Real Options, Risk Governance, and Value-at-Risk (VAR)

1
Real Options, Risk Governance, and Value-at-Risk
(VAR)
2
What is a real option?

• Real options exist when managers can influence
  the size and risk of a projects cash flows by
  taking different actions during the projects
  life in response to changing market conditions.
• Alert managers always look for real options in
  projects.
• Smarter managers try to create real options.

3
Introduction to Real Options

• Alternative, yet complementary, approach to
  DCF-based Capital Budgeting.
• Many corporate investments (especially
  strategic ones) have embedded options.
• Overlooking these options can lead to
• under-valuing investment projects.
• Using Real Options approach can improve project
  management as well as valuations.

4
Types of Real Options

• Abandonment
• Contraction
• Temporary suspension
• Permanent
• Switch / Transition
• Change Product Mix
• Change Input Mix
• Technical Obsolescence

• Wait / Timing
• Resolve Uncertainty
• Identify Demand
• Expansion
• Existing Products
• New Geographic Markets
• Growth
• New Products
• RD

5
Four Procedures for Valuing Real Options

• 1.DCF analysis of expected cash flows, ignoring
  the option.
• 2.Qualitative assessment of the real options
  value.
• 3.Decision tree analysis.
• 4.Standard model for a corresponding financial
  option.

6
Analysis of a Real Option Example of a Basic
Project

• Initial cost 70 million, Cost of Capital
  10, risk-free rate 6, cash flows occur for 3
  years.

7
Approach 1 DCF Analysis (ignoring option)

• E(CF) .3(45).4(30).3(15)
• 30.
• PV of expected CFs (30/1.1) (30/1.12)
  (30/1/13)
• 74.61 million.
• Expected NPV 74.61 - 70
• 4.61 million

8
Procedure 2 Qualitative Assessment

• The value of any real option increases if
• the underlying project is very risky
• there is a long time before you must exercise the
  option
• This project is risky and has one year before we
  must decide, so the option to wait is probably
  valuable.

9
Procedure 3 Decision Tree Analysis (Implement
only if demand is not low.)
10
Projects Expected NPV if Wait

• E(NPV)
• 0.3(35.70)0.4(1.79) 0.3 (0)
• E(NPV) 11.42

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Procedure 4 Use the existing model of a
financial option.

• The option to wait resembles a financial call
  option-- we get to buy the project for 70
  million in one year if value of project in one
  year is greater than 70 million.
• This is like a call option with a strike price of
  70 million and an expiration date of one year.

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Inputs to Black-Scholes Model for Option to Wait

• X strike price cost to implement project
  70 million.
• rRF risk-free rate 6.
• t time to maturity 1 year.
• S (or P) current stock price 67.82 see
  following spreadsheet.
• s2 variance of stock return 14.2 see
  following spreadsheet.

13
Discounted Cash Flow Valuation and Value-Based
Management

• Link to Real Options Valuation Excel file
• FM 12 Ch 13 Mini Case.xls (Brigham Ehrhardt
  file)

14
Relation between Financial Options Real Options
15
Calculating the NPV Quotient (NPVq)

• _____ NPVq lt 1.0________NPVq gt 1.0_____
• Negative NPV Positive NPV
• Calls Out-of-Money Calls In-the-Money

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Using Black-Scholes to Price a Real Option

• Identify 5 key Inputs to B-S OPM
• Initial Investment X 100
• Current Assets Worth S 90
• Assets Riskiness s 40
• Deferral Time 3 years
• Risk-free Rate 5
• Note that current NPV -10 but NPVq 1.04
• Using B-S OPM method, the Options worth
• .284 90 25.56 !!
• Above analysis shows that this might be a
  promising project in the future (the option to
  wait is valuable).

17
Tomato Gardens Real Options
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Real Option Implementation Issues

• Need to Simplify Complex Projects.
• Difficulties in Estimating Volatility (use
  simulation, judgment, coefficient of variation)
• Checking Model Validity (distributions, decision
  trees).
• Interpreting Results
• (sensitivity analysis is a must!)

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Overview of Risk Governance Issues

• Key Risk Management Responsibilities of Senior
  Managers / Board Members
• Board / Senior Management must approve firms
  risk management policies and procedures.
• Ensure that operating team has requisite
  technical skills to execute the firms policies
  and procedures.
• Evaluate the performance of the risk management
  activity on a periodic basis.
• Maintain oversight of the risk management
  activity (possibly with a board sub-committee).

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Ways to Measure Manage Risk

• Value-at-Risk (VAR) has become a popular summary
  measure of risk.
• VAR is most useful when measuring market-based
  risks of financial companies (less meaningful for
  many non-financial companies).
• Precursors to VAR (and still in use)
• Maturity Gap
• Duration and the Value of a 1 basis point change
• Convexity plus Duration
• Option-based Measures (delta, gamma, vega).

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Why VAR has Become so Popular

• VAR provides a succinct, dollar-based summary
  measure of risk which allows management to
  aggregate risks.
• Also, traditional risk measures had several
  weaknesses
• They could not be aggregated over different types
  of risk factors/securities.
• They do not measure capital at risk.
• They do not facilitate top-down control of risk
  exposures.
• VAR is easy for senior management to interpret
  It measures the maximum dollar amount the firm
  can lose over a specified time horizon at a
  specified probability level (e.g., the 1-day VAR
  with 99 confidence is 5M)
• (See Spreadsheet)

22
Calculating VAR (Three Methods)

• Can calculate VAR via two types of simulation
  methods and one analytic method.
• Historical Simulation
• Identify Factors affecting market values of
  securities in the portfolio
• Simulate future values of these Factors using
  Historical Data
• Use the simulated Factor values to estimate the
  value of the portfolio several times (usually
  1,000 or more times)
• Create a histogram of the portfolios expected
  change in value and identify the relevant
  probability level for the VAR calculation (e.g.,
  find the change in portfolio that occurs at the
  lowest 1 of the distribution).

23
Calculating VAR (cont.)

• Monte Carlo Simulation
• Follow the same steps as in the Historical
  Simulation method except you use Monte Carlo
  techniques to obtain the simulated Factor values
  (step 2 of the previous slide).
• Analytic Variance-Covariance Method
• Can be simpler to estimate since you dont need
  the entire distribution of Factor values (summary
  measures will suffice).
• Specify Distributions and Payoff Profiles (e.g.,
  normal and linear).
• Decompose Securities into Simpler
  Transactions/Buckets.
• Estimate Variances/Covariances of Standard
  Transactions
• Calculate VAR based on standard definition of
  variance.

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Strengths / Weaknesses of the Three VAR Methods

• Historical Simulation does not assume specific
  distributions for the securities and uses
  real-world data but it requires pricing models
  for all instruments and allows limited
  sensitivity analysis.
• Monte Carlo Simulation makes it easier to do
  sensitivity analysis but requires the analyst to
  specify asset distributions as well as pricing
  models (also, one step removed from real-world
  prices).
• Analytic Method is intuitively simpler and does
  not require any pricing models but it is not
  conducive to sensitivity analysis and cannot
  handle non-linear payoff profiles such as options.

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Differences in VAR Estimates from the Three
Methods

• Empirical Tests to date, tests of the three
  methods suggest that the approaches can yield
  similar results when
• Portfolio payoffs are linear.
• 95 confidence level is used.
• There are not many large outliers in the
  historical data set.
• Where Differences can Occur biggest differences
  can occur between the 2 simulation approaches and
  the analytic method when
• Non-linear payoffs are a significant share of the
  portfolio and they do not cancel out (e.g., long
  a large number of put options).
• Large number of outliers in the historical data
  set.
• 99 or higher confidence level is used.

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Choosing between the Methods

• As in much of life, It Depends!
• If the portfolio has linear (or weakly
  non-linear) payoffs, then the Analytic method
  might be best.
• If the portfolio has strongly non-linear payoffs,
  then the two Simulation methods are better.
• If stress-testing and sensitivity analysis are
  needed, then Monte Carlo Simulation is the
  preferred method (however, it can be very complex
  to remove all possible arbitrage opportunities
  from the simulation).

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Who Should Use VAR?

• Firms that have their values determined primarily
  by financial market risks should use VAR (e.g.,
  Investment banks, Brokers/Dealers, as well as
  CBs and Insurance Cos with active trading
  portfolios).
• Firms that have their values determined by growth
  opportunities or growth options probably should
  not use VAR as their primary risk measure
• (e.g., high tech or bio tech firms).
• For firms with growth options, a VAR estimate is
  typically not relevant because the real value of
  these companies comes from non-traded assets
  where no-arbitrage arguments typically do not
  hold.

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Implementing VAR

• Parameter Selection
• Time Horizon (e.g., 1-day or 10-day VAR)
• Confidence Level (usually 95 or 99)
• Variance-Covariance Data (unstable correlations
  vs. 1.0)
• Other Important Issues
• Sensitivity Analysis (how sensitive is the VAR
  estimate to the data set used in the analysis?)
• Scenario Analysis (worst case vs. standard
  case)
• Stress-testing (how does VAR change as the above
  parameters change?)
• Back-testing (how good have past VAR estimates
  been in relation to actual portfolio changes?)