Bodoff: Capital Allocation by Percentile Layer

Question 1

External forces dictating how much capital an insurance firm should hold

Answer 1

Regulators

Rating agencies

Investors

Question 2

Kreps allocation of capital

Answer 2

Really the allocation of the required rate of return on capital

Question 3

VaR approach of allocating capital (Bodoff)

Answer 3

Allocates capital only to those components that contribute to one particular loss scenario

Question 4

TVaR approach for allocating capital

Answer 4

Holds capital for average loss event even at the given percentile; still ignores losses below the tail threshold

Question 5

Percentile layer of capital

Answer 5

Question 6

Layer of capital

Answer 6

Question 7

Conditional exceedance probability for event (i)

Answer 7

Question 8

Two reasons loss event tends to receive a larger percentage allocation in the upper layers than lower layers

Answer 8

1. In upper layer, allocating to fewer events
2. In upper layers, allocating wider layer of capital (percentile layer tends to widen as loss amount increases)

Question 9

“Horizontal procedure” of capital allocation

Answer 9

Allocating each layer of capital to all losses that penetrate the layer

Question 10

“Vertical procedure” of marginal capital allocation

Answer 10

Takes each loss event and allocates capital to it for all layers it penetrates

Question 11

Horizontal then vertical

Answer 11

Question 12

Vertical then horizontal

Answer 12

Question 13

Allocation of capital by layer

Answer 13

Question 14

Three things a loss event’s allocated capital depends on

Answer 14

1. Probability of loss event
2. Severity of loss event
3. Loss event’s inability to share burden with other loss events (dissimilarity in severity to other loss events)

Question 15

Advantages for capital allocation by percentile layer

Answer 15