11 - Return on Capital

Question 1

What are the benefits of capital allocation?

Answer 1

1) Pricing - take account of cost of capital to support business
2) Risk selection - to select the risks that best employ the available capital
3) Performance measurement - To assess the performance relative to the capital
4) Performance attribution - Between business units, classes and UWs - which could be used for remuneration
5) Strategic Decision Making - Assessing a new opportunity or future UW strategy

Question 2

What are the two main challenges to incorporating capital costs?

Answer 2

1) Developing frameworks to measure performance and drive profit enhancement
2) Incorporating appropriate target loadings in premium rates to reflect the true cost of capital

Question 3

What are the desirable attributes of a capital allocation method?

Answer 3

1) Be consistent with the modeled capital for the whole business
2) Reflect the risk of individual business segments relative to one another and the business as a whole
3) Be justifiable and consistent
4) Reflect the interrelationships between risks, in particular reflect diversification benefits

Question 4

What are the two main elements of capital cost?

Answer 4

1) Capacity Occupation Cost

2) Capital Call Cost

Question 5

Describe Capacity occupation cost

Answer 5

This is the opportunity cost to compensate a firm for missing out on other opportunities.

Typically described as a risk adjusted hurdle rate, its the difference between the safe investments required by regulation and the the higher return investments available if free to invest.

Question 6

Describe Capital Call Cost

Answer 6

This is a risk loading that compensates for the potential erosion of capital to pay claims.
This should depend not only on the probability of call but also the distribution of the amount of a capital call.
We also should consider the the reduction in future uw capacity as a result of the call (known as capcity downtime)

Question 7

Give a simple pricing formula involving cost of capital

Answer 7

Premium = expected loss +capital *cost of capital (consumptive and non consumptive)

Question 8

What two elements need to be selected in order to allocate capital

Answer 8

A risk measure

A capital allocation method

Question 9

What are the desirable characteristics of a risk measure

Answer 9

Easy to communicate and apply
Observable, measurable and not manipulable
Consistent with perception of risk
Quantifies risk in a manner that is understandable
Consistent with the basis used to aggregate capital
Results in an internally consistent allocation of diversification benefits
Results in a coherent allocation

Question 10

What 4 conditions are needed for a risk statistic to be coherent?

Answer 10

1) Monotonicity- if one portfolio is always worth more than another it cannot be riskier
2) Linear homogeneity - Scaling a portfolio by a constant will change the risk by the same proportion
3) Sub-additivity - Combining two portfolios will not create more risk
4) Translational Invariance - adding a portfolio with a known guaranteed outcome to an existing portfolio reduces the risk by a guaranteed outcome

Question 11

What are some common risk measures:

Answer 11

Variance/semi variance
VAR
TAIL VAR
Expected policyholder default
Transformed loss measure

Question 12

Advantages/Disadvantages to Variance?

Answer 12

+ widely understood

- Not coherent as not monotonic

Question 13

Advantages/Disadvantages to VAR?

Answer 13

+ widely understood

- Not coherent as fails sub additivity

Question 14

What measures are coherent?

Answer 14

Tail VAR

Transformed loss measure

Question 15

List some capital allocational methods

Answer 15

Proportional
Marginal last in
game theory
Equalise relative risk

Question 16

What characteristics are required for a allocation method to be coherent?

Answer 16

1) Diversification benefit- allocation to sub portfolio should be the same as when considered separately
2) Symmetry- if the risk of two portfolios is the same, the allocation should be the same
3) Cash in a sub portfolio reduces allocation accordingly

Question 17

What three issues are there with deciding a capital rate?

Answer 17

1) Deciding the overall cost of capital for the firm- what do you base this on?
2) The relationship between the amount of capital allocated, the different capital requirements faced by the firm and actual amount of capital held by the firm
3) Whether the cost of capital rate should be equal for all business lines.

Question 18

List 11 issues with Capital allocation an actuary is likely to face

Answer 18

1) Gathering sufficient quality data
2) Sensitivity to specific assumptions
3) Selection of appropriate risk measures
4) Ensuring consistency with companies broader enterprise risk management framework
5) Communication and interpretation of results across business
6) Sufficient staff and resources to embed capital considerations into decision making
7) Incorporation of capital loads at risk level
8) Allowance for fixed capital costs such as operations - flat or proptional?
9) Help UWs appreciate the gearing of returns on capital and hence the significance of pricing terms and conditions
10) Convincing senior management of the benefits of ROC methodology
11) Evolving the methods over time as understanding of risk improves.