Cummins - Allocation of Capital

Question 1

-insurer needs to hold capital to

Answer 1

assure policyholders that their claims will be paid in event that they are larger than initially anticipated

Question 2

even though the entire capital of insurer is available to pay claims arising out of any specific policy or line

Answer 2

it is often useful to allocate capital to make better pricing and underwriting decisions

Question 3

capital allocation can assist with

Answer 3

value maximization

Value maximization: management can determine whether a line is producing sufficient return to cover its cost of capital

Question 4

various metrics that are based on allocated capital can be used to determine if value is being maximized

Answer 4

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

Question 5

2 methods to determine Cost of capital

Answer 5

1. 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
2. perform regressions on data of multiline insurers to derive cost of capital by line

Question 6

Friction Costs in general

Answer 6

• 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

Question 7

3 sources of friction costs

Answer 7

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

Question 8

Capital Allocation Techniques

Answer 8

Risk Based Capital, RBC

CAPM

VaR

Insolvency Put Option/EPD Ratio

Merton-Perold

Myers-Read

Question 9

Risk Based Capital, RBC

Answer 9

level of capital that must be held in order to avoid regulatory intervention

Question 10

RBC: reasons why not to use

Answer 10

• 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

Question 11

RBC advantage

Answer 11

Relatively simple to calculate and find input values

Question 12

CAPM: use

Answer 12

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

Question 13

problems with CAPM

Answer 13

1. CAPM only reflects systematic UW risk (UW risk correlated with market portfolio), does not reflect other risks
2. β of each line is hard to estimate
3. rates of return are impacted by other factors in addition to β

Question 14

VaR

Answer 14

• VaR calculates the loss associated with a given confidence level
• VaR analysis can be used to calculate exceedance probability, ε

Question 15

Exceedance probability

Answer 15

probability that actual losses will exceed expected losses plus allocated capital

Question 16

Exceedance probability can be used to

Answer 16

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

Question 17

issues with VaR

Answer 17

1. firm may not have enough capital to achieve probability
2. approach does not consider the impact of diversification
3. does not reflect amount by which losses will exceed resources in event that exceedance level is breached

Question 18

advantage with VaR

Answer 18

A consistent risk measure that can be used to compare between lines of business, companies, etc.

Question 19

Expected Policyholder Deficit, EPD

Answer 19

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

Question 20

how EPD can be used to allocate capital

Answer 20

-capital can be allocated to achieve equivalent ratios of EPD to liabilities among lines

Question 21

EPD advantage over VaR

Answer 21

it reflects the severity of losses (more impacted by potential severity of tail losses)

Question 22

EPD does not account for

Answer 22

diversification

Question 23

Merton-Perold Method is based on

Answer 23

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

Question 24

to derive the required amount of risk capital

Answer 24

tweak the EPD methodology because interested in marginal impact of line on capital required to achieve a certain EPD

Question 25

M-P recognizes

Answer 25

impact of diversification

Question 26

M-P method allocates ..

Answer 26

• 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

Question 27

Myers-Read Method aims to

Answer 27

equalize the marginal default values across LOBs

Question 28

Myers-Read Method: how does it differ from M-P

Answer 28

1. M-R looks at impact of very small changes to loss liabilities as opposed to adding entire business units;
2. M-R allocates 100% of capital, so avoids problem of how to deal with excess capital

Question 29

decisions should focus on

Answer 29

EPD

EPD provides more info than VaR

Question 30

using allocation model that reflects

Answer 30

the impact of diversification will lead to better decisions as diversification does have value

Question 31

cost of capital that is allocated to line

Answer 31

spread cost

Question 32

capital allocation must account for

Answer 32

asset and liability risk as well as the covariability between assets and liabilities

-capital allocation should factor in duration and maturity of liabilities

Question 33

decision making should drive the design of

Answer 33

data system -> annual data is insufficient to allocate capital appropriately

Question 34

firms that allocate capital successfully will

Answer 34

make better pricing, UW, and entry/exit decisions, creating value for shareholders