09a risk and uncertainty.ppt

8/16/2019 09A Risk and Uncertainty.ppt

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Risk and Uncertainty

King’s College

King's College, MBA - 2015 1


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Risk Analysis

King's College, MBA - 2015


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Motivation

To make effective investment decisions,one must understand risk.

Decision makers sometimes know withcertainty the outcomes associated with

each possible course of action.



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Motivation Contd..

Example: A firm with Rs.100,000 in cash

Decision to make:

(1) Invest in a 30-day Treasury bill yielding 6%

interest (2) Prepay a 10% bank loan

Which course of action to take? Choose (1) => Rs.493 interest income after 30 days

Choose (2) => Rs.822 interest expense savings after 30 days

Choose (2) provides Rs.329 additional 1-month return



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Defnition o Risk and Uncertainty

- Risk/Uncertainty: Both concepts deal withthe probability of loss or the chance of

adverse outcomes

- Risk: All possible outcomes of managerialdecisions and their probabilities are not

completely known

- Uncertainty: The possible outcomes andtheir probabilities are uncertain



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General Risk Categories

Business Risk " t#e c#ance o$ loss associated %it# a given&anagerial decision ty(ically a )y-(rod*ct o$ t#e *n(redicta)levariation in (rod*ct de&and and cost conditions

Market Risk " t#e c#ance t#at a (ort$olio o$ invest&ents can lose&oney )eca*se o$ overall s%ings in $inancial &arkets

Inflation Risk " t#e danger t#at a general increase in t#e (ricelevel %ill *nder&ine t#e real econo&ic val*e o$ cor(orateagree&ents

Interest-rate Risk " anot#er ty(e o$ &arket risk t#at can a$$ectt#e val*e o$ cor(orate invest&ents and o)ligations

Credit Risk " t#e c#ance t#at anot#er (arty %ill $ail to a)ide )y itscontract*al o)ligations



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General Risk Categories Contd..

Liuidit! Risk " t#e di$$ic*lty o$ selling cor(orateassets or invest&ents t#at #ave only a $e% %illing)*yers or are ot#er%ise not easily trans$era)le at$avora)le (rices *nder ty(ical &arket conditions

"eri#ati#e Risk " t#e c#ance t#at volatile $inancialderivatives s*c# as co&&odity $*t*res and indeo(tions co*ld create losses )y increasing rat#ert#an decreasing (rice volatility

Curren$! Risk " t#e c#ance o$ loss d*e to c#anges int#e do&estic c*rrency val*e o$ $oreign (ro$its

%t&er Risks (erational Risk, .yste&ic Risk etc/



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Probability

- (ro)a)ilit! likeli#ood o$ (artic*lar o*tco&eocc*rring, denoted )y p. #e n*&)er p is al%ays)et%een ero and one/

- *reuen$! esti&ate o$ (ro)a)ility, p=n/N, %#ere n is n*&)er o$ ti&es a (artic*lar o*tco&e

occ*rred d*ring N trials/



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Investment Decision Under Risk andUncertainty

Probability Distribution "is$rete +ro)a)ilit!

distri)ution deals %it# events6%#ose states o$ nat*re6 are

discrete/ #e event6 is t#e stateo$ t#e econo&y/ #e states o$nat*re6 are recession, nor&al, and)oo&/

Continuous +ro)a)ilit!

distri)ution deals %it# events6%#ose states o$ nat*re6 arecontin*o*s val*es/ #e event6 is(ro$its, and t#e states o$ nat*re6are vario*s (ro$it levels/

EventState of Economy

P (probabilty)

Recession 0.2

Normal 0.6

Boom 0.2



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Payo Matrix MethodA ta)le t#at s#o%s o*tco&es associated %it# eac# (ossi)le state o$ nat*re/

State of Economy Project A Project B Probability of State of Economy

Recession $4,000 $0 0.2

Normal $5,000 $5,000 0.6

Boom $6,000 $2,000 0.2

Project A more !esirable in a recession.

Project B more !esirable in a boom.

"n a normal economy, t#e rojects offer t#e same rofit otential.%ecision to &a'e(

A firm m)st c#oose only one of t#e t*o in+estment rojects c#oose Project A

or Project B-.



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Exected !al"e

#e (ayo$$s o$ all events x 1, x 2, 7, x N

#e (ro)a)ility o$ eac# event p1, p2, 7, pN

8(ected val*e o$ x:

89:; is a %eig#ted-average (ayo$$, %#ere t#e %eig#ts arede$ined )y t#e (ro)a)ility distri)*tion/

Use t#e (ayo$$ &atri in t#e (revio*s slide, toget#er %it# t#e(ro)a)ility o$ eac# state o$ t#e econo&y/

p x p x p x p x x EV i N

i

i N N ∑=

=+++=

22...-



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000,5$2.0000,6$6.0000,5$2.0000,4$- =•+•+•= A EV

400,5$2.0000,2$6.0000,5$2.00$- =•+•+•= B EV

Exected roft oPro#ect $ and % "nderdierent econo&ic

states o nat"re



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!ariance and 'tandard Deviation

9ariance and .tandard


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For project A, what are the variance and standard deviation? EV(A) = $5,000

Variance (σ2) = ($4,000-5,000)2(.2) + ($5,000-$5,000)2(.6) + ($6,000-$5,000)2(.2)

(σ2) = ($1,000)2(.2) + ($0)2(.6) + ($1,000)2(.2) (σ2) = $400,000 (units are in terms of squared dollars)

σ A= $632.46

For project B, what are the variance and standard deviation? EV(B) = $5,400 Variance (σ2) = ($0-5,400)2(.2) + ($5,000-$5,400)2(.6) + ($12,000-$5,400)2(.2)

(σ2) = 5,832,000 + 96,000 + 8,712,000 (units are in terms of squared dollars) (σ2) = 14,640,000 (units are in terms of squared dollars)

σB= $3,826.23

Project B has a larger standard deviation; therefore it is the riskier project



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Risk Meas"re&ent Absolute Risk:- Overall dispersion of possible payoffs

- Measurement: variance, standard deviation

- The smaller variance or standard deviation, thelower the absolute risk.

-Relative Risk- Variation in possible returns compared with the

expected payoff amount- Measurement:coefficient of Variation (CV),

- The lower the CV, the lower the relative risk. EV

CV σ =



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Project A

EV(A) = $5,000

σ A= $632.46

Project B

EV(B) = $5,400

σ B= $3,826.23

Coefficient of variation

CV A = = 0.1265

CVB = = 0.7086

Coefficient of variation measures the relative risk; the variationin possible returns compared with the expected payoff amount.

σ A

E V A, -

C V E V

=

σ

σ B

E V B, -



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Risk Aversion

characterizes decision makers who seek to avoid or minimize risk.

Risk Neutrality

characterizes decision makers who focus on expected returns anddisregard the dispersion of returns.

Risk Seeking (Taking)

characterizes decision makers who prefer risk.

Risk $ttit"des



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Scenario: A decision maker has two choices, a sure thing and a riskyoption, and both may/may not yield the same expected value.

Risk-averse behavior:

Decision maker takes the sure thing

Risk-neutral behavior:

Decision maker is indifferent between the two choices

Risk-loving (or seeking) behavior:Decision maker takes the risky option

Risk $ttit"des



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Typically, consumers and investors displayrisk-averse behavior, especially when

substantial sums of money are involved. Riskaversion is the general assumption behinddecision models in managerial economics.

Utility (heory and Risk $nalysis



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Risk $ttit"des

Risk averter) di&inishing

MURisk ne"tral) constantMURisk lover) increasing MU

:MU;

:MU;

:MU;



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Examples of utility functions

Let w = income (or profit) or more generally wealth, w > 0

U w w

U w w

U w w

U w w

, -

, - l n

, -

, -

=

=

=

= +

2

. 0

M U w w

w

M U w w

M U w w

M U w

, -

, -

, -

, -

= =

=

=

=

−

2

2

2

.

2

Which utility function is consistent with risk-seeking behavior?

Which utility function is consistent with risk neutrality?

Which utility function is consistent with risk aversion?



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Example:

Suppose that Anita’s utility function is given by where w represents total wealth.(a)Is Anita risk averse, risk loving, or risk neutral?

MU diminishes with increases in w.

Anita is risk averse.

U w w, - =


U w

M U w

w

=

= =

−

2

2

2

2

09a risk and uncertainty.ppt

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