ERA 2 TIA Flashcards

1
Q

What are the major differences in the 1st and 2nd
evolutionary step in Decision Analysis?

A
  • Use of Distributions for the inputs instead of
    fixed amounts
  • Output is also a Distribution
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2
Q

What is the major difference between the 2nd and 3rd
evolutionary step in Decision Analysis?

A

Use a Risk Preference (Utility) function to value
the possible outcomes

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3
Q

What is the argument that the 3rd evolutionary step
in Decision Analysis is Unnecessary

A

Firms only compensate owners for systemic risk,
since the firm-specific risk is averaged out.

therefore, no need for formulations of corporate risk preferences; only systemic risk should be managed

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4
Q

Name some reasons why companies should pay
attention to firm-specific risk (3)

A
  • Management cannot easily separate firm-specific
    vs. systemic risk
  • Some risks are instantaneous, and can’t be
    managed through discounting
  • market based information is too noisy to use for
    cost-benefit analysis
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5
Q

Owners and Management want corporate policy that
makes risk management decisions more (4):

A
  • Objective
  • Consistent
  • Repeatable
  • Transparent
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6
Q

Spetzler parameterizes a Utility function for
management. What are the benefits of using a Utility function to
make decisons? (3)

A
  • Transparent
  • Objective
  • Mathematical
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7
Q

Walls identifies an efficient set of portfolios for the
firm to invest in. Why is this not sufficient to select the best portfolio?

A

We need the company risk preference to select the
optimal portfolio along the efficient frontier

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8
Q

According to Mango what 3 questions does Walls ask?

A
  • How much risk are we willing to tolerate
  • How much reward are we willing to give up for a given
    reduction in risk
  • Are the risk-reward tradeoffs along the efficient frontier
    acceptable to us?

The first two come from the parameterized utility function
It’s possible there are no options on the efficient frontier that
are acceptable

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9
Q

Why is allocating capital considered irrelevant? (2)

A
  • All of the company’s capital supports each policy
  • Allocating cost of capital is preferred
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10
Q

What risk sources should capital be allocated to?

A
  • Risk taking sources (eg. products)
  • Non Risk taking sources (eg. credit risk)
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11
Q

What is RORAC?

A

Return On Risk Adjusted Capital
1. Allocate Capital on a risk adjusted basis
2. Apply a company wide hurdle rate to determine
the cost of capital in $
3. This is a form of cost of capital

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12
Q

How do Merton & Perold define the cost of capital?

A

Amount to purchase a guarantee that the firm will
meet its obligations

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13
Q

How do we use Cost of Capital to determine if a
course of action is suitable?

A

EVA = NPV − [Cost of Capital] > 0

Economic Value Added

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14
Q

Under Capital Allocation, how do we determine if a
course of action is suitable?
for example a purchase of additional reinsurance

A

NPV > Cost of Capital
[Net Reinsurance Cost] < −∆ Capital · [Hurdle Rate]

That is the benefit to cost of capital should be greater than
the reinsurance cost
Reinsurance Premium 30m
Expected Reinsurance Benefit 20m
Net Reinsurance Cost 10m

```

∆ Capital -100m
Hurdle Rate 12%

```

10m < 12m
Cost < Benefit
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15
Q

What is Value at Risk VaRα?

A

The loss at the αth percentile.

VaRα = E[Y|F(Y) = α]

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16
Q

What is Tail Value at Risk TVaRα?

A

The average loss excess of the percentile α

TVaRα = E[Y|F(Y) > α]

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17
Q

What is Excess Tail Value at Risk XTVaRα?

A

Conceptually, the expected losses are funded by premium.
The excess is funded by capital - This is what XTVaR
represents.

XTVaRα = E[Y | F(Y) > α] − E[Y]

= TVaRα - Mean

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18
Q

What is Expected Policyholder Deficit EPD?

A

If capital is set as VaRα then EPD is the expected loss given default, times the probability of default.

EPD = (TVaRα − VaRα) · (1 − α)

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19
Q

Why does Venter not recommend VaR as a risk
measure for insurance companies?

A

It is too simplistic for insurers, which tend to use a number of
risk measures, many of which are more informative than VaR

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20
Q

Why shouldn’t we use a 1-in-3000 year risk metric? (3)

A
  • Not able to accurately measure the losses so deep in the tail
  • Selection of 1-in-3000 is arbitrary
  • Better to choose probability levels that are less remote, but still impact the company
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21
Q

What features does the following risk measure have? (2)
E[Y · e^(cY/EY)]

A
  • Captures all the moments
  • Usually only exists if there is a maximum loss
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22
Q

What is the Value of the Default Put Option?

A

The market cost of purchasing insurance to cover any losses, when in default.

If VaRα is the capital level, then EPD is the expected unconditional loss, and the Default Put is the Market Value.

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23
Q

What is a Probability Transform?
How can we use it to calculate risk measures?

A
  • A probability transform changes the density function -
    usually increasing the the density of worse losses
  • A risk measure (such as mean) can be calculated on the
    transformed probabilities
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24
Q

What is the Esscher Transform?

A

f^*(y) = k · e^y/c · f(y)

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25
What is a Complete Market?
A market where any risk can be sold
26
What Probability Transforms are favored in incomplete markets? (2)
* Minimum Martingale Transform (MMT) * Minimum Entropy martingale Transform (MET) * They give reasonable approximations for reinsurance prices
27
What transform can be used to model prices for bonds and catastrophe bonds?
The Mean under the Wang transform closely approximates the market value for bonds and catastrophe bonds
28
How to calculate Blurred VaRα?
Uses η(p) to weigh the losses, with the most weight at Y = F^−1(α), and the weight decreasing to either side. ``` E[Y · η(F(Y))] η(p) = e^[−θ(p−α)^2] ``` Large θ makes it tight around α
29
What market considerations should an insurer take into account when setting capital?
* Some customers want a well capitalized insurer, others want a better price * A company with 80% renewal business could afford to lose 20% of capital - this would be a meaningful risk metric
30
Why is TVaR a better risk measure than VaR at a given percentile for setting capital levels?
VaR is the minimum loss excess of a percentile TVaR is the average loss excess of a percentile
31
What is a co-measure?
For a risk measure: `ρ(Y) = E[h(Y) · L(Y)| g(Y)]` We have a co-measure `r(Xj) = E[h(Xj) · L(Y)| g(Y)]` We require h() to be additive: h(x + y) = h(x) + h(y) The co-measures sum to the risk measure ρ(Y) = ∑ r(Xj)
32
Are co-measures marginal?
Up to 1 co-measure will be marginal
33
Co-measure of VaR
r(Xj) = E[Xj | F(Y) = α] The expected loss in unit j when the firm has a loss at the αth percentile h(Y) = Y ; L(Y) = 1 ; g(Y) = F(Y) = α
34
Co-measure of TVaR
r(Xj) = E[Xj | F(Y) > α] The expected loss in unit j when the firm has a loss excess of the αth percentile h(Y) = Y ; L(Y) = 1 ; g(Y) = F(Y) > α
35
Co-measure of Standard Deviation
r(Xj) = Cov(Xj,Y) / Stdev(Y) This is the Marginal Co-measure h(Y) = Y − EY ; L(Y) = (Y − EY) / Stdev(Y); g(Y) = True
36
What is the Co-measure of EPD?
r(Xj) = (CoTVaRα − CoVaRα) · (1 − α) This is analogous to the definition of EPD.
37
What makes an allocation a Marginal Method?
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.
38
What is a suitable allocation? Are marginal allocations suitable?
An allocation is suitable if a small increase to a unit that has a higher return on capital than the company (average), leads to an increase in the return on capital for the company. Yes. A marginal allocation will always be Suitable
39
What is a scalable risk measure?
ρ(aY) = a · ρ(Y)
40
How to directly calculate a marginal allocation from the risk measure?
r(Xj) = lim e→0 [ρ(Y + e · Xj) − ρ(Y)]/e **this is the definition of a derivative
41
What is risk adjusted profit?
Pj / r(Xj) Pj = profit from unit j r(Xj) is the allocated risk measure For this to be true risk adjusted profit, need: r(Xj) ∝ Market Value of Risk
42
Why would we use multiple risk measures to calculate risk adjusted profit?
* We don’t know Market Value, so we use several risk measures - and hope they indicate a consistent result
43
How can we use a Stop-Loss to allocate cost of capital? (4)
* The Market Price of a stop loss is the cost of capital * Could use the Mean on Transformed probabilities * Minimum Entropy Transform * Mean + 30% Standard Deviation
44
How can options be used to allocate cost of capital? Why aren’t Options considered a good solution?
Use the Option Value of: The right of the business unit to call on the capital of the firm Timing is not fixed, thus they are difficult to value
45
Why is allocating Capital considered Arbitrary and Artificial?
* Arbitrary - different risk measures give different allocations, so the allocations are different * Artificial - each business unit has access to the capital of the entire firm, not just a portion of it
46
List Advantages of Economic Capital (4)
* Unifying Measure for all risks across an organization * More Meaningful than RBC or Capital Adequacy Ratios * Firm Quantifies Risks via Probability Distributions * Framework for setting acceptable risk levels
47
What is the difference between Expected Policyholder Deficit and Value of Default Put at some percentile α
EPD is the expected losses excess of VaRα Value of Default Put is the Market Value of protecting against losses excess of VaRα
48
What properties does a scalable risk measure have?
It is both Marginal and Additive
49
What is the Marginal Decomposition of E[Y · e^cy/EY]?
50
If we use a risk measure to allocate capital and calculate a Risk-Adjusted Return, What property would we like our risk measure to have?
That the Risk Measure is Proportional to the Market Value of Risk ρ(Y) ∝ [Market Value of Risk]
51
What 2 Definitions of Cost of Capital are Proposed
* Value the Option - right to call on the capital of the firm * value of stop loss reinsurance
52
What were common capital requirements prior to the 1990’s in the US? (2)
Leverage Ratios: Premium / Surplus < 3.0 Reserves / Surplus < a a might be 3
53
What ratios were used for Solvency I regulations in the EU
Equivalent to the higher of: Premium / Surplus and Incurred Claims / Surplus
54
What is a major weakness of using leverage ratios to determine capital requirements?
They do not distinguish between lines of business
55
How are Capital Requirements set under a Factor model?
A different factor is multiplied by each of the following to set the capital requirement: *Premium *Reserves *Receivables (Credit) *Assets These are summed, with a diversity benefit reducing the total
56
How do Factor models distinguish between lines of business?
Factors that apply to Premium, Reserves, Assets, Credit can differ by line of business
57
How does AM Best respond to companies that have high reinsurance recoverables?
Increases the Credit charge for companies with a high Reinsurance Recoverables / Surplus
58
What capital requirements for credit risk are in place in the UK? (2)
* Premium ceded to one reinsurer cannot exceed 20% of gross premium * Recoverables from one insurance group cannot exceed 100% of surplus
59
What scenario testing is required in Canada?
Static Scenarios
60
What stochastic scenario tests are required in the UK?
1 year 99.5% survival 3 years 98.5% survival 5 years 97.5% survival Basically 0.5% per year Australia just has the 1 year test
61
What inputs does stochastic modeling require? (4)
* Forecast Financials for 1-5 years * Probability Distributions * Dependencies * Reflection of Management responses
62
What is Accumulation Risk? How do firms consider it in their models?
Exposure to catastrophic events affecting a large number of insureds Most models use periods of 1-in-100 or 1-in-250 years, and include natural perils such as: Wind, Hail, Earthquake
63
What is Asset Liability Matching?
Matching focused on hedging interest rate risk
64
How is Asset Liability Modeling different from Asset Liability Matching? (2)
* Modeling looks at Assets, Liability and Future Premiums * Seeks to exploit hedges of any sort
65
When doing ALM, why do companies focus on Assets more than Liabilities?
Assets are much more liquid than insurance liabilities
66
What 4 portfolios did Venter consider in his analysis of ALM?
* Assets Only * Known Liabilities and Cash Flows (timing) * Liabilities and Timing are variable * Going Concern
67
What does Venter conclude for optimal ALM under an **Assets Only** portfolio? (3)
* Treasuries are Risk Free * Stocks are Risky * Look for alternatives along the Efficient Frontier
68
What does Venter conclude for optimal ALM under a **Known Liabilities and Cash Flow** portfolio? (3)
* Short Duration investments leads to Reinvestment Risk * Long Duration investments leads to Interest Rate Risk * Accounting bases that discount will have different results
69
What does Venter conclude for optimal ALM under a **Liabilities and Timing are variable** portfolio? (2)
* A model that incorporates asset and liability fluctuations is required * inflation sensitive liabilities complicates this analysis
70
What does Venter conclude for optimal ALM under a **Going Concern** portfolio? (3)
* Need to Model: Premium, Losses, Expense and Income * Has flexibility to use premium cash flows to pay claims if asset prices are depressed * Need an enterprise wide model
71
In what situation are Tax Exempt Bonds Preferred?
In Profitable periods
72
In what situation are Taxable Bonds preferred?
In Unprofitable periods (U/W losses reduce taxable income from bonds)
73
What did the Valuation, Finance & Investment Committee conclude about duration matching under **Statutory Accounting**? (3)
* Bonds are amortized, not marked to market * Liabilities are not discounted * Duration matching is not effective because neither assets nor liabilities move with interest rate changes
74
What did the Valuation, Finance & Investment Committee conclude about duration matching under **GAAP Accounting**? (3)
* Bonds are marked to market * Liabilities are not discounted * Only somewhat effective
75
What did the Valuation, Finance & Investment Committee conclude about duration matching under an **Economic Balance Sheet**? (5)
* Bonds are market to market * Liabilities are discounted * Matching results in Low interest rate risk * Short Duration investments leads to Reinvestment Risk * Long Duration investments leads to Interest Rate Risk
76
Why is investing in assets with long duration considered a trade off?
The longer duration creates interest rate risk But, since the yield curve slopes upward it also generates additional return
77
How can equities be used as a hedge?
* Hedge against Inflation * Impact can be tested with an enterprise risk model The conclusions will depend on the assumptions in the macroeconomic model
78
What future research is recommended? (Asset-Liability Management) (2)
* Correlations are poorly understood * Models of Unpaid Losses are Not explanatory models
79
What is a naive way to value reinsurance?
Add up the cash flows: Premium Paid − Recoveries If this "cost" is greater than zero, the reinsurance was not valuable
80
What cash flows need to be considered when valuing a reinsurance program? (4)
+ Reinsurance Premium Paid + Reinstatement Premium − Commission Received − Reinsurance Recoveries
81
What 3 paradigms does Venter use to measure the value of reinsurance?
* Quantify Stability and its Value * Reinsurance as Capital * Reinsurance impact on Market Value
82
List the first 4 methods used to quantify Stability
83
List Methods 5 & 6, which use very good and very bad outcomes, to quantify stability
5. Var1% : very favorable outcome 6. Worst Loss : not very useful because it is too extreme and too volatile
84
Methods 7, 8, & 9 to quantify stability focus on the Premium minus Losses
7. Graph Density function of [Premium − Losses] for each reinsurance program 8. Graph Distribution function 9. Table showing the results at various percentiles for each reinsurance program
85
Methods 10 & 11 to quantify stability are visual representations
10. **Space Needle Chart** * The height of each box represents the percentiles * The area is proportional to the probability that the result lies within that range 11. **Cost Benefit Diagram** * Graph the Result at a given percentile against the cost of the reinsurance program for several programs * For a given percentile, we prefer programs with a better result and lower cost * You can graph this for multiple percentiles
86
Method 12 to quantify stability uses Pre-Tax Net Income
12. Table showing the Pre-Tax Net Income at different percentiles
87
Methods 13 & 14 to quantify stability use Financial Ratios
88
Method 15 to quantify stability can compare many reinsurance programs at once
89
How does Venter calculate Capital Consumed?
−PV[Premium + Reserves − Losses − Expenses] eg. If losses are large, we need capital to make up the difference.
90
Define Net Cost of Reinsurance
Present Value of all Reinsurance Cash Flows [Net Cost of Reinsurance] = PV[Reinsurance Premiums − Recoveries]
91
What does Venter recommend when using XTVaRα to set capital?
* Don’t select a high α * Instead select a lower α, and use a multiple of XTVaR e.g. 6 · XTVaR90% OR 4.5 · XTVaR95%
92
How can we estimate the the lifetime capital required for one year of premium?
* Calculate the reserves as-if the current book of business had been in force for several years * Calculate the capital requirement considering both the premium, and the as-if reserves * When calculating the reserves for prior AY’s, trend back the premium from this year
93
How much of a price discount do insureds demand relative to Expected Policyholder Deficit (EPD)?
10 to 20 times EPD
94
How much does a 1% decrease in capital affect the pricing level?
A 1% decrease in capital → 1% loss in pricing level
95
How much does a 1% increase in standard deviation of earnings affect pricing level?
A 1% increase in standard deviation of earnings → 0.33% decrease in pricing level
96
How much does a ratings downgrade or upgrade affect business growth?
Upgrade 3% Business Growth Downgrade 5-20% reduction in business