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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.

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## Materials for Lecture 16

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**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**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**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**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**Portfolio Analysis Models**• Portfolio analysis with three stocks or investment • Find the best combination of the three • Note Corr Coef.**Portfolio Analysis Models**• Nine portfolios analyzed are 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**Portfolio Analysis Models**• Next how does the preferred portfolio change as the investor considers investments with low correlation**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**Portfolio Analysis Models**• A portfolio (P6) is ranked second followed by P5**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**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)**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**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, etc.**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**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**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**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%**Bid Analysis in Business**• Bids if you ignore the risk • Average Cost is $350,850 Stochastic Analysis yields the following**Bid Analysis in Business**• Because we are uncertain about the cost of facilitators and researchers we can run a scenario analysis on these costs**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

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