Enterprise Risk Management & Capital Budgeting under Dependent Risks: An Integrated Framework

Tianyang Wang, Colorado State University(with Jing Ai, The University of Hawaii)

Motivations

• Enterprise risk management (ERM) help companies optimize operational decisions.

• Risk management and capital budgeting are two critical components of the dynamic corporate decision process. They naturally connected by the dependent risk exposures and a variety of other synergetic relationships within an intricate corporate structure

• It is challenging is to fully encompass the two components into the overall corporate decision making.

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• Enterprise risk management– “Coordinate” decisions of other corporate activities

• Froot et al. 1993 and Froot and Stein (1998)– Incorporated in the decision making process

• Ai et al. (2010)

• Capital budgeting– Modeling the internal allocation process

• The NPV standard (Graham and Harvey 2001, Graham et al. 2010)

– Agency problems • “Centralized” vs. “Delegated” (Marino and Matsusaka 2005)

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Literature Review

OverviewDevelop an integrated framework that allows to design optimal investment and risk management strategies jointly and endogenously• Characterize an optimal decision making problem with–Evaluations of capital requirements, cash flow potentials, and risk exposures first within each division –Corporate level optimal decisions in a multi-division, multi-project, multi-period environment–Fully accounting for dependent risks across business divisions and time periods–Simultaneously obtaining optimal risk management strategies• Uses the intuitive interface of decision tree as an auxiliary step

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• Solve an optimization problem of the corporate decision maker in capital allocation

• Model structure– Objective function: Maximize her appropriate utility function – Corporate “state of nature” tree: probability tree structure to capture

dependent risk within and across divisions and periods, using the copula model

– Characterize cash flows of the corporate project portfolio with the tree structure and a set of constraints • Logical consistency • Capital resource• Risk

– Incorporate RM strategies by recognizing cost and adjusting future cash flow positions

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Model Set-Up

Model Set-Up• Mapping decisions onto the corporate state of nature tree

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An Illustrative Example

• Consider a financial services company with a two-period planning horizon – Two business divisions: loan and insurance, each with one

potential project to invest in– In period 1, both are subject to market risk – In period 2, loan division is subject to credit risk and insurance

division is subject to actuarial pricing risk– These risks are dependent – The CEO makes investment decisions at the corporate level, given

an initial capital budget, by maximizing her expected utility from the final resource position at the end of the two-period horizon

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• Build the corporate state of nature tree with dependent risks • Distributional and dependency assumptions

– We use scaled beta distributions for its flexibility

– Correlation Structure among Risks

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An Illustrative Example

• Characterize cash flows of the corporate project portfolio– Investment requirements, risk-free interest rate, etc.

Decision For Investment ($ million) Notation

Division 1 (t=0) 7 Inv1(1)

Division 1 (t=1) 6 Inv1(2)

Division 2 (t=0) 7 Inv2(1)

Division 2 (t=1) 6 Inv2(2)

Initial Resources (Inv0) 30

Risk-Free Interest Rate 6%

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An Illustrative Example

An Illustrative Example

• Decision making process for division 1

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An Illustrative Example

• Decision making process for division 2

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• The corporate state of nature tree

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An Illustrative Example

An Illustrative Example• Objective function

– Using the mean-risk model, the CEO maximizes the certainty equivalent, CE = Expected future cash flow (EVT) – Risk

– Using lower semi-absolute deviation (LSAD) as the risk measure to focus on expected downside risk

– Risk = risk aversion coefficient (0.5)*LSAD• Model constraints

– Logical consistency constraints

– Capital resource constraints – Risk constraints Incorporating risk management strategies

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Optimal DecisionsX1,0,Y 1 α1,0 0.012X1,0,N 0 α2,0 0.737X1,1,Y 1 α1,1 0X1,1,N 0 α1,2 0.644X1,2,Y 1 α1,3 1X1,2,N 0 α2,1 0X1,3,Y 1 α2,2 0.592X1,3,N 0 α2,3 1X2,0,Y 1 X2,0,N 0 X2,1,Y 1 X2,1,N 0 X2,2,Y 1 X2,2,N 0 X2,3,Y 1 X2,3,N 0

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Optimal Decisions (ignoring risk dependence)X1,0,Y 1 α1,0 0X1,0,N 0 α2,0 0X1,1,Y 1 α1,1 0.581X1,1,N 0 α1,2 0.980X1,2,Y 1 α1,3 0.538X1,2,N 0 α2,1 0X1,3,Y 1 α2,2 0X1,3,N 0 α2,3 0X2,0,Y 0X2,0,N 1X2,1,Y 0X2,1,N 0X2,2,Y 0X2,2,N 0X2,3,Y 0X2,3,N 0

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Comparison of Optimal Values and Risk Exposures

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Project Valuation with risk free rate 33.71

Forgoing Hedging

Assumption of Independent Risks and No

Hedging

Assumption of Independent

Risks Complete Model

Optimal Value 45.87 46.13 46.60 47.90Value of Capital Budgeting and

Hedging Strategies 12.16 12.42

12.89 14.19

Diff% from The Complete Model -14.31% -12.47%

-9.16% 0.00%

Comparison of Risk Exposure

• Capital budgeting– Studying optimal capital budgeting in a multi-

divisional firm with dependent risk exposures.• Corporate risk management and ERM– Operationalizing the concepts of ERM in

incorporating risk management into the corporate decision making process.

• Decision analysis– Solve problem of capital budgeting and enterprise

risk management.

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Summary

Thank You!

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