Materials for Lecture 16 Read Chapters 13 and 14 Lecture 16 Portfolio Analyzer Low Corr.xlsx Lecture...

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

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

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


• 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 with three stocks or investments

• Find the best combination of the three• Note Corr Coef.


• Nine portfolios analyzed, expressed as percentage combinations of Investments 1-3


• 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


• 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

P1

P2

P3

P4

P5

P6

P7P8

P9

0.0970

0.0980

0.0990

0.1000

0.1010

0.1020

0.1030

0.1040

0.1050

0.1060

0.1070

0.1080

0.000000 0.000002 0.000004 0.000006 0.000008 0.000010 0.000012

ARAC

P1 P2 P3 P4 P5 P6 P7 P8 P9


• Next how does the preferred portfolio change as the investor considers investments with low correlation


• The results for simulating 9 portfolios where the individual investments have low correlation and near equal means

• Portfolios still have lower relative risk


• A portfolio (P6) is ranked second followed by P5

Stochastic Efficiency with Respect to A Function (SERF) Under a Neg. Exponential Utility Function

P1

P2

P3

P4

P5

P6

P7P8

P9

0.08

0.09

0.09

0.09

0.09

0.09

0.09

0.09

0.09

0.09

0.09

0 1E-06 2E-06 3E-06 4E-06 5E-06 6E-06 7E-06 8E-06

ARAC

P1 P2 P3 P4 P5 P6 P7 P8 P9


• 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

Strategic Asset Allocation Guidelines

Portfolio Objective

HighCurrentIncome

ConservativeIncome

Income with

Growth

Growth with

Income

Growth Aggressive

Growth

Asset Class

Cash Equivalent 5% 5% 5% 5% -- --

Short/Intermediate Investment-Grade Bonds

20% 30% 20% 10% -- --

Long Investment-Grade Bonds 50% 40% 25% 20% -- --

Speculative Bonds 15% -- -- -- -- --

Real Estate 10 % 5% 5% 5% -- --

U.S. Large-Cap Stocks -- 20% 30% 30% 55% 40%

U.S. Mid-Cap Stocks -- -- 10% 15% 20% 20%

U.S. Small-Cap Stocks -- -- -- 10% 15% 20%

Foreign Developed Stocks -- -- 5% 5% 10% 15%

Foreign Emerging Market Stocks

-- -- -- -- -- 5%


• 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)


• 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


• 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.


• 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


• 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


• 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:

- P(costs > 375,000) = 33.89%- P(costs > 400,000) = 16.67%- P(costs > 425,000) = 2.4%

- P(costs > 350,000) = 50.5%


• The bid if you ignore the risk– Average Cost is $350,850

Stochastic Analysis yields the following


• Because we are uncertain about the cost of facilitators and researchers we can run a scenario analysis on these costs


• 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

Contractor’s Bid Analysis

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

390000 395000 400000 405000 410000 415000 420000 425000 430000

Pro

b

CDF of Total Costs (black line) and Bid Price (red line)

TC Bid

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

-6000 -4000 -2000 0 2000 4000 6000 8000 10000

Pro

b

CDF of Profits given a bid of 400000

-10000 -5000 0 5000 10000 15000

PDF Approximation of Profits Given a Bid Price of 400000

-0.03 -0.02 -0.01 0.00 0.01 0.02 0.03

PDF Approximation for Rate of Return Given a Bid Price of 400000

ROR

CDF of Profits for Alternative Bid Prices

CDF

0

0.2

0.4

0.6

0.8

1

-100000 -50000 0 50000 100000 150000

Pro

b

P/L: 1 P/L: 2 P/L: 3 P/L: 4 P/L: 5

Materials for Lecture 16 Read Chapters 13 and 14 Lecture 16 Portfolio Analyzer Low Corr.xlsx Lecture...

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