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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) 5 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.) 8 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? 10 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? 11 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 12 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. 13 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 14 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 15