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Presented By:

Omkar Inamdar

( Roll No. 70)

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` Risk Must make a decision for which the outcome is not

known with certainty

Can list all possible ou

tcomes & assign probabilities tothe outcomes

` Uncertainty Cannot list all possible outcomes

Cannot assign probabilities to the outcomes

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` Table or graph showing all possible

outcomes/payoffs for a decision & the probability

each outcome will occur

` To measure risk associated with a decision Examine statistical characteristics of the probability

distribution of outcomes for the decision

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` Expected value (or mean) of a

probability distribution is:

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Where Xi is the ith outcome of a decision,

pi is the probability of the ith outcome, and

n is the total number of possible outcomes

n

i i

i

E( X ) p X !

! ! 1

Expected value of X

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` Does not give actual value of the random

outcome

` Indicates average value of the outcomes if therisky decision were to be repeated a large

number of times

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` Variance is a measure of absolute risk

` Measures dispersion of the outcomes about the meanor expected outcome

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n

x i i

i

p ( X E( X ))W!

! ! 2 2Variance(X)

The higher the variance, the greaterthe risk associated with a probabilitydistribution

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` Standard deviation is the square root of thevariance

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The higher the standard deviation,the greater the risk

xW ! Variance(X)

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` When expected values of outcomes differ

substantially, managers should measure

riskiness of a decision relative to its

expected value using the coefficient ofvariation Ameasure of relative risk

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E( )

W

Y ! !

Standard deviation

Expectedvalue

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` No single decision rule guarantees profits will

actually be maximized

` Decision rules do not eliminate risk Provide a method to systematically include risk in the

decision making process

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Expected

value rule

Mean-

variance

rules

Coefficient of

variation rule

Choose decision with highest expected value

Given two risky decisions A & B:

If A has higher expected outcome & lowervariance than B, choose decision A

If A & B have identical variances (or standarddeviations), choose decision with higherexpected value

If A & B have identical expected values,

choose decision with lower variance (standarddeviation)

Choose decision with smallest coefficient ofvariation

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` For a repeated decision, with identical

probabilities each time Expected value rule is most reliable to maximizing

(expected) profit

Average return of a given risky course of action

repeated many times approaches the expected value

of that action

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` For a one-time decision under risk No repetitions to average out a bad outcome

No best rule to follow

` Rules should be used to help analyze & guidedecision making process As much art as science

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` Risk averse If faced with two risky decisions with equal expected

profits, the less risky decision is chosen

` Risk loving Expected profits are equal & the more risky decision is

chosen

` Risk neutral Indifferent between risky decisions that have equal

expected profit

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