DUALITY AND GLOBALITY IN RISK MANAGEMENT STRATEGGY

DUALITY AND GLOBALITY IN RISK MANAGEMENT STRATEGGY

DUALITY

The essence of duality is that in managing risks one can:

Address the cause of the risk – i.e. remove the risk

Address the effect of the risk - i.e. mitigate the consequences of the risk for the firm

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Table 8-1

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DUALITY AND NON-LINEAR TAXES

Ex. A firm purchases a capital asset at a cost of $1 billion which generates an income stream over a five year period of either

$132 mil. With probability ½

$532 mil. With probability ½

E(Earnings) = ½(132) + ½(532) = 332

Depreciation is straight-line (i.e. equal installments over 5 years).

i.e. the tax rate shield from depreciation is 200 million per year

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The tax rate is 34%. The expected tax liability is ½(.34(532-200) + ½ (0) = 56.44m

The expected net present value isE(NPV) = -1000mil + 5(332m – 56.44) = 377.8

If earnings turn out to be 532m actual taxes are(532-200).34 = 112.88m

If earnings turn out to be 132m actual taxes are 0 since the firm has an after tax loss(132-200) < 0

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Consider 2 strategies1) A hedge strategy – that removes the risk2) A tax arbitrage strategy – that mitigates the effect of the risk

Hedge Strategy

If the firm can hedge its earnings to fix earnings at their E(V) of 332, expected tax is reduced to

.34(332-200) = 44.88

and the E(NPV) is increased to

E(NPV) = -1000m + 5(332m-44.88m) = 435.6m

which is greater than the unhedged value of 377.8m 7


Tax Arbitrage Strategy A 2nd firm has earnings of either 1bil or 2bil. If this firm were to buy the asset just described it would always have sufficient income to fully utilize

the depreciation deduction.

This benefit is .34(200m) = 68m

Ignoring the time value of money, the firm could buy the machine and lease it back to the 1st firm at 132m without losing money.

200 Annual Cost

(68) Tax Savings132m Net cost to Firm 2

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The gain comes from the double deduction of depreciation by firm 2 and the lease payments by firm 1 and from the full utilization of the depreciation tax shield.

Even if firm 1 cannot deduct the lease payments, its expected after- tax annual income is

½(532 – 132) + ½(132 – 132) – .34[½(532) + ½(132)] = 87.12m

for a expected. NPV of

E(NPV) = 5 87.12m = 435.6m

This is identical to the hedging case

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Suppose this is done.

Firm 1’s expected taxable income is

1/2(532m-132m).34 + ½(132m-132).34 = 68m

The expected. NPV is now

E(NPV1) = 5(200m-68m) = 660m

which is even higher than when the firm hedges

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DUALITY AND BANKRUPTCY COSTS

A firm has value distributed as follows

Value Prob100 0.1

300 0.2500 0.4

700 0.2900 0.1

which has expected value of 500. The firm has debt with a face value of 200. Bankruptcy costs are 50

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Value of Debt

V(D) = .1(100-50) + .2(200)+.4(200)+.2(200)+.1(200) = 185

Value of Equity

V(E) = .1(0) + .2(300-200) + .4 (500-200) + .2(700-200) + .1(900-200) = 310

Value of Assets

V(A) = 185 + 310 = 495

which is E(V) of 500 less E(BC) of 5.

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Hedge Strategy Suppose the firm is able to fix its value at 500 –T where T is the transaction cost of the hedge.

Unless T > 300 the firm will always have enough funds to pay its debt. The probability of bankruptcy falls to zero. Hence E(BC) = 0

Suppose the cost of the hedge is T = 2 The value of the firm with the hedge is 498 with

Value of debt = 200Value of equity = 298 13


Equity appears to decrease in value with the hedge.

If the hedge is implemented after the bonds are issued this is indeed the case.

The increase in value is captured by the bondholders.

This is a form of the asset substitution problem.

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However, if the shareholders can precommit to the hedge prior to selling the bonds, the bondholders will pay 200 instead of 185 for the bonds raising firm value to

500 - 2 + 15 = 513

with

Value of bonds = 200

Value of equity = 313

which is > 310

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Leverage Strategy Another strategy is to reduce the firm’s leverage Suppose the firm reduces the debt to 100.

Then there is no probability of default and E(BC) = 0 Value of debt

V(D) = .1(100) + .2 (100) + .4(100) + .2(100) +.1(100) = 100 Value of Equity

V(E) = .1(100-100) + .2 (300-100) + .4(500-100) + .2(700-100) + .1(900-100) = 400 Value of Firm

V(A) = 100+400 = 500 which is >495 16

DUALITY AND AGENCY COSTS: ASSET SUBSTITUTION

Ex. Earnings can be either 100 or 200 with probability ½ each

The expected value is

V(A) = 150.

Firm has senior debt with a face value of 100.

Since the debt is covered in both states

V(D) = 100

V(E) = 150 -100 = 50

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All risk is diversifiable. The firm can select one of the following news investments:

Capital Cost

PV Earnings

Prob. E(NPV)

Project A 200 220 1 20

Project B 200 20 ½ -35

310 ½

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The firm issues junior debt with a face value of 200.

Transaction costs in the event of bankruptcy are 100.

Consider the net value of the firm:

*Firm is bankrupt since CF < 300

Project A Project B

Ret. From Original Ops.

220 prob = 1 20 prob = ½ 310 prob = ½

100, prob = ½ 320 prob = ½ 20* prob = ¼ 410 prob = ¼

200, prob = ½ 420 prob = ½ 120* prob = ¼ 510 prob = 1/419


Value of firm if A is chosen

V(A) = ½ (320) + ½ (420) = 370

V(OD) = ½ (100) + ½ (100) = 100

V(ND) = ½ (200) + ½ (200) = 200

V(E) = ½ (20) + ½ (120) = 70

Value of firm if B is chosenV(A) = ¼ (20+120+410+510) = 265

V(OD) = ¼ (20+100+100+100) = 80

V(ND) = ¼ (0+20+200+200) = 105

V(E) = ¼ (0+0+110+210) = 80 20


Shareholders would prefer the negative NPV project B to the positive NPV project

Classic asset substitution problem.

However, the new debt holders would anticipate this and pay no more than 105 for new debt with a face value of 200 face value debt.

Shareholders will not make up the difference

200-105= 95,

since their gain from project B is only 80-50 = 30.

Promises that the firm will do A are not, by themselves, convincing.

As a result, the firm can do neither A nor B.21


Hedge Strategy

Suppose the firm can credibly commit itself to hedge the risk from new projects.

The lottery of project B between payoffs of 20 and 310 is replaced with a sure payoff of 165.

If so, then project B is no longer in shareholders interest.

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Value if A is chosen:

V(A) =½ (320+420) = 370

V(OD) = ½ (100+100) = 100

V(ND) = ½ (200+200) = 200

V(E) = 370 – 100 – 200 = 70

Value if B is chosen:

V(A) = ½ (165 + 365) = 265

V(OD) = ½ (100+100) = 100

V(ND) = ½ (65+200) = 132.5

V(E) = ½ (0 + 65) = 32.5 23


If project B is chosen bankruptcy still occurs in the low value state since 100+165< 300.

If project A is selected, new bondholders would be willing to pay 200 for new debt of face 200,

The project can be financed, and shareholders are

70 – 50 = 20 better off.

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Leverage Strategy

Changing the source of financing for the new project can also solve the asset substitution problem.

Suppose the project were funded 50% with new debt and 50% with new equity.

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Value if A is chosen:

V(A) = ½ (320 + 420) = 370

V(OD) = ½ (100+100) = 100

V(ND) = ½ (100+100) = 100

V(E) = ½ (120+220) = 170

Value of firm if B is chosen

V(A) ¼ (20+220+410+510) = 290

V(OD) = ¼ (20+100+100+100) = 80

V(ND) = ¼ (0+100+100+100) = 75

V(E) = ¼ (0+20+210+310) = 135 26


Bankruptcy occurs when both projects have low values.

Shareholders prefer project A.

So, new debt with face = 100 can be issued for 100.

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CLASSIFYING RISK MANAGEMENT STRATEGIES

We know there are a number of factors that make risk costly to firms including:

tax non-linearities

bankruptcy cases

asset substitution and underinvestment

crowding out of new investment

managerial risk aversion

Some risk management strategies address some of these costs while other risk management strategies address all of these costs.

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If a firm faces interest rate risk, then interest rate futures/swaps address all of the costs that arise from that source of risk.

However, the costs arising from other sources of risk are not addressed.

On the other hand, a leverage strategy addresses bankruptcy and investment-related costs regardless of the source(s) of risk.

As Table 8.2 shows, there is a lot of overlap between different risk management strategies.

Some RM strategies cut across functional boundaries within the firm.

But this just means that risk management strategy needs to determined fairly high up in the corporation (at/near CFO)

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ASSET AND LIABILITY HEDGES

Hedging – a hedge is focused in that it addresses a specific form of risk.

That is, we usually think of a specific hedging instrument as paired with a specific source of risk:

E.g., Insurance policy for liability risk

Forwards or swaps for exchange rate and/or interest rate risk

Some risks may be difficult to hedge

e.g., inflation risk

There is an important distinction between asset hedges and liability hedges.

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Asset Hedge – An asset hedge is an asset that provides an offsetting cash flow to that of another asset.

An asset hedge can be represented as a portfolio, F, with an amount X invested in 2 assets:

Base asset, B, with return RB and

Hedge asset, H, with return RH.

The capital X invested is allocated over the two assets in the ratio (1:h).

The correlation coefficient between RB and RH is < 0.

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We have

F = X(RB + hRH)

If = -1, then there exists some h* such that F is riskless

var(F) = var(X(RB + h*RH)) = 0

For example, an insurance policy has cash flows that are negatively correlated with the value of the asset insured.

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Liability Hedge – Instead of a hedging asset, the portfolio has a liability , L, with return RL, such that

F = X(RB – hRL)

and corr(RB, RL) > 0.

Here the value of the liability rises/falls when the value of the asset rises/falls.

e.g., covered call writing: the value of the liability (short call) is positively correlated with the value of the asset (long stock).

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LEVERAGE AND FINANCING STRATEGIES

Leverage Management - Reducing leverage reduces the agency cost between creditors and shareholders.

It also puts the firm in a stronger position to access capital markets following a loss.

An alternative to reducing leverage is to reduce dividends to build up retained earnings

Post-Loss Financing - Issuing equity after a loss can partly address some of the costs of risk.

It may be costly to do so, however.

Post-loss financing may have greatest value if a loss introduces a liquidity crunch w/o impacting franchise value.

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LEVERAGE AND FINANCING STRATEGIES

Contingent Financing – contingent financing simply fixes the terms of post-loss financing in advance.

This can range from simple lines of credit possibly with fixed interest rates to long positions in equity put options, which may include additional conditions for exercises (like insurer’s CatEPuts).

Other Contingent Leverage Strategies – Including an option in debt to convert it to common stock allows the firm to unlever following a loss.

This reverse convertible debt or callable convertible debt gives the firm an option.

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OTHER RISK MANAGEMENT STRATEGIES

Compensation Management – A risk management formula for compensation contract design balances the need to provide incentives to managers through performance-related compensation and the risk premium needed in such (risky) compensation contracts.

Tax Management – Expected tax liabilities increase as the earnings risk of a firm increases.

Tax management strategies are designed to linearize the tax schedule and include hedging risks and leasing.

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RIFLES AND SHOTGUNS

Focused and Global Strategies – Rifles and Shotguns

Some risk management strategies are holistic, whereas others are specific to a type of risk.

However, a holistic risk management approach can make use of targeted strategies.

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RIFLES AND SHOTGUNS

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DUALITY AND GLOBALITY IN RISK MANAGEMENT STRATEGGY