Cummins - Allocation of Capital Flashcards
-insurer needs to hold capital to
assure policyholders that their claims will be paid in event that they are larger than initially anticipated
even though the entire capital of insurer is available to pay claims arising out of any specific policy or line
it is often useful to allocate capital to make better pricing and underwriting decisions
capital allocation can assist with
value maximization
Value maximization: management can determine whether a line is producing sufficient return to cover its cost of capital
various metrics that are based on allocated capital can be used to determine if value is being maximized
RAROC: if RAROC>cost of capital, insurer should continue to devote resources to the line, but if it not, firm will have to take some action
EVA: formula quantifies the value added to firm for a given line
2 methods to determine Cost of capital
- base it on cost of capital of a monoline firm that writes the same line, but the issue is that it will be difficult to find firms that write only the one line and have similar UW standards
- perform regressions on data of multiline insurers to derive cost of capital by line
Friction Costs in general
- capital of insurers will be invested in marketable securities
- friction costs reduce return on capital
- insurer needs to account for these costs when determining whether a line is earning the appropriate rate of return
3 sources of friction costs
agency and informational costs: management may behave opportunistically and therefore fail to achieve the owner’s objective of value maximization
current tax system results in double taxation: investing in securities via insurance companies produces lower after tax returns than purchasing securities directly
various regulations may force the insurer to hold inefficient investment portfolios (too much capital); for most insurers, this generates no real cost as they generally would hold more capital than regulatory requirement anyway
Capital Allocation Techniques
Risk Based Capital, RBC
CAPM
VaR
Insolvency Put Option/EPD Ratio
Merton-Perold
Myers-Read
Risk Based Capital, RBC
level of capital that must be held in order to avoid regulatory intervention
RBC: reasons why not to use
- believes that this is not wise to use as basis to allocate because:
1. factors used in derivation are of questionable accuracy
2. calculations are often based on book value instead of market
3. ignores several important sources of risk
RBC advantage
Relatively simple to calculate and find input values
CAPM: use
not used to allocate the surplus, but determines the required rate of return for each line
- achieved by decomposing the aggregate β of firm to determine βs by LOB
- required rate of return can then be calculated
- shows that each line is essentially paying interest for use of PH funds and receiving a return which is based on systematic risk
problems with CAPM
- CAPM only reflects systematic UW risk (UW risk correlated with market portfolio), does not reflect other risks
- β of each line is hard to estimate
- rates of return are impacted by other factors in addition to β
VaR
- VaR calculates the loss associated with a given confidence level
- VaR analysis can be used to calculate exceedance probability, ε
Exceedance probability
probability that actual losses will exceed expected losses plus allocated capital
Exceedance probability can be used to
allocate capital: 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 losses
- lines with higher level of risk will require more capital relative to expected losses
issues with VaR
- firm may not have enough capital to achieve probability
- approach does not consider the impact of diversification
- does not reflect amount by which losses will exceed resources in event that exceedance level is breached
advantage with VaR
A consistent risk measure that can be used to compare between lines of business, companies, etc.
Expected Policyholder Deficit, EPD
calculates the expected value of the difference between the obligation owed to the claimant and the amount actually paid
-deficit to policyholders = max(0,L-A); equivalent to the payoff of a put option an so expected deficiency to the policyholder should be equal of the put option
how EPD can be used to allocate capital
-capital can be allocated to achieve equivalent ratios of EPD to liabilities among lines
EPD advantage over VaR
it reflects the severity of losses (more impacted by potential severity of tail losses)
EPD does not account for
diversification
Merton-Perold Method is based on
risk capital, which is smallest amount that needs to be invested to insure the value of firm’s net assets against a loss in value relative to risk free investment of those net assets
to derive the required amount of risk capital
tweak the EPD methodology because interested in marginal impact of line on capital required to achieve a certain EPD
M-P recognizes
impact of diversification
M-P method allocates ..
- method allocates less than 100% of risk capital
- allocating all capital would cause firm to reject projects that would add to its market value
- excess capital can be then allocated to corporate level
Myers-Read Method aims to
equalize the marginal default values across LOBs
Myers-Read Method: how does it differ from M-P
- M-R looks at impact of very small changes to loss liabilities as opposed to adding entire business units;
- M-R allocates 100% of capital, so avoids problem of how to deal with excess capital
decisions should focus on
EPD
EPD provides more info than VaR
using allocation model that reflects
the impact of diversification will lead to better decisions as diversification does have value
cost of capital that is allocated to line
spread cost
capital allocation must account for
asset and liability risk as well as the covariability between assets and liabilities
-capital allocation should factor in duration and maturity of liabilities
decision making should drive the design of
data system -> annual data is insufficient to allocate capital appropriately
firms that allocate capital successfully will
make better pricing, UW, and entry/exit decisions, creating value for shareholders
