Decision Making Under Uncertainty and Risk 1 By Isuru Manawadu B.Sc in Accounting Sp. (USJP), ACA, AFM 31130.

Decision Making Under Uncertainty and Risk

1

By Isuru Manawadu

B.Sc in Accounting Sp. (USJP), ACA,

AFM 31130AFM 31130

Learning Outcomes

After studying this session you will be able to:

Risk, uncertainty and probabilityMeasuring UncertaintyExpected valueAdvantages and disadvantages of expected valueVarianceSlandered DeviationExpected utility Theory

Decisions

• Decision making without taking uncertainty into consideration

• Decision making under uncertainty

Decision making under uncertainty

• Non probabilistic Approach• Probabilistic Approach

Decision Making Models

• Identified Objective

• Identified alternatives

• Identified states of nature

• Possible outcomes

• Measurement of the value of payoffs

• Select the best course of action

Question 01

Araliya PLC is reviewing its marketing policy for next budget period. It has developed two new product A and B. But it only has sufficient recourses to launch one of them.

Required to;

Illustrate the application of decision making model concept to solve the above problem.

AnswerStep Remarks

Objective Maximize the profit

Decision alternatives Product AProduct BDo nothing

Status of nature Competitors will;Do nothingIntroduce comparable productIntroduce a superior product

Possible outcomes Slight increase in profitSlight decrease in profitLarge increase in profitLarge decrease in profitNo change in profit

Measure payoff

Select best course of action

Risk, Uncertainty and Probability

Risk- Applied where there are several possible outcome and there is a relevant past experience with statistical evidence enabling a qualified degree of prediction of the possible out come.

Uncertainty- Where there are several possible outcome but there is little previous statistical evidence to enable the possible outcomes to be predicted.

Risk, Uncertainty and ProbabilityCont….

Probability- Quantification of uncertainty or measurement of degree of risk.

Risk and uncertainty

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

known with certainty

• Can list all possible outcomes & assign probabilities to the outcomes

Uncertainty• Cannot list all possible outcomes

• Cannot assign probabilities to the outcomes

Probability

• Objective Probability

• Subjective Probability

Probability Distribution

• Discrete probability distributionProbability will be assigned to finite number of

possible outcomes

• Continuous probability distributionUsed for the continuous variables and point

estimate of probabilities are not possible.

Measuring Risk with Probability Distributions• Table or graph showing all possible

outcomes/payoffs for a decision & the probability each outcome will occur.

• To measure risk associated with a decisionExamine statistical characteristics of the probability

distribution of outcomes for the decision

Probability Distribution for Sales

Expected value

The expected value is calculated by multiplying each of the financial outcomes by its associated probability.

Expected Value

Expected value (or mean) of a probability distribution is:

1

n

i ii

E( X ) Expected value of X p X

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

Expected Value

• Does not give actual value of the random outcome

• Indicates “average” value of the outcomes if the risky decision were to

be repeated a large number of times

Question 02Kalana PLC is consedering whether to make product A or B. The estimated sales demand for the product A and B are uncertain. A detail investigation of possible sales demand for each product gives the following probability distribution of the profit for each product.

Product A Probability Distribution

Product B Probability Distribution

Outcome Profit (in

Mn)Estimated

Probability

Outcome Profit (in

Mn)Estimated

Probability600 0.1 400 0.05700 0.2 600 0.1800 0.4 800 0.4900 0.2 1000 0.25

1000 0.1 1200 0.2

Expected Value - Advantages

• Simple to understand and calculate• Represents whole distribution by a single

figure• Arithmetically takes account of the

expected variabilities of all outcomes

Expected Value - Disadvantages

• By representing the whole distribution by a single figure it ignores the other characteristics of the distribution Eg. Range of skewness.

•Make the assumption that the decision maker is risk neutral.

Variance

Variance is a measure of absolute risk• Measures dispersion of the outcomes about the

mean or expected outcome

• The higher the variance, the greater the risk associated with a probability distribution

2 2

1

n

X i ii

Variance(X) = p ( X E( X ))

Identical Means but Different Variances

Standard Deviation

• Standard deviation is the square root of the variance

• The higher the standard deviation, the greater the risk

X Variance( X )

Probability Distributions with Different Variances

Coefficient of Variation

When expected values of outcomes differ substantially, managers should measure riskiness of a decision relative to its expected value using the coefficient of variation

A measure of relative risk

Standard deviation

Expected value E( X )

Decisions Under Risk

• 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

Question 03

Calculate Variance, standard deviation and coefficient of variance for the probability distribution provided in the question 02

Product A Probability Distribution Product B Probability Distribution

Outcome Profit (in Mn)

Estimated Probability

Outcome Profit (in Mn)

Estimated Probability

600 0.1 400 0.05

700 0.2 600 0.1

800 0.4 800 0.4

900 0.2 1000 0.25

1000 0.1 1200 0.2

Expected value rule

Mean-variance rules

Coefficient of variation rule

Summary of Decision Rules Under Conditions of Risk

Choose decision with highest expected value

Given two risky decisions A & B:

• If A has higher expected outcome & lower variance than B, choose decision A

• If A & B have identical variances (or standard deviations), choose decision with higher expected value

• If A & B have identical expected values, choose decision with lower variance (standard deviation)

Choose decision with smallest coefficient of variation

Which Rule is Best?

• 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

• 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 & guide decision making process• As much art as science

Which Rule is Best?

Expected Utility Theory

• Actual decisions made depend on the willingness to accept risk

• Expected utility theory allows for different attitudes toward risk-taking in decision making• Managers are assumed to derive utility from

earning profits

Managers make risky decisions in a way that maximizes expected utility of the profit outcomes

• Utility function measures utility associated with a particular level of profit• Index to measure level of utility received for a

given amount of earned profit

Expected Utility Theory

1 1 2 2 n nE U( ) p U( ) p U( ) ... p U( )

• Risk averseIf faced with two risky decisions with equal expected profits, the less risky decision is chosen

• Risk lovingExpected profits are equal & the more risky decision is chosen

• Risk neutralIndifferent between risky decisions that have equal expected profit

Manager’s Attitude Toward Risk

Pay off tables

The application of probability concept to business decision making, pay off table refer to a matrix that provides pay-offs for all the possible combinations of decision alternatives and events

This can be used to solve problems that involve only one decision variable.

Alternative 01 Alternative 02 Alternative 03

Event 01 Pay-off Pay-off Pay-off

Event 01 Pay-off Pay-off Pay-off

Event 01 Pay-off Pay-off Pay-off

Expected value (EV)

EV – Alternative o1

EV – Alternative o2

EV – Alternative o3

Layout of a pay-off table

Question 04A book shop sells expensive monthly magazine at Rs. 1,000 per copy. The purchasing price of a magazine is Rs. 600 per copy. Bookshop can not return any unsold copies at the month end. How ever, they can sell those at Rs. 500 per copy to a local bookshop.

The probability distribution for the monthly demand is as follows.

Demand per month Probability

4 0.10

5 0.35

6 0.30

7 0.25

Thank you