Materials for Lecture 16

bugenigmaΛογισμικό & κατασκευή λογ/κού

30 Οκτ 2013 (πριν από 3 χρόνια και 9 μήνες)

53 εμφανίσεις

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


Strategic Asset Allocation Guidelines


Portfolio Objective


High

Current

Income



Conservative

Income


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%

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
)


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



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


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 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


Contractor’s Bid Analysis

CDF of Profits for Alternative Bid Prices