John A. Major, ASA
Financial Frictions: No Country
for Old Cost Accountants
RCM-1 Logic, Fallacies, and Paradoxes in
Risk/Profit Loading in Ratemaking
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!
2
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
3
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
4
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
Wt  W0    t  X t
capital (equity,
surplus, risk reserve)
constant
premium
inflow
W
compound
Poisson
loss outflow
ruin
t
Filip Lundberg Harald Cramér
6
1957 de Finetti model
Wt  W0    t  X t  Dt
dividends to
shareholders
Bruno de Finetti
7
Optimal dividends


t
M w  max E  1  r  Dt W0  w
 t 0

Optimal dividend strategy maximizes
the shareholder value of the firm.
friction:
bankruptcy
terminates operations
and dividend flows
(Ignoring signaling effects.)
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Typical solution is a “dividend barrier”
dividend payments instead of retained earnings
“dividend
barrier”
W
t
9
Model insurance company
Wt  W0    t  X t  Dt
Surplus (W) currently = $9, BCAR = 180,
ratings boundary at W = $5.
friction:
customer
risk aversion
Inflow = $1/yr above boundary,
$0.25/yr below boundary.
Cat risk l = 0.5; exponential
severity: mean = $1.
friction:
external finance
not available
Valuation rate r is 1%.
  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?
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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
friction:
risk management
is costly
 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?
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Solution
60
Ratings cliff
5
Value
of the
firm
W
k
Franchise value M-W
climbs rapidly around
cliff, then levels off.
Constant above W=15.4
40

k, 0

k , j 20
0
0
5
10
W
Reinsurance
strategy
1
U
k, j
20
k
Purchase reinsurance
when W between 8, 10.
Above, not worth it;
below, not effective enough
5
0.5
0
0
5
10
W
Dividend
strategy
15
1
15
20
k
Optimal capital = 15.4;
dividend above that,
retain earnings below.
If W<2, go out of business.
5
D
k, j
C
k, j
0.5
0
0
5
10
W
k
15
20
Dividend back to left edge
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Shareholder value added by XOL
0.15
Utilization
0.1

k, 0
1

k, 1
Value added
=M(w;Uopt) - M(w;U=0)
. 0.17
U
k, 0
0.05
0
0
5
10
W
15
20
k
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
friction:
external finance
is costly
 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
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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
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