ERA 2 TIA Flashcards
What are the major differences in the 1st and 2nd
evolutionary step in Decision Analysis?
- Use of Distributions for the inputs instead of
fixed amounts - Output is also a Distribution
What is the major difference between the 2nd and 3rd
evolutionary step in Decision Analysis?
Use a Risk Preference (Utility) function to value
the possible outcomes
What is the argument that the 3rd evolutionary step
in Decision Analysis is Unnecessary
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
Name some reasons why companies should pay
attention to firm-specific risk (3)
- 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
Owners and Management want corporate policy that
makes risk management decisions more (4):
- Objective
- Consistent
- Repeatable
- Transparent
Spetzler parameterizes a Utility function for
management. What are the benefits of using a Utility function to
make decisons? (3)
- Transparent
- Objective
- Mathematical
Walls identifies an efficient set of portfolios for the
firm to invest in. Why is this not sufficient to select the best portfolio?
We need the company risk preference to select the
optimal portfolio along the efficient frontier
According to Mango what 3 questions does Walls ask?
- 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
Why is allocating capital considered irrelevant? (2)
- All of the company’s capital supports each policy
- Allocating cost of capital is preferred
What risk sources should capital be allocated to?
- Risk taking sources (eg. products)
- Non Risk taking sources (eg. credit risk)
What is RORAC?
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
How do Merton & Perold define the cost of capital?
Amount to purchase a guarantee that the firm will
meet its obligations
How do we use Cost of Capital to determine if a
course of action is suitable?
EVA = NPV − [Cost of Capital] > 0
Economic Value Added
Under Capital Allocation, how do we determine if a
course of action is suitable?
for example a purchase of additional reinsurance
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
~~~
What is Value at Risk VaRα?
The loss at the αth percentile.
VaRα = E[Y|F(Y) = α]
What is Tail Value at Risk TVaRα?
The average loss excess of the percentile α
TVaRα = E[Y|F(Y) > α]
What is Excess Tail Value at Risk XTVaRα?
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
What is Expected Policyholder Deficit EPD?
If capital is set as VaRα then EPD is the expected loss given default, times the probability of default.
EPD = (TVaRα − VaRα) · (1 − α)
Why does Venter not recommend VaR as a risk
measure for insurance companies?
It is too simplistic for insurers, which tend to use a number of
risk measures, many of which are more informative than VaR
Why shouldn’t we use a 1-in-3000 year risk metric? (3)
- 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
What features does the following risk measure have? (2)
E[Y · e^(cY/EY)]
- Captures all the moments
- Usually only exists if there is a maximum loss
What is the Value of the Default Put Option?
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.
What is a Probability Transform?
How can we use it to calculate risk measures?
- 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
What is the Esscher Transform?
f^*(y) = k · e^y/c · f(y)
What is a Complete Market?
A market where any risk can be sold
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
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
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
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
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
What is a co-measure?
For a risk measure:ρ(Y) = E[h(Y) · L(Y)|g(Y)]
We have a co-measurer(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)
Are co-measures marginal?
Up to 1 co-measure will be marginal
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
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
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
What is the Co-measure of EPD?
r(Xj) = (CoTVaRα − CoVaRα) · (1 − α)
This is analogous to the definition of EPD.
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.
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
What is a scalable risk measure?
ρ(aY) = a · ρ(Y)
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
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
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
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
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
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
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
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
What properties does a scalable risk measure have?
It is both Marginal and Additive
What is the Marginal Decomposition of E[Y · e^cy/EY]?
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]
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
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
What ratios were used for Solvency I regulations in
the EU
Equivalent to the higher of:
Premium / Surplus
and
Incurred Claims / Surplus
What is a major weakness of using leverage ratios to
determine capital requirements?
They do not distinguish between lines of business
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
How do Factor models distinguish between lines of
business?
Factors that apply to Premium, Reserves, Assets,
Credit can differ by line of business
How does AM Best respond to companies that have
high reinsurance recoverables?
Increases the Credit charge for companies with a
high
Reinsurance Recoverables / Surplus
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
What scenario testing is required in Canada?
Static Scenarios
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
What inputs does stochastic modeling require? (4)
- Forecast Financials for 1-5 years
- Probability Distributions
- Dependencies
- Reflection of Management responses
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
What is Asset Liability Matching?
Matching focused on hedging interest rate risk
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
When doing ALM, why do companies focus on Assets more than Liabilities?
Assets are much more liquid than insurance
liabilities
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
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
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
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
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
In what situation are Tax Exempt Bonds Preferred?
In Profitable periods
In what situation are Taxable Bonds preferred?
In Unprofitable periods
(U/W losses reduce taxable income from bonds)
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
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
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
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
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
What future research is recommended? (Asset-Liability Management) (2)
- Correlations are poorly understood
- Models of Unpaid Losses are Not explanatory
models
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
What cash flows need to be considered when valuing
a reinsurance program? (4)
+ Reinsurance Premium Paid
+ Reinstatement Premium
− Commission Received
− Reinsurance Recoveries
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
List the first 4 methods used to quantify Stability
List Methods 5 & 6, which use very good and very
bad outcomes, to quantify stability
- Var1% : very favorable outcome
- Worst Loss : not very useful because it is too extreme
and too volatile
Methods 7, 8, & 9 to quantify stability focus on the
Premium minus Losses
- Graph Density function of [Premium − Losses]
for each reinsurance program - Graph Distribution function
- Table showing the results at various percentiles
for each reinsurance program
Methods 10 & 11 to quantify stability are visual
representations
-
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 -
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
Method 12 to quantify stability uses Pre-Tax Net
Income
- Table showing the Pre-Tax Net Income at
different percentiles
Methods 13 & 14 to quantify stability use Financial
Ratios
Method 15 to quantify stability can compare many
reinsurance programs at once
How does Venter calculate Capital Consumed?
−PV[Premium + Reserves − Losses − Expenses]
eg. If losses are large, we need capital to make up the
difference.
Define Net Cost of Reinsurance
Present Value of all Reinsurance Cash Flows
[Net Cost of Reinsurance] =
PV[Reinsurance Premiums − Recoveries]
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%
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
How much of a price discount do insureds demand
relative to Expected Policyholder Deficit (EPD)?
10 to 20 times EPD
How much does a 1% decrease in capital affect the
pricing level?
A 1% decrease in capital
→
1% loss in pricing level
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
How much does a ratings downgrade or upgrade
affect business growth?
Upgrade 3% Business Growth
Downgrade 5-20% reduction in business
