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1. Materials for Lecture 16 • Read Chapters 13 and 14 • Lecture 16 Portfolio Analyzer Low Corr.xls • Lecture 16 Portfolio Analyzer High Corr.xls • Lecture 16 Insurance Analyzer.xls • Lecture 16 Stochastic Bid Analysis.xls • Lecture 16 Research Bid Analysis.xls

2. Portfolio and Bid Analysis Models • Many business decisions can be couched in a portfolio analysis framework • A portfolio usually 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

3. Portfolio Analysis Models • Basis for portfolio analysis – overall risk of a business can be reduced by investing in two risky instruments rather than one • This always holds true if the correlation between the risky investments is negative • Markowitz discovered this result 50+ years ago • Old saw: “Don’t put all of your eggs in one basket” is the foundation for portfolio analysis

4. 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 • Mid West used to raise corn and feed cattle • Irrigated west grow cotton and alfalfa • Undiversified portfolio is grow corn and sorghum • 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

5. Portfolio Analysis Models • Portfolio analysis with three stocks or investment • Find the best combination of the three • Note Corr Coef.

6. Portfolio Analysis Models • Nine portfolios analyzed are percentage combinations of Investments 1-3

7. 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

8. Portfolio Analysis Models • Preferred is 100% invested in Invest 1 • Next best thing is P6, then P5

9. Portfolio Analysis Models • Next how does the preferred portfolio change as the investor considers investments with low correlation

10. Portfolio Analysis Models • The results for simulating 9 portfolios where the individual investments have low correlation and near equal means • Portfolios still have lower relative risk

11. Portfolio Analysis Models • A portfolio (P6) is ranked second followed by P5

12. Portfolio Analysis Models • How are portfolios observed in the investment world? • The following is a portfolio mix recommendation prepared by a major brokerage firm • The words are changed but see if you can find the portfolio for extremely risk averse and slightly risk averse investors

13. Strategic Asset Allocation Guidelines

14. Portfolio Analysis Models • Simulation does not tell you the best portfolio, but tells you the rankings of alternative portfolios • Steps to follow for portfolio analysis • Select investments to analyze • Gather returns data for period of interest – annual, monthly, etc. based on frequency of changes • Simulate stochastic returns for investment i (or Ỹi) • Multiply returns by portfolio j fractions or Rij= Fj * Ỹi • Sum returns across investments for portfolio j or Pj = ∑ Rij sum across i investments for portfolio j • Simulate on the total returns (Pj) for all j portfolios • SERF ranking of distributions for total returns (Pj)

15. Portfolio Analysis Models • Typical portfolio analysis might look like: • Assume 10 investments so stochastic returns are Ỹi for i=1,10 • Assume two portfolios j=1,2 • Calculate weighted returns Rij = Ỹi * Fij where Fij is fraction of funds invested in investment i for portfolio j • Calculate total return for each j portfolio as Pj = ∑ Rij

16. 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

17. 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, etc.

18. Bid Analysis in Business • Bids for new projects can be couched in terms of a stochastic simulation problem • The KOV is the actual bid price • 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

19. 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 component • Labor costs = f( hourly, contract labor, professional labor, management time, etc.) • Gets 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

20. 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

21. 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 Simulation 1000 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: - P(costs > 375,000) = 33.89% - P(costs > 400,000) = 16.67% - P(costs > 425,000) = 2.4% - P(costs > 350,000) = 50.5%

22. Bid Analysis in Business • Bids if you ignore the risk • Average Cost is \$350,850 Stochastic Analysis yields the following

23. Bid Analysis in Business • Because we are uncertain about the cost of facilitators and researchers we can run a scenario analysis on these costs

24. Bid Analysis in Business • Example of a bid analysis for building a house Activity Cost of Materials • Site Preparation 5K, 10K, 20K • Concrete 50K – 60K • Steel 75K, 80K, 90K • Lumber 80K – 100K • Electrical 30K • Sheetrock 21K – 25K • Exterior Walls 41K – 45K • Paint 18K – 25K • Floor Covering 18K – 22K • Interest Rate 7% – 8.5% • Overhead 30K – 35K • Profit Residual

25. Contractor’s Bid Analysis

26. CDF of Profits for Alternative Bid Prices