensation for three elements:compensation for three elements:

Time: a return ofTime: a return of 22..33% is required for the pure time% is required for the pure timevalue of money.value of money.

Inflation: is anticipated to beInflation: is anticipated to be 33% over the year.% over the year. Thus, at the time (to)$Thus, at the time (to)$10001000 buys one basket ofbuys one basket of

goods & services.goods & services. To buy the same basket of goods & services atTo buy the same basket of goods & services at

(t(t11) (one year later) $) (one year later) $10301030 is needed.is needed.


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Required ReturnRequired Return

However, different investment categoriesHowever, different investment categoriescarry different degrees of uncertainty aboutcarry different degrees of uncertainty about

the outcome of investment.the outcome of investment. Therefore, investors require different riskTherefore, investors require different risk

premiums on top of the RFR to reflect thepremiums on top of the RFR to reflect theperceived level of extra risk.perceived level of extra risk.

Thus: Required Return = RFR + RiskThus: Required Return = RFR + Riskpremium.premium.


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Coping with Risk and Uncertainty in InvestmentCoping with Risk and Uncertainty in InvestmentDecisionsDecisions

There are a number of differentThere are a number of differentapproaches to risk analysisapproaches to risk analysis

1.1. Subjective or informal approachSubjective or informal approach2.2. NPV/payback approachNPV/payback approach

3.3. RiskRisk adjusted discount rate approachadjusted discount rate approach

4.4. Probability distribution approachProbability distribution approach5.5. SimulationSimulation

6.6. Sensitivity analysisSensitivity analysis


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Subjective or Informal Approach:Subjective or Informal Approach:

The subjective approach is widely used because itThe subjective approach is widely used because itis simple and inexpensive.is simple and inexpensive.

For example, a firm compute the NPV for a projectFor example, a firm compute the NPV for a project

and make investment decisionsand make investment decisions based upon the decisionbased upon the decision--makers subjective feelingsmakers subjective feelings

about the projects risk in relation to its potential returns.about the projects risk in relation to its potential returns. If two mutually exclusive investments havingIf two mutually exclusive investments having

approximately the same NPV are being evaluatedapproximately the same NPV are being evaluated The decisionThe decision--maker would likely choose the one he ormaker would likely choose the one he orshe felt to be the least risky.she felt to be the least risky.


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Subjective or Informal Approach:Subjective or Informal Approach:

On the other hand, if the two projects hadOn the other hand, if the two projects hadsignificantly different NPVs, as well assignificantly different NPVs, as well as

different levels of perceived risk, thedifferent levels of perceived risk, thedecision is not quite simpledecision is not quite simple

In such a case, the decisionIn such a case, the decision--maker mustmaker mustdecide if the traditional risk of a project isdecide if the traditional risk of a project isbeing compensated for with sufficientlybeing compensated for with sufficientlyhigher returns.higher returns.


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NPVNPV--Payback ApproachPayback Approach::

Many firms combine the NPV method with theMany firms combine the NPV method with thepayback approach in an attempt to considerpayback approach in an attempt to considerproject risk.project risk.

As you remember, the payback period of a projectAs you remember, the payback period of a projectis the number of years required before net cashis the number of years required before net cashflows just equal the initial investment.flows just equal the initial investment.

If one agrees that estimates of cash flows that aIf one agrees that estimates of cash flows that aproject may generate become less certain theproject may generate become less certain the

farther into the future one goes,farther into the future one goes, then applying a payback cutoff point whenthen applying a payback cutoff point when

analyzing projects can be viewed as a way ofanalyzing projects can be viewed as a way ofreducing this future uncertainty.reducing this future uncertainty.


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::Payback ApproachPayback Approach--NPVNPV

For example, a firm may require that allFor example, a firm may require that allacceptable projects have a positive NPVacceptable projects have a positive NPV

when net cash flows are discounted at thewhen net cash flows are discounted at thecost of capital and have a payback of lesscost of capital and have a payback of lessthan five years.than five years.

This approach is widely used because it isThis approach is widely used because it isboth simple and inexpensive to apply.both simple and inexpensive to apply.


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NPVNPV--Payback ApproachPayback Approach::

However, it does suffer from some notable weakness.However, it does suffer from some notable weakness.1.1. The choice of a payback cutoff criterion is purely subjective and notThe choice of a payback cutoff criterion is purely subjective and not

directly related to the variability of returns from the project.directly related to the variability of returns from the project.2.2. Some investments have relatively certain cash flows that extend farSome investments have relatively certain cash flows that extend far

into the future, While others do not.into the future, While others do not.3.3. By setting a payback cutoff point of, say five years, the risk associatedBy setting a payback cutoff point of, say five years, the risk associatedwith the cash flows that are expected during the first four years iswith the cash flows that are expected during the first four years isignored.ignored.

4.4. Some projects will be more risky than others during this startSome projects will be more risky than others during this start--up period.up period.

In spite of these weaknesses, many firms have found thisIn spite of these weaknesses, many firms have found this

approach to be helpful in screening investmentapproach to be helpful in screening investmentalternatives.alternatives.


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::adjusted Discount Rate Approachadjusted Discount Rate Approach--RiskRisk

With the riskWith the risk--adjusted discount rate approach theadjusted discount rate approach therate at which future cash flows are discounted inrate at which future cash flows are discounted incalculating the present value of a project is equalcalculating the present value of a project is equal

to the firms required rate of return plus a to the firms required rate of return plus a riskriskpremium.premium. Thus, the net present value (NPV) of a projectThus, the net present value (NPV) of a project

would be equal to:would be equal to:

NPV = ANPV = Atttt

(( 11 ++ kk*)*)


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RiskRisk--adjusted Discount Rate Approachadjusted Discount Rate Approach::

Where:Where: k* is the riskk* is the risk--adjusted discount rate, &adjusted discount rate, & At is the cash outlay or inflow for each period tAt is the cash outlay or inflow for each period t ..

The risk premium is a function of the amount of riskThe risk premium is a function of the amount of riskassociated with a given project.associated with a given project. Rather than treating the riskRather than treating the risk--adjusted discount rate as aadjusted discount rate as a

continuous variable that is different for every project, acontinuous variable that is different for every project, asmall number of risk classes can be set up with a differentsmall number of risk classes can be set up with a different

risk premium being given to each class.risk premium being given to each class. Projects would then be assigned to one of the classes.Projects would then be assigned to one of the classes. Three classesThree classes low ; medium ; and high risk.low ; medium ; and high risk.


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RiskRisk--adjusted Discount Rate Approachadjusted Discount Rate Approach::

Cash flows or projects that are classified as lowCash flows or projects that are classified as lowrisk might be assigned a riskrisk might be assigned a risk--premium ofpremium of 00percentpercent

And would thus be discounted at the firmsAnd would thus be discounted at the firmsstandard required rate of return for examplestandard required rate of return for example 1010%.%. Projects of a medium risk might be assigned aProjects of a medium risk might be assigned a

riskrisk--premium ofpremium of 33%, for example and the cash%, for example and the cashflows would be discounted at (flows would be discounted at (1010 ++ 33) =) = 1313%%

High risk projects might be assigned a riskHigh risk projects might be assigned a risk--premium ofpremium of 88%, for example, and the cash flows%, for example, and the cash flowswould be discounted at (would be discounted at (1010 ++ 88) =) = 1818%.%.


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::adjusted Discount Rate Approachadjusted Discount Rate Approach--RiskRisk

The problem with this approach are twofold:The problem with this approach are twofold:1.1. The assignment of riskThe assignment of risk--premium is somewhat arbitrary.premium is somewhat arbitrary.

there is little theoretical basis or empirical evidence to suggestthere is little theoretical basis or empirical evidence to suggestthe use of any particular values.the use of any particular values.

2.2. Once risk classes are established, the assignment of a particularOnce risk classes are established, the assignment of a particularproject to one of the classes is subjective.project to one of the classes is subjective.

Risk was defined as the dispersion of the possibleRisk was defined as the dispersion of the possiblereturns of a project.returns of a project.

Thus, without an explicit consideration of this dispersion,Thus, without an explicit consideration of this dispersion,it is difficult to establish objective guidelines for assigningit is difficult to establish objective guidelines for assigninginvestment projects to one of the risk classes.investment projects to one of the risk classes.


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::Probability Distribution ApproachProbability Distribution Approach

With the probability distribution approach, explicitWith the probability distribution approach, explicitconsideration is given to the possible dispersion in theconsideration is given to the possible dispersion in thefuture cash flows of an investment project.future cash flows of an investment project.

This can be done by requiring the decisionThis can be done by requiring the decision--maker tomaker toassess the possible range of the likelihoodsassess the possible range of the likelihoods

(probabilities) of cash flows that may result each period(probabilities) of cash flows that may result each periodfrom acceptance of the project.from acceptance of the project. Using elementary probability concepts, this information isUsing elementary probability concepts, this information is

then combined to obtainthen combined to obtain the mean,the mean,

standard deviation, andstandard deviation, and probability distribution of the net present value of the project.probability distribution of the net present value of the project.


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Probability Distribution ApproachProbability Distribution Approach::

Using the standard deviation of net presentUsing the standard deviation of net presentvalue as a measure of the risk associatedvalue as a measure of the risk associated

with the projectwith the project (dispersion in the possible net present value)(dispersion in the possible net present value)

The decisionThe decision--maker can weigh the risk andmaker can weigh the risk andexpected return based on his or her ownexpected return based on his or her ownutility preference in choosing whether toutility preference in choosing whether toaccept or reject the project.accept or reject the project.


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In arriving at an overall assessment of the desirability ofIn arriving at an overall assessment of the desirability ofthe investmentthe investment

The decisionThe decision--maker would be required to have an explicitlymaker would be required to have an explicitlyor implicitly defined tradeor implicitly defined trade--off function between risk andoff function between risk and

expected return.expected return. Thus, while the probability distribution approach does notThus, while the probability distribution approach does not

do away with the necessity of integrating the twodo away with the necessity of integrating the twodimensions of risk and expected return in arriving at andimensions of risk and expected return in arriving at anoverall measure of desirability,overall measure of desirability,

It has the advantage of forcing the decisionIt has the advantage of forcing the decision--maker to focusmaker to focusattention on the relevant variables, namely:attention on the relevant variables, namely: The expected return &The expected return & Dispersion in the returnsDispersion in the returns


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Let us now consider some of the steps tat are required inLet us now consider some of the steps tat are required inmeasuring the expected return and risk by the probabilitymeasuring the expected return and risk by the probabilitydistribution approach:distribution approach:

The periodThe period-- byby-- period cash flows of a project are assumedperiod cash flows of a project are assumed

to beto be random variables,random variables, whose probability distributions canwhose probability distributions canbe specified by the decisionbe specified by the decision--maker.maker. The specification of a probability distribution over the rangeThe specification of a probability distribution over the range

of possible cash flows in a future period can be difficult.of possible cash flows in a future period can be difficult. One way to simplify the procedure, and at the same time toOne way to simplify the procedure, and at the same time to

capture the element of uncertainty involved, is to ask thecapture the element of uncertainty involved, is to ask thedecisiondecision--maker to specify a small number of possiblemaker to specify a small number of possiblevalues andvalues and

Then to assign probabilities to these values.Then to assign probabilities to these values.


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The decisionThe decision--maker would then be asked tomaker would then be asked torepeat this procedure for the next period.repeat this procedure for the next period.

This procedure would be repeated for asThis procedure would be repeated for asmany periods as the investment project wasmany periods as the investment project wasexpected to yield cash flows.expected to yield cash flows.

In order to proceed with the analysis,In order to proceed with the analysis,

consider the following threeconsider the following three--period example.period example.


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Suppose the firm is considering a project involvingSuppose the firm is considering a project involvingthe introduction of a new product that is expectedthe introduction of a new product that is expectedto have a lifetime of two years.to have a lifetime of two years.

Management has specified the possible valuesManagement has specified the possible valuesand probabilities of the cash out flows for theand probabilities of the cash out flows for theproject during the current year (yearproject during the current year (year 00))

And the conditional cash flows during each of theAnd the conditional cash flows during each of thenext two years.next two years.


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For example:For example: The decisionThe decision--maker can be asked to givemaker can be asked to give

Most likelyMost likely Optimistic andOptimistic and Pessimistic estimates of the cash flow duringPessimistic estimates of the cash flow during

the next period for a given project.the next period for a given project.

Next he or she would be asked to assessNext he or she would be asked to assesssubjectively the relative chances of each ofsubjectively the relative chances of each ofthese outcomes occurring.these outcomes occurring.


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For example,For example, 33 inin 55,, 11 inin 55, and, and 11 inin 55respectively.respectively.

From these estimates one can assign theFrom these estimates one can assign the

respective probabilities of .respective probabilities of .6060, ., .2020 and .and .2020 to theto thethree outcomes.three outcomes. The decisionThe decision--maker would then be asked to repeatmaker would then be asked to repeat

this procedure for the next periodthis procedure for the next period

This procedure would be repeated for as manyThis procedure would be repeated for as manyperiods as the investment project was expected toperiods as the investment project was expected toyield cash flows.yield cash flows.


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The assessment of the probabilities ofThe assessment of the probabilities ofthe possible periodthe possible period--byby--period cash flowsperiod cash flowsfor a project can be simplified if eitherfor a project can be simplified if either

one of two assumptions can be madeone of two assumptions can be madeabout these cash flows.about these cash flows.1.1. If the realized cash flows of a project areIf the realized cash flows of a project are

independent from period to period.independent from period to period.

Then the expected net present value and standardThen the expected net present value and standarddeviation can be calculated asdeviation can be calculated as


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E(NPV) =E(NPV) = E(AE(Att))____________ tt(( 11 + r )+ r )

22

Sdv (NPV) = Sdv (NPV) = tt____________22 tt((11 + r )+ r )

Where E(AWhere E(Att) : is the expected cash flow in period) : is the expected cash flow in period tt r is the riskr is the risk--free rate andfree rate and

22

SdvSdv is the variance of the cash flows in period tis the variance of the cash flows in period t


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Assuming that the cash flows are independentAssuming that the cash flows are independentover time,over time, then the expected net present value (discounted at thethen the expected net present value (discounted at the

riskrisk--free rate offree rate of 55%) is%) is 11..2020 andand The standard deviation isThe standard deviation is 11..5858

When the cash flows are assumed to be perfectlyWhen the cash flows are assumed to be perfectlycorrelated,correlated, the expected net present value isthe expected net present value is 11..2020 andand

The standard deviation isThe standard deviation is 22..5858


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Example:Example: Analysis of return & Risk when cash flows are eitherAnalysis of return & Risk when cash flows are eitherindependent or perfectly correlatedindependent or perfectly correlated

yearyear00 yearyear11 yearyear22cash cash cashcash cash cashFlow probability flow probability flow probabilityFlow probability flow probability flow probability--1010 ..2020 ++88 ..3030 ++88 ..2525--1111 ..6060 ++77 ..5050 ++66 ..5050--1212 ..2020 ++66 ..2020 ++44 ..2525

E(AE(A00) =) = --1111..00 E(AE(A11) = +) = +77..11 E(AE(A22) = +) = +66..00

variancevariance(A(A00) = .) = .4040 variance(Avariance(A11) = .) = .4949 variance(Avariance(A22) = .) = .2020

Std(AStd(A00) = .) = .6363 std(Astd(A11) = .) = .7070 std(Astd(A22) =) = 11..4141


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1.1. Assuming that the cash flows are independentAssuming that the cash flows are independent::..

77..1 61 6..00E(NPV) =E(NPV) = --1111..00 + ++ + 22 = += + 11..2020

((11..0505) ( ) (11..0505))

..49 249 2..00

std(NPV)std(NPV) = .= .4040 + ++ + 22 == 11..5858

((11..0505) ( ) (11..0505))


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2.2. Assuming that the cash flows are perfectly correlated:Assuming that the cash flows are perfectly correlated:

77..1 61 6..00

E(NPV) =E(NPV) = --1111..00 + ++ + 22 = += + 11..2020((11..0505) ( ) (11..0505))

..70 170 1..4141

std(NPV)std(NPV) = .= .6363 ++ ++ 22 == 22..5858

((11..0505) ( ) (11..0505))


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End of LectureEnd of Lecture 22

Lecture 2 - Risk Management

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