Decision Making Under Uncertainty and Risk 1 By Isuru Manawadu B.Sc in Accounting Sp. (USJP), ACA, AFM 31130 AFM 31130
Jan 02, 2016
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