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Risk

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Theory: Non-Systematic Risk Based on Information Flow and Liquidity ... Cummins, J. David, (1990), Multi-Period Discounted Cash Flow Ratemaking Models in ... – PowerPoint PPT presentation

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Title: Risk


1
Risk ReturnParameter Estimation
  • David Appel, Ph.D.
  • Milliman Robertson
  • Richard A. Derrig, Ph.D.
  • Senior Vice President
  • Automobile Insurers Bureau of MA

Casualty Actuarial Society Seminar on
Ratemaking March 12, 2001 Las Vegas, NV
2
Agenda
  • Risk and Return Models
  • Time Value of Money
  • Cash Flow Patterns Levels
  • Measuring Risk - CAPM
  • IRR Models
  • Allocating Capital
  • Calendar Year Acct Models
  • Risk Premium Project (COTOR)
  • Summary

3
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4
Risk and Return Models
  • Net Present Value Model
  • Valuation of Policyholder Flows
  • Internal Rate of Return Model
  • Valuation of Shareholder Flows
  • Calendar Year Accounting Model
  • Valuation of Company Acct
  • Returns

5
Risk and Return Models
  • Net Present Value Model
  • PV(P) PV(L) PV(E) PV(T)
  • Internal Rate of Return Model PV(Shareholder
    Inv. - Shareholder Dividends) 0
  • Calendar Year Accounting Model
  • Return on Surplus Return on Investment
  • Return on Underwriting

6
Risk and Return Models Family Tree
Profit Models
Historical
Prospective
CASH FLOW
ACCOUNTING
CYAM
ISO STATE-X
NPV (policyholder perspective)
IRR (shareholder perspective)
7
Time Value of Money
  • Premiums and Capital In
  • Expenses and Claims Out
  • Risk-Free Interest Rates
  • Risky Investments

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14
Cash Flow Patterns Levels
  • Premium Payments
  • Finance Charges
  • Acquisition Costs
  • General Expense
  • Premium Taxes
  • Capital Investment
  • Investment Income
  • Income Taxes

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16
Cash Flow Patterns Levels
  • Premium Payments
  • Finance Charges
  • Acquisition Costs
  • General Expense
  • Premium Taxes
  • Capital Investment
  • Investment Income
  • Income Taxes

17
Cash Flow Patterns LevelsIncome Taxes
  • Federal (35 Marginal Rate)
  • Change in Unearned Premium Reserve
  • Underwriting Earned Premium - Formula Discounted
    Loss Reserves
  • Investment Deductions by Asset Class
  • Deduct 70 Stock Dividends
  • Deduct 85 Tax-Exempt Bond Income
  • Alternate Minimum Tax
  • Idea 20 Minimum Rate on Net Income
  • Actual Consolidated Tax Returns
  • State (Specific Rate)
  • MA Flat of Investment Income

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19
Measuring Risk
  • Cost of Capital
  • Capital Asset Pricing Model
  • (CAPM)
  • Equity, Asset and Liability Betas
  • Market Risk Premium
  • Dividend Growth Models
  • Risk-Adjusted Discount Rates

20
Capital Asset Pricing Model(CAPM)
  • Investors are compensated for non-diversifiable
    (i.e., systematic) risk only
  • radj rfree ? x (rmarket - rfree)
  • where,
  • radj risk adjusted return
  • rfree return on risk free investments
  • rmarket return on the market
  • ? systematic risk coefficient

21
Capital Asset Pricing Model(Theoretical
Relationship)
Expected Return
Expected Return
20.1
R 15.4
?
Risk Premium
Rf 6.0
1.0
1.5
? Risk
R rf ? (market risk premium)
22
Capital Asset Pricing Model(Observed Empirical
Relationship)
Return
Expected Return
Empirical Observation
?
Risk Premium
Beta, Firm Size, Market/Book ratio Returns are
higher than predicted for Low Beta Small
Size Low M/B
23
CAPM Anomalies
Returns higher for Low beta firms Small
firms Low M/B firms Insurers tend to
be Average beta Relatively small market
cap Relatively low market/book Also, insurers
subject to interest rate risk not priced by CAPM
24
CAPM Issues
  • Sample Selection
  • Estimation of beta
  • Value Line, SP,Merrill Lynch, Wilshire
  • Market risk premium
  • Ibbotson Associates
  • Greenwich Associates

25
Capital Asset Pricing Model Beta Coefficients
Sources Value Line Investment Survey, Part 3,
The Ratings Reports, June 2, 2000 and June 30,
2000.
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28
Excess Market Risk Premium
  • Definition MRP RM - RF
  • RF depends on horizon length
  • RF T-Bill, Int. Govt, Long Govt.
  • MRP RM-Tbill,
  • RM-Int .Govt.
  • RM-Long Govt.

29
Excess Market Risk Premium
  • Problem 1 How Do I Estimate MRP Value?
  • Problem 2 Does RF Beta MRP Work?

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37
Simple CAPM is DeficientAdd Small Stock Effect
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39
IRR - Relevant Cash Flows
  • Shareholders commit equity capital to support
    sale of insurance
  • In return, receive rights to cash flows from
    underwriting and investment activities
  • - Underwriting cash flow (net of tax)
  • - Investment income on reserves and surplus
  • - Flow of surplus
  • IRR cash flows conditional on accounting
    conventions (usually SAP) and tax rules

40
IRR - Algebra
IRR r discount rate such that
(Cfi) (1 r)-i 0
Set price such that IRR target return (COK)
41
IRR - Key Inputs/Assumptions
  • Cash Flow Patterns (especially premium loss)
  • Investment Yield Rate (usually current yield)
  • Leverage (reserves/premiums/other)
  • Surplus Runoff (flow/block)

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IRR CASH FLOWS IN NOMINAL AND PRESENT VALUE
Final NPV of Final Time Cash Flow Cash
Flow 0 -75.0 -75.0 1 68.0 58.4 2 15.6
11.5 3 8.1 5.1 SUM 0.0 IRR
16.5
44
Setting Target Returns(a.k.a. Estimating Cost of
Capital)
  • Two Important Methods
  • Dividend valuation (DCF) model
  • CAPM
  • Also, comparable earnings

45
DCF Model
Price of stock equals present value of future
cash flows
P o
If D grows at constant annual rate, g, then
and
46
DCF Issues
  • Sample selection
  • Estimation of growth rate (g)
  • - Historical data or analysts forecasts
  • - Earnings, dividends or book value
  • Single growth rate or multi-stage model

47
Discounted Cash Flow Analysis Estimated Dividend
Yield
Estimated Dividend Yield
21th Century ACE Limited Allmerican
Finan Allstate Corp. Amer Intl Group American
Finan Berkley (W.R.) Chubb Cincinnati Fin Fremont
General GAINSCO HCC Ins Holdings HSB
Group Hartford Finan Mercury General Ohio
Casualty Old Republic Progressive RLI
Corp Reliance Selective St. Paul Transatlantic Uni
trin XL Capital Limited SAFECO Average
3.0 1.9 0.5 2.8 0.2 3.7 2.6 2.1 2.2 7.6 1.4 1.1 5.
7 1.6 3.8 4.4 3.3 0.4 1.8 nil 3.2 3.1 0.6 7.0. 3.6
3.5 2.84
Sources Value Line Investment Survey, Part 3,
The Ratings Reports, June 2, 2000 and June 30,
2000
48
Discounted Cash Flow Analysis Earnings Per Share
Experience
Sources Value Line Investment Survey, Part 3,
The Ratings Reports, June 2, 2000 and June 30,
2000.
49
Discounted Cash Flow Analysis Earnings Per Share
Experience
Sources Value Line Investment Survey, Part 3,
The Ratings Reports, June 2, 2000 and June 30,
2000.
50
Allocating Capital
  • Standard Allocations
  • Premium
  • Liabilities
  • Discounted Liabilities
  • Myers-Cohn Allocation
  • Myers-Read

51
Calendar Year Accounting Model - CYAM
Total Return (UW Profit IY Reserves) IY
Surplus Return on Operations Return from
Investment of Surplus Return on Operations
Return attributable to undertaking the risk
of the insurance transaction
52
CYAM - Algebra
Set Total Return Target Return (COK) and Solve
for UW?
53
CYAM - Key Inputs/Assumptions
  • Investment Yield Rate i
  • Investible Balance
  • Leverage
  • i is usually embedded yield
  • is usually estimated using recent
    historical data
  • is usually normative value rarely varies
    by line

54
CYAM - Likely Problems
  • Embedded yield not necessarily good proxy for
    expected earnings rate
  • Investible balance may be distorted due to
    variations in historical growth or loss
    experience
  • Leverage is typically insensitive to risk
  • and,
  • TIMING OF CASH FLOWS IS IGNORED

55
CALENDAR/ACCIDENT YEAR ANALYSIS STEADY STATE /
GROWTH RATE 0
AY1 AY2 AY3 AY4 0 -75.0 1
68.0 -75.0 2 15.6 68.0 -75.0 3 8.1 15.6
68.0 -75.0 4 8.1 15.6 68.0 5 8.1
15.6 6 8.1

Calendar Year ROE (6815.68.1)/75
22.3
56
CALENDAR/ACCIDENT YEAR ANALYSIS STEADY STATE /
GROWTH RATE 16.5
NPV OF AY1 AY2 AY3 AY4
AY4 0 -75.0 1 68.0 -87.4 2 15.6 79.2
-101.8 3 8.1 18.2 92.3 -118.5
-118.5 4 9.4 21.2 107.5
92.3 5 11.0 24.7
18.2 6 12.8 8.1 Calendar
Year ROE (92.318.28.1)/101.8 16.5
57
CALENDAR/ACCIDENT YEAR ANALYSIS STEADY STATE /
GROWTH RATE 25.0

NPV OF AY1 AY2 AY3
AY4 AY4 0 -75.0 1 68.0 -93.8 2 15.6
85.0 -117.2 3 8.1 19.5 106.3
-146.5 -146.5 4 10.1 24.4 132.8
114.0 5 12.7 30.5 22.5 6
15.8 10.0
Calendar Year ROE (106.319.58.1)/117.2
14.2
58
Model Outputs
  • NPV Underwriting Profit Provision
  • IRR Expected Return to Capital
  • CYA Return to Capital
  • Actual or Expected
  • Model Outputs Consistent if Inputs
  • are Consistent

59
Other Issues
  • Guaranty Funds
  • Residual Markets
  • Reinsurance
  • Default Risk
  • Risk Premium Project
  • Excess Capital

60
CAS Risk Premium Project
  • Committee on Theory of Risk
  • Discount Rate for Liabilities
  • Literature Review
  • Actuarial Process and Parameter Risk
  • Financial Systematic Risk
  • Academic Dave Cummins, Rich Phillips
  • Industry Bob Butsic, Rich Derrig
  • http//casact.org/cotor/rpp.htm

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62
Small Stock Effect/Sum Beta
  • Small Stock Effect Smaller Decile (MKT CAP)
    Returns Exceed CAPM Expected
  • Theory Non-Systematic Risk Based on Information
    Flow and Liquidity
  • Practice Deciles 5 to 10, 1926-1998 0.87 (5)
    to 3.75 (10) Excess of CAPM
  • Example MA Companies 1.3
  • Ibbotson, Kaplan Peterson (1997)
    Cross-Autocorrelations in Returns Sum Beta
    adds One Lag Sum ? ? ?-1
  • Sum Beta Explains Some of Small Stock Effect

63
Full Information Beta
  • Problem Public Firms not all Pure Play
  • Solution Industry Equity Beta via
  • Sales Weighted Full
  • Market Regression
  • P C Equity Beta 12/31/1998 of 0.92
    3/31/2000 of 1.15

64
Surplus Allocation
  • Surplus by Company stands behind all lines
  • Surplus by Line needed to allocate taxes and
    other by line Costs.
  • Myers-Read (1999) Theory Allows Unique Additive
    Allocation of Capital by Fairness to Guaranty
    Fund Criteria and Options Pricing Methods
  • Properties Higher Line Covariance with Liab
    (Asset) Portfolio Implies Higher (Lower) Surplus
  • Key Equation Default Option F (Liabilities,
    Assets, A/L)

65
Loss Distribution Betas
  • CAPM Loss Beta (Fairley, 1979) has
  • ? F(A,L,T,S, More (?)), No Default
  • Problem All Liability Dollars Have Same Risk
  • Butsic (1999) Unique Surplus Allocation if
    Price Homogeneity (Same Marginal Default Option).
  • Surplus Allocation Across Coverage Layers (Loss
    Distribution)
  • Layer Beta and Surplus Increasing by Limit
  • Risk Loads by Layer
  • Example Catastrophe Risk, Layer Betas 0.18 to
    8.29
  • Stay Tuned for More Developments

66
References
  • Almagro, Manuel and Thomas L. Ghezzi, (1988),
    Federal Taxes Provisions Affecting
    Property-Casualty Insurers, Proceedings of the
    Casualty Actuarial Society, LXXV.
  • Brealey, Richard A. and Stewart C. Myers, (2000),
    Principles of Corporate Finance, Sixth Edition,
    McGraw-Hill Higher Education.
  • Butsic, Robert P., (1991), Loss Reserve Valuation
    Using A Risk-Adjusted Discounting Interest Rate,
    Managing the Insolvency Risk of Insurance
    Companies, J. David Cummins and R. A. Derrig
    (Eds), Kluwer Academic Publishers
  • Butsic, Robert P., (1999), Capital Allocation
    for Property-Liability Insurers A Catastrophe
    Reinsurance Application, Casualty Actuarial
    Society Forum, Spring.
  • Cummins, J. David, (1990), Asset Pricing Models
    and Insurance Ratemaking, ASTIN Bulletin, 202.

67
References
  • Cummins, J. David, (1990), Multi-Period
    Discounted Cash Flow Ratemaking Models in
    Property-Liability Insurance, Journal of Risk
    Insurance, 571, 79-109, March.
  • Cummins, J. David , (1988), Risk-Based Premiums
    for Insurance Guaranty Funds, Journal of Finance,
    43, 823-839, September.
  • Derrig, Richard A., (1994), Theoretical
    Considerations of the Effect of Federal Income
    Taxes on Investment Income in Property-Liability
    Ratemaking,Journal of Risk and Insurance, 614,
    691-709, December
  • Derrig, Richard A., (1989), Solvency Levels and
    Risk Loadings Appropriate for Fully Guaranteed
    Property-Liability Insurance Contracts A
    Financial View, Financial Models of Insurance
    Solvency, J. David Cummins and R. A. Derrig
    (Eds), Kluwer Academic Publishers
  • Doherty, Neil A. and James R. Garven, (1991),
    Capacity and the Cyclicality of Insurance
    markets, Third International Conference on
    Insurance, Finance and Solvlency, Rotterdam, The
    Netherlands, May.

68
References
  • Fairley, William B., (1979), Investment Income
    and Profit Margins in Property-Liability
    Insurance Theory and empirical Results, The Bell
    Journal of Economics, 10, 192-210, Spring.
  • Kaplan, Paul D. and James D. Peterson, (1998),
    Full-Information Industry Betas, Financial
    Management, Summer.
  • Ibbotson, Roger G, Paul D. Kaplan and James D.
    Peterson, (1997), Estimates of Small Stock Betas
    are Much Too Low, Journal of Portfolio
    Management, Summer.
  • Mahler, Howard C., (1985), An Introduction to
    Underwriting Profit Models, Proceedings of the
    Casualty Actuarial Society, Volume LXXII.
  • Myers, Stewart C. and Richard A. Cohn, (1987), A
    Discounted Cash Flow Approach to
    Property-Liability Insurance Rate Regulations,
    Fair Rate of Return in Property-Liability
    Insurance, J. David Cummins and Scott E.
    Harrington (Eds).
  • Myers, Stewart C. and James A. Read, Jr., (2000),
    Capital Allocation for Insurance Companies, AIB
    Working Paper, Nov.

69
Summary
  • Models follow policyholder or
  • shareholder perspectives
  • Cash flows are modelled according
  • to perspective
  • Pricing models are prospective
  • and by line of business
  • Capital must be allocated
  • Model outputs are consistent
  • with consistent parameters
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