Risk

Risk

Certainty v Risk

• As human beings, we tend to live mentally in a world of certainty– examples

• Psychologically, that’s usually an illusion

Certainty v Risk

• Truth is all situations have some risk

• Risk can usually be measured in some way and the branch of mathematics that attempts to measure risk is called probability

Certainty v Risk

• There are actually three conditions– Certainty– Risk – Uncertainty

• Uncertainty occurs when we cannot estimate risk

Random variables

• In probability, we look for random variables.

• Random variables are numbers whose values we don’t know with certainty.

• Examples: expenses, revenues, completion times.

Most likely or expected values

• There are several ways to try to work with random variables.

• A common approach is to use a most likely or expected value.

• We did that with CP/M-based project management

Most likely or expected values

• Also, we use this approach frequently in real life.

• We use most-likely estimates for– How long it will take us to get somewhere– What an item with “go for” on Ebay– Note that what we might get as a Birthday gift

is a guess, but it’s not a most likely value. Random variables are numbers.

Most likely or expected values

• A major problem with expected values are they don’t say anything about variability

• Example:– If you take 20 minutes to get to school, that’s

an expected value– Sometimes you will be early and sometimes

late. Sometimes you will be very early and sometimes very late.

• How do we get at variability?

What if analysis

• Example: linear programming sensitivity analysis• Linear programming assumes certainty, but

sensitivity analysis lets us look at what might happen if something happens differently than expected.

• Weakness– Bias based on manager’s judgment, so decisions

could be better– Burns time: many iterations needed

Probability distributions

• A die is a random variable. Roll it and it will have a value.

• Roll dice and tally.• The tally represents a model of the risk

association with rolling the dice. – Rolling a 2 is riskier than a 7.– Rolling a 1 is impossible.

• Models of risk are generically referred to as probability distributions

Probability distributions

• Probability distributions are the best available tool for addressing risk.

Excel Random Number Generator RAND()

RAND( ) gives you a uniform random number on the interval 0, 1

0 1

Pr{RAND( )}

RAND( )

Using RAND( )

To create a uniform random number between a and b, you can use

= a + (b – a) * rand( )

For example, to create a series of numbers between 5 and 12 you would use

= 5 + (12 – 5)*rand( )

Using ROUND()

• Can be used to round to obtain whole numbers or to specify the number of decimal digits in a number.

• Example: round(3.2643,0) gives 3

• Example: round(3.2643,1) gives 3.3

Dice rolling simulation spreadsheet