Measuring Risk

Risk = The Range of Possible Outcomes.

Measuring Risk is defined statistically as measuring the "variability" around an expected outcome value. This is otherwise known as the Coeeficient of Variation (or Risk).

The Square Root of the Sum of the Squared Variabilities x Probabilities = Standard Deviation or Risk.
The Coefficient of Variation of Risk = Standard Deviation/Expected Outcome Value.

Example:
A business is considering investing in the launch of a new product.
The range of possible profit outcomes is as follows:

Profit $15,000 Probability 15% Weighted $ 2,250
Profit $25,000 Probability 50% Weighted $12,500
Profit $35,000 Probability 20% Weighted $ 7,000
Profit $45,000 Probability 15% Weighted $ 6,750 Expected Value $28,500.

Variability and Standard Deviation.

Profit $15,000. Variability -13,500 Squared 182,250,000. x 15% = 27,337,500
Profit $25,000. Variability -3,500 Squared 12,225,000. x 50% = 6,112,500
Profit $35,000. Variability -6,500 Squared 42,250,000. x 20% = 8,450,000
Profit $45,000. Variability -16,500 Squared 272,250,000. x 15% = 40,837,500
Sum of squared variabilities $83,736,000
Standard deviation $9,150.74
Expected Value = $28,500
Coefficient of Variation = 32.1%

A high Coefficient such as is the outcome in this example indicates that project is subject to stastically higher uncertainity and variability.