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

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

4 Types of Real Options Abandonment Abandonment Contraction Contraction Temporary suspension Temporary suspension Permanent Permanent Switch / Transition Switch / Transition Change Product Mix Change Product Mix Change Input Mix Change Input Mix Technical Obsolescence Technical Obsolescence Wait / Timing Resolve Uncertainty Identify Demand Expansion Existing Products New Geographic Markets Growth New Products R&D

5 Four Procedures for Valuing Real Options 1.DCF analysis of expected cash flows, ignoring the option. 2.Qualitative assessment of the real option’s 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. Initial cost = $70 million, Cost of Capital = 10%, risk-free rate = 6%, cash flows occur for 3 years. DemandProbability Annual cash flow High30%$45 Average40%$30 Low30%$15

7 Approach 1: DCF Analysis (ignoring option) E(CF) =.3($45)+.4($30)+.3($15) E(CF) =.3($45)+.4($30)+.3($15) = $30. PV of expected CFs = ($30/1.1) + ($30/1.12) + ($30/1/13) PV of expected CFs = ($30/1.1) + ($30/1.12) + ($30/1/13) = $74.61 million. Expected NPV = $ $70 Expected NPV = $ $70 = $4.61 million

8 Procedure 2: Qualitative Assessment The value of any real option increases if: The value of any real option increases if: the underlying project is very risky the underlying project is very risky there is a long time before you must exercise the option 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. 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.) NPV this $35.70 $1.79 $0.00 Cost 0Prob Scenario a -$70$45 30% $040%-$70$30 30% $0 Future Cash Flows Discount the cost of the project at the risk-free rate, since the cost is known. Discount the operating cash flows at the cost of capital. Example: $35.70 = - $70/ $45/ $45/ $45/ See FM12 Ch 13 Mini Case.xls for calculations later in this set of slides.

10 Project’s Expected NPV if Wait E(NPV) = E(NPV) = [0.3($35.70)]+[0.4($1.79)] + [0.3 ($0)] [0.3($35.70)]+[0.4($1.79)] + [0.3 ($0)] E(NPV) = $11.42 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. 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. 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. X = strike price = cost to implement project = $70 million. r RF = risk-free rate = 6%. r RF = risk-free rate = 6%. t = time to maturity = 1 year. t = time to maturity = 1 year. S (or P) = current stock price = $67.82 see following spreadsheet. S (or P) = current stock price = $67.82 see following spreadsheet. σ 2 = variance of stock return = 14.2% see following spreadsheet. σ 2 = 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: Link to Real Options Valuation Excel file: FM 12 Ch 13 Mini Case.xls (Brigham & Ehrhardt file) FM 12 Ch 13 Mini Case.xls (Brigham & Ehrhardt file) FM 12 Ch 13 Mini Case.xls FM 12 Ch 13 Mini Case.xls

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  Variance of Return Time value of money r Risk-free Rate

15 Calculating the NPV Quotient (NPV q ) _____ NPV q 1.0_____ Negative NPVPositive NPV Calls Out-of-MoneyCalls In-the-Money

16 Using Black-Scholes to Price a Real Option Identify 5 key Inputs to B-S OPM: Identify 5 key Inputs to B-S OPM: Initial Investment = X = $100 Initial Investment = X = $100 Current Asset’s Worth = S = $90 Current Asset’s Worth = S = $90 Asset’s Riskiness =  = 40% Asset’s Riskiness =  = 40% Deferral Time = 3 years Deferral Time = 3 years Risk-free Rate = 5% Risk-free Rate = 5% Note that current NPV = -10 but NPVq = 1.04 Note that current NPV = -10 but NPVq = 1.04 Using B-S OPM method, the Option’s worth = Using B-S OPM method, the Option’s worth =.284 * $90 = !! Above analysis shows that this might be a promising project in the future (the option to wait is valuable). 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 < 1.0) In the Money (NPVq > 1.0) Very Low Exercise Never Exercise Now Low Doubtful: NPV<0; NPV q <1; &  2 is low. Wait if possible. Otherwise, exercise early. High Less Promising: NPV < 0 and NPV q < 1; but  2 is high. Very Promising: NPV 1

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

19 Overview of Risk Governance Issues Key Risk Management Responsibilities of Senior Managers / Board Members: Key Risk Management Responsibilities of Senior Managers / Board Members: 1. Board / Senior Management must approve firm’s risk management policies and procedures. 2. Ensure that operating team has requisite technical skills to execute the firm’s policies and procedures. 3. Evaluate the performance of the risk management activity on a periodic basis. 4. 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. 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). 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): Precursors to VAR (and still in use): Maturity Gap Maturity Gap Duration and the Value of a 1 basis point change Duration and the Value of a 1 basis point change Convexity plus Duration Convexity plus Duration Option-based Measures (delta, gamma, vega). 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. VAR provides a succinct, dollar-based summary measure of risk which allows management to aggregate risks. Also, traditional risk measures had several weaknesses: Also, traditional risk measures had several weaknesses: They could not be aggregated over different types of risk factors/securities. They could not be aggregated over different types of risk factors/securities. They do not measure capital at risk. They do not measure capital at risk. They do not facilitate top-down control of risk exposures. 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) 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) (See Spreadsheet) (See Spreadsheet) (See Spreadsheet)

22 Calculating VAR (Three Methods)… Can calculate VAR via two types of simulation methods and one analytic method. Can calculate VAR via two types of simulation methods and one analytic method. Historical Simulation: Historical Simulation: 1. Identify Factors affecting market values of securities in the portfolio 2. Simulate future values of these Factors using Historical Data: 3. Use the simulated Factor values to estimate the value of the portfolio several times (usually 1,000 or more times) 4. Create a histogram of the portfolio’s 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: 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). 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: Analytic Variance-Covariance Method: Can be simpler to estimate since you don’t need the entire distribution of Factor values (summary measures will suffice). Can be simpler to estimate since you don’t need the entire distribution of Factor values (summary measures will suffice). 1. Specify Distributions and Payoff Profiles (e.g., normal and linear). 2. Decompose Securities into Simpler Transactions/Buckets. 3. Estimate Variances/Covariances of “Standard Transactions” 4. 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. 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). 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. 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: Empirical Tests – to date, tests of the three methods suggest that the approaches can yield similar results when: Portfolio payoffs are linear. Portfolio payoffs are linear. 95% confidence level is used. 95% confidence level is used. There are not many large outliers in the historical data set. 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: 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). 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. Large number of outliers in the historical data set. 99% or higher confidence level is used. 99% or higher confidence level is used.

26 Choosing between the Methods As in much of life, “It Depends!” 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 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 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). 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 CB’s and Insurance Co’s with active trading portfolios). Firms that have their values determined primarily by financial market risks should use VAR (e.g., Investment banks, Brokers/Dealers, as well as CB’s and Insurance Co’s 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 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. 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: Parameter Selection: Time Horizon (e.g., 1-day or 10-day VAR) Time Horizon (e.g., 1-day or 10-day VAR) Confidence Level (usually 95% or 99%) Confidence Level (usually 95% or 99%) Variance-Covariance Data (unstable correlations vs. +1.0) Variance-Covariance Data (unstable correlations vs. +1.0) Other Important Issues: Other Important Issues: Sensitivity Analysis (how sensitive is the VAR estimate to the data set used in the analysis?) Sensitivity Analysis (how sensitive is the VAR estimate to the data set used in the analysis?) Scenario Analysis (worst case vs. “standard” case) Scenario Analysis (worst case vs. “standard” case) Stress-testing (how does VAR change as the above parameters change?) 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?) Back-testing (how good have past VAR estimates been in relation to actual portfolio changes?)