Portfolio Allocation Model

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
• CBToolsOptQuest
• Wizard takes you through the process of
  specifying the optimization model.
• Defining the objective What is it you want to
  maximize or minimize?