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?

Simple Spreadsheet Model

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%)

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 (toolsdigital drop box).

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?

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!

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.

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?