Real Options, Risk Real Options, Risk Governance, and Value-at-Risk Governance, and Value-at-Risk

(VAR)(VAR)

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What is a real option? What is a real option?

Real options exist when Real options exist when managers can managers can influenceinfluence the size and risk of a the size and risk of a project’s cash flows by taking project’s cash flows by taking differentdifferent actions during the project’s life in actions during the project’s life in response to changing market conditions.response to changing market conditions.

Alert managersAlert managers always always look forlook for real real options in projects.options in projects.

Smarter managersSmarter managers try to try to createcreate real real options.options.

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Introduction to Real OptionsIntroduction to Real Options

AlternativeAlternative, yet , yet complementarycomplementary, approach to , approach to DCF-based Capital Budgeting.DCF-based Capital Budgeting.

Many corporate investments (especially Many corporate investments (especially “strategic” ones) have “strategic” ones) have embedded optionsembedded options..

Overlooking these options can lead to Overlooking these options can lead to

under-valuingunder-valuing investment projects. investment projects. Using Real Options approach can Using Real Options approach can improve improve

project managementproject management as well as as well as valuationsvaluations..

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Types of Real OptionsTypes of Real Options

AbandonmentAbandonment ContractionContraction

Temporary Temporary suspensionsuspension

PermanentPermanent Switch / TransitionSwitch / Transition

Change Product MixChange Product Mix Change Input MixChange Input Mix Technical Technical

ObsolescenceObsolescence

Wait / TimingWait / Timing Resolve UncertaintyResolve Uncertainty Identify DemandIdentify Demand

ExpansionExpansion Existing ProductsExisting Products New Geographic New Geographic

MarketsMarkets GrowthGrowth

New ProductsNew Products R&DR&D

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Four Procedures for Four Procedures for Valuing Real OptionsValuing Real Options

1.1.DCF analysisDCF analysis of expected cash flows, of expected cash flows, ignoringignoring the option. the option.

2.2.QualitativeQualitative assessment of the real assessment of the real option’s value.option’s value.

3.3.Decision treeDecision tree analysis. analysis.

4.Standard model for a corresponding 4.Standard model for a corresponding financial optionfinancial option..

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Analysis of a Real Option: Analysis of a Real Option: Example of a Basic ProjectExample of a Basic Project

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

Demand ProbabilityAnnual

cash flow

High 30% $45

Average 40% $30

Low 30% $15

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Approach 1: Approach 1: DCF Analysis (ignoring option)DCF Analysis (ignoring option)

E(CF) =.3($45)+.4($30)+.3($15) E(CF) =.3($45)+.4($30)+.3($15)

= $30.= $30. PV of expected CFs = ($30/1.1) + PV of expected CFs = ($30/1.1) +

($30/1.12) + ($30/1/13) ($30/1.12) + ($30/1/13)

= $74.61 million.= $74.61 million. Expected NPV = $74.61 - $70 Expected NPV = $74.61 - $70

= = $4.61$4.61 million million

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Procedure 2: Procedure 2: Qualitative AssessmentQualitative Assessment

The value of any real option increases The value of any real option increases if:if: the underlying project is very riskythe underlying project is very risky there is a long time before you must there is a long time before you must

exercise the optionexercise the option This project is risky and has one year This project is risky and has one year

before we must decide, so the option to before we must decide, so the option to wait is wait is probablyprobably valuable. valuable.

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Procedure 3: Decision Tree Procedure 3: Decision Tree Analysis Analysis (Implement (Implement only ifonly if demand demand is is notnot low.) low.)

NPV this

$35.70

$1.79

$0.00

Cost

0 Prob. 1 2 3 4 Scenarioa

-$70 $45 $45 $4530%

$0 40% -$70 $30 $30 $3030%

$0 $0 $0 $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 = -$70/1.06 + $45/1.12 + $45/1.13 + $45/1.13. See FM12 Ch 13 Mini Case.xls for calculations later in this set of slides.

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Project’s Expected NPV Project’s Expected NPV if Waitif 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) = E(NPV) = $11.42$11.42

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Procedure 4: Use the existing Procedure 4: Use the existing model of a financial option.model of a financial option.

The option to wait resembles a financial The option to wait resembles a financial call option-- we get to “buy” the project call option-- we get to “buy” the project for $70 million in one year if value of for $70 million in one year if value of project in one year is greater than $70 project in one year is greater than $70 million.million.

This is like a This is like a call optioncall option with a with a strike strike price of $70 millionprice of $70 million and an expiration and an expiration date of one year. date of one year.

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Inputs to Black-Scholes Model Inputs to Black-Scholes Model for Option to Waitfor Option to Wait

X = strike price = cost to implement X = strike price = cost to implement project = $70 million.project = $70 million.

rrRFRF = risk-free rate = 6%. = risk-free rate = 6%. t = time to maturity = 1 year.t = time to maturity = 1 year. S (or P) = current stock price = $67.82 S (or P) = current stock price = $67.82

see following spreadsheet. see following spreadsheet. σσ22 = variance of stock return = 14.2% = variance of stock return = 14.2%

see following spreadsheet.see following spreadsheet.

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Discounted Cash Flow Valuation and Discounted Cash Flow Valuation and Value-Based ManagementValue-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) (Brigham & Ehrhardt file)

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Relation between Financial Relation between Financial Options Options & Real Options& Real Options

Corporate ProjectCorporate Project VariableVariable Financial Call Financial Call OptionOption

Expenditures to Expenditures to acquire assetacquire asset

XX Exercise PriceExercise Price

PV of acquired PV of acquired assetasset

SS Stock PriceStock Price

Time that decision Time that decision can be deferredcan be deferred

tt Time to ExpirationTime to Expiration

Riskiness of assetRiskiness of asset Variance of ReturnVariance of Return

Time value of Time value of moneymoney

rr Risk-free RateRisk-free Rate

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Calculating the NPV Quotient Calculating the NPV Quotient (NPV(NPVqq))

__________ NPV NPVqq < 1.0 < 1.0________||________NPVNPVqq > 1.0 > 1.0__________

Negative NPVNegative NPV Positive NPVPositive NPV

Calls Out-of-MoneyCalls Out-of-Money Calls In-the-MoneyCalls In-the-Money

)(es)Expenditur Capital(

Flows)Cash Net (

XPV

S

PV

ExpectedPVNPVq

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Using Black-Scholes to Price Using Black-Scholes to Price a Real Optiona Real Option

Identify Identify 5 key Inputs5 key Inputs to B-S OPM: to B-S OPM: Initial Investment = X = $100Initial Investment = X = $100 Current Asset’s Worth = S = $90Current Asset’s Worth = S = $90 Asset’s Riskiness = Asset’s Riskiness = = 40% = 40% Deferral Time = 3 yearsDeferral Time = 3 years Risk-free Rate = 5%Risk-free Rate = 5%

Note that Note that current NPVcurrent NPV = = -10-10 but NPVq = but NPVq = 1.041.04 Using B-S OPM method, the Option’s worth = Using B-S OPM method, the Option’s worth =

.284 * $90 = .284 * $90 = +25.56 !!+25.56 !! Above analysis shows that this might be a Above analysis shows that this might be a

promising project promising project in the futurein the future (the option to (the option to wait is valuable)wait is valuable)..

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““Tomato Gardens” & Real Tomato Gardens” & Real OptionsOptions

Cumul. Cumul. VariancVariancee

Out of the Out of the Money (NPVq < Money (NPVq <

1.0)1.0)

In the Money In the Money

(NPVq > 1.0)(NPVq > 1.0)

Very LowVery Low Exercise Exercise NeverNever Exercise Exercise NowNow

LowLow Doubtful:Doubtful: NPV<0; NPV<0; NPVNPVqq<1; & <1; & 22 is is low.low.

WaitWait if possible. if possible. Otherwise, exercise Otherwise, exercise early.early.

HighHigh Less Promising:Less Promising: NPV < 0 and NPVNPV < 0 and NPVqq < 1; but < 1; but 22 is high. is high.

Very Promising:Very Promising:

NPV < 0 but NPVNPV < 0 but NPVqq > > 11

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Real Option Implementation Real Option Implementation IssuesIssues

Need to Need to SimplifySimplify Complex Projects. Complex Projects.

Difficulties in Difficulties in Estimating VolatilityEstimating Volatility (use (use simulation, judgment, coefficient of simulation, judgment, coefficient of variation)variation)

Checking Checking Model ValidityModel Validity (distributions, (distributions, decision trees).decision trees).

Interpreting Results:Interpreting Results: (sensitivity analysis is (sensitivity analysis is a must!a must!))

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Overview of Risk Governance Overview of Risk Governance IssuesIssues

Key Risk Management Responsibilities of Senior Key Risk Management Responsibilities of Senior Managers / Board Members:Managers / Board Members:

1.1. Board / Senior ManagementBoard / Senior Management must must approve firm’s risk approve firm’s risk management policies and proceduresmanagement policies and procedures..

2.2. Ensure that Ensure that operating team has requisite technical skillsoperating team has requisite technical skills to execute the firm’s policies and procedures.to execute the firm’s policies and procedures.

3.3. Evaluate the performanceEvaluate the performance of the risk management of the risk management activity on a periodic basis.activity on a periodic basis.

4.4. Maintain oversightMaintain oversight of the risk management activity of the risk management activity (possibly with a board sub-committee).(possibly with a board sub-committee).

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Ways to Measure & Manage RiskWays to Measure & Manage Risk Value-at-RiskValue-at-Risk (VAR) (VAR) has become a popular has become a popular

summary measure of risk.summary measure of risk. VAR is VAR is mostmost useful when measuring market- useful when measuring market-

based risks of financial companies (based risks of financial companies (lessless meaningful for many non-financial companies).meaningful for many non-financial companies).

Precursors to VAR (and still in use):Precursors to VAR (and still in use): Maturity GapMaturity Gap Duration and the Value of a 1 basis point changeDuration and the Value of a 1 basis point change Convexity plus DurationConvexity plus Duration Option-based Measures (delta, gamma, vega).Option-based Measures (delta, gamma, vega).

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Why VAR has Become so PopularWhy VAR has Become so Popular VARVAR provides a succinct, provides a succinct, dollar-based summary measuredollar-based summary measure

of risk which allows management to of risk which allows management to aggregate risksaggregate 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 They could not be aggregated over different types of risk

factors/securities.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 VAR is easyeasy for senior management to interpret: for senior management to interpret: It It measures the maximum measures the maximum dollar amountdollar amount the firm can lose the firm can lose over a specified over a specified time horizontime horizon at a specified at a specified probability probability levellevel (e.g., the 1-day VAR with 99% confidence is $5M) (e.g., the 1-day VAR with 99% confidence is $5M)

(See Spreadsheet)

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Calculating VAR (Three Methods)Calculating VAR (Three Methods)……

Can calculate VAR via Can calculate VAR via twotwo types of simulation types of simulation methods and methods and oneone analytic method. analytic method.

Historical Simulation: Historical Simulation: 1.1. Identify FactorsIdentify Factors affecting market values of securities in the affecting market values of securities in the

portfolioportfolio2.2. Simulate future valuesSimulate future values of these Factors using Historical Data: of these Factors using Historical Data:3.3. Use the simulated Factor values to Use the simulated Factor values to estimate the value of the estimate the value of the

portfolio several timesportfolio several times (usually 1,000 or more times) (usually 1,000 or more times)4.4. Create a histogramCreate a histogram of the portfolio’s expected change in of the portfolio’s expected change in

value and value and identify the relevant probability levelidentify the relevant probability level for the VAR for the VAR calculation (e.g., find the change in portfolio that occurs at calculation (e.g., find the change in portfolio that occurs at the lowest 1% of the distribution).the lowest 1% of the distribution).

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Calculating VAR Calculating VAR (cont.)(cont.) Monte Carlo Simulation: Monte Carlo Simulation:

Follow the Follow the same steps same steps as in the Historical Simulation methodas in the Historical Simulation method exceptexcept you use you use Monte Carlo techniquesMonte Carlo techniques to obtain the to obtain the simulated Factor values (step 2 of the previous slide).simulated Factor values (step 2 of the previous slide).

Analytic Variance-Covariance Method:Analytic Variance-Covariance Method: Can beCan be simpler to estimate simpler to estimate since you don’t need the entire since you don’t need the entire

distribution of Factor values (summary measures will suffice).distribution of Factor values (summary measures will suffice).1.1. Specify Distributions and Payoff ProfilesSpecify Distributions and Payoff Profiles (e.g., normal and (e.g., normal and

linear).linear).2.2. Decompose SecuritiesDecompose Securities into Simpler Transactions/Buckets. into Simpler Transactions/Buckets.3.3. Estimate Variances/CovariancesEstimate Variances/Covariances of “Standard Transactions” of “Standard Transactions”4.4. Calculate VAR based on Calculate VAR based on standard definition of variancestandard definition of variance..

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Strengths / Weaknesses of the Strengths / Weaknesses of the Three VAR MethodsThree VAR Methods

Historical SimulationHistorical Simulation does does notnot assume specific distributions for assume specific distributions for the securities and uses real-world data the securities and uses real-world data butbut it requires pricing it requires pricing models for models for allall instruments and allows limited sensitivity instruments and allows limited sensitivity analysis.analysis.

Monte Carlo SimulationMonte Carlo Simulation makes it easier to do sensitivity analysis makes it easier to do sensitivity analysis butbut requires the analyst to specify asset distributions requires the analyst to specify asset distributions as well asas well as pricing models (also, one step removed from real-world prices).pricing models (also, one step removed from real-world prices).

Analytic MethodAnalytic Method is intuitively simpler and does not require any is intuitively simpler and does not require any pricing models pricing models butbut it is it is notnot conducive to sensitivity analysis conducive to sensitivity analysis and cannot handle and cannot handle non-linearnon-linear payoff profiles such as options. payoff profiles such as options.

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Differences in VAR Estimates Differences in VAR Estimates from the Three Methodsfrom the Three Methods Empirical TestsEmpirical Tests – to date, tests of the three methods – to date, tests of the three methods

suggest that the approaches can yield suggest that the approaches can yield similarsimilar results when: results when: Portfolio payoffs are Portfolio payoffs are linearlinear.. 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 OccurWhere Differences can Occur – biggest – biggest differencesdifferences can can occur between the 2 simulation approaches and the analytic occur between the 2 simulation approaches and the analytic method when:method when: Non-linearNon-linear payoffs are a payoffs are a significant sharesignificant share of the portfolio of the portfolio andand they they do do

not cancel outnot cancel out (e.g., long a large number of put options). (e.g., long a large number of put options). Large number of outliersLarge number of outliers in the historical data set. in the historical data set. 99% or higher confidence level is used.99% or higher confidence level is used.

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Choosing between the MethodsChoosing between the Methods As in much of life, As in much of life, “It Depends!”“It Depends!”

If the portfolio has If the portfolio has linearlinear (or weakly non-linear) (or weakly non-linear) payoffs, then the payoffs, then the Analytic methodAnalytic method might be best. might be best.

If the portfolio has If the portfolio has strongly non-linearstrongly non-linear payoffs, then payoffs, then the the two Simulation methodstwo Simulation methods are better. are better.

If If stress-testingstress-testing and and sensitivity analysissensitivity analysis are needed, are needed, then then Monte Carlo SimulationMonte Carlo Simulation is the preferred method is the preferred method (however, it can be very complex to remove all (however, it can be very complex to remove all possible arbitrage opportunities from the simulation).possible arbitrage opportunities from the simulation).

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Who Should Use VAR?Who Should Use VAR? Firms that have their values determined primarily by Firms that have their values determined primarily by

financial market risks financial market risks shouldshould use VAR (e.g., Investment use VAR (e.g., Investment banks, Brokers/Dealers, as well as CB’s and Insurance banks, Brokers/Dealers, as well as CB’s and Insurance Co’s with active trading portfolios).Co’s with active trading portfolios).

Firms that have their values determined by growth Firms that have their values determined by growth opportunities or “growth options” probably opportunities or “growth options” probably should notshould not use use VAR as their primary risk measure VAR as their primary risk measure (e.g., high tech or bio tech firms).(e.g., high tech or bio tech firms).

For firms with growth options, a VAR estimate is typically For firms with growth options, a VAR estimate is typically notnot relevant because the real value of these companies relevant because the real value of these companies comes from comes from non-traded assetsnon-traded assets where no-arbitrage where no-arbitrage arguments typically arguments typically do notdo not hold. hold.

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Implementing VARImplementing 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. Variance-Covariance Data (unstable correlations vs.

+1.0)+1.0)

Other Important Issues:Other Important Issues: Sensitivity AnalysisSensitivity Analysis (how sensitive is the VAR (how sensitive is the VAR

estimate to the data set used in the analysis?) estimate to the data set used in the analysis?) Scenario AnalysisScenario Analysis (worst case vs. “standard” case) (worst case vs. “standard” case) Stress-testingStress-testing (how does VAR change as the above (how does VAR change as the above

parameters change?)parameters change?) Back-testingBack-testing (how good have past VAR estimates (how good have past VAR estimates

been in relation to actual portfolio changes?)been in relation to actual portfolio changes?)