Chapter 12: Risk, Capital Budgeting, and Diversification

1
Chapter 12 Risk, Capital Budgeting, and
Diversification

• How to incorporate Risk into the model Monte
  Carlo Simulation
• Return and Risk
• Optimal Portfolio

2
Simulation

• 1. Start with the standard capital budgeting
  problem
• 2. We add uncertainty into the problem. What if
  some of input variables change in the future?
• A. Sensitivity how the result changes with
  respect to a change in some variables. Sometimes
  it is sensitive, sometimes not. We focus on the
  variables to which the results are sensitive.
  Skip Exhibit 12-3, 4, and 5.
• B. Scenario Analysis (review this in Chapter 11)
• C. Monte Carlo Simulation Full-scale scenario
  with probability distribution You need to install
  ExcSim Add-ins on the Website. Also may skip page
  405-408.
• New functions Monte Carlo Simulation

3
Basic Statistics and Excel functions

• Expected Return Average ( )
• Variance VAR ( )
• Standard Deviation STDEV ( )
• Covariance COVAR ( , )
• Correlation CORREL ( , )
• Probability Distribution Possible events (Cash
  flow) and its probability

4
Basic Statistics and Excel functions

• Expected Return
• Variance
• Probability Distribution Possible events (X
  Cash flow) and its probability ( P )

5
Basic Statistics and Excel functions

• Standard Deviation Squared Root of Variance
• These are expected numbers. In practice we use
  the estimated numbers (sample mean, sample
  variance, etc.)

6
Basic Statistics (Estimates) and Excel functions

• Expected Return Average ( )
• Variance VAR ( )
• Standard Deviation STDEV ( )
• Covariance COVAR ( , )
• Correlation (Rho) CORREL ( , )

7

• The Objective of Portfolio Management
• Maximize Portfolio return and minimize
  Portfolio risk.

8

• PORTFOLIO RETURN with 2 assets
• E(RP) X1 E(R1) (1-X1) E(R2)
• where X1 and (1-X1) are the investment weights
  for asset 1 and asset 2 and
• E(R1) and E(R2) are the expected returns on
  asset 1 and asset 2.
• RISK
• ?2P X21 ?21 2X1(1-X1)RHO12 ?1?2
  (1-X1)2 ?22
• OR
• ?2P X21 ?21 2X1(1-X1)COV12
  (1-X1)2 ?22

9

• RISK (Measured by variance or standard deviation
  of returns)
• ?2P X21 ?21 2X1(1-X1)RHO12 ?1?2
  (1-X1)2 ?22 OR
• ?2P X21 ?21 2X1(1-X1)COV12
• (1-X1)2 ?22

10
Optimal Portfolio Problem

• Choose the investment weight (X1, X2) so that
  portfolio risk is minimized, given a portfolio
  return.
• Solver Function
• Read Chapter 12