Goldfarb - capital allocation

Question 1

capital allocation methods

Answer 1

Proportional Allocation Based on Risk Measure

Incremental Allocation

Marginal Allocation

Co-Measures Approach

Question 2

Proportional Allocation Based on Risk Measure

Answer 2

• capital is allocated based on distribution of a given risk measure
• calculates standalone risk measures for each risk source and then allocates the total risk capital in proportion to the separate risk measures

**capital is allocated proportional to paricular risk measure

Question 3

Incremental Allocation

Answer 3

• incremental contribution of particular risk to risk measure is derived and used as basis of allocation
• allocate capital based on the marginal impact on risk capital due to adding the entire line to the remainder of the business (other lines)

**capital is allocated proportional to marginal impact on risk capital

Allocated capital i = [risk measure(all sources)-risk measure(all ex-source i)]/Ʃ[risk measure(all sources)-risk measure(all ex-source i)] * total risk capital

Question 4

Marginal Allocation

Answer 4

• marginal methods are based on marginal increments of the risk
• allocate capital based on the marginal impact on risk capital due to increasing the exposure of the line by incremental portions

Question 5

Myers-Read

Answer 5

method is based on fact that total potential losses usually exceed the assets of firm and therefore view insurer’s owners as essentially having an option to default on obligation

-Myers-read method allocates capital to equalize the marginal impact of each business unit on the value of the option

Question 6

Myers-Read relationship

Answer 6

-capital allocated to a line is proportional to covariability with loss portfolio and inversely proportional to covariability with asset portfolio

Question 7

Myers-Read advantage and disadvantages

Answer 7

-method usually produces a more appropriate result than incremental allocation but may not be practical if risk sources can’t be represented proportional to revenue/expected losses or if it is difficult to determine marginal impact

• not developed to determine the risk adjusted capital requirement
• requires significantly more quantitative resources than other methods -> mathematical challenges have indicated that it may not be appropriate for most insurance applications

Question 8

Co-Measures Approach

Answer 8

particular risk measure first has to be adopted to determine capital requirement of entire firm

Co-measure: derived by calculation the equivalent risk measures for individual business unit in cases where firmwide measures exceed a threshold

-capital is allocated proportional to co-measure

**co-measure(i) is value of particular risk based on risk measure of entire firm

Question 9

5 examples of applications of risk adjusted performance metrics

Answer 9

1. assessing capital adequacy: when deciding whether insurers have sufficient capital
2. setting risk management priorities: insurer can identify the segment/activity that is generating the most risk capital
3. evaluating alternative risk management strategies: insurer can examine the impact of risk management strategy on RAROC
4. risk adjusted performance measurement
5. insurance policy pricing

Question 10

regulators and rating agencies ask several questions

Answer 10

does the firm have enough capital to meet PH obligations

• does management understand the source of risks in business
• does management actively measure/manage its exposure to risk

Question 11

important to note that RAROC measurement and subsequent conclusions are highly sensitive to

Answer 11

capital allocation method that is adopted

Question 12

RAROC can be used directly in insurance pricing & assumption

Answer 12

insurer can set a price that would target a specific RAROC

• one method is to determine additional risk margin that needs to be added to current premium in order to arrive at target
• note assumption made that risk margin is earning same expected rate of investment return as premiums

Question 13

Investment Income on Allocated Capital

Answer 13

• definition of economic profit above did not include the investment income expected to be earned on risk capital
• target return is actually technically an excess return over investment rate
• for it to be true target return, investment return on risk capital would need to be included

Question 14

methods in the industry that are commonly used to derive the

Cost of Risk Capital variable

Answer 14

CAPM and the Fama French models

there are a number of issues with using these models

Question 15

issues with CAPM model being used to derive cost of risk capital variable

Answer 15

CAPM as hurdle rate issue = Each line of business has different amounts of risks and different amounts of surplus supporting it. Hence the same rate for all lines is not appropriate.

• definition of risk used by CAPM is systematic risk associated with investment but RAROC is based on totally different type of risk (difference between cash flow’s expected value and values in tail)
• denominator of RAROC is understated since it does not account for franchise value and as result, RAROC value is overstated

Question 16

firms often use inconsistent time horizons when assessing the aggregate risk profile

Answer 16

market risk is often based on 1 year period and insurance risks are based on ultimate liability (which would include payments over multiple years)

• one suggested solution is to look at all risks over potential lifetime
• it is much more difficult to quantify some parameters over the long term

Question 17

some firms have had trouble when using a return measure that is significantly different to GAAP or SAP

Answer 17

-some practitioners reduce the return measure by cost of stranded capital

Question 18

stranded capital

Answer 18

excess of actual capital over risk capital

Question 19

methods discussed to allocate capital were based on

Answer 19

tail measures of risk

• this methodology allocated more of capital to segments with most skewed losses
• even though this may make sense from a regulatory or risk management perspective, it may not be the most appropriate in terms of guiding business decisions

Question 20

alternative approach to tail measures of risk

Answer 20

is to instead focus on less extreme events that would still impact the credit rating, financial strength, or ability to operate as going concern

Question 21

diversification assumption selected will have a material impact on

Answer 21

derivation of aggregate risk profile

allocation of risk capital

RAROC calculation

Question 22

even though RAROC methodology can be extremely useful

Answer 22

it should not be the only metric used to drive decisions

because of material impact of diversification