Brehm Chapter 2 Flashcards
(27 cards)
Decision Analysis - using simultions to drive corporate decision making
Evolution of Decision Analysis > Deterministic Project Analysis
Deterministic Project Analysis
* single forecast of future cash flows, present value, IRR
* incorporate uncertainty judgementally
Decision Analysis - using simultions to drive corporate decision making
Evolution of Decision Analysis > Risk Analysis
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
Decision Analysis - using simultions to drive corporate decision making
Evolution of Decision Analysis > Certainty Equivalent
Argument for/against
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)
Internal Risk Model (IRM) > Corporate Risk Tolerance
IRM Process, what is corporate risk tolerance, what are it’s drivers
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
Internal Risk Model (IRM) > Cost of Capital Allocated / Cost Benefit Analysis
IRM Process
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)
Decision Analysis > Risk Measures > Moment Based Measures
Examples, Disadvantage, alternatives
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
Decision Analysis > Risk Measures > Tail-Based Measures
Examples, Disadvantages
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
Decision Analysis > Risk Measures > Probability Measures
What is it? Examples
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
Decision Analysis > Risk Measures > Generalized Moments
What is it? Examples
Generalized moments - E[random variable] that is NOT powers of that variable
Example:
* TVaR = E[X | F(X) > p]
* Spectral risk measures
Decision Analysis > Required Capital
Drivers/considerations
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)
Decision Analysis > Capital Allocation/Decomposition > Proportional Allocation & co-measures
Steps for proportional allocation?
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
Co-Measures: Overall Risk Measure & Allocated Capital
Conditions, examples
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]
Decision Analysis > Capital Allocation/Decomposition > Marginal Method
What is it? Advantages, Condition required, Examples
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
Decision Analysis > Capital Allocation/Decomposition > Allocating Cost of Capital
Allocations: Arbitrary vs. Artificial
Formula for cost of capital ($), how to I quantify value of BU?
Cost of Capital ($) = 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
Regulatory & Rating Agency Capital Adequacy Models > Leverage Ratios / IRIS Ratios
Disadvantages of Leverage Ratios
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
Regulatory & Rating Agency Capital Adequacy Models > Risk Based Capital (RBC) Models
Differences in RBC modles (US, CA, Japan, AM Best, S&P)
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)
Regulatory & Rating Agency Capital Adequacy Models > Scenario Testing
What does scenario testing feature?
Features:
* correlations among risks
* reflections of management responses to adverse financial results (for multi-yr models)
Regulatory & Rating Agency Capital Adequacy Models > Risk Based Capital (RBC) Models > Evaluate Capitalization Strategy
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
Asset-Liability Management > Asset-Liability Matching
What is it
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
Asset-Liability Management Scenario > Asset Portfolio w/ No Liabilities
Considerations:
Considerations:
* short term treasuries are considered risk free
* high yield assets (stock/bonds) are risky
Asset-Liability Management Scenario > Asset Portfolio w/ Fixed Liabilities
Considerations:
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
Asset-Liability Management Scenario > Asset Portfolio w/ Variable Liabilities
Consideration, concerns
Considerations:
* more complicated than duration matching, especially if liabilities are inflation sensitive
* create a model that reflects asset/liability fluctuations over time
Asset-Liability Management Scenario > Going Concern
Considerations
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
Asset-Liability Management > Modeling Approach
Steps, potential issues/future research needed
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