Brehm Chapter 2 Flashcards

(27 cards)

1
Q

Decision Analysis - using simultions to drive corporate decision making

Evolution of Decision Analysis > Deterministic Project Analysis

A

Deterministic Project Analysis
* single forecast of future cash flows, present value, IRR
* incorporate uncertainty judgementally

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2
Q

Decision Analysis - using simultions to drive corporate decision making

Evolution of Decision Analysis > Risk Analysis

A

Risk Analysis
* distributions created for important variables, then used in a Monte Carlo simulation
* generated a distribution of PV of cash flows
* incorporate uncertainty judgementally

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3
Q

Decision Analysis - using simultions to drive corporate decision making

Evolution of Decision Analysis > Certainty Equivalent

Argument for/against

A

Certainty Equivalent - improves the “incorporate uncertainty judgementally”
* uses utility function (i.e. corporate risk preference) to quantify risk judgement
* formalizes judgement so that it can be consistently applied
* before, there could be firm-specific risk from the management’s judgement

Arguments against:
* investors care less about firm-specific risk, because it’s diversifiable
* investors will not demand a risk premium to firm-specific risk, so management should be indifferent to firm-specific risk
* overly detailed and unnecessary

Arguments for:
* difficult for management to determine firm-specific risk vs systematic risk
* risk-adjusted rate mostly reflects risks in the future, but the insurer also needs to worry about risks that may arise instantly
* market based data is noisy and difficult for management to conduct cost-benefit analysis
* shareholder want to maximize market value = book (current) + franchise value (future)

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4
Q

Internal Risk Model (IRM) > Corporate Risk Tolerance

IRM Process, what is corporate risk tolerance, what are it’s drivers

A

IRM Process
1. Start with aggregate loss distribution
2. quantifies impact of possible aggregate loss outcomes on the corporation
3. assign a cost of each impact
4. allocate cost back to the risk sources

Corporate Risk Tolerance - needed in steps 2 & 3
* measures the firm’s risk tolerance
* depend on insurer’s size, finacial resources, volatility tolerance

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5
Q

Internal Risk Model (IRM) > Cost of Capital Allocated / Cost Benefit Analysis

IRM Process

A

IRM Process
1. Start with aggregate loss distribution
2. quantifies impact of possible aggregate loss outcomes on the corporation
3. assign a cost of each impact
4. allocate cost back to the risk sources

Cost of Capital Allocated - step 4 (theoretical) (covered later)
* allocate risk capital first and then using it to assign cost of capital
* cost of capital ($) = risk adjusted capital * hurdle rate = RORAC

Cost Benefit Analysis - 1 approach is EVA (covered later)
* EVA = NPV Return - Cost of Capital (covered more in Cummins Capital)
* grow units with EVA ≥ 0 (consistent with firm value maximization)

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6
Q

Decision Analysis > Risk Measures > Moment Based Measures

Examples, Disadvantage, alternatives

A

Moment-Based Measures use the moment of a random variable
* Examples - Var & SD

Disadvantages
* favorable deviations are treated the same as unfavorable deviations
* As quadratic risk measures (e.g. Var & SD), these might understate market attitudes to risk

Alternatives
* semi-SD - only based on unfavorable deviations
* skewness - uses a higher moment, better capture market attitudes to risk
* exponential moments - captures the effect of large losses on the risk exponentially, better capture market attitude to risk

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7
Q

Decision Analysis > Risk Measures > Tail-Based Measures

Examples, Disadvantages

A

Tail-Based Measures are driven by large losses only
* Disadvantage - may be inappropriate b/c even average losses would have an impact on risk

Examples:
* VaR
* TVaR
* XTVaR = TVaR - E[X]
* EPD = (TVaR - VAR) * p
* Value of default option: value of an option that would cover all default probability

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8
Q

Decision Analysis > Risk Measures > Probability Measures

What is it? Examples

A

Probability Measures - transforms the probability towards unfavorable outcomes
* then calculate a risk measure that is based on these new transformed probability

Examples
* E[X] using transformed probability (i.e. CAPM and Black-Scholes uses transformed means)
* WTVaR instead of TVaR (originally treats all large loss the same)
* Wang transform

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9
Q

Decision Analysis > Risk Measures > Generalized Moments

What is it? Examples

A

Generalized moments - E[random variable] that is NOT powers of that variable
Example:
* TVaR = E[X | F(X) > p]
* Spectral risk measures

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10
Q

Decision Analysis > Required Capital

Drivers/considerations

A

Customer reaction
* some customers care about the capital held and the financial rating of an insurer
* if insurer’s rating improves –> growth increases slowly
* if rating deteriorates –> rapid decline in business

Capital requirements of rating agencies
* different rating agencies require different amounts of capital held

Relative profitability of new vs renewal business
* renewal business typically more profitable
* important for insurer that they have enough capital to retain their renewal book (worst case just don’t write NB)

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11
Q

Decision Analysis > Capital Allocation/Decomposition > Proportional Allocation & co-measures

Steps for proportional allocation?

A

Allocate the overall risk to each BU (Capital Allocation)
* Calculate overall risk measure
* Calculate risk measure for each BU
* Allocate overall risk measure to each BU in proportion to their risk measure

Estimate the contributions of each BU to the overall risk (co-measure, Capital Decomposition)
* define risk measure as an average of compy results under certain conditions (i.e. TVaR: S(x) > p)
* contributions from each BU is the average of the BU’s results
* more detail in “Brehm Formula” flashcards

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12
Q

Co-Measures: Overall Risk Measure & Allocated Capital

Conditions, examples

A

Overall risk measure:
* ρ(Y) = E[h(Y) * L(Y) | g(Y)]
* h is an additive function h(X+Y) = h(X) + h(Y)
* L is any function that conditional EV exists

Capital allocated to BU Xj:
* r(Xj) = E[h(Xj) * L(Y) | g(Y)]
* since h is additive, then sum[ r(Xj) ]= ρ(Y)

Examples
* TVaR = ρ(X) = E[X | S(X) > p] –> r(Xj) = E[Xj | S(X) > p]
* XTVaR = ρ(X) = E[ (X - E[X]) | S(X) > p] –> r(Xj) = E[ (Xj - E[Xj] ) | S(X) > p]

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13
Q

Decision Analysis > Capital Allocation/Decomposition > Marginal Method

What is it? Advantages, Condition required, Examples

A

Marginal method - the impact to insurer’s overall risk due to a small change in the volume of a BU, should be allocated to the BU
* consistent with financial theory of pricing in proportion to marginal cost
* used to optimize strategy
* all marginal decomps are also co-measures

Condition required
* BU is able to increase/decrease book in a homogeneous fashion (w/o changing loss distribution, LR). Example - quota share
* ρ(aY) = aρ(Y) ~ risk measure is scalable (aka. PH - positive homogenous, homogenous of degree 1)

Examples
* VaR, TVaR
* SD, (NOT Varience)
* Exponential moment
* XTVaR when condition is a quantile (NOT fixed $ amount)

Capital Allocated to BU Xj
* r(Xj) = Δρ(Y) / Δρ(Xj) = [ ρ(Y + εXj) - ρ(Y) ] / ε as ε –> infinity

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14
Q

Decision Analysis > Capital Allocation/Decomposition > Allocating Cost of Capital

Allocations: Arbitrary vs. Artificial

Formula for cost of capital ($), how to I quantify value of BU?

A

Cost of Capital ($) = Capital * hurdle rate
Value of BU = EVA = NPV Return (Profit) - Cost of Capital
* each BU incurs a cost (of capital) due to its right to access the capital of the insurer
* can also be calculated using options pricing

Allocating capital is:
* arbitrary- different risk measures result in different allocations
* artificial - each BU can access all of insurer’s capital, rather than just their allocation portion

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15
Q

Regulatory & Rating Agency Capital Adequacy Models > Leverage Ratios / IRIS Ratios

Disadvantages of Leverage Ratios

A

Regulators and rating agency originally focused on leverage ratio (i.e prem/surplus ≤ 3.0)
* does not different by class of business
* do not factor in others risks besides underwriting risks

IRIS Ratios - still used today but given less weight than other capital adequacy measures
* fail 4 or more ratios –> regulatory scruntiny
* GWP / Surplus, NWP / Surplus, 2 yr operation ratio, investment yield, etc

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16
Q

Regulatory & Rating Agency Capital Adequacy Models > Risk Based Capital (RBC) Models

Differences in RBC modles (US, CA, Japan, AM Best, S&P)

A

RBC model reflects multiple types of risks and outputs the minimum capital that insurer should hold
* based on insurer’s risk exposure (unlike leverage ratios)
* risks including invested asset, credit, premium, and reserve risk

Differences among RBC Models (US, CA, Japan, AM Best, S&P):
* AM Best and S&P determine if insurer is viable long term –> have higher factors
* regulatory models look at 1 year likelihood of insolvency –> lower factors
* differing covariance adjustment (so that sum of the risk charges < total required capital)

17
Q

Regulatory & Rating Agency Capital Adequacy Models > Scenario Testing

What does scenario testing feature?

A

Features:
* correlations among risks
* reflections of management responses to adverse financial results (for multi-yr models)

18
Q

Regulatory & Rating Agency Capital Adequacy Models > Risk Based Capital (RBC) Models > Evaluate Capitalization Strategy

A

RBC models used to compare capitalization strategies

Issue surplus note - will increase surplus but less than a dollar-for-dollar basis:
* interest on the note is assumed > cost of capital
* size of the note is very large, > 20% of capital
* increase the amount of invested assets, increasing asset risk and required capital
* rating agency (AM Best) reduces the surplus benefit of the surplus note
* cannot be repaid for 10 years

Purchasing reinsurance reduces required capital
* partially offset by an increase in credit risk
* more costly than surplus note on a one-year basis
* long term, insurer’s profits are projected to increase surplus, decreasing the reinsurance needed

19
Q

Asset-Liability Management > Asset-Liability Matching

What is it

A

Asset-Liability Management - managing asset portfolio, generate optimal portfolio
* interest rate risk
* also inflation, credit, market risk

Asset-Liability Matching - maintaining an investment portfolio that has the same duration as the liability portfolio
* protects insurer against interest rate changes

20
Q

Asset-Liability Management Scenario > Asset Portfolio w/ No Liabilities

Considerations:

A

Considerations:
* short term treasuries are considered risk free
* high yield assets (stock/bonds) are risky

21
Q

Asset-Liability Management Scenario > Asset Portfolio w/ Fixed Liabilities

Considerations:

A

Considerations - reinvestment risk:
* if rates drop, investment income may not be enough to pay for liabilities (shorter term treasuries)
* if rates increase, asset values will likely fall, may not be enough to pay liabilities (longer term investments)
* can be addressed by duration matching

22
Q

Asset-Liability Management Scenario > Asset Portfolio w/ Variable Liabilities

Consideration, concerns

A

Considerations:
* more complicated than duration matching, especially if liabilities are inflation sensitive
* create a model that reflects asset/liability fluctuations over time

23
Q

Asset-Liability Management Scenario > Going Concern

Considerations

A

If the conditions for liquidation are not favorable:
* insurer can continue to operate and make payments
* need to model the current business operation, asset and liability

24
Q

Asset-Liability Management > Modeling Approach

Steps, potential issues/future research needed

A

Steps:
1. Start with the model of asset classes (stock, bonds), existing liability (reserves), and current business operations
2. Define risk metrics (VaR, TVaR, etc)
3. Define return (ROE, earnings)
4. Define time horizon, timing of the analysis
5. Define constraints (regulators)
6. Run model for multiple investment/UW/reinsurance strategies (create simulations)
7. Construct an efficient frontier based on different scenarios

Potential issues with enterprise wide modeling, future research needed:
* Correlations between LOBs and between assets and liabilities
* Unpaid losses based on economic dat have not been developed yet

25
Measuring Reinsurance Value > **Cost Benefit Analysis** | What are costs ($), benefits ($), net benefit ($)
Cost: premiums that are ceded to the reinsurer Benefit: recoveries and ceding commissions received from the reinsurer Net Benefit = Benefit - Cost * **often negative** * losses are paid many years later, primary insurer **loses investment income** * even if net benefit was positive, reinsurer will increase price * reinsurer exist to make money too
26
Measuring Reinsurance Value > **Reinsurance Benefits** | Benefits
Stability * protect capital * improves predicability of earnings * assurance to policyholders * cost = ceded prem - recoveries Frees up capital * insurer is able to hold less capital * Marginal ROE (reinsurance) = cost / capital reduction. If ROE < target return, good decision to buy reinsurance Adds market value to the firm * investors like more stability
27
Measuring Reinsurance Value > Reinsurance Benefits > **Marginal ROE** | Formula + how to derive denominator
Marginal ROE Stability = cost of reinsurance / capital consumed * If ROE < target return, good decision to buy reinsurance * cost of reinsurance can be change in NPV How to derive capital reduction: * theoretical model - derive from **risk metrics** from **enterprise risk model** * practical model - determine required capital by referring to **rating agency/regulatory requirement**