1. Portfolio Allocation Model How to invest in different asset classes? Different people have different objectives/goals. Returns from investments are inherently random. How can we take this uncertainty into account and still make a reasonable decision?

2. Simple Spreadsheet Model

3. Asset Return Uncertainty (annualized) Money Market –Uniform(minimum 2%, maximum 4%) Income –Normal(mean 5%, stdev 5%) Growth & Income –Normal(mean 7%, stdev 12%) Aggressive Growth –Normal(mean 11%, stdev 18%)

4. Crystal Ball Define Assumption Cells for the annual returns Define Forecast Cell Set Simulation Settings (Number trials = 1000) Run Simulation View & Analyze Results Run other two scenarios, complete summary table Compare alternatives (If no disk) Upload model to Blackboard Drop Box (tools  digital drop box).

5. Results Summary Statistics –Mean, standard deviation, minimum, maximum, standard error Frequency Distribution –Graphical, table of percentiles Interactive use of frequency chart –What is the probability that the dollar return will be worse than $X? –What are the quartiles of the return distribution? What do they mean? –If I invest this way, at least how much should I be prepared to lose about 5% of the time?

6. Goals/Objectives Performance is a function of asset returns as well as asset allocation. We cannot control returns, but we can control the allocation. What is the “best” allocation? –Depends on the performance measure!

7. Constrained Optimization Objective (maximizing or minimizing) Constraints Decision Variables Basic Question: What are the values of the decision variables which 1) satisfy the constraints, and 2) maximize or minimize the objective? We will be using Solver soon in the course; however, Crystal Ball has a tool called OptQuest built in. OptQuest is good for models which incorporate uncertainty, but is much slower than Solver for deterministic models.

8. OptQuest Build simulation model: define assumptions, forecast cells, and decision cells CBTools…OptQuest Wizard takes you through the process of specifying the optimization model. Defining the objective: What is it you want to maximize or minimize?