ERM Ch.2 Flashcards
3 steps in the evolutionary process
- Deterministic Project Analysis
- Risk Analysis
- Certainty Equivalent
Risk Management Decisions should be
- Objective
- Consistent
- Repeatable
- Transparent
Steps to allocate cost of risk
- Estimate an Aggregate Loss Distribution
- Quantify the impact of the loss outcomes on the organization
- Assign a cost to each amount of impact
- Attribute (allocate) the cost back to each risk source
Corporate risk tolerance depends on
- Organization’s size
- Financial resources
- Abiltiy & willingness to tolerate volatility
Advantages of Economic Capital
- Provides a unifying measure for all risks across an organization
- More meaningful to management than formulaic RBC or capital adequacy ratios
- Forces firm to quantify the risks it faces & combine them into a probability distribution
- Provides a framework for setting acceptable risk levels for the organization as a whole & for individual business units
Asset Liability Modeling Approach
- Start w/ models of asset classes, liabilities & current business operations
- Define risk metrics
- Define return metrics
- Time Horizon
- Constraints
- Simulations
- Efficient frontier graph
- Liabilities, in particular future loss reserves, can be modified
- Results should be reviewed to identify the simulations that the preferred portfolio performed poorly
Value of Reinsurance
- Provides stability
- Frees up captial
- Adds to the value of the firm
Deterministic Project Analysis
Singe deterministic forecast of cash flows. Calculate a NPV or IRR. May do sensitivity analysis by varying some of the input assumptions. Uncertainity is handled judgementally.
Risk Analysis
The critical inputs have a distribution. These are fed into the model, and the output is a distribution of outcomes. Can be NPV or IRR. Uncertainty is handled judgementally, though a good portion has been moved into the distributions.
Certainty Equivalent
Has the additional step of running the output through a utility function. Formalizes some of the risk assessment so it can be applied consistently.
Should we strive for certainty equivalent?
Argument 1: Since the investors in the company are only compensated for systemic risk, and not compensated for firm-specific risk; the company shouldn’t be concered with firm-specific risk.
Argument 2: Hard to identify systemic vs. firm-specifc risk. Market-based information is too noisy for management to be able to do a proper CBA and make tradeoff decisions.
Market Value
Book Value + Franchise Value
2 papers analyzed by Mango - Spetzler
- Measure the utility curve for managers of a firm
- Which minimum level (p) would you accept a project
- Compared risk tolerance of different managers within a firm
- Create a transparent, objective mathematical expression of the corporation’s risk/reward tradeoffs
2 papers analyzed by Mango - Walls
- Focused on oil projects - Upfront investment -> Project may either succeed or fail
- Certainty Equivalent - The fixed amount that the firm is indifferent between taking the risky portfolio or the fixed amount
- Calculates the efficient frontier of portfolios & then uses the risk tolerance of the firm to select where on the frontier to select the best portfolio
- Questions:
- How much risk are we willing to tolerate?
- How much reward are we willing to give up for a given reduction in risk & vice versa?
- Are the risk-reward tradeoffs available along the efficient frontier acceptable to us?
One method to allocate the cost of risk capital
- Allocate Capital in a risk adjusted way
- Apply a hurdle rate to determine the cost of captial for each business unit
- Called Return on Risk-Adjusted Capital - RAROC
Economic Value Added
NPV - Cost of Capital
Why do we prefer skewness over standard deviation?
There is evidence that standard deviation does not capture market attitudes to risk, so we can add higher moments
XTVaR - Excess Tail Value at Risk
TVaR - Mean
EPD - Expected Policyholder Deficit
(TVaR - VaR) * (1- alpha)
Transforms - Why & Types
Want a way to recognize that large losses are worse for the firm, in more than a linear way
- Types:
- Minimum Martingale Transform (reins. prices)
- Minimum Entropy Martingale Transform (reins. prices)
- Wang Transform (market prices for bonds/CAT bonds)
Allocating the company risk measure to each business unit…
- Allows the company to measure the amount of risk each business unit contributes to the company
- Can be used to set capacity & policy limits for each business unit
- Can be used to calculate risk-adjusted profitability
3 ways to allocate a risk measure of a firm to its business units:
- Proportional Method
- Calculate the risk measure for each business unit, p(Xj), & allocate the risk measure for the company, p(Y), in proportion to p(Xj)
- TVaR
- Calculate the average losses in unit j, when the firm has losses excess of the (alpha)th percentile
- VaR
- Calculate the expected value fo the losses in unit j when the firm has losses at the (alpha)th percentile
Scalable Risk Measure
Risk measure are scalable if increasing (or decreasing) the size of the business by a small factor also increases (reduces) the risk measure by the same factor
Marginal Allocation
An allocation is marginal if the change to the company’s risk measure from a small change in a single business unit is attributed to that business unit.
Can get proportional growth (shrinkage) in two ways:
- Reinsruance
- Growth
How to measure the risk adjusted profit of a business unit
Profits of the unit/Allocation
Pj/r(Xj)
Allocate cost of capital
- Set equal to the value fo the righ to call upon the capital of the firm
- Charge the market valeu of a stop-loss for the business unit
- Start w/ the expected value of the stop-loss
- Use a probability transform & the theory of pricing in incomplete markets (Min. Entropy Martingale Transform)
Allocating capital is ___ and ___
Arbitrary & Artificial
3 accounting methods & effect on hedging
- Statutory Accounting:
- Little hedge from duration matching
- Bonds are amortized not marked to market
- LIabilities are not discounted
- GAAP Accounting:
- Duration matching is not effective
- Bonds are marketed to market
- Liabilities are not discounted
- Economic Balance Sheet:
- Duration matching results in low interest rate risk
- Assets are marked to market
- Liabilities are discounting
*
Net Benefit of Reinsurance
= | Change in Cost of Capital| - |Net Cost of Reinsurance|
If >0 then Accept
ROE - Reinsurance
= Net Cost of Reinsurance / Change in Capital
Accept if less than the cost of capital
Theoretical Models vs. Practical Models
Theoretical - from a risk model (Ex: VaR, TVaR)
Practical - use capital requirements from rating agencies or regulators (Ex: BCAR, S&P)
Pro & Con of Practical Model
- Pro: Easier to implement, since it doesn’t require modeling the distribution of lossses & their correlations
- Con:Not accurate though, because the measurement of risk is based on proxies, not the actual risk itself
- Solution: Have a model that looks a year out. It would take the current state & projections for nex year. Predict the probability of falling below certain thresholds. The capital could then be set so that the proability of this is less than 10%
As-If Reserves
Calculate the reserves, as if the company has been writing the same book the last several years
Need to adjust for inflation
As-If Reserves Advantages
- It can measure the impact of accumulated risk caused by correlated risk factors
- The reinsurance can be applied to the current AY & the as-if reserves providing a more valid measure of the accumulated risk & captial used over the full-life of the AY
Capital Consumed
=-PV(Premium + Reserves - Losses - Expenses)
