modules/module06.txt

MODULE NAME:
Module 06 – Decisions Under Risk

LEARNING OBJECTIVES:
- Calculate the expected value of a choice with two or more outcomes
- Summarize the process and applications of decision trees to decision-making
- Sketch and interpret a decision tree
- Describe the process and applications of Monte Carlo simulations to decision-making
- Create and interpret a Monte Carlo simulation of a business investment decision

KEY POINTS:
• Expected Value (EV): The rational decision rule is to choose the option with the highest positive expected value. EV is a probability-weighted average of all possible outcomes, calculated using E(x)=Σxp(x). Decision-makers can be risk averse (require payoff > EV), risk neutral (accept payoff = EV), or risk seeking (accept payoff < EV).
• Decision Trees: Used for analyzing path-dependent decisions under uncertainty. Tree structure maps potential futures using: square nodes (choices), lines (path-dependency), circle nodes (chance events). Solve by mapping choices left to right, then calculate values right to left to find optimal (highest EV) path. Shows value of options like quit or expand. Challenge: assigning numerical values to non-quantifiable outcomes and accurately estimating probabilities.
• Monte Carlo Simulations: Computational method that "embraces randomness" to model situations with significant uncertainty. Useful for complex systems in project management and finance. Process: (1) Replace uncertain inputs with random variables (values are random but statistical distribution is known), (2) Run simulation thousands of times, (3) Generate distribution of possible outcomes, (4) Average of outcomes = expected value. In Excel: use RANDBETWEEN(bottom,top) to add risk, create scenario outputs with data table, summarize with AVERAGE and STDEV.S functions and histogram.