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List 3 categories of insurance u/w risk

1. Loss reserves on prior policy years: potential adverse development
2. U/W for the current policy year
3. property catastrophe risk



Contrast CAT Bond with traditional reinsurance

Credit Risk:
-CAT bonds are much safer since they are fully collaterized
-Reinsurance credit risk is a major concern at this magnitude
-Highest layers usually have the highest profit margins
- Investors will accept lower spreads from CAT bonds since they offer diversification benefits (low correlation with investment returns)
-Multi year bonds are available
-Reinsurance is usually only offered for one year period



List advantages of using Freq/Sev distributions instead of Loss Reserve Distribution Models in quantifying u/w risk

- It is easier to account for growth in the volume of business/inflation can be more accurately reflected
- Changes in limit and deductibles can be more easily reflected
- The impact of deductibles on frequency can be accounted for
- The treatment of the split of loss between insured, insurer & reinsurer can be mutually consistent



Describe the insolvency put option (EPD) method to allocate capital

EPD: Cost of protection against insolvency at given level

Objective is to achieve equivalent ratios of EPD to liabilities among lines.
Find the level of assets needed to have the same EPD ratio



Describe two issues why comparing RAROC with cost of capital determined by CAPM or Fama-French model

- Risk in CAPM is the systematic risk associated with an investment. RAROC risk is based on the difference between the cash flow’s expected value and the values in the tail.
- The denominator of the RAROC calculation is understated, since it does not account for the
franchise value.



What happens to capital requirement under lognormal distribution of LOSSES (vs normal) in the EPD method

It increases, where the difference increases as the coefficient of variation increases. This is because the probability of large losses is higher under lognormal (higher tail)



List 3 factors that is slowing the growth of risk linked securities market

- Regulatory issues
- Accounting issues
- Tax issues



What are sources of exposure to credit risk

- Marketable securities/derivatives/swap positions
- Insured’s contingent premiums and deductibles receivables.
- Reinsurance recoveries



Give the insolvency put option (EPD) method of capital allocation advantages and disadvantages

Over VaR, this approach reflects the severity of the losses.
The main problem is that it does not account for diversification.



Describe 3 problems with CAPM model of capital allocation

1. CAPM only reflects the systematic underwriting risk. It does not reflect other risks

2. βi is hard to estimate

3. the rates of return are impacted by other factors in addition to β



List the criterias that need to be satisfied by the RBC method

- The standard needs to be the same for all types of insurers (personal vs commercial; primary vs reinsurers)
- The RBC needs to be objectively determined (2 insurers with the same risk exposure need to have the same RBC requirements)
- The approach should be able to distinguish between items that differ materially in level of riskiness



How can the EPD value be compared to an option depending on the riskiness of asset and liabilities?

Liability is risky and the asset riskless:
Call option on the losses with exercise price equal to the value of the assets at the end of the year.
Assets are risky and liabilities riskless:
Put option on the ending assets: because in the event where the asset value (stock price) is less than the
liability (exercise price), the difference will be “put” to the policyholders.



Describe two way to determine if a line of business is profitable

RAROC: if RAROC is greater than the cost of capital, the insurer should continue to devote resources to the line.
- EVA(Economic Value Added): this formula quantifies that value added to the firm from a given line:
𝐸𝑉𝐴𝑖=𝑁𝐼𝑖−𝑟𝑖 * 𝐶𝑖
𝐸𝑉𝐴𝑂𝐶𝑖=𝑁𝐼𝑖 / 𝐶𝑖 − 𝑟𝑖



List problems with the use of economic profit as an income measure

- Ignores franchise value
- May make less sense to management, as the economic values often do not reconcile to GAAP accounting
- Management may have difficulty justifying their decisions to external parties, as these parties only have access to statutory & GAAP accounting



Briefly describe the issues when rating structured product on the same scale as single-name corporate bonds

Rating agencies did not understand the impact of errors in the correlation assumptions on the default probabilities



Describe the exceedance probability method in capital allocation

The appropriate amount of capital for each line is the amount which will equalize the exceedance probability among lines. Because the expected losses between lines usually differ in size, the above equation is usually adjusted to express everything in terms of ratios to expected loss: 𝑃[𝐿𝑜𝑠𝑠𝑖𝐸(𝐿𝑜𝑠𝑠𝑖)>1+𝐶𝑖𝐸(𝐿𝑜𝑠𝑠𝑖)]=𝜀𝑖



Briefly describe 3 modules of CAT models

- Stochastic module/Hazard module: generate the events that can occur, including the location, intensity, etc.
- Damage (vulnerability) module: derives the damage that would arise from an event, based on exposure information
- Financial analysis module: applies the insurance/reinsurance terms to the losses to determine
the financial impact to the insurer



Described risk-based capital

Amount of capital needed to protect against the risks to
which it is exposed



List ways to facilitate growth of CAT bond market according to Cummins

- Distribute information to researchers
- Regulatory reporting of CAT info when industry losses exceed threshold
- Account for reinsurance credit quality in regulatory capital requirements



Describe 2 methods to determine the cost of capital of each line

1. Base it on the cost of capital of a monoline firm that writes the same line. However, it will be difficult to find firms that write only the one line, and which have similar underwriting characteristics

2. Perform regressions on the data of multiline insurers to derive cost of capital by line



List and briefly describes the different allocation methods

1. Proportional Allocation Based on a Risk Measure
Allocates the total risk capital in proportion to the separate risk measures
2. Incremental Allocation
Allocate capital based on the marginal impact on risk capital due to adding the entire line
3. Marginal Allocation
Marginal impact on risk capital due to increasing the
exposure of the line by incremental portions
4. Co-Measure
Calculate risk measure of individual unit in case where total losses exceed threshold



Define structure finance

Structured finance involves pooling financial assets and creating a capital structure of claims (tranches)
against these pools.



What should be the accounting basis of RBC calculations and why?

Market value accounting is preferable for solvency assessment, as in the event of an insurer’s failure, the items of the balance sheet are liquidated at the market rates. Not accounting bias as with accounting book value basis.



When are the economic capital and risk capital may be equal

Remove conservartism from loss reseves or risk margin from premiums in risk capital



List some considerations when using Myers-Read method in capital allocation

- Not developed to determine the risk adjusted capital requirement
-Requires significantly more quantitative resources than other methods
- Mathematical challenges have indicated that may not be appropriate for most insurance applications



Give the Merton-Perold method of capital allocation advantages and disadvantages

A: Recognises the impact of diversification
D: Does not allocate 100% of capital, which can create a bias in risk-adjusted return measures



List reasons why subprime repackaged mortgage (CMOs) were biased against investors

- Higher probability of default due to lower credit quality of borrowers
- Lower recovery values, because when the assets do need to be sold, they are often sold under financial pressure
- High level of default correlation due to pooling mortgages from similar geographic areas/vintages.
- Due to the CDO2 structure, the impact of errors in the estimates is magnified.



List the 3 general types of triggers of CAT bond payments

1. Indemnity trigger: Based in insurer's actual losses
2. Index trigger: Based on an index of industry losses
3. Hybrid trigger: Blend of more than one trigger



Describe catastrophe risk swaps and its advantages/disadvantages

Swap between 2 (re)insurers which are exposed to
different types of catastrophic risk. The swap defines a specified amount of money that needs to be paid by each reinsurer in the occurrence of a specified event

- The (re)insurer reduces some of its core risk, and achieves diversification
- Lower transaction costs than some of the other securities

- It is difficult to create a swap that achieves parity
- Can create more exposure to basis risk that some other types of contracts
- Not prefunded



What needs to be done to correlation when elements are on opposite side of the balanche sheet

It needs to be multiplied by -1



What is the criticism of tail-based methods to determine capital allocation?

They ignore losses below the threshold



Describe 3 methods to quantify dependency in CAT models (and disadvantages)

1. Empirical analysis of Historical Data.
Disadvantages include:
a. usually there is insufficient data to calculate the historical dependency
b. there is little insight as to how the dependencies will change during tail events
2. Subjective Estimates: advantages include:
a. can account for the tail events
b. reflects the user’s intuition
Disadvantages include:
a. the number of risk categories increases, the number of dependency parameters that need to be estimated increases exponentially
3. Explicit Factor Models: these link the variability of the risks to common factors



Describe the two alternative views of capital allocation by percentile layer

1) Horizontal procedure: Allocating each layer of capital to the loss events that penetrate the layer
2) Vertical procedure: Allocating capital to each loss events based upon the layers that it penetrates



Describe the impact of default probabilities on tranches for ABS structured finance

As the default probability increases,
- The expected payoff on the collateral decreases monotonically. This impacts the tranches.
- The sensitivity of the tranches to the probability depends on their seniority



List 2 disadvantages of bond default probabilities as a threshold for risk measures

- Does not address which credit rating should be targeted
- Does not account for the risk of downgrade



Describe ways to derive the threshold for risk measures used in determining capital

- Bond default probabilities at a Selected Credit Rating Level: capital to keep probability of default of the firm equal to the probability of default of a bond with a specific credit rating.
- Management’s risk preferences: a threshold based on the risk tolerance of management.
- Arbitrary default probability: an arbitrary percentile that is relatively easy to measure. No need to estimate values at very low probability of occurrences, where a lot
of uncertainty exists.



Describe 3 unique aspects of reinsurance recoveries that makes it difficult to estimate credit risk

- Definition of “default” : consideration to impact of reinsurer credit rating downgrade in capacity to pay full value of losses
- Substantial contingent exposure: insurer's adverse development may increase recoverables and therefore exposure to credit risk
- Reinsurance credit risk is highly correlated with the underlying insurance risk



Describe catastrophic equity puts and its advantages/disadvantages

It’s an option. The insurer purchases the put from the writer, and in return, receives the right to issue
preferred stock to the writer at a specified price on the occurrence of a specified event.
- The insurer will be able to raise equity after a catastrophe, when its stock price is likely to be
- Lower transaction costs than CAT bonds, as no need to form a SPR
- Not collateralized, so exposes the insurer to credit risk
- If the insurer issues preferred stock, the value of the existing shares will be diluted



Describe the Merton-Perold method to allocate capital

Interested in the marginal impacts of a line on the capital required to achieve a certain EPD. Look at additional capital needed when adding the line of business



List disadvantages of management’s risk preferences as a threshold for risk measures

- will be difficult to get management to articulate and agree on a threshold
- May differ to the preferences of directors and shareholders
- ignores risk, which is an important consideration to compare to reward
- managers will likely be focused on a number of issues that concern policyholders, and it may be hard to isolate the estimate of the threshold to just the probability of default



How are Asset backed securities CDO created and why?

Due to the high level of risk, mezzanine tranches are often difficult to sell. In order to sell these, some
dealers have repackaged mezzanine tranches from several different asset backed securities into a new



Explain why a loss would receive a higher allocation in the upper layers than in the lower layers in the capital allocation by layer method

- There are a fewer events that pierce the layer (Losses divided into fewer losses)
- The layer of capital is wider because the incremental increase to severity of each event tends to increase in size. (Usually losses at higher percentile rare but severe)



Give exceedance probability method of capital allocation advantages and disadvantages

- Consistent risk measure that can be used to compare between LoB, companies, etc.

- The firm may not have enough capital to achieve a certain exceedance probability
- This approach does not consider the impact of diversification
- This does not reflect the amount by which losses will exceed the resources in the event that the exceedance level is breached



Describe some reasons why structure finance market grew substantially in the years leading up to the 2008 crisis

1. Seemingly attractive yields: Biased by historical default rate and failed recognition of high systematic risk assumed
2. Extreme market optimism: Housing prices would keep increasing and subprime mortgage default rates would stay low
3. Too little appreciation for fragility of ratings:
Very sensitive to assumptions. Capital requirements and decisions based on them.
4.Perverse incentives for rating agencies: Paid by issuer, not investors
5. Perverse incentives for banks: Collected huge fees for creating the structured finance products.



What happens to capital requirement under lognormal distribution of ASSETS (vs normal) in the EPD method

It decreases, because under lognormal assets cannot be negative.



Give two advantages of issuing the CAT bonds offshore

- Lower transaction costs
- Off-shore jurisdictions have demonstrated that they can perform very well in issuing and settling
the securities



Give the Myers-Read method of capital allocation advantages

Account for diversification
Allocates 100% of the capital (avoid the problem of dealing with excess capital)



Describe and give advantage (1) and disadvantages of the Risk-based capital (RBC) method of capital allocation

This is the level of capital that must be held in order to avoid regulatory intervention.

Relatively simple to calculate and find input value
- Factors used in the derivation of the RBC are of questionable accuracy
- Calculations are often based on book value instead of market
- RBC ignores several important sources of risk



Describe the main advantage of Industry Loss Warranties (ILW)

There is a possibility that the risk linked securities may not be treated as reinsurance by regulators.
An ILW is one type of security that does not suffer from this problem



Briefly describe risk measures used to derive the necessary amount of capital

- Percentile Risk Measure: provides the capital required to achieve a certain probability of ruin.
- Conditional Tail Expectation (CTE): the mean loss of all the losses that exceed a certain percentile. (TVaR)
- Expected Policyholder Deficit Ratio: discussed in Butsic. This metric is less arbitrary than CTE (no percentile)



List 3 type of indices in an index trigger in CAT bond

1. Industry loss indices: Estimated losses to the industry
2. Modeled loss indices: output from a model of CAT modeling firm to generate either industry losses or losses speciific to a sponsoring insurer
3. Parametric indices: triggered by specified physical measures of an event (weather related measures)



Give on advantage and a disadvantage of the RAROC as a risk adjusted performance measurement

A: Factors the level of risk into the performance measurement
D: Highly sensitive to the capital allocation method that is adopted



Describe different participants interactions in the structure of a typical bond

- Pays premium to SPR
- Receives fund from the SPR if CAT occurs
-Sells bond to investors and invest proceeds in highly rated (safe) investment
-Collects premium from insurer and pay in case of CAT
-Return money to investors if not CAT occurs
-Provide initial funds to SPR (bond price)
-Receive interest payment and principal at maturity if no CAT
Trust account:
-SPR maintains fund in trust account until it is paid out



Describe the Myers-Read method to allocate capital

This method looks at the impact of very small changes to lossliabilities by line of business on the required capital. It aims to equalize the marginal default values across LOB



Give 2 ways to reduce basis risk in CAT bonds and make it a less speculative instrument

- Base the payment on narrowly defined geographic indices
- Dual-trigger contracts (where the insurer cannot collect more than its net loss)



Describe moral hazard and basis risk in CAT bonds

Moral hazard: the risk that the insurer may artificially increase the losses in order to qualify for
reimbursement (H: Indemnity L: Parametric, Modeled)
Basis risk: the risk that the defined trigger is not very closely related to the insurance company’s
exposure (H: Parametric L: Indemnity)



List advantages of sidecars

- Transactions are usually off-balance sheet, and therefore the sidecars can be used to improve the reinsurer’s leverage
- Can be formed quickly with minimal documentation/administration costs



List the advantages of capital allocation by layer

1. Allocates capital to the entire range of loss events (not only extreme)
2. Tends to allocate more capital to events that are more likely
3. Tends to allocate significantly more capital to events that are more severe
4. Eliminates the need to select an arbitrary percentile level as a basis for allocating capital
5. Always allocate 100% of the capital



Describe risk-linked securities

Risk linked securities enable insurance risk to be transferred to the capital market, providing the
insurance market with additional capacity: catastrophes that are large relative to the resources of
insurers will often still be small relative to the size of capital markets.



List and briefly describe the 3 components of loss reserve risk (from insurance risk)

- Process risk: risk that actual results will deviate from their expected value due to the random variation inherent in the claim development process
- Parameter risk: risk that the actual expected value of the liability differs from the actuary’s estimate of the expected value due to inaccurate parameters
- Model risk: risk that the actual expected value of the liability differs from the actuary’s estimate of the expected value due to the use of the wrong model



Briefly describe methods to estimate u/w risk (from insurance risk)

- Loss ratio distribution model
- Frequency & severity model: Construct an aggregate distribution based on separate frequency and severity models.
- Inference from reserve risk models: Inferring the risk from new business with unconditional models generated from conditional reserve models (from inforce policies).



Define exceedance probability

Probability that the actual losses will exceed expected losses plus allocated capital.



What was the consequence of the increase of non-conforming mortgages and decreasing quality of subprime borrowers

- Ratio of mortgage values to home prices increased
- Increased use of second lien loans
- Increased issuance of mortgages with low/no documentation



What is Bodoff proposal for the new definition of VaR?

Hold enough capital EVEN for the 99th percentile. This means losses below the percentile selected is also considered



Describe different risk-based capital measures

- Regulatory Required Capital (min. requirements)
- Rating Agency Required Capital: to achieve a specific credit rating
- Economic Capital: the amount of capital necessary to provide the firm with a certain probability of achieving a specific objective over the time horizon.
- Risk Capital: the amount of capital that needs to be provided by the shareholders to cover the risk that the liabilities may exceed the funds already provided



What are the assumptions made in order for ABS to be rated AAA?

- Rating based on anticipated likelihood of default
- Assume that these high risk assets are not correlated to each other and with the market as a whole
-Senior tranches are safeguarded by junior tranches (true if uncorrelated)



Why is historical experience from catastrophe events less reliable for future losses

- Events are rare
- Exposures change over time
- Severities change over time due to changes in the building materials & designs



Define sidecars in risk linked securities

These are special purpose vehicles formed by insurers or reinsurers to provide additional capacity to
write reinsurance.
Sidecars are mainly capitalized by private investors, but can be funded by insurers and reinsurers as



List and briefly describe 3 frictions costs that reduce the return on capital of a line of business

1. Agency & Informational costs: management may behave opportunistically, and therefore fail to achieve the owner’s objective value maximization

2. the current tax system results in double taxation: investing in securities via insurance companies produces lower after tax returns than purchasing the securities directly

3. Various regulations may force the insurer to hold inefficient investment portfolios. Note that for most insurers, this generates no real cost, as they generally would hold more capital than the regulatory requirement anyway



List problems with looking at change in value of insurance liabilities over a year only

- There is little available methods/data to estimate the timing of the recognition of adverse loss
- The “change in value” perspective for loss reserves will not be totally consistent with market risk, as it will most likely focus on the best estimate of the reserve. Market risk, which is based on market value, includes a risk margin
- The information that would result in the revaluation of the liabilities is often not available over the short term



Describe the condition in ILW for payment to be made and 2 categories of payment that can be made

This security has dual-triggers that need to be satisfied for the loss to be paid:
- Retention trigger: based on the incurred loss of the insurer
- Warranty trigger: based on an industry wide loss index

ILWs have 2 categories of payments that can be made:
- Binary trigger: full payment is made once both triggers are satisfied
- Pro rata trigger: payoff depends on the magnitude by which the loss exceeds the warranty



List the advantages of a SPR in a CAT bond

- Shields the investors from general business risk of the insurer
- Financing costs for the issuer will be lower
- Transaction cost is more transparent than a debt issue since funds are in a trust and released according to specific criteria



Describe different income measures used in the RAROC calculation

- GAAP Net Income: calculated using GAAP accounting. (management decisions)
- Statutory Net Income: calculated using Statutory accounting rules
- IASB Fair Value: based on Fair value accounting. Removes the accounting biases of various accounting conventions
- Economic Profit: the change in “economic value” of the firm over a period (assets are recorded at market value, and liabilities are discounted).



Describe two objectives possibly targeted by economic capital

- Solvency objective: that the firm can meet its existing obligations to policyholders
- Capital Adequacy Objective: that the firm can continue to pay dividends/grow premiums/maintain a certain financial strength



Explain why it may be appropriate not to allocate 100% of available capital (M-P method)

One reason is that allocating all the capital would cause the firm to reject projects that would add to its
market value.
The excess capital can then be allocated to the “corporate” level.



Describe the role of banks in the structured finance situation during the crisis

- Investment banks had the incentive to keep dealing in structured finance business even as the U/W standards fell, due to the huge short term profits.
- The banks actually held the senior tranches that were
not sold, as the capital requirements were low, and also because the tranches were considered to be safe.



Why were risk linked securities initially received with low interest (4)

- Thinnest of the market
- Possible counterparty risk on the occurrence of a major catastrophe
- Insurer’s wanting to avoid disrupting long term relationships with reinsurers
- Excessive basis risk



Describe different capital measures that are not risk based

- Actual Committed Capital: the actual capital provided by the shareholders
- Market Value of Equity



List the advantages of EPD method according to Butsic

- Measure dollar severity of insolvency risk
- EPD can consistently measure insolvency risk in such a way that a standard minimum level of protection is applied to all classes of policyholders and insurers



Describe the impact of correlation on tranches for ABS structured finance

As the correlation increases,
- The risk shifts from the junior to the senior tranche
- The expected payoff on the junior tranche increases relative to the baseline, and the expected payoff on the mezzanine falls



List 5 applications to risk adjusted performance metrics

1. Assessing Capital Adequacy: when deciding whether insurers have sufficient capital, regulators and rating agencies ask several questions
2. Setting Risk Management Priorities: the insurer can identify the segment/activity that is generating the most risk capital
3. Evaluating Alternative Risk Management Strategies: the insurer can examine the impact of a Risk Management strategy on RAROC
4. Risk Adjusted Performance Measurement
5. Insurance Policy Pricing



List different ways to generate aggregate distribution in Freq/Sev model to quantify u/w risk

- Analytical solution
- Numerical method: numerical approximation
- Approximation: based on the mean, variance of the collective risk model
- Simulation



Under CAPM capital allocation, what is the formula for the Beta of equity

B(e) = B(A) * (1 + k1+ k2) + B1*s1 +B2*s2

Where :
ki= Li / E
si = Pi / E
Bi = Insurance risk Beta


Under CAPM capital allocation, what is the formula for the required rate of return of a line i?

What is the combined ratio?

ri = -ki*rf + Bi*(rm -rf)

Where ki = Li / E

Combined ratio = 1 - ri


What is the formula for the alternative formula for Franchise Value and the duration?

F =
(cr*S*(a+by-y)) / ((1+y)*(1+y-cr))

D =
(a-b+1) / ((1+y)*(a+by-y)) + 1/(1+y-cr)