Section C: ERM Flashcards
Brehm Chapter 1:
Enterprise Risk Management
ERM is the process of systematically and comprehensively identifying critical risks, quantifying their impacts and implementing integrated strategies to maximize enterprise value.
Brehm Chapter 1: Key Aspects of ERM
Key Aspects of ERM
- An effective ERM program should be a regular process not a one time event
- Risks should be considered on an enterprise-wide basis
- should consider risks other than insurance risks
- ERM focuses on risks that have a significant impact on the value of the firm (material impact)
- Risk can be positive or negative; its the fact that the actual outcomes stray from expected
- Risks must be quantified as best as possible including correlations among risks
- should be on overall portfolio basis
- Strategies must be implemented to avoid, mitigate or exploit risk factors
- To maximize firm value, should examine the tradeoff between risk and return
Brehm Chapter 1: Types of Insurance Company Risk Factors
Insurance Hazard Risk - risk assumed by the insurer for a premium
- Underwriting - risk due to non-cat losses from current exposures
- Accumulation/Cat-risk - risk due to cat losses from current exposures
- Reserve Deterioration - risk due to losses from past exposures
Financial Risk - risk in the insurer’s asset portfolio due to volatility in interest rates, foreign exchange rates, equity prices, credit quality, and liquidity
Operational Risk - risk associated with the execution of the company’s business
- actions taken by the company
- e.g. execution of IT systems, policy service systems
Strategic Risks - the risks of strategic choices made by the company
- the risk of choosing the wrong plan
Brehm Chapter 1:
Enterprise Risk Management Process
The ERM process can be described as a sequence of steps:
Diagnose - firm conducts a risk assessment to determine material risks that exceed a company-defined threshold
- General Environment - political uncertainties, government policies, macroeconomic changes, catastrophes, etc.
- Industry - supply (input market) and demand (product market) changes, competitive uncertainties
- Firm Specific - labour changes, liability (product, pollution, employment), R&D
Analyze - risks that exceed a company threshold are modelled as best as possible:
- risks are quantified with probability distributions of potential outcomes
- recognize correlation among risk factors
Implement - implement various activities to manage the risks
- risk avoidance
- reduce risk occurrence
- risk mitigation
- risk transfer
- retain the risk
Monitor - monitor the actual outcomes vs. expected and update plans
Brehm Chapter 1: Goal Enterprise Risk Modeling
Goal is to understand and quantify the relationships among risks from assets, liabilities and underwriting.
Enterprise Risk Models combine several risk sub-models to produce an overall risk profile of the business.
Brehm Chapter 1: Enterprise Risk Modeling
These models help with the insurer with important management functions and strategic decisions such as:
- Determining capital needed to support risk, maintain ratings, etc.
- Identifying significant sources of risk and cost of capital to support those risks
- Setting reinsurance strategies
- Planning growth
- Managing asset mix
- Valuing companies for M&A
Brehm Chapter 1:
Elements Needed for Effective ERM Model
A good enterprise risk model has the following characteristics:
- Model reflects relative importance of various risks to business decisions
- Modelers have deep knowledge of the fundamentals of those risks
- Model includes mathematical techniques to reflect the relationships among risks (dependencies/correlations)
- Modelers have a trusted relationship with senior management
Brehm Chapter 1:
What are the essential elements of the enterprise risk model?
- Underwriting Risk
- Reserve Risk
- Asset Risk
- Dependencies/Correlations
Brehm Chapter 1: Essential Elements of Enterprise Risk Model
Underwriting Risk
1. Loss Frequency and Severity Distributions
- Used to quantify loss potential
2. Pricing Risk
- Risk of reserve deficiency due to underpricing which may go unnoticed for some time (until losses accumulate)
- Underwriting Cycle
3. Parameter Risk
- Risk from mist-estimated parameters, imperfect model form, unmodeled risks
4. Catastrophe Modeling Uncertainty
- Uncertainty in 3rd party CAT models (e.g. probability of event/loss)
Brehm Chapter 1: Essential Elements of Enterprise Risk Model
Underwriting Risk - Parameter Risk
Estimation Risk - misestimation of model parameters due to imperfect data
- the risk that the form and parameters of the frequency/severity distributions don’t reflect the true form and parameters
Projection Risk - changes over time and the uncertainty in the projections of these changes. (e.g driving increases since fuel is cheaper, criminals attack security vehicles because banks are more secure)
- examples of projections include trending frequency and severity to future periods AND loss development
Event Risk - events outside the company’s control that impact frequency/severity trends (e.g. class action, asbestos, new cause of loss, etc.)
Systematic Risk - risk that cannot be diversified away and affects many policies (such as inflation)
- do not improve when volume is added
Brehm Chapter 1: Essential Elements of Enterprise Risk Model
Reserving Risk
Reserving Risk
- Risk that reserve develop differently than expected
- Reserve uncertainty impacts the amount of capital required and the time the capital must be held
- A model can understate both a reserve estimate and reserve uncertainty
- need a model of reserve uncertainty in an enterprise risk model
Brehm Chapter 1: Essential Elements of Enterprise Risk Model
Asset Risk
Asset Risk
- Model asset risk by generating probabilistic scenarios based on historical patterns and testing the insurer’s strategy against the scenarios, taking into account the scenario likelihood
- Model should account for:
- bonds
- equities
- foreign exchange/interest rates
Note: key aspect is modeling scenarios consistent with historical patterns so its realistic
Brehm Chapter 1:
Sources of Dependency
Sources of Dependency
- Inflation rates, interest rates, equity values, etc. are correlated and should be modeled as such in a macroeconomic model
- UW cycles, insurance loss trends and reserve development are correlated across lines of business and with each other
- CATs and other event risk are often correlated across lines of business
Brehm Chapter 1:
Modeling Dependency
- Modeling tail dependency in extreme events is crucial when developing an enterprise risk model
- Use copulas to incorporate dependency if there’s higher correlation in the tail
- Correlation through a multivariate normal distribution has a low tail dependency
Brehm Chapter 1:
Why default avoidance isn’t the most important reference point to set capital
- Default avoidance is about protecting current policyholders
-
To protect shareholders, the company should avoid significant partial losses of capital that could damage franchise value
- could impact customer base, agency relationships, reputation
- Loss that would cause a significant rating downgrade is more meaningful reference point than total default
Brehm Chapter 1:
Meaningful reference points for setting capital besides default
- Maintaining enough capital to avoid rating downgrade below certain level
- Maintaining enough capital to service renewal business
- if writing renewal business requires 80% capital than an appropriate reference point is a 20% loss of capital
- Maintaining enough capital so insurer thrives after a catastrophe (not just survives)
- Holding enough capital to maximize insurers franchise value
Brehm Chapter 1:
Challenge when using extreme reference points to set capital
- Model is least reliable in the extreme tail (e.g. exhausting all captial)
- Little data far in the tail
- Results are senstive to assumptions about the distribution
- Far tail is poorly understood
Brehm Chapter 2: Corporate Decision Making using ER Model
What is the three-step evolutionary process?
- Deterministic Project Analysis
- Risk Analysis
- Certainty Equivalent
*Trying to determine cashflows to use in IRR or NPV calculation to see how risks impact the value of the firm. Based on this info, company can make decisions.
Brehm Chapter 2: Corporate Decision Making using ER Model
Deterministic Project Analysis
Deterministic Project Analysis
- Uses a single deterministic forecast to estimate present value or IRR
- Uncertainty is handled judgementally by decision makers
Brehm Chapter 2: Corporate Decision Making using ER Model
Risk Analysis
Risk Analysis
- Use forecasted distributions of the critical variables in a Monte Carlo simulation to calculate a distribution of present value of cashflows
- simulating cashflows on a discounted basis based on risks deemed important or influential
- helps to see the risk’s impact on company’s cashflows
- The risk judgment is intuitive applied by decision makers
- a.k.a. Dynamic Financial Analysis (DFA)
Brehm Chapter 2: Corporate Decision Making using ER Model
Certainty Equivalent
Certainty Equivalent
- Similar to risk analysis but quantifies the risk judgement with a corporate preference or utility function for consistency
- so judgement can be consistently applied
Brehm Chapter 2: Corporate Decision Making using ER Model
For a public firm, why might a certainty equivalent approach with a corporate risk preference be undesirable?
- Diversified investors only care about risk that cannot be diversified away in their portfolios (systematic risk) so they won’t care about firm-specific risk as this can be diversified away
- If management’s goal is to maximize shareholder value, they should also ignore firm-specific risk
- Issues with this - difficult to determine which risks are systematic and which ones are firm-specific.
- Also, market-based signals such as the risk adjusted discount rate, lack the refinement and discriminatory power that managers need to make cost-benefit and tradeoff decisions for mitigation or hedging
Brehm Chapter 2: Corporate Decision Making using ER Model
There are 5 major elements in internal risk modeling. Brehm focuses on the 5th one.
What are the sub-components of the 5th component?
- Corporate Risk Tolerance
- Cost of Capital Allocated
- Cost Benefit Analysis on Mitigation and Hedging
Brehm Chapter 2: Corporate Decision Making using ER Model
Decision making with IRM: We desire a mechanism with the following steps:
Step 1: Determine an aggregate loss distribution with many sources of risk (e.g. lines of business)
Step 2: Quantify or assess the impact of possible aggregate loss outcomes on the company
Step 3: Assign a cost to each amount of impact
- how much is the risk costing the company
Step 4: Attribute the cost back to the risk sources
- allocated the cost back to the line of business or other source (market risk, etc.)
Brehm Chapter 2: Corporate Decision Making using ER Model
Internal Risk Model (IRM): Corporate Risk Tolerance
Corporate Risk Tolerance
- Corporate Risk Tolerance is needed to quantify the impact of possible aggregate loss outcomes and assign a cost to each amount (impact)
- Combination of the following factors is Corporate Risk Tolerance:
- organization size
- financial resources
- ability and willingness to tolerate volatility
Brehm Chapter 2: Corporate Decision Making using ER Model
Internal Risk Model (IRM): Cost of Capital Allocated
Cost of Capital Allocated
- Cost of risk capital is allocated to the individual risk sources (e.g. line of business)
- RAROC = Risk-Adjusted Captial • Hurdle Rate*
Brehm Chapter 2: Corporate Decision Making using ER Model
Internal Risk Model (IRM): Cost-Benefit Analysis for Risk Mitigation
Cost Benefit Analysis for Risk Mitigation
- Any risk mitigation effort with a positive EVA is worth doing. This means the reduction of capital cost is greater than the cost of risk-mitigation.
- EVA = NPV Return - Cost of Capital*
- Cost of Capital = Risk Capital • Hurdle Rate
- Using the EVA approach determines the cost of capital directly
- If we use the capital allocation approach (where we have allocated capital) we would pursue activities where the decrease in capital required exceeds the cost of implementation.
Brehm Chapter 2: Risk Measures & Capital Allocation
Advantages of Economic Capital
Advantages of Economic Capital
- Provides unifying measure for all risks across an organization
- More meaningful to management than risk-based capital or capital adequacy ratios
- Forces the firm to quantify the risks it faces and combine them into a probability distribution
- Provides a framework for setting acceptable risk levels for an organization as a whole AND for individual business units
Brehm Chapter 2: Risk Measures & Capital Allocation
Moment-Based Measures:
Advantages & Disadvantages
Moment-Based Measures - use the moment of a random variable
- random variable could be change in capital over an accounting period
- measured by variance, standard deviation, skewness, etc.
Advantages
- Reflects all losses in the distribution
Disadvantages
- Standard Deviation treats favourable deviations the same as unfavourable ones
- Exponential Moment - responds better to large losses*
- Semi-Standard Deviation - only uses unfavourable deviations*
- Skewness or higher moments may reflect market attitude better*
Brehm Chapter 2: Risk Measures & Capital Allocation
Tail-Based Measures: VaR
Advantages & Disadvantages
VaR - percentile of the probability distribution
Advantages
- Emphasizes large losses
Disadvantages
- Only looks at one point in the distribution
Brehm Chapter 2: Risk Measures & Capital Allocation
Tail-Based Measures: TVaR
Advantages & Disadvantages
TVaR - expected loss given a loss above a selected percentile of the probability distribution
- VaR uses one point as the expected loss (e.g. 99th percentile) while TVaR uses the average of all the losses above the 99th percentile)
Advantages
- Reflects losses that exceed VaR
Disadvantages
- Losses are reflected linearly in the tail
Brehm Chapter 2: Risk Measures & Capital Allocation
Tail-Based Measures: XTVaR
XTVaRp% = TVaRp% - Mean
- The mean loss might be funded by other means (other than capital such as premium) so capital is only needed for losses above the mean.
Brehm Chapter 2: Risk Measures & Capital Allocation
Tail-Based Measures: Expected Policyholder Deficit (EPD)
EPD = (TVaRp% - VaRp%) • (1-p%)
- For EPD, the probability level is set so that the capital is VaR at that level.
- The (TVaRp% - VaRp%) term is the expected value of default conditioned on that a default occurs.
- The second term, (1-p%), makes the first term unconditional so it becomes the expected value of default.
Brehm Chapter 2: Risk Measures & Capital Allocation
Tail-Based Measures: Value of Default Option
Value of Default Option
When capital and/or reinsurance is exhausted, the firm has the right to default on its obligations and put the claims to the policyholders.
The market value of this risk is the value of the default put option which can be estimated based on option pricing.
Brehm Chapter 2: Risk Measures & Capital Allocation
Probability Transforms
- Probability transforms measure risk by shifting the probability towards the unfavourable outcomes and then computing a risk measure with transformed probabilities
Examples:
- Expected loss with transformed probabilities
- Minimum martingale transform and minimum entropy martingale transform, Wang transform
- Weighted risk measures: WVaR, WTVaR, WXTVaR
- losses twice as large are twice as bad - for example, removes the linearity in the tail for TVaR which assumes that each loss above the tail gets the same weight (simple average in tail)
Brehm Chapter 2: Risk Measures & Capital Allocation
Generalized Moments
Generalized Moments - expectations of a random variable that are NOT simply powers of that variable.
Example:
- Blurred VaR, which adds weight to losses around the percentile so we are not just looking at the loss percentile
Brehm Chapter 2: Risk Measures & Capital Allocation
The amount of capital an insurance is required to hold is a function of several things:
The amount of capital an insurance is required to hold is a function of several things:
- Customer Reaction - some care about insurers ratings so if the rating drops there could be a decline in business (more likely to see greater impact when rating decline vs. improve)
- Capital Requirements of Rating Agencies - different requirements differ by agency
-
Comparative Profitability of New and Renewal Business - renewal business tends to be more profitable due to more informed pricing and underwriting
- e.g. if renewals comprise 80% of the book then the insurer should be able to maintain 80% of its capital (coming from renewal business which is more profitable). Therefore, in a bad year if the company wishes to maintain this, then they should hold enough capital so that 20% of its capital could cover the adverse event.
Brehm Chapter 2: Risk Measures & Capital Allocation
Purpose of Capital Allocation
Purpose of Capital Allocation
- helps to show the contribution of each business unit to the overall risk
- can be used for calculating the risk-adjusted profitability by line of business and also setting capacity controls for those lines
Brehm Chapter 2: Risk Measures & Capital Allocation
Risk Allocation can be done in two ways
- Allocate the overall risk to the individual business units
- Estimate the contributions of the individual units to the overall risk
Brehm Chapter 2: Risk Measures & Capital Allocation
Proportional Capital Allocation
Proportional Capital Allocation
- Allocates total risk down to business units
Steps:
- Calculate overall risk measure
- Calculate the risk measure for each individual business unit
- Allocate the overall risk measure to the individual business units in proportion to their individual risk measures
Brehm Chapter 2: Risk Measures & Capital Allocation
Allocating Captial - Risk Decomposition
Risk Decomposition
- Decomposition uses co-measures to calculate the contribution of each business unit to the overall risk measure.
- e.g. Co-TVaR
Brehm Chapter 2: Risk Measures & Capital Allocation
Allocating Captial - Marignal Allocation
Marginal Allocation
- Measures the change to the total risk measure for the company if there is a small change in a business unit’s volume
- The change to the total risk measure is assigned to the business unit.
Marginal Impact of the jth business component:
r(Xj) = lim as ε→0 {[⍴(Y+εXj) - ⍴(Y)] / ε}
Brehm Chapter 2: Risk Measures & Capital Allocation
Allocating Captial - Marignal Allocation
Advantages
Advantages
- Marginal allocation also produces co-measures
- Marginal attributions sum to the total risk measure
- Leads to consistent strategic implications
- e.g. growing a business with an above average profit-to-risk ratio increases the company’s profit-to-risk ratio
Brehm Chapter 2: Risk Measures & Capital Allocation
Risk-Adjusted Profitability
If the risk measure is proportional to the market value of risk, then a higher risk-adjusted profitability ratio means a business unit is more profitable relative to its risk.
Risk-Adjusted Profitability Ratio = Profit / Risk Measure
Brehm Chapter 2: Risk Measures & Capital Allocation
Allocating the Cost of Capital
Allocating the cost of capital to business units sets a minimum profit target to each unit.
- If a business unit’s profit exceeds the minimum profit target, this excess is added to the firm
The cost of capital reflects the risk that a business unit has the right to access the insurer’s entire capital.
Brehm Chapter 2: Risk Measures & Capital Allocation
Disadvantages of Allocating Capital Compared to Allocating the Cost of Capital
Disadvantages of Allocating Capital
- it’s arbitrary because different risk measures allocate capital differently
- it’s artificial because each business unit has access to the entire company’s capital
Brehm Chapter 2: Regulatory and Rating Agency Capital Adequacy Models
Practical Models for Setting Capital:
Leverage Ratios
- Leverage ratios are generally a per dollar of surplus measure such as premium to surplus or reserve to surplus
- Can be used to compare to a threshold for testing capital adequacy (12 IRIS ratios)
Advantages
- Easy to calculate and monitor
Disadvantages
- Doesn’t distinguish between lines of business
- Ignores risks other than underwriting risks
Brehm Chapter 2: Regulatory and Rating Agency Capital Adequacy Models
Practical Models for Setting Capital:
Risk-Based Capital Models
Risk-based capital models combine multiple aspects into a single number.
Included Risk Aspects:
- Invested Asset Risk
- Credit Risk
- Premium Risk
- Reserve Risk
- Accumulation/CAT Risk (not in US or S&P models)
- Covariance Adjustment (in some models US and AM Best)
Brehm Chapter 2: Regulatory and Rating Agency Capital Adequacy Models
Practical Models for Setting Capital:
Risk-Based Capital Models - Reasons for Significant Differences between RBC Models
Different Model Uses
- Rating agency models (AM Best, Moody’s, S&P) focus on long-term viability of the firm
- Regulatory models (MCT, US RBC, etc.) focus on 1-year solvency so these models will have relatively lower factors
Covariance Adjustment
- Models with a covariance adjustment (like AM Best) will have relatively higher factors than models without it (like S&P)
- the covariance adjustment will reflect that not all risks will occur at the same time: reflects the independence between risks so that that overall capital is less than the sum of the individual risks
Brehm Chapter 2: Regulatory and Rating Agency Capital Adequacy Models
Practical Models for Setting Capital:
Scenario Testing
An insurer may do its own risk assessment using scenario testing or stochastic modeling which would be reviewed by a regulator.
Requirements:
- A one to five year financial projection model
- Probability distributions for sources of uncertainty
- Correlations between risks
- Management responses to adverse financial results
Brehm Chapter 2:
Asset-Liability Management
Asset Liability Management - the analysis and management of the asset portfolio, reflecting current liabilities, future cash flows, future premium flows, and the existing asset and liability portfolios.
The GOAL of ALM is to help the insurer make better risk-return decisions.
*more extensive than just asset-liability matching
Brehm Chapter 2:
Asset-Liability Matching
Asset-Liability Matching - setting an investment portfolio to have the same duration as the duration of the liability portfolio to protect the firm from changing interest rates.
Brehm Chapter 2:
Additional Risks and Actions that ALM Considers
Beyond interest rate risk, ALM considers:
- Inflation Risk
- Credit Risk
- Market Risk
- Equities and Reinsurance as methods for hedging
Brehm Chapter 2:
Layers of Complexity in ALM
Each item below adds complexity - we start off with just the asset portfolio then start adding the liabilities, timing and then UW cashflows.
- Analysis of the asset portfolio in isolation (risk vs. return)
- Adding fixed liabilities into the analysis
- reinvestment risk if asset duration is shorter
- risk of selling depressed assets if asset duration is longer (interest rates high)
- Adding variability to the amount/timing of liability cash flows
- Adding variable underwriting cash flows
With the above real-world complexities, a true enterprise-risk model is needed.
Brehm Chapter 2:
How does a company’s choice of risk-return metrics impact the optimal investment strategy?
Statutory Accounting Metrics
Since bonds are amortized and liabilities are not discounted, this approach show little hedging from duration-matching.
GAAP Accounting Metrics
Bonds are valued at market value, but this also shows little hedging form duration-matching.
True Economic Metrics
Duration-matching lowers interest rate risk, but including cash flows complicates the analysis.
Brehm Chapter 2:
Asset-Liability Modeling Steps
Step 1: Model assets, existing liabilities and current business operations
Step 2: Define risk metrics, can be income based or balance sheet based
Step 3: Define return metrics - income or balance sheet based (should be consistent with step 2)
Step 4: Set the analysis time horizon - single year or multi-year
Step 5: Include Model Constraints - regulatory restraints
Step 6: Run the model - with different investment, underwriting and reinsurance strategies, calculating risk-return metrics
Step 7: Plot an efficient frontier based on the different portfolios
Step 8: Test the effects of different reinsurance structures
Step 9: Review simulations where portfolios performed poorly
- hedging strategies or new policies may help to reduce downside risk
Brehm Chapter 2:
Naive Approach to Measuring Reinsurance Value
Comparing ceded premium (cost of reinsurance) to reinsurance recoveries and ceding commissions (benefit) over many years typically shows a negative benefit.
Reinsurance expect to make a profit, so simple cost-benefit analysis is a poor way to assess reinsurance value.
Brehm Chapter 2: Measuring Reinsurance Value
Paradigm 1
Reinsurance Provides Stability (Paradigm 1)
- Protects surplus from adverse results
- Improves predictability of earnings and growth
- Improves customer confidence that they’ll recover insured losses
- Ceded Premium - Recoveries*
- is a better cost measure under this paradigm
Brehm Chapter 2: Measuring Reinsurance Value
Paradigm 2
Reinsurance is a Substitute for Risk Capital (Paradigm 2)
- Increased stability lowers required risk capital
- ROE Cost of Reinsurance = Reinsurance Cost / Capital Freed*
If the ROE cost of reinsurance is less than the company’s target return, getting reinsurance is a good deal (i.e. want a small ratio).
Brehm Chapter 2: Measuring Reinsurance Value
Paradigm 3
Reinsurance adds value (Paradigm 3)
- Ideally, we could measure the value of reinsurance by the incremental increase in market value to the company.
Brehm Chapter 2:
Disadvantage of the Quantifying Stability Paradigm for Measuring Reinsurance Value
Disadvantage
Significant judgement is needed to evaluate the benefit of stability against the net cost of reinsurance for the different programs.