ERM Ch.2

Question 1

3 steps in the evolutionary process

Answer 1

• Deterministic Project Analysis
• Risk Analysis
• Certainty Equivalent

Question 2

Risk Management Decisions should be

Answer 2

• Objective
• Consistent
• Repeatable
• Transparent

Question 3

Steps to allocate cost of risk

Answer 3

• 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

Question 4

Corporate risk tolerance depends on

Answer 4

• Organization’s size
• Financial resources
• Abiltiy & willingness to tolerate volatility

Question 5

Advantages of Economic Capital

Answer 5

• 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

Question 6

Asset Liability Modeling Approach

Answer 6

• 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

Question 7

Value of Reinsurance

Answer 7

• Provides stability
• Frees up captial
• Adds to the value of the firm

Question 8

Deterministic Project Analysis

Answer 8

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.

Question 9

Risk Analysis

Answer 9

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.

Question 10

Certainty Equivalent

Answer 10

Has the additional step of running the output through a utility function. Formalizes some of the risk assessment so it can be applied consistently.

Question 11

Should we strive for certainty equivalent?

Answer 11

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.

Question 12

Market Value

Answer 12

Book Value + Franchise Value

Question 13

2 papers analyzed by Mango - Spetzler

Answer 13

• 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

Question 14

2 papers analyzed by Mango - Walls

Answer 14

• 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?

Question 15

One method to allocate the cost of risk capital

Answer 15

• 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

Question 16

Economic Value Added

Answer 16

NPV - Cost of Capital

Question 17

Why do we prefer skewness over standard deviation?

Answer 17

There is evidence that standard deviation does not capture market attitudes to risk, so we can add higher moments

Question 18

XTVaR - Excess Tail Value at Risk

Answer 18

TVaR - Mean

Question 19

EPD - Expected Policyholder Deficit

Answer 19

(TVaR - VaR) * (1- alpha)

Question 20

Transforms - Why & Types

Answer 20

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)

Question 21

Allocating the company risk measure to each business unit…

Answer 21

• 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

Question 22

3 ways to allocate a risk measure of a firm to its business units:

Answer 22

• 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

Question 23

Scalable Risk Measure

Answer 23

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

Question 24

Marginal Allocation

Answer 24

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.

Question 25

Can get proportional growth (shrinkage) in two ways:

Answer 25

* Reinsruance * Growth

Question 26

How to measure the risk adjusted profit of a business unit

Answer 26

Profits of the unit/Allocation Pj/r(Xj)

Question 27

Allocate cost of capital

Answer 27

* 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)

Question 28

Allocating capital is ___ and \_\_\_

Answer 28

Arbitrary & Artificial

Question 29

3 accounting methods & effect on hedging

Answer 29

* 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 *

Question 30

Net Benefit of Reinsurance

Answer 30

= | Change in Cost of Capital| - |Net Cost of Reinsurance| If \>0 then Accept

Question 31

ROE - Reinsurance

Answer 31

= Net Cost of Reinsurance / Change in Capital Accept if less than the cost of capital

Question 32

Theoretical Models vs. Practical Models

Answer 32

Theoretical - from a risk model (Ex: VaR, TVaR) Practical - use capital requirements from rating agencies or regulators (Ex: BCAR, S&P)

Question 33

Pro & Con of Practical Model

Answer 33

* 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%

Question 34

As-If Reserves

Answer 34

Calculate the reserves, as if the company has been writing the same book the last several years Need to adjust for inflation

Question 35

As-If Reserves Advantages

Answer 35

* 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

Question 36

Capital Consumed

Answer 36

=-PV(Premium + Reserves - Losses - Expenses)