The Effective Duration of Liabilities for Property-Liability ...

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The Effective Duration of Liabilities for Property-Liability ...

  1. 1. An Overview of Capital Management for Property/Casualty Insurers <ul><li>Rick Gorvett, FCAS, MAAA, ARM, FRM, Ph.D. </li></ul><ul><li>Actuarial Science Program </li></ul><ul><li>University of Illinois at Urbana-Champaign </li></ul><ul><li>Casualty Actuarial Society </li></ul><ul><li>Washington, DC </li></ul><ul><li>July, 2003 </li></ul>
  2. 2. Agenda <ul><li>“Capital management” and its inclusiveness </li></ul><ul><li>Putting capital management in a financial services industry context : a look at the banking world </li></ul><ul><li>The financial theory underlying capital management </li></ul><ul><li>Discussion of cost of capital </li></ul><ul><li>Capital management for property / casualty insurance </li></ul>
  3. 3. “ Capital Management” and its Inclusiveness
  4. 4. What is Meant by “Capital” and “Capital Management” <ul><li>“ Capital ” (and surplus) </li></ul><ul><ul><li>Assets less liabilities </li></ul></ul><ul><ul><li>Owners’ equity </li></ul></ul><ul><ul><li>Support for (riskiness of) operations </li></ul></ul><ul><ul><li>Thus, supports profitability and solvency of firm </li></ul></ul><ul><li>“ Capital Management ” </li></ul><ul><ul><li>Determine need for and adequacy of capital </li></ul></ul><ul><ul><li>Plans for increasing or releasing capital </li></ul></ul><ul><ul><li>Strategy for efficient use of capital </li></ul></ul>
  5. 5. Types and Measures of Capital <ul><li>Statutory </li></ul><ul><ul><li>Inherently conservative; solvency perspective </li></ul></ul><ul><li>GAAP </li></ul><ul><ul><li>Going concern; income statement orientation </li></ul></ul><ul><li>Risk-based capital </li></ul><ul><ul><li>Required capital based on risk attributes and promulgated charges </li></ul></ul><ul><li>Economic </li></ul><ul><ul><li>Required capital in order to achieve a specified solvency standard </li></ul></ul>Actual Theoretical
  6. 6. Why Do We Care About Managing Capital? <ul><li>Leads to solvency and profitability </li></ul><ul><li>Benefits of solidity and profitability </li></ul><ul><ul><li>Higher company value </li></ul></ul><ul><ul><li>Happy claimholders (policyholders, stockholders,...) </li></ul></ul><ul><ul><li>Better ratings </li></ul></ul><ul><ul><li>Less unfavorable regulatory treatment </li></ul></ul><ul><ul><li>Ability to price products competitively </li></ul></ul><ul><ul><li>Customer loyalty </li></ul></ul><ul><ul><li>Potentially lower costs </li></ul></ul>
  7. 7. The Problem With Capital <ul><li>A certain amount of capital is needed in order to promote solvency </li></ul><ul><ul><li>Thus, need to be able to raise capital </li></ul></ul><ul><li>But.... If there is too much capital, profitability (as measured by return on equity) will suffer </li></ul><ul><ul><li>Thus, need to be able to efficiently deploy capital </li></ul></ul>
  8. 8. What Does Capital Management Entail? Capital Management Capital Structure Financial Risk Mgt. Setting Objectives Raising Capital Strategic Planning Liability Valuation Asset Allocation Product Pricing
  9. 9. Putting Capital Management in a Financial Services Industry Context : A Look at the Banking World
  10. 10. Banks: How They Improved <ul><li>“ After the near-death experience of the late 1980s and early 1990s, banks began to invest where the rewards for investing were not just higher but also better in relation to the amount of risk they were taking—in other words, they started looking at risk-adjusted returns. This meant that they began to jettison businesses that were insufficiently profitable.” </li></ul><ul><li>“ What worries banks most, however, is not that their fees might drop, but that their main business—lending, which still accounts for most of their revenues—would come a cropper. That is where most of their capital is at risk. And that is why their favourite gripe is about the bankers at Basle.” </li></ul><ul><li>- “Renaissance Men,” Economist , 4/15/99 </li></ul>
  11. 11. From the Fed: Bank Capital <ul><li>BOARD OF GOVERNORS OF THE FEDERAL RESERVE SYSTEM DIVISION OF BANKING SUPERVISION AND REGULATION </li></ul><ul><li>SR 99-18 (SUP) </li></ul><ul><li>July 1, 1999 </li></ul><ul><li>SUBJECT: Assessing Capital Adequacy in Relation to Risk at Large Banking Organizations and Others with Complex Risk Profiles </li></ul>
  12. 12. From the Fed: Bank Capital (cont.) <ul><li>“ ....increasing emphasis on banking organizations' internal processes for assessing risks and for ensuring that capital, liquidity, and other financial resources are adequate in relation to the organizations' overall risk profiles.” </li></ul><ul><li>“ ....one of the most challenging issues faced by bankers and supervisors is how to integrate the assessment of an institution's capital adequacy with a comprehensive view of the risks it faces.  Simple ratios - including risk-based capital ratios - and traditional rules of thumb no longer suffice in assessing the overall capital adequacy of many banking organizations, especially large institutions and others with complex risk profiles such as those significantly engaged in securitizations or other complex transfers of risk.” </li></ul><ul><li>(continued) </li></ul>
  13. 13. From the Fed: Bank Capital (cont.) <ul><li>“ ....this letter directs supervisors and examiners to evaluate internal capital management processes to judge whether they meaningfully tie the identification, monitoring, and evaluation of risk to the determination of the institution's capital needs.” </li></ul><ul><li>“ ....this letter describes the fundamental elements of a sound internal capital adequacy analysis - identifying and measuring all material risks, relating capital to the level of risk, stating explicit capital adequacy goals with respect to risk, and assessing conformity to the institution's stated objectives - as well as the key areas of risk to be encompassed by such analysis.” </li></ul><ul><li>(continued) </li></ul>
  14. 14. From the Fed: Bank Capital (cont.) <ul><li>“ Current industry practice :   Most institutions consider several factors in evaluating their overall capital adequacy: a comparison of their own capital ratios with regulatory standards and with those of industry peers; consideration of identified risk concentrations in credit and other activities; their current and desired credit agency ratings, if applicable; and their own historical experiences including severe adverse events in the institution's past.  Some more sophisticated banks also use risk modeling techniques and scenario analyses to evaluate risk, but generally have not yet incorporated such analyses formally into their overall assessment of capital adequacy.” </li></ul><ul><li>(continued) </li></ul>
  15. 15. From the Fed: Bank Capital (cont.) <ul><li>Fundamental Elements of a Sound Internal Capital Adequacy Analysis </li></ul><ul><li>1) Identifying and measuring all material risks </li></ul><ul><li>2) Relating capital to the level of risk </li></ul><ul><li>3) Stating explicit capital adequacy goals with respect to risk </li></ul><ul><li>4) Assessing conformity to the institution's stated objectives </li></ul><ul><li>Composition of Capital </li></ul><ul><li>“ ....it has been the Board's long-standing view that common equity (that is, common stock and surplus and retained earnings) should be the dominant component of a banking organization's capital structure and that organizations should avoid undue reliance on noncommon equity capital elements.” </li></ul>
  16. 16. Basle I <ul><li>1988 Basle Accord </li></ul><ul><li>By 1992, banks had to have a capital ratio of 8% </li></ul><ul><li>Capital ratio = {amount of available capital} / {risk-weighted assets} </li></ul><ul><li>“Risk-weighted assets” </li></ul><ul><ul><li>Only explicitly identifies two types of risks: (1) credit risk; (2) market risk </li></ul></ul><ul><ul><li>Other risks presumed to be covered implicitly </li></ul></ul>
  17. 17. Basle II <ul><li>Ongoing; have issued third Consultative Document (comments due by 7/31/03) </li></ul><ul><li>New Accord includes three “pillars”: (1) minimum capital requirements; (2) supervisory review of capital adequacy; (3) public disclosure </li></ul><ul><li>Pillar 1: proposals to modify definition of risk-weighted assets </li></ul><ul><ul><li>Changes to treatment of credit risk </li></ul></ul><ul><ul><li>Explicit treatment of operational risk </li></ul></ul>
  18. 18. The Financial Theory Underlying Capital Management
  19. 19. Steps in the Financial Risk Management (FRM) Process <ul><li>Determine the corporation’s objectives </li></ul><ul><li>Identify the risk exposure (e.g., FX risk) </li></ul><ul><li>Quantify the exposure (e.g., measure volatility) </li></ul><ul><li>Assess the impact (DFA) </li></ul><ul><li>Examine financial risk management tools </li></ul><ul><li>Select appropriate risk management approach </li></ul><ul><li>Implement and monitor program </li></ul>
  20. 20. Finance Theory and Capital Management <ul><li>Why bother to worry about financing or FRM (or any risk management), in light of the capital structure irrelevance proposition? </li></ul><ul><li>Modigliani-Miller (1958): if financing does matter, it must be because of one or more of: </li></ul><ul><ul><li>Tax effects – convex tax function </li></ul></ul><ul><ul><li>Financial distress / bankruptcy costs </li></ul></ul><ul><ul><li>Effects on future investment decisions </li></ul></ul>
  21. 21. Pre-FRM Post-FRM
  22. 22. Derivatives Use Among Insurers <ul><li>Activity during 1994 </li></ul><ul><ul><li>Cummins, Phillips, Smith (1997) </li></ul></ul><ul><ul><li>142 P/C insurers (7%) used derivatives in 1994 </li></ul></ul><ul><ul><li>Larger companies more likely to use derivatives than smaller companies </li></ul></ul><ul><ul><li>Most often used contracts for P/C insurers: </li></ul></ul><ul><ul><ul><li>Foreign currency forwards </li></ul></ul></ul><ul><ul><ul><li>Equity options </li></ul></ul></ul><ul><ul><li>Other (FX) activity in 1994 in: </li></ul></ul><ul><ul><ul><li>Foreign currency swaps </li></ul></ul></ul><ul><ul><ul><li>Foreign currency futures </li></ul></ul></ul><ul><ul><ul><li>Foreign currency options </li></ul></ul></ul>
  23. 23. Derivatives Use Among Insurers (cont.) <ul><li>Anecdotal evidence from SEC 10-K filings </li></ul><ul><ul><li>Specific mentions re: FX risk include: </li></ul></ul><ul><ul><ul><li>Currency swaps </li></ul></ul></ul><ul><ul><ul><li>Foreign currency forwards </li></ul></ul></ul><ul><ul><ul><li>Asset-liability management </li></ul></ul></ul><ul><ul><ul><li>Sensitivity analysis with respect to hypothetical changes in exchange rates </li></ul></ul></ul><ul><ul><ul><li>Investments in foreign currencies </li></ul></ul></ul><ul><ul><ul><li>Cash flows from foreign operations, to fund investments in foreign currencies </li></ul></ul></ul>
  24. 24. Capital Structure - Theory <ul><li>To finance ops., firm can issue debt or equity </li></ul><ul><li>“ Capital Structure ”: firm’s mix of securities </li></ul><ul><li>Does this mix selection affect firm value? </li></ul><ul><li>Miller & Modigliani said “No” (in perfect capital markets) </li></ul><ul><ul><li>Firm value is determined by its real assets – value is independent of capital structure </li></ul></ul><ul><ul><li>Capital structure irrelevant (for fixed investment decisions, no taxes, no costs of financial distress) </li></ul></ul><ul><ul><li>Allows separation of investment and financing decisions </li></ul></ul>
  25. 25. Capital Structure - Reality <ul><li>Modigliani-Miller Proposition: capital structure decision is irrelevant to firm value, under certain “friction-free” assumptions (e.g., no taxes) </li></ul><ul><li>But: in reality , there are taxes </li></ul><ul><li>There are also costs associated with financial distress </li></ul>
  26. 26. Interest Tax Shield <ul><li>Tax-deductibility of interest may make some debt in the capital structure attractive </li></ul><ul><li>Discount the interest tax shield by the rate demanded by investors holding the debt </li></ul><ul><li>PV (tax shield) = t ( r d D ) / r d = t D </li></ul><ul><li>(assumes debt in perpetuity) </li></ul><ul><li>Value of firm increases by PV (tax shield): </li></ul><ul><li>Value of firm = value if all equity-financed </li></ul><ul><li>+ PV (tax shield) </li></ul>
  27. 27. Costs of Financial Distress <ul><li>However.... </li></ul><ul><li>Increasing debt  increasing risk and increasing likelihood of distress, which has costs associated with it – e.g., </li></ul><ul><ul><li>Costs of shareholder – bondholder conflicts </li></ul></ul><ul><ul><li>Costs of potential bankruptcy </li></ul></ul><ul><ul><li>Costs associated with inability to operate optimally / efficiently </li></ul></ul><ul><ul><li>Costs associated with bond provisions / compliance </li></ul></ul>
  28. 28. Sample Debt / Equity Tradeoff Chart Debt / Equity Ratio Firm Value PV(tax shield) PV(costs fin. distress)
  29. 29. Other Capital Structure Issues <ul><li>More on debtholder–shareholder conflicts </li></ul><ul><ul><li>Projects / investments: more risky versus less risky </li></ul></ul><ul><ul><li>High versus low dividend payouts </li></ul></ul><ul><ul><li>Pack-it-in versus keep-hanging-on </li></ul></ul><ul><li>Financing “pecking order” theory </li></ul><ul><ul><li>Order of preference: (1) internal financing; (2) issue debt; (3) issue equity </li></ul></ul><ul><ul><li>More profitable / cash flow  don’t need external </li></ul></ul><ul><ul><li>External can send adverse signals </li></ul></ul>
  30. 30. Issuing Securities <ul><li>Initial public offerings </li></ul><ul><ul><li>Engage an underwriter(s) </li></ul></ul><ul><ul><li>File SEC registration statement </li></ul></ul><ul><ul><li>Prospectus (“red herring”) </li></ul></ul><ul><li>General cash offers </li></ul><ul><ul><li>Similar steps to those for IPO above </li></ul></ul><ul><ul><li>SEC Rule 415: shelf registration </li></ul></ul><ul><ul><li>Announcement of equity issue: empirically, small decline in stock price </li></ul></ul><ul><ul><ul><li>Signal to investors </li></ul></ul></ul><ul><ul><ul><li>Puzzle re: long-run underperformance </li></ul></ul></ul>
  31. 31. Issuing Securities (cont.) <ul><li>Private placements </li></ul><ul><ul><li>Significant on debt side </li></ul></ul><ul><ul><li>Less costly; flexible </li></ul></ul><ul><ul><li>Counterparty concerns; less liquid </li></ul></ul><ul><li>Costs of security issuance </li></ul><ul><ul><li>Accounting and legal </li></ul></ul><ul><ul><li>Underwriting </li></ul></ul><ul><ul><ul><li>Spread </li></ul></ul></ul><ul><ul><ul><li>Possibility of underpricing securities </li></ul></ul></ul>
  32. 32. Dividends <ul><li>Declared by board of directors </li></ul><ul><li>Once declared, an obligation </li></ul><ul><li>Modigliani & Miller: dividend policy is irrelevant in a world without taxes, transaction costs, etc. </li></ul>
  33. 33. Types of Dividends <ul><li>Regular cash divs .: expect to maintain </li></ul><ul><li>Extra dividend : may not be repeated </li></ul><ul><li>Special dividend : unlikely to be repeated </li></ul><ul><li>Liquidating dividend : </li></ul><ul><ul><li>When going out of business </li></ul></ul><ul><ul><li>Distribution of assets (“return of capital”) </li></ul></ul><ul><li>Stock dividend : shares of company or subsidiary </li></ul><ul><ul><li>For company: conserves cash </li></ul></ul><ul><ul><li>For investor: not taxed until sold </li></ul></ul>
  34. 34. Limits on Dividends <ul><li>By bondholders </li></ul><ul><ul><li>Covenants prevent the distribution of the firm’s assets as dividends to stockholders </li></ul></ul><ul><ul><li>Company can’t issue a liquidating dividend if funds are needed for protection of creditors </li></ul></ul><ul><li>By state law </li></ul><ul><ul><li>Prohibits paying dividend that would make the company insolvent </li></ul></ul><ul><ul><li>Prohibits paying dividends out of legal capital </li></ul></ul>
  35. 35. Dividend Viewpoints <ul><li>Tax effects  low dividend preferable </li></ul><ul><li>Investor preferences  high dividend payouts </li></ul><ul><li>Somewhere in-between are those who subscribe to the original MM proposition that dividend policy is irrelevant </li></ul>
  36. 36. Share Repurchase <ul><li>Alternative to paying cash dividends </li></ul><ul><li>Often used when </li></ul><ul><ul><li>Company has accumulated lots of cash </li></ul></ul><ul><ul><li>Wants to replace equity with debt </li></ul></ul><ul><li>Methods of repurchase </li></ul><ul><ul><li>Open market </li></ul></ul><ul><ul><li>General tender offer to all or small shareholders </li></ul></ul><ul><ul><li>Direct negotiations with major shareholder </li></ul></ul><ul><li>Repurchased shares seldom de-registered and canceled </li></ul>
  37. 37. Liquidity Ratios <ul><li>Indicators of riskiness, financial strength </li></ul><ul><li>Short-term “cashability” </li></ul><ul><li>More reliable values for liquid assets </li></ul><ul><li>Short-term  can become out of date </li></ul><ul><li>Possibly seasonal </li></ul><ul><li>Ratios: </li></ul><ul><ul><li>Current ratio = current assets / current liabilities </li></ul></ul><ul><ul><li>Quick ratio = (cash + marketable securities + </li></ul></ul><ul><ul><li>receivables) / current liabilities </li></ul></ul><ul><ul><li>Cash ratio = (cash + marketable securities) / </li></ul></ul><ul><ul><li>current liabilities </li></ul></ul>
  38. 38. Leverage Ratios <ul><li>Measures of financial leverage (capital structure) </li></ul><ul><li>Ratios (other definitions are possible): </li></ul><ul><ul><li>Leverage Ratio = assets / equity </li></ul></ul><ul><ul><li>= 1+ (debt/equity) </li></ul></ul><ul><ul><li>Debt ratio = long-term debt / </li></ul></ul><ul><ul><li>(long-term debt + equity) </li></ul></ul><ul><ul><li>(Here, long-term debt includes value of leases) </li></ul></ul><ul><ul><li>Times interest earned = EBIT / interest expense </li></ul></ul><ul><ul><li>(Numerator sometimes includes depreciation) </li></ul></ul>
  39. 39. Market Value Ratios <ul><li>Combine accounting (book) and stock (market) data </li></ul><ul><li>Ratios: </li></ul><ul><ul><li>Price-earnings ratio = stock price / EPS </li></ul></ul><ul><ul><li>Earnings yield = EPS / stock price = 1 / (P/E) </li></ul></ul><ul><ul><li>Market-to-book ratio = stock price / </li></ul></ul><ul><ul><li>book value per share </li></ul></ul><ul><ul><li>Dividend yield = dividend per share / stock price </li></ul></ul><ul><ul><li>Tobin’s q = MV of firm / replacement cost </li></ul></ul>
  40. 40. Profitability Ratios <ul><li>Measures of profitability and efficiency </li></ul><ul><li>Ratios: </li></ul><ul><ul><li>Sales to total assets (or asset turnover ) = </li></ul></ul><ul><ul><li>sales / average total assets </li></ul></ul><ul><ul><li>Profit margin = EBIT / sales </li></ul></ul><ul><ul><li>Average collection period = </li></ul></ul><ul><ul><li>[(average receivables) / sales] x 365 </li></ul></ul><ul><ul><li>Also: ROE, ROA, Payout Ratio </li></ul></ul><ul><li>(Note: Usually use averages for snapshot figures when comparing them with flows) </li></ul>
  41. 41. Other Ratios <ul><li>Capital ratios </li></ul><ul><ul><li>E.g., capital / liabilities; capital / assets; capital / {weighted asset formula} </li></ul></ul><ul><li>NAIC IRIS ratios – e.g., </li></ul><ul><ul><li>Premium / surplus </li></ul></ul><ul><ul><li>Change in premium writings </li></ul></ul><ul><ul><li>Surplus aid to surplus </li></ul></ul>
  42. 42. International Differences <ul><li>United States </li></ul><ul><ul><li>Companies widely held </li></ul></ul><ul><ul><li>Rely largely on financial markets </li></ul></ul><ul><li>Germany </li></ul><ul><ul><li>Cross-holdings of companies; layered ownership </li></ul></ul><ul><ul><li>Greater “reliance” on banking system </li></ul></ul><ul><li>Japan </li></ul><ul><ul><li>“ Kiretsu”: network of companies, usually organized around a major bank </li></ul></ul><ul><ul><li>Most financing from within the group </li></ul></ul>
  43. 43. Debtholders vs. Shareholders Who’s Interested in What? Firm Value Probability Debtholders Shareholders
  44. 44. Option Values: Payoff Charts <ul><li>Call -- long position: </li></ul><ul><li>Call -- short position: </li></ul><ul><li>Put -- long position: </li></ul><ul><li>Put -- short position: </li></ul>Payoff X S T X X X S T S T S T
  45. 45. Payoff and Profit/Loss Profiles Long a Call Option S T Profit/Loss Payoff X Call Premium
  46. 46. Black-Scholes Option Pricing Model <ul><li>Variables required </li></ul><ul><li>1. Underlying stock price </li></ul><ul><li>2. Exercise price </li></ul><ul><li>3. Time to expiration </li></ul><ul><li>4. Volatility of stock price </li></ul><ul><li>5. Risk-free interest rate </li></ul>
  47. 47. Black-Scholes Formula <ul><li>V C = S N(d 1 ) - X e -rt N(d 2 ) </li></ul><ul><li>where </li></ul><ul><li>d 1 = [ln(S/X)+(r+0.5  2 )t] /  t 0.5 </li></ul><ul><li>d 2 = d 1 -  t 0.5 </li></ul><ul><li>where N( ) = cumulative normal distribution, </li></ul><ul><li>S = stock price, </li></ul><ul><li>X = exercise price, </li></ul><ul><li>r = continuously compounded risk-free interest rate, </li></ul><ul><li>t = number of periods until exercise date, and </li></ul><ul><li> = std. dev. per period of continuously </li></ul><ul><li>compounded rate of return on the stock </li></ul>
  48. 48. Options & Capital Structure <ul><li>Both components of capital structure, equity and debt can be viewed within the option (contingent claim) framework </li></ul><ul><li>Thus, we can bring powerful valuation tools from option / contingent claim theory to bear on questions of capital structure, firm value, pricing of insurance policies, etc. </li></ul>
  49. 49. Options & Capital Structure (cont.) <ul><li>Equity : residual claim on value of the firm </li></ul><ul><ul><li>Contingent value after other claimholders </li></ul></ul><ul><ul><li>If firm defaults, equityholders put the company onto the debtholders </li></ul></ul><ul><ul><li>This reflects equityholders’ limited liability </li></ul></ul>Equity Payoff Firm Asset Value L
  50. 50. Options & Capital Structure (cont.) <ul><li>Debt : claim on firm assets takes priority relative to equity </li></ul><ul><ul><li>Value contingent upon firm asset value </li></ul></ul><ul><ul><li>Bondholders hold the assets and write a call to the equityholders </li></ul></ul>Debt Payoff Firm Asset Value L
  51. 51. Applying the Option Pricing Model to Insurance* <ul><li>Use option pricing to determine the value of each claim on an insurer’s assets </li></ul><ul><li>Policyholders’ Claim = H </li></ul><ul><li>Government’s Tax Claim = T </li></ul><ul><li>Owners’ Claim = V </li></ul><ul><li>* Neil Doherty and James Garven, 1986, “Price Regulation in Property-Liability Insurance: A Contingent Claims Approach,” Journal of Finance , December </li></ul>
  52. 52. Option Pricing Model Applied to Insurance Stockholder Value Terminal Asset Value 0 Taxes Liabilities Beg. Assets
  53. 53. Value of Various Claims at the End Of the Period <ul><li>Policyholders’ claim </li></ul><ul><li>H 1 = MAX{MIN[L,Y 1 ],0} </li></ul><ul><li>Government’s tax claim </li></ul><ul><li>T 1 = MAX{t[i(Y 1 -Y 0 )+P-L],0} </li></ul><ul><li>Owners’ claim </li></ul><ul><li>V e = Y 1 - H 1 - T 1 </li></ul>
  54. 54. <ul><li>S 0 = Initial equity </li></ul><ul><li>P = Premiums (net of expenses) </li></ul><ul><li>Y 0 = Initial assets = S 0 + P </li></ul><ul><li>R = Investment rate </li></ul><ul><li>k = Funds generating coefficient </li></ul><ul><li>Y 1 = Ending assets </li></ul><ul><li>= S 0 + P + (S 0 + kP)R </li></ul><ul><li>L = Losses </li></ul><ul><li>t = Tax rate </li></ul><ul><li>i = Portion of investment income that is taxable </li></ul>where:
  55. 55. Determine The Value Of These Claims At The Beginning Of The Period <ul><li>V(Y 1 ) = Market value of asset portfolio </li></ul><ul><li>C[A;B] = Value of call option with exercise price of B on asset with value of A </li></ul><ul><li>E(L) = Expected losses </li></ul><ul><li>H 0 = V(Y 1 ) - C[Y 0 ;E(L)] </li></ul><ul><li>T 0 = tC[i(Y 1 - Y 0 ) + P 0 ;E(L)] </li></ul><ul><li>V e = V(Y 1 ) - H 0 - T 0 </li></ul><ul><li>= C[Y 0 ;E(L)] - tC[i(Y 1 - Y 0 ) + P 0 ;E(L)] </li></ul>
  56. 56. Use Of Option Pricing To Set Insurance Premiums <ul><li>To determine the “fair” premium, the premium level is determined for which the owners’ claim is equal to the initial equity. Thus, the owners receive a “fair” investment return. </li></ul>
  57. 57. Discussion of Cost of Capital
  58. 58. Cost of Capital <ul><li>Weighted Average Cost of Capital (WACC) = weighted average of firm’s (after-tax) financing source costs </li></ul><ul><li>WACC = r s w s + r p w p + r d (1 – t) w d </li></ul><ul><li>where r = cost, w = weight, t = tax rate, s = </li></ul><ul><li>common stock, p = preferred stock, and </li></ul><ul><li>d = debt </li></ul>
  59. 59. Cost of Capital <ul><li>Cost of capital can be used as a hurdle rate against which to measure investment decisions. </li></ul><ul><li>Weights are the long-run proportions of the various financing sources comprising the firm’s capital structure </li></ul><ul><li>Key is to determine the costs, or rates, associated with each financing source </li></ul><ul><ul><li>Can use CAPM, APT, etc. </li></ul></ul>
  60. 60. Capital Asset Pricing Model E(R i ) = R f +  i [E(R m ) - R f ] where: E = expected value operator R i = return on an asset R f = risk free rate R m = return on market portfolio  i = Cov(R i ,R m ) /  2 (R m ) = systematic risk
  61. 61. Arbitrage Pricing Model <ul><li>The APM is similar to the CAPM with regard to classifying risk as either diversifiable or non-diversifiable . </li></ul><ul><li>The APM does not require investors to be concerned only with market risk. </li></ul><ul><li>The APM allows consideration of any number of factors to influence the risk of an investment. </li></ul>
  62. 62. Arbitrage Pricing Model (cont.) R i = a i + b ij I j + e i R = realized rate of return a = intercept b = sensitivity of return to index I = value of index e = error term i = asset indicator j = factor indicator  n j = 1
  63. 63. An Alternative Hurdle Rate Approach* <ul><li>CAPM ignores existing portfolio when contemplating price / capital needed to support one more risk </li></ul><ul><li>Add a factor to the CAPM </li></ul><ul><ul><li>Reflects correlation of new risk with existing portfolio </li></ul></ul><ul><ul><li>Incremental capital to maintain existing target probability of ruin </li></ul></ul>* Froot and Stein, “A New Approach to Capital Budgeting for Financial Institutions,” Journal of Applied Corporate Finance , Summer 1998. Also, Froot, “A Fundamental Framework for Managing Capital Risk,” in Managing Capital and Expectations Through Effective Risk Management , Guy Carpenter
  64. 64. Capital Management for Property / Casualty Insurance
  65. 65. The Insurer’s Capital Challenge <ul><li>“ Four separate but related troubles are to blame. The first is falling premiums. The second is falling interest rates. The third is stagnant growth. And the fourth is excess capital. Too much capacity and too little demand feed on each other, reducing premiums further still.” </li></ul><ul><li>“ The insurance industry is in trouble. The main reason is that it has too much capital. Shareholders should ask firms to give it back to them” </li></ul><ul><li>“ The one thing that insurers do have some power over is the amount of capital in their business. Indeed, managing that capital—both its amount and its cost—ought to be the essence of an insurance manager’s job description.” </li></ul><ul><li>- “Capital Punishment,” Economist , 1/16/99 </li></ul>
  66. 66. Alternatives to Capital <ul><li>“ Insurers are discovering what bankers know as securitisation: the process of assembling mortgages, credit-card receivables or even business loans into securities that provide reasonably predictable income streams and principal repayments. This sort of financial engineering has been going on for decades in America.... Its big advantage is that, once the assets have been sold, the issuer need no longer set aside capital to cover potential losses; instead, the capital can be redeployed more profitably. Insurers are only now waking up to the potential benefits.” </li></ul><ul><li>- “An Earthquake in Insurance,” Economist , 2/26/98 </li></ul>
  67. 67. New Risks  New Capital Needs <ul><li>“ ....insurers have started bundling traditional and non-traditional risks—exchange-rate, business interruption, fire, and so on—and selling their clients protection against all of them with so-called “multi-trigger” policies.” </li></ul><ul><li>“ Having thus widened their (insurers’) definition of risk, they then teamed up with investment banks to devise new sources of capital to pledge against it. Traditionally, insurance capital was what was paid up by the shareholders of insurance companies. But in future it may include savings stored in banks, pension funds and mutual funds.” </li></ul><ul><li>- “The New Financiers,” Economist , 9/2/99 </li></ul>
  68. 68. An Opportunity for Actuaries <ul><li>“ International banks, and their regulators, are wrangling over the level of additional capital that banks should be made to carry, as a cushion, against so-called ‘operational risk’ that might damage a bank’s health or even the financial system. Operational risk includes anything from computer failure and postal strikes to fraud and cock-ups of Baring-style proportions. Insurance companies.... have joined the fray, offering to replace bank capital with new-fangled insurance cover.” </li></ul><ul><li>“ Most insurers think a capital-markets solution for operational risk is a distant goal. The nearer one is to bring their centuries of actuarial skills to bear to help banks save capital, and so to tap a rich new market of, potentially, 30,000 banks.” </li></ul><ul><li>- “Capital Cushion Fight, Economist , 6/7/01 </li></ul>
  69. 69. Problems for Insurers <ul><li>“ The insurance industry is in poor shape, particularly in Europe.... ....the biggest reason to worry about their (European insurers’) solvency is their over-investment in equities. Three years ago, on average they had 30-40% of their assets invested in equities, though some British insurers had as much as 80%. This is in stark contrast to American insurers, which invest, on average, only about a fifth of their assets in shares.” </li></ul><ul><li>“ Regulators in some countries impose a ceiling on equity investment. In Germany, for instance, there is a statutory limit of 35%. In America, the controls are imposed via higher capital requirements for investing in equities.” </li></ul><ul><li>(continued) </li></ul>
  70. 70. Problems for Insurers (cont.) <ul><li>“ To strengthen their balance sheets, insurers and reinsurers have become increasingly creative at finding new ways to raise capital. Those most in need have turned to their shareholders with a rights issue.” </li></ul><ul><li>“ Some P&C insurers raised new capital in order to be able to take on new business, rather than out of any desperation for cash.” </li></ul><ul><li>“ Shedding assets has been another way to raise cash and pay for the sins of the past.” </li></ul><ul><li>- “Poor Cover for a Rainy Day”, Economist , 3/6/03 </li></ul>
  71. 71. Canadian Regulation <ul><li>“ Dynamic Capital Adequacy Testing” (DCAT) </li></ul><ul><li>“ (DCAT) is the process of analyzing and projecting the trends of a company’s capital position given its current circumstances, its recent past, and its intended business plan under a variety of future scenarios…. The DCAT process is to include the running of a base scenario and several adverse scenarios…” </li></ul><ul><li>-- Canadian Institute of Actuaries, Dynamic </li></ul><ul><li>Capital Adequacy Testing – Life and </li></ul><ul><li>Property and Casualty </li></ul>
  72. 72. Canadian Regulation (cont.) <ul><li>“ (One possible approach would consist of…) … ‘stress-testing’ of the risk category in question… Stress-testing means a determination of just how far the risk factor in question has to be changed in order to drive the company’s surplus negative during the forecast period, and then evaluating if that degree of change is plausible or not. When stochastic models with reasonable predictability are available, an adverse scenario would be considered plausible if all remaining probability in the tail beyond this scenario is in the range of 1% to 5%.” </li></ul><ul><li>-- Ibid </li></ul>
  73. 73. Canadian Regulation (cont.) <ul><li>“… the concept of capital adequacy envisioned by DCAT extends beyond the balance sheet at a specific date to the continued vitality of the organization… The principal goal of this process is to help prevent insolvency by arming the company with the best information on the course of events that may lead to capital depletion, and the relative effectiveness of alternative corrective actions.” </li></ul><ul><li>-- Canadian Institute of Actuaries, ibid. </li></ul>
  74. 74. Capital Management for Insurers – Issues <ul><li>Determine the economic (required) capital </li></ul><ul><li>Make adjustments to actual capital position, if necessary </li></ul><ul><li>“Allocate” capital </li></ul><ul><li>Measure performance relative to capital </li></ul><ul><li>Deploy capital most efficiently </li></ul>
  75. 75. Strategies for Managing Capital <ul><li>If capital is inadequate (i.e., actual < economic) </li></ul><ul><ul><li>Raise new capital </li></ul></ul><ul><ul><ul><li>Internal: retained earnings; realizing capital gains </li></ul></ul></ul><ul><ul><ul><li>External: equity; debt; surplus notes </li></ul></ul></ul><ul><ul><li>Reduce risk level of firm </li></ul></ul><ul><ul><ul><li>Reduce exposures </li></ul></ul></ul><ul><ul><ul><li>Reinsurance </li></ul></ul></ul><ul><ul><ul><li>Strengthen underwriting standards </li></ul></ul></ul><ul><ul><ul><li>Reduce financial risks </li></ul></ul></ul>
  76. 76. Strategies for Managing Capital (cont.) <ul><li>If there is excess capital (i.e., actual > econ.) </li></ul><ul><ul><li>Payout to shareholders </li></ul></ul><ul><ul><ul><li>Increase dividends </li></ul></ul></ul><ul><ul><ul><li>Repurchase shares </li></ul></ul></ul><ul><ul><li>Greater capital investment activity </li></ul></ul><ul><ul><ul><li>New lines or areas of insurance </li></ul></ul></ul><ul><ul><ul><li>Acquisitions </li></ul></ul></ul><ul><ul><li>Increase risk level of firm </li></ul></ul>
  77. 77. Other Issues in Capital Mgt. <ul><li>Controlling expenses </li></ul><ul><li>Uncovering “hidden” capital </li></ul><ul><li>Managing dividends </li></ul><ul><li>Managing reinsurance </li></ul><ul><li>Managing asset allocation, buying, and selling </li></ul>
  78. 78. Applying RAROC <ul><li>RAROC = Risk-adjusted return on capital </li></ul><ul><ul><li>Emerged from the banking industry </li></ul></ul><ul><li>Reflects expected return on economic capital </li></ul><ul><li>Applied to insurance* </li></ul><ul><ul><li>Aggregate (accounting for correlations) risk measures and economic capital across all risks </li></ul></ul><ul><ul><li>Reattribute economic capital back to sources of risk </li></ul></ul><ul><ul><li>Measure capital productivity and performance </li></ul></ul>* Nakada, Shah, Koyuoglu, and Collignon, “P&C RAROC: A Catalyst for Improved Capital Management in the Property and Casualty Insurance Industry,” Journal of Risk Finance , Fall 1998

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