150 likes | 182 Views
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
E N D
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!
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
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
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)
1930 Cramér-Lundberg model compound Poisson loss outflow capital (equity, surplus, risk reserve) constant premium inflow ruin W t Filip Lundberg Harald Cramér
1957 de Finetti model dividends to shareholders Bruno de Finetti
Optimal dividends Optimal dividend strategy maximizes the shareholder value of the firm. (Ignoring signaling effects.) friction: bankruptcy terminates operations and dividend flows
Typical solution is a “dividend barrier” dividend payments instead of retained earnings “dividend barrier” W t
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? Model insurance company 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. friction: external finance not available Cat risk l = 0.5; exponential severity: mean = $1. Valuation rate r is 1%.
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
Solution Ratings cliff Franchise value M-W climbs rapidly around cliff, then levels off. Constant above W=15.4 Value of the firm M Rein- surance strategy Purchase reinsurance when W between 8, 10. Above, not worth it; below, not effective enough U Optimal capital = 15.4; dividend above that, retain earnings below. If W<2, go out of business. Dividend strategy D Dividend back to left edge
Shareholder value added by XOL U Utilization Value added =M(w;Uopt) - M(w;U=0) D M 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.
If recapitalization is available friction: external finance is costly • 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
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