Financial Frictions: No Country Financial Frictions: No Country for Old Cost Accountantsfor Old Cost Accountants

John A. Major, ASAJohn A. Major, ASA

RCM-1 Logic, Fallacies, and Paradoxes in RCM-1 Logic, Fallacies, and Paradoxes in Risk/Profit Loading in RatemakingRisk/Profit Loading in Ratemaking

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Modigliani & Miller (1958)

If: – taxes are neutral– capital markets are efficient– borrowing and lending are fair– financing decisions are uninformative– no bankruptcy cost

Then:– Leverage (gearing) doesn’t matter– Dividend policy doesn’t matter– Risk management doesn’t matter

But: – they do!

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What is a financial friction?

Something that violates M&M assumptions.

Explains why leverage, dividend policy, and r.m. do matter.

Examples:– taxes– transaction costs– capital market restrictions– agency problems– bankruptcy costs– customer credit sensitivity– information asymmetry

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Why care about financial frictions?

Fair value of liabilities

Fair value accounting

Economic balance sheet

Market Consistent Embedded Value

Convergence: securitization / insuratization

CFO as risk manager

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Modeling frictions is not just about estimating costs

Typical approach– pick a friction (e.g. agency cost of holding capital)– relate it to an underlying quantity (e.g., amount of surplus)– find or guess a cost rate or spread (e.g., 2%)– multiply– Voilà! We have our frictional cost. – Insert as a line item into valuation.

As you will see in the following example (working paper available) – this makes no sense at all

(possible exception: double taxation)

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1930 Cramér-Lundberg model

tt XtWW 0

capital (equity, surplus, risk reserve)

constantpremium

inflow

compoundPoisson

loss outflow

t

W

Harald CramérFilip Lundberg

ruin

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1957 de Finetti model

ttt DXtWW 0

dividends toshareholders

Bruno de Finetti

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Optimal dividends

wWDrEwMt

tt

00

1max

Optimal dividend strategy maximizes the shareholder value of the firm.(Ignoring signaling effects.)

friction:bankruptcy

terminates operations and dividend flows

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Typical solution is a “dividend barrier”

t

W

dividend payments instead of retained earnings

“dividendbarrier”

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Model insurance company

Expected net profits = $0.5 above, -$0.25 below ratings boundary.

Can still make a profit under the boundary – with some luck

What is optimal dividend policy? What is market value of the firm?

ttt DXtWW 0

Cat risk = 0.5; exponential severity: mean = $1.

Inflow = $1/yr above boundary, $0.25/yr below boundary.

Surplus (W) currently = $9, BCAR = 180, ratings boundary at W = $5.

Valuation rate r is 1%.

friction: external finance

not available

friction:customer

risk aversion

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But wait! Let’s make it more interesting…

Available XOL program modifies net cat losses

Attachment = $3 (41-yr RetPer), limit = $1 (110-yr RetPer).

Full cover Expected Loss = $0.016, r/i premium = $0.070

Purchase any fraction of cover U, 0-100%, paying prorata premium.

Applies to all cats, no reinstatement premium required.

What is optimal utilization U? What value does it add to the firm?

friction: risk management

is costly

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0 5 10 15 200

20

40

60

Wk

,k 0

,k j

5

Wk

0 5 10 15 200

0.5

1

U,k j

5

Wk

0 5 10 15 200

0.5

1

D,k j

C,k j

5

Wk

Solution

Valueof thefirm

Rein-surancestrategy

Dividendstrategy

Ratings cliffFranchise value M-Wclimbs rapidly around cliff, then levels off.Constant above W=15.4

Purchase reinsurancewhen W between 8, 10.Above, not worth it;below, not effective enough

Optimal capital = 15.4;dividend above that,retain earnings below.If W<2, go out of business.

Dividend back to left edge

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Shareholder value added by XOL

0 5 10 15 200

0.05

0.1

0.15

,k 0

,k 1

.1 U,k 0

0.17

Wk

Value added

Utilization

=M(w;Uopt) - M(w;U=0)

Note: availability of XOL adds value, even for states of W where it is not being purchased;this is the value of holding a reinsurance purchase option.

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If recapitalization is available

If costly, depends on cost

As cost is lowered from “infinite” to zero…– optimal capital level (div barrier) steadily moves down– value of the firm steadily increases– “go out of business” threshold is pushed down and out– recapitalization is used everywhere under the ratings cliff (W=5)– XOL purchase at 8 ≤ W ≤ 10 is gradually zeroed out– XOL purchase comes in again at 5 ≤ W ≤ 6– XOL purchase zeroed out again as recapitalization is used

above the ratings cliff

At zero cost, a version of Modigliani-Miller results– optimal capital at W = 7.5: to dividend above, recapitalize below– no reinsurance

friction: external finance

is costly

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Conclusion: “frictional effects” are complex phenomena

Nonlinear

Interact with each other

Dynamic– operate on probability distribution of future earnings trajectories

Interact with management strategies

Not generally amenable to cost-accounting approach