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• Many business decisions can be couched in a portfolio analysis framework
• A portfolio analysis refers to comparing investment alternatives
• A portfolio can represent any set of risky alternatives the decision maker faces
• For example an insurance purchase decision can be framed as a portfolio analysis if many alternative insurance coverage levels exist
Portfolio Analysis Models
• Basis for portfolio analysis – overall risk can be reduced by investing in two risky instruments rather than one IF:– This always holds true if the correlation
between the risky investments is negative
– Markowitz discovered this result 50+ years ago while he was a graduate student!
– Old saw: “Don’t put all of your eggs in one basket” is the foundation for portfolio analysis
Portfolio Analysis Models
• Application to business – given two enterprises with negative correlation on net returns, then we want a combination of the two rather than specialize in either one– Mid West used to raise corn and feed cattle– Irrigated west grew cotton and alfalfa
• Undiversified portfolio is grow only corn• Thousands of investments, which ones to
include in the portfolio is the question?– Own stocks in IBM and Microsoft– Or GMC, Intel, and Cingular
• Each is a portfolio, which is best?
Portfolio Analysis Models
• Portfolio analysis with three stocks or investments
• Find the best combination of the three• Note Corr Coef.
Portfolio Analysis Models
• Nine portfolios analyzed, expressed as percentage combinations of Investments 1-3
Portfolio Analysis Models
• The statistics for the 9 simulated portfolios show variance reduction relative to investing exclusively in one instrument
• Look at the CVs across Portfolios P1-P9, it is minimized with portfolio P7
Portfolio Analysis Models
• Preferred is 100% invested in Invest 1• Next best thing is P6, then P5
Stochastic Efficiency with Respect to A Function (SERF) Under a Neg. Exponential Utility Function
where Fij is fraction of funds invested in investment i for portfolio j
• Calculate total return for each j portfolio as Pj = ∑ Rij
Bid Analysis in Business
• Businesses are often asked to prepare bids for uncertain projects, such as:– Build a house– Build a road or bridge– Build an airplane
• Past experiences help in bid preparation– The cost categories are commonly
known– But what of the risks? – Risks are taken into consideration based
on perceived risks or past experience
Bid Analysis in Business
• How fixed price bids work– Contractors provide a fixed price bid– Must deliver finished product at a fixed
price– If costs exceed expectations, they must
absorb cost excesses in terms of reduced profits which could turn into losses
– Risks are: price of inputs (materials), cost & performance of sub-contractors, performance of materials, performance of finished product, liability for environmental quality during project, interest rate, weather, etc.
Bid Analysis in Business
• Bids for new projects can be couched in terms of a stochastic simulation problem
• The KOV is the simulated cost vs. bid• Objective of management: submit a
bid price that is low enough to get accepted, but high enough to insure a profit– Sounds like game theory?– We can set it up as a simulation model
with the objective that the bid insures an x% chance of a profit
Bid Analysis in Business
• Model formulation– KOV is the bid and probability of a profit– Bid = Sum of costs + Desired Profit– Stochastic variables are any factor which
affects the cost and are uncertain• Break each cost category into its basic
professional labor, management time, etc.)• Get estimates of the PDF for each labor cost
item from an expert in that field• Materials costs are risky, get estimates of
PDFs from experts for each material
Bid Analysis in Business
• Example model to bid on a research project
• Example is for an international research project
• Start with a simplified budget for the project
• Notice all of the uncertainties
Category Quantity Cost
Researchers
3 to 6 $35,000 each
Grad Students
1 or 2 $15,000 each
Local Facilitators
2 or 3 $10,000 each
Secretarial 1 $24,000
Fringe Benefits
40% of salaries
Travel 10 to 15 trips
$2-$3,000 each
Materials $5 to $8,000
Stochastic Bid Analysis- Deterministic Best Case/Worst Case
- Lowest Cost is $244,100 or the “Best Case” scenario- Average Cost is $350,850 or the “No Risk” scenario- Highest Cost is $462,600 or the “Worst Case” scenario
- Stochastic Results of Budget Simulation1000 iterations
- Mean $351,379- Minimum $266,419 Note: This is much higher than the “Worst Case”- Maximum $440,159 Note: This is less than the “Best Case”
Probability of under bidding project for alternative bids: