08_CumminsCapital Flashcards
Briefly describe the uniqueness of debt capital for insurance companies.
An insurer’s debt capital is provided by its customers in the form of premiums.
Unlike bondholders, insurance policyholders are unable to protect themselves against insolvency through diversification.
Briefly describe two methods for determining the cost of capital for a LOB for a firm that writes multiple LOBs.
- Pure play technique – estimates the cost of capital by examining mono-line “pure-play” firms that only write that LOB
- Full-information betas technique – estimates the cost of capital by running
regressions on data from other multi-line firms
Briefly describe four reasons why it is unwise to use the RBC formula to allocate capital.
- The regulatory risk charges may not be accurate
(For example, some of the charges are based
on worst-case scenarios rather than statistical concepts such as variances and co-variances.
In addition, the formula ignores correlations among the firm’s businesses) - The regulatory risk charges are based on book value rather than market value
- The regulatory risk charges ignore important sources of risk such as interest rate risk
- There is no theoretical foundation for the RBC formula
Briefly describe two reasons why RBC is still important despite its limitations.
- RBC identifies most of the important risks faced by insurer
- Regulatory capital may serve as constraint on some of the firm’s activities due to RBC solvency thresholds
The required UW return for each LOB can be thought of as the sum of two components. Briefly describe each component.
- Each LOB implicitly pays interest for the use of policyholder funds (−𝑘_i 𝑟_F)
- Each LOB receives a rate of return based on the systematic risk of the
LOB (𝛽_i(𝑟_M − 𝑟_F))
Under the CAPM “allocation” method, we are not actually allocating capital by LOB. Explain what is actually happening.
Instead of allocating capital by LOB, we charge each LOB for at least the CAPM cost of capital.
Which reflects the LOB beta coefficient and leverage ratio
Briefly describe three issues with the CAPM approach described in Cummins
Capital.
- CAPM reflects systematic underwriting risk, which is the correlation of underwriting performance with the market portfolio. However, insurers are also concerned about the risk of extreme events, which is not captured in the CAPM return
- LOB underwriting betas are difficult to estimate
- Rates of return are driven by factors other than beta. CAPM fails to capture these other factors
Explain how capital is allocated using the VaR allocation approach.
Capital is allocated to each LOB such that each LOB’s exceedence probability equals the target exceedence probability.
Briefly describe three problems with using VaR for capital allocation.
- A firm may not have enough capital to ensure that all LOBs meet the specified exceedence probability. If this occurs, the firm can raise the probability level or raise more capital
- The stand-alone exceedence probabilities do not reflect diversification across LOBs
- The VaR approach does not reflect the amount by which losses might exceed the exceedence probability level
Describe (in words) the “Insolvency Put Option.”
The Insolvency Put Option draws upon option pricing theory. Consider a firm with random assets A and liabilities L that is subject to default risk. The liabilities are assumed to be payable one period from now. If A > L at the liability maturity date, then the policyholders receive the value of the liabilities.
If A < L, then the owners of the firm default on the liability payment and the policyholders receive the assets of the firm. This is equivalent to a put option on A with a strike price of L. This put option is known as the insolvency put option.
Explain how capital is allocated to LOB under the Insolvency Put Option (i.e. Expected Policyholder Deficit (EPD)) approach.
Capital is allocated to LOB such that each LOB achieves an EPD ratio equal to the target EPD ratio.
Briefly describe two advantages and one disadvantage of the EPD approach to capital allocation.
Advantages
1. It considers the expected value of the amount that can be lost rather than just providing the probability of exceeding a specific loss amount
2. It is consistent with the theory around pricing risky debt contracts
Disadvantages
1. It does not reflect diversification across LOBs
2. It considers each LOB separately
Describe “risk capital” as used in the Merton-Perold allocation method.
Risk capital is defined as the smallest amount that can be invested to insure the value of the firm’s net assets (i.e. total assets minus the default-risk-free value of the firm’s policyholder liabilities) against a loss in value relative to the risk-free investment of those net assets. Thus, risk capital can be viewed as the value of an option that guarantees that the firm will receive no less than its net assets at the option maturity date.
Identify two sources of risk capital.
- If there is no default risk, risk capital is supplied entirely by the firm
- If there is default risk, risk capital is partially supplied by the liability holders
Describe the steps used to allocate capital under the Merton-Perold allocation method (assume the firm writes three LOBs).
- Calculate the risk capital for each two-LOB combination. For a firm with three LOBs, there would be three two-LOB combinations (LOB 1 and 2, LOB 1 and 3, LOB 2 and 3)
- Calculate the risk capital for the firm in total. Subtract each two-LOB combination to calculate the marginal capital required to add the third LOB to the firm
Define “corporate” capital under the Merton-Perold allocation method.
Explain how the presence of corporate capital leads to the acceptance of more projects/LOBs under the Merton-Perold allocation method.
Corporate capital is the capital not allocated to a specific LOB. Under the M-P method, the sum of the marginal capital amounts is less than the required capital for the firm in total. This difference is corporate capital.
The presence of corporate capital leads to higher EVA and RAROC metrics since there is less capital being allocated. Thus, profitable projects or LOBs that may have been rejected under other methods may be accepted under the M-P method.
Does the Merton-Perold allocation method consider diversification?
Yes! The sum of the stand-alone EPD capital figures for each LOB is greater than the EPD capital figure for the firm in total. This reflects the diversification across LOBs.
Describe the main difference between the Merton-Perold and Myers-Read allocation methods.
The M-P method allocates capital at the margin by adding entire LOBs to the firm, whereas the M-R method allocates capital at the margin by determining the effects of extremely small changes in loss liabilities for each LOB.
Does “corporate” capital exist under the Myers-Read allocation method?
No! The M-R method provides a full allocation of the total firm capital.
Assume a LOB has a large covariance with the insurer’s total losses. Explain how the capital allocation to this LOB is impacted.
Assume a LOB has a large covariance with the insurer’s total assets. Explain how the capital allocation to this LOB is impacted.
LOBs with large covariances with the insurer’s total losses receive a larger capital allocation. This is because a larger covariance with the loss portfolio increases the overall risk level of the firm. Thus, these LOBs should receive a larger capital allocation.
LOBs with large covariances with the insurer’s total assets receive a smaller capital allocation. This is because a larger covariance with the asset portfolio decreases the overall risk level of the firm (acts as a natural hedge). Thus, these LOBs should receive a smaller capital allocation.
Explain why a firm might prefer to use the M-R method over the M-P method.
Explain why a firm might prefer to use the M-P method over the M-R method.
Why might an insurer prefer to use the M-R method over the M-P method?
* The M-R method allocates the full capital of the firm
* Since the M-R method is a micro allocation method, it aligns more closely with the normal operations of a firm. Firms typically make small changes to an existing portfolio (ex. pricing and underwriting changes)
Why might an insurer prefer to use the M-P method over the M-R method?
* The M-P method might be preferable when a firm is adding entire businesses to the firm
Describe the three biggest sources of frictional costs.
- Agency and informational costs – Agency costs are incurred when managers of firms behave opportunistically in a way that fails to maximize firm value. Informational costs are incurred through adverse selection and moral hazard to the extent that these things are not mitigated through proper pricing and underwriting
- Double taxation – Insurer investment income is taxed twice by the federal government, producing lower investment income than what could be obtained by investing directly in the market
- Regulatory costs – Regulatory costs are incurred in the form of an “option.” Regulators have the right to seize control of an insurer if regulatory thresholds are triggered
Note that these frictional costs give way to a spread between fair market returns and insurer investment returns. This spread cost represents the cost above and beyond the cost of capital caused by the fact that the capital was held by insurers rather than directly invested in the capital market. When cost of capital is allocated to a line, we are essentially allocating the spread cost.
List the seven conclusions offered up by Cummins at the end of the paper (these are good ones to know).
- EPD provides more information than VaR
- Using an option model that reflects diversification leads to better decision making regarding the pursuit of projects or LOBs
- The cost of capital allocated to a line is the spread cost
- Capital allocation should consider both asset and liability risk and allow for covariability between assets and liabilities
- Capital allocation should consider the duration and maturity of liabilities
- The decision-making system should inform the design of the data system. In other words, we start by figuring out which methods we want to use to make decisions. Then, we design our data system such that we have the required information to implement those methods
- Successful firms will be the ones that implement capital allocation and other financial decision-making techniques
- Line A: Short-tailed property catastrophe reinsurance
- Line B: Long-tailed casualty reinsurance
Explain which line of business (A or B) should receive a higher allocation of capital for each of premium, and interest rate risk.
Premium risk: Line A
Line A has a greater chance at mispricing given the volatility of catastrople losses. (注意：如果不是CAT则short tail不会有这个问题）Reinsurance is priced for the average year. However, most years there will be few losses and other years (infrequently) will have very large losses. There is also model risk involved due to lack of historical experience, which introduces additional pricing risk.
Interest rate risk: Line B
The longer tail means the investments supporting the reserves need to have a longer duration and are more dependent on interest rate changes. Short term investments such as those supporting the shorter tailed line are not subject to interest rate fluctuations.
