econ finance

8/2/2019 Econ Finance

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Page 1Economic and Financial Perspectives on the Demand for Reinsurance

Economic and Financial Perspectives

on the Demand for Reinsurance

James R. Garven and Joan Lamm-TennantHankamer School of Business, Baylor University

GeneralCologne Re

Finance Department WorkshopFebruary 14, 2003

Chapter 10 in Rational Reinsurance Buying, Nick Golden (editor),

London: Risk Books (January 2003), pp. 163-186.


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Corporate Risk Management Todays seminar kicks off our spring 2003 workshop series, which is organized

around the theme "Corporate Risk Management". Primary insight: Risk management policy and financing policy are

complementary. This complementarityis captured by the term integrated riskmanagement. Integrated risk management from the medias perspective:

"The business of financing companies is converging with the business of insuring them."

(see "The New Financiers," The Economist, September 2, 1999). Integrated risk management from the finance professions perspective:

Froot, K. A., D. S. Scharfstein and J. C. Stein, 1993, "Risk Management: CoordinatingCorporate Investment and Financing Policies",Journal of Finance, 48 (Dec.), pp. 1629-58(hereafter, FSS)

Brealey, Richard A. and Stewart C. Myers (2002). Financing and Risk Management. NewYork: McGraw Hill.

Integrated risk management from the risk management professions perspective : Garven, J. R. and R. D. MacMinn, 1993, "The Underinvestment Problem, Bond Covenants

and Insurance",Journal of Risk and Insurance, 60 (Dec.), pp. 635-46.

Doherty, N. A. (2000). Integrated Risk Management: Techniques and Strategies forManaging Corporate Risk. New York: McGraw-Hill (required textbook for FIN/RMI 4335and FIN/RMI 5335).


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Under what conditions is risk management irrelevant?

In a frictionless economy, risk management is a pointlessactivity.

Shareholders can adjust the risk profile of their portfolios bydiversifying or shifting their assets.

Healthy companies that suffer unwelcome financial shocks can always

approach the capital markets for funding. Adverse shocks to a company's cash flow typically create

indirect costs.

These costs might stem from the threat of costly bankruptcy andfinancial distress, the difficulties of raising funds to finance corporate

strategies or the consequences of these shocks to stakeholders.

Risk management can help lessen these threats and therebyboost and sustain the value of the company.


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Under what conditions is risk management irrelevant?

Proposition 1: Risk management is irrelevant if and only if

there are no market frictions; e.g., transaction costs, taxes, regulations, etc., there is no moral hazard, and there is no adverse selection.

Proof. Suppose the above conditions hold. The firm may alter its risk profile by transferring risk to or from a counterparty. Investors may also alter their risk profiles by trading the firms shares along with the

shares of other firms. Suppose the firm seeks to reduce the risk of its shares by transferring risk to a

counterparty. While some investors might approve of such a change, others might have an

appetite for more risk that can be satisfied by buying shares in other riskier firms. Since investor risk management is a perfect substitute for corporate risk

management, shares of firms that differ only with respect to risk managementpolicy must sell for the same price Otherwise, arbitrage profits are available by shorting the (relatively) undervalued shares

and going long in the (relatively) overvalued shares.


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Under what conditions is risk management relevant?

What happens to the theory of corporate risk management if

Proposition 1 assumptions are violated? We will show how violations of Proposition 1 assumptions

represent sufficient conditions in order for corporate riskmanagement to matter.

Alternative Hypotheses Asymmetric taxes (due to progressive marginal tax rates as well

as incomplete tax loss offsets)

Direct and indirect costs related to financial distress (e.g., costsof bankruptcy and moral hazard).

Asymmetric information (adverse selection)

Role of managerial compensation contract design


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Implications of Proposition 1 assumption violations

1. Firm-specific risk affects the value of the corporation

Consequently, diversification may be of some value as a corporate risk managementstrategy.

2. Firm-specific risk matters irrespective of the nature of investor riskpreferences What matters is the impact of risk upon the firms tax exposure, magnitude of transaction

and agency costs.

3. Risk management and financing policies have complementary

economic and financial consequences. Coordination of financial and risk management policies enables the firm to expand its debt

capacity (cf. FSS (1993) and GM (1993)).

4. Risk management is the unifying principle for all business managementdisciplines (not just finance, economics, and RMI). E.g., marketing may be viewed as a risk management strategy to manage uninsurable

business risks such as loss of competitive position, product substitution and obsolescence.


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Asymmetric Taxes

Consider corporate tax effects.

In most industrialized countries, corporate income tax rates arestate contingent, varying as a function of the level of income;typically, dt/dp > 0 (aka the progressive tax rate problem).

Tax authorities typically limit the firms ability to deduct the full

value of corporate losses (aka the incomplete tax loss offsetproblem).

Mathematically, these features imply that firms face non-linear,or convex tax schedules in which varying marginal tax ratesintroduce a firm-specific source of risk; typically, a risk more

effectively managed by the firm than by its shareholders.


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Economic and Financial Perspectives on the Demand for Reinsurance

Tax Convexity

Definition of tax convexity(Jensens Inequality):

If a functionf(x) is convex, thenE(f(x)) >f(E(x)).

Taxes are convex because the tax on fully hedged

incomef(E(x)) is less than the tax on unhedged income(E(f(x)).


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Tax Linearity

A B C

T(A)

T(C)

E(tax) = T(B)

$


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Tax Convexity

Corporate Earnings

Taxes

payable

A B C

T(A)

T(B)

T(C)

E(Tax) =.5T(A)+.5T(C)


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Tax Convexity Numerical ExampleStrategy 1: Retain Risk

LossOutcome

Probability Taxable Income Taxes After-Tax Income

No Loss 50% $1,000,000 $350,000 $650,000Loss 50% $500,000 $75,000 $425,000

Strategy 2: Transfer (Insure) Risk

LossOutcome

Probability Taxable Income Taxes After-Tax Income

No Loss 50% $750,000 $187,500 $562,500

Loss 50% $750,000 $187,500 $562,500

Comparing the two risk management strategies listed above, the effect of insuring risk is tosimultaneously reduce the volatility and increase the expected value of after-tax income:

Strategy 1 Expected Taxable Income = 50% $1,000,000 50% $500,000 = $750,000.

Strategy 1 Expected Taxes = 50% $350,000 50% $75,000 = $212,500.

Strategy 1 Expected After-Tax Income = 50% $650,000 50% $425,000 = $537,500.

Strategy 2 Expected Taxable Income = 50% $750, 000 50% $750, 000 = $750,000.

Strategy 2 Expected Taxes = 50% $187,500 50% $187,500 = $187,500.

Strategy 2 Expected After-Tax Income = 50% $562,500 50% $562,500 = $562,500.


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The Incomplete Tax Loss Offset Problem

Incomplete tax loss offsets make the problem evenworse.

Tax-loss offsets are incomplete in the sense that firmsare limited in their ability to write off, for tax purposes,

the full value of corporate losses. Thus gains are taxedat a higher rate than losses are rebated.

The government holds a fractional position in a calloption on the firm's assets; this options exercise price is

the sum of the promised payment to bondholders plusother tax write-offs (typically items such as depreciationallowances).


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Payoff to the Government (T1)

$

BY1

1

Y

B

T1 = tMax[Y1-TS,0]

TS

TS


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After-tax Payoffs to Bondholders (D1) andShareholders (S1-T1)

$

BY1

1Y

B

T1

TS

TS S1

D1

S-T1 1


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Tax Convexity in the Real World

Tax convexity in the real world is quite a bit more

complicated than in our numerical example, and itcan vary significantly from firm to firm.

For any given firm, the degree of tax convexitydepends not only upon the schedule of marginaltax rates published by the tax authorities, but alsoupon a number of firm-specific characteristics,including past, present and future expected profitability, whether the firm is subject to the alternative minimum

tax, and whether the firm has any investment tax credits or net

operating loss carrybacks and carryforwards.


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Direct Costs of Financial Distress

If a firm goes bankrupt under the U.S. Bankruptcy

law, the costs of distributing its assets fall on thecreditors of the firm ex post.

Legal fees

Court fees Accounting Costs

Incentive costs for managers under bankruptcy courtreview might be different than profit maximizing contracts

entered into prior to bankruptcy. These constitute the direct and indirect costs of

bankruptcy.


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Even if the firm doesnt fail, there are indirect costs

related to financial distress.

Underinvestment. Because owners and creditors shareunequally (asymmetrically) in gains and losses,

circumstances may arise where firms (in the absence ofproper risk management) may rationally reject positiveNPV projects.

Risk Shifting(asset substitution). Risk management can

mitigate the risk shifting problem by reducingex antethepotential benefits that can be gained by increasing therisk of the firm after a debt issue.

Indirect Costs of Financial Distress


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Underinvestment Problem

State Pr(s) L(s) Vu(s)=-L(s) I(s) Vr(s)=-I(s)no loss 50% $1000 $0 $1000 $0 $1000

loss50% $1000 $800 $200 $600 $400

value now $1000 $400 $600 $300 $700

The Unlevered, Uninsured Firm


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The Levered, Uninsured Firm (B=$700)

State Pr(s) L(s) Du(s) Su(s) I(s) Dr(s) Sr(s)no loss 50% $1000 $0 $700 $300 $0 $700 $300

loss 50% $1000 $800 $200 $0 $600 $400 $0value now $1000 $400 $450 $150 $300 $550 $150

Underinvestment Problem (Contd.)


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Levered, Insured Firm (Bc=$500 & d=$500)

State Pr(s) L(s) I(s) pc(s) = I(s)-d *= -I(s)+pc(s) Dc(s) Sc(s)no loss 50% $1,000 $0 $0 $0 $1,000 $500 $500

loss 50% $1,000 $800 $600 $100 $500 $500 $0value now $1,000 $400 $300 $50 $750 $500 $250



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Effect of Transaction Costs (Bl = $600 & d = $400)

State Pr(s) L(s) I(s) pl(s) = I(s)-d *=-I(s) + pl(s) Dl(s) Sl(s)no loss 50% $1,000 $0 $0 $0 $1,000 $600 $400

Loss 50% $1,000 $800 $600 $200 $600 $600 $0value now $1,000 $400 $300 $100 $800 $600 $200



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Who pays agency and bankruptcy costs?

Shareholders bear these costs ex ante.

Bondholders know that if the firm has anasymmetric payoff structure, there is a moral hazardproblem, in that shareholders benefit from rippingoff bondholders!

In the absence of legally enforceable guaranteesagainst such moral hazards, bondholders have nochoice but to discount bond prices to account for

this risk. Consequently, the cost of debt is higher tosuch a firm.

Ex ante, firms want to convince potential bondinvestors that the likelihood of bankruptcy is low.


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Why Does Risk Management Matter - Summary

Why does risk management matter? Answers sofar include:

Asymmetric taxes

Bankruptcy risk and related costs

Bankruptcy costs include direct costs of thebankruptcy process (e.g., legal fees, accountingfees and court costs), plus indirect costs such as

value foregone due to suboptimal contracting. Lowering bankruptcy risk also reduces costs

related to other agency problems such asunderinvestment and asset substitution.


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Pre- versus Post-loss Financing Suppose a firm suffers a loss involving the destruction of a

physical asset such as a manufacturing facility. Rebuilding (reinvestment) will make sense only if the NPV of

the rebuilt facility is positive and greater than any otheralternative use of the capital.

Reinvestment can be financed two ways:

Post-loss methods typically involve the use of traditional debt andequity instruments to finance rebuilding costs.

Post-loss methods incur costs due to adverse selection andmoral hazard.

Pre-loss methods involve the use of insurance or some other formof hedging.

the firm must commit cash up front; there also may betransaction costs incurred in implementing the hedge.


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Pre- versus Post-loss Financing

The decision to use pre- or post-loss financing comes

down to comparing the marginal costs and benefits ofeach approach.

One benefit of pre-loss versus post-loss financing is

that pre-loss financing guarantees liquidity at a futuredate on favorable terms.

Following a loss, the unhedged firm might experiencedifficulty raising additional capital on favorable terms.


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Pecking Order Theory Adverse selection in equity markets

Announcement of a secondary stock offering drives down theprices of currently outstanding shares because investors believemanagers are more likely to issue equity when existing sharesare overpriced.

This represents an adverse selection problem in the equitymarket!

Therefore firms prefer internal equity since funds can beraised without conveying adverse signals; consequently,internal equity is a cheaper source of financing than

external equity. If external financing is required, firms issue debt first

and equity as a last resort (because there is less room fordifferences in opinion about what debt is worth).


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Pecking Order Theory of Risk Mgmt.

Now suppose an unhedged firm suffers a lossof liquidity (e.g., a major manufacturingfacility is destroyed).

The loss in liquidity curtails the firms

internally financed investment projects.

This results in a real economic loss to thefirm.

Risk management policies should ensure thata company always has the cash available tomake value-enhancing investments.


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Managerial Compensation Contract Design

Agency costs exist because managers do not

necessarily have the same objectives asshareholders. Stockholders prefer that managers maximize (the

risk-adjusted discounted value of) profits. Managers are interested in maximizing expected

utility.

We can devise a management compensation

scheme that attempts to reconcile theseconflicting objectives. Managers also bear corporate risks and therefore

need to be properly compensated for risk bearing.


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Risk and Managers

Risk averse managers have natural

incentives to reduce their firm's exposureto risk.

The manager is often not well-diversifiedsince her human and financial capital maybe closely tied to the firms financial

performance.

Thus a risk averse manager may use hedgingto reduce her exposure to corporate riskeven if it does not increase firm value.


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Designing a Managerial Compensation Contract

Assume that shareholders are risk neutral, but the

manager is risk averse with utility U = W.5. Assume that interest rates are zero; thus the value of

the firms shares is simply the expected value ofcorporate net cash flow.

Irrespective of the manner in which the contract isstructured, the firm must offer the manager acompetitive salary package. Suppose that competitive managerial labor market conditions

imply that competitive certainty equivalent salary is $300,000per year.

Thus the compensation contract must provide the managerwith expected utility of at least U($300,000) = $300,000.5 =547.72.


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Now suppose an all-equity firms value

will be $500 million or

$1000 million

each with a 1/2 probability

If hedged the firms value will be $780

million; thus the hedge has a positive NPVof $30 million.

Will the manager find it in her self-interest toimplement this hedge?



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Designing a Managerial Compensation Contract Consider three alternative managerial compensation contractsa

fixed salary, direct share ownership, and executive stock options.1. Fixed salary of $300,000 causes the manager to be indifferent

about implementing the hedge because the decision to hedgedoes not affect her welfare.

2. Direct share ownership. Manager receives a portion (x) ofvalue of earnings and no salary. This incentive scheme mustprovide expected utility of at least U($300,000)=547.72. Solvefor x:

547.72 < 0.5(500,000,000x)0.5 + 0.5(1,000,000,000x)0.5

1095.45 < (500,000,0000.5 + 1,000,000,0000.5)(x)0.51095.45 < 53983.46 (x)0.5

0.02029 < x0.5

x > 0.000412.


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2. Direct share ownership (continued) Therefore, lets assume that the manager receives .0412%

of the firm.

With the hedge E(U) = ( x*$780 Mill).5 = (0.000412 *$780

Mill).5

= 566.89. Without the hedge E(U) =.5(0.000412*500M ).5

+.5(0.000412*1000M).5 = 547.72.

Thus, E(U) is higher w/ hedge and shareholders are also

better off; consequently the direct share ownershipscheme is superior to the flat salary scheme, since it doesa better job of aligning shareholder and managerialincentives.


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Stock option assumptions: Manager receives no salary nor shares of stock. There are 10 million shares outstanding; consequently, the value of a

share of stock is either $50 or $100.

Manager receives options to purchase 60,000 shares of stock at a price of$80 per share.

The expected profit per option isE(profit) =.5*(Max(share price-$80,$0) =.5*($0)+.5*($20)=$10.

The expected profit and utility from holding options topurchase 60,000 shares are:E(profit) =.5(0 x 60,000) + .5($20 x 60,000) = $600,000, and

E(U) =.5(0 x 60,000).5 + .5($20 x 60,000).5 = 547.72.

The optimal decision here is to not hedge, because E(U) ishigher without the hedge (547.72) than with it (0).



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Summary of Numerical Example

Type of contract Contract Design Expected Utility What to do?

Fixed Salary Fixed Salary of$300,000

EU = 547.72 nomatter what

Indifferent betweenhedging and nothedging

Direct ShareOwnership

Manager owns x =.00412% of the firm

EU = 566.89 withhedging; EU =

547.72 withouthedging

Hedge

Options Manager ownsoption to purchase60,000 shares ofstock, exercise price

of $80.

EU = 0 withhedging; EU =547.72 withouthedging;

Dont Hedge


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Some What ifs on CompensationCEQ Income $300,000

U(Wceq) 547.7226

# Shares 10,000,000Risk Aversion Coefficient 0.5

Option 1 Exercise Price $80



Fixed Salary Share Ownership Option 1 Option 2 Option 3

Salary $300,000 $0 $0 $0 $0

Ownership fraction 0.0000% 0.0412% 0.0000% 0.0000% 0.0000%Options 0 0 60,000 40,000 30,000

No Hedge

p(s) V(s) U(V(s)) U(V(s)) U(V(s)) U(V(s)) U(V(s))

50% $500,000,000 547.7226 453.7482 0.0000 0.0000 0.0000

50% $1,000,000,000 547.7226 641.6969 1095.4451 1095.4451 1095.4451

547.7226 547.7226 547.7226 547.7226 547.7226

HedgePrice $220,000,000


50% $780,000,000 547.7226 566.7313 0.0000 565.6854 734.8469

50% $780,000,000 547.7226 566.7313 0.0000 565.6854 734.8469


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Some What Ifs on CompensationCEQ Income $300,000

U(Wceq) 547.7226

# Shares 10,000,000Risk Aversion Coefficient 0.5




Fixed Salary Share Ownership Option 1 Option 2 Option 3

Salary $300,000 $0 $0 $0 $0

Ownership fraction 0.0000% 0.0412% 0.0000% 0.0000% 0.0000%Options 0 0 60,000 40,000 30,000

No Hedge


50% $500,000,000 547.7226 453.7482 0.0000 0.0000 0.0000

50% $1,000,000,000 547.7226 641.6969 1095.4451 1095.4451 1095.4451

547.7226 547.7226 547.7226 547.7226 547.7226

HedgePrice $280,000,000


50% $720,000,000 547.7226 544.4979 0.0000 282.8427 600.0000

50% $720,000,000 547.7226 544.4979 0.0000 282.8427 600.0000


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Managerial Compensation Summary

Firms that offer incentive (direct shareownership) compensation are likely to hedgerisk.

Firms that offer flat salary may still hedge,but the incentives to do so are weaker (sincethe linkage between utility and risk isindirect).

Managers paid in stock options are not likelyto hedge.


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Managerial Compensation Summary

From a risk sharing view, it makes sense formanagers to be paid salaries and for risk to beprimarily borne by shareholders.

However, from an incentive view, it makes sense to

align interests of shareholders and managers in theform of incentive compensation.

This trade-off can be at least partially avoided if thefirm hedges risks that are largely outside managerial

control. This permits firms to use incentive compensation

without unnecessarily burdening managers with risksthat are outside their control.


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Empirical Predictions

Keep in mind the theoretical arguments wehave advanced:

Risk management can add value by reducing

taxes. Risk management can add value by reducing the

cost of financial distress.

Risk management can add value by facilitating

optimal investment.

Whether the firm manages risk depends upon thenature of the managerial compensation contract.


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Empirical Findings

Risk management to reduce taxes

Dolde (1995) reports a statistically significantpositive relationship between tax loss carryforwards and the use of risk management

instruments. Nance, Smith & Smithson (1993) and Mian (1994)

find a statistically significant positive relationshipbetween tax credits and the use of risk

management instruments. Garven and Lamm-Tennant (2000) show that the

demand for reinsurance is greater for insurers thatinvest in tax-exempt securities.


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Empirical Findings

Risk management to reduce the cost of financialdistress.

Dolde and Samant (1996) find a statistically significantpositive relationship between the use of risk managementand leverage.

Mayers and Smith (1990) show that demand forreinsurance is negatively related to credit standing(assigned by a rating agency); i.e., less credit-worthyinsurers reinsure more.

Garven and Lamm-Tennant (2000) show that demand forreinsurance is positively related to the insurers financial

leverage.


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Empirical Findings

Risk management to facilitate optimal investment.

Nance, Smith & Smithson; Geczy, Minton & Schrand; andDolde all find a statistically significant positive relationshipbetween the firm's R&D expenditures and its use of riskmanagement.

Samant (1996) finds a statistically significant positiverelationship between the market-to-book value ratio and theuse of risk management.

Empirical evidence cited by Froot, Scharfstein and Stein (1993)suggests that for each dollar of unhedged loss, project budgetswill be cut by about 30 cents.

Minton and Schrand (1999) find that capital expenditure forfirms with high cash flow volatility is about 19% below averageand expenditures for those with low volatility is about 11%above average.


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Empirical Findings

Risk management as a function of managerial riskaversion.

Tufano (1996) finds managerial equity positions positivelycorrelated with risk management in gold firms, and

negative relationship between risk management and largermanagerial options.

Geczy, Minton and Schrand (1997) find that managerialequity positions are positively correlated with foreign

exchange risk management by nonfinancial firms; also, anegative relationship between risk management and largermanagerial options.

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