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.

Demand Probability Annual cash flow
High 30 45
Average 40 30
Low 30 15
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

11
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.

12
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
Corporate Project Variable Financial Call Option
Expenditures to acquire asset X Exercise Price
PV of acquired asset S Stock Price
Time that decision can be deferred t Time to Expiration
Riskiness of asset s2 Variance of Return
Time value of money r Risk-free Rate
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

16
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
Cumul. Variance Out of the Money (NPVq lt 1.0) In the Money (NPVq gt 1.0)
Very Low Exercise Never Exercise Now
Low Doubtful NPVlt0 NPVqlt1 s2 is low. Wait if possible. Otherwise, exercise early.
High Less Promising NPV lt 0 and NPVq lt 1 but s2 is high. Very Promising NPV lt 0 but NPVq gt 1
18
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!)

19
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).

20
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).

21
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.

24
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.

25
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.

26
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).

27
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.

28
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?)