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

2. Portfolio and Bid Analysis Models 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

3. 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

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 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?

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

6. Portfolio Analysis Models Nine portfolios analyzed, expressed as 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 Portfolio Objective High Current Income Conservative Income Income with Growth Growth with Income Growth Aggressive Growth Asset Class Cash Equivalent5% -- Short/Intermediate Investment- Grade Bonds 20%30%20%10%-- Long Investment-Grade Bonds50%40%25%20%-- Speculative Bonds15%-- Real Estate10 %5% -- U.S. Large-Cap Stocks--20%30% 55%40% U.S. Mid-Cap Stocks-- 10%15%20% U.S. Small-Cap Stocks-- 10%15%20% Foreign Developed Stocks-- 5% 10%15% Foreign Emerging Market Stocks-- 5%

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 Ỹ i ) –Multiply returns by portfolio j fractions or R ij = F j * Ỹ i –Sum returns across investments for portfolio j or P j = ∑ R ij sum across i investments for portfolio j –Simulate on the total returns (P j ) for all j portfolios –SERF ranking of distributions for total returns (P j )

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

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, interest rate, weather, etc.

18. 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

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.) 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

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 CategoryQuantityCost Researchers3 to 6$35,000 each Grad Students 1 or 2$15,000 each Local Facilitators 2 or 3$10,000 each Secretarial1$24,000 Fringe Benefits 40% of salaries Travel10 to 15 trips $2-$3,000 each Materials$5 to $8,000

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 The bid 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 ActivityCost of Materials –Site Preparation5K, 10K, 20K –Concrete50K – 60K –Steel75K, 80K, 90K –Lumber80K – 100K –Electrical30K –Sheetrock21K – 25K –Exterior Walls41K – 45K –Paint18K – 25K –Floor Covering18K – 22K –Interest Rate7% – 8.5% –Overhead 30K – 35K –Profit Residual

25. Contractor’s Bid Analysis

26. CDF of Profits for Alternative Bid Prices