Flashcards in Cummins - Capital Deck (53)

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1

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Capital allocation

(Cummins - Capital)

### determination of the amount of a firm's equity capital that is assigned to each project or LOB

2

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Firm mission

(Cummins - Capital)

### maximize market value

3

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Uses for capital allocation (2)

(Cummins - Capital)

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1. measure performance by LOB by ensuring each LOB is making adequate profit to cover its cost of capital

2. making LOB pricing and UW decisions

4

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Measures of return (3)

(Cummins - Capital)

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1. risk-adjusted return on capital (RAROC)

2. economic value added (EVA)

3. economic value added on capital (EVAOC)

5

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Risk-adjusted return on capital (RAROC(i))

(Cummins - Capital)

### RAROC = net income after tax & interest expense / allocated capital

6

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Measuring return adequacy using RAROC

(Cummins - Capital)

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compare RAROC to cost of capital (aka hurdle rate or required return)

if RAROC >= cost of capital - LOB/project adds to firm value

if RAROC < cost of capital - LOB/project is reducing firm value

7

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Potential firm actions if a LOB is reducing firm value (3)

(Cummins - Capital)

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1. re-pricing the LOB

2. tightening UW standards

3. withdrawing from the LOB

8

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Economic value added (EVA) - definition and formula

(Cummins - Capital)

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measure of return on investment in excess of its required return

EVA = net income - required return * allocated capital

9

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Measuring return adequacy using EVA

(Cummins - Capital)

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EVA >= 0 means LOB adds value to the firm

EVA < 0 means LOB is reducing firm value

10

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Economic value added on capital (EVAOC)

(Cummins - Capital)

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rate of return form of EVA

EVAOC = EVA / allocated capital

11

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Methods to determine the cost of capital for a LOB (2)

(Cummins - Capital)

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1. pure play approach

2. full information betas

12

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Pure play approach to estimating the cost of capital for a LOB

(Cummins - Capital)

### estimates cost of capital by finding mono-line "pure play" firms exclusively offering a single LOB

13

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Reasons the pure play approach is difficult (2)

(Cummins - Capital)

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1. few mono-line firms exist

2. even if a mono-line firm is found, it may have significantly different UW risk characteristics

14

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Full information betas approach to estimating the cost of capital for a LOB

(Cummins - Capital)

### estimates cost of capital by running a regression on a multi-line firm's data

15

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Reason the full information betas approach is difficult

(Cummins - Capital)

### often lack data needed

16

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Capital allocation techniques (5)

(Cummins - Capital)

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1. risk-based capital (RBC)

2. capital asset pricing model (CAPM)

3. value at risk (VaR)

4. insolvency put option/expected policyholder deficit (EPD)

5. marginal allocation methods

17

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Reasons RBC should not be used for capital allocation (5)

(Cummins - Capital)

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1. based on worst-case scenario instead of statistical concepts

2. ignores correlations

3. based on book value (vs. market value)

4. ignore important sources of risk such as interest rate risk

5. has no theoretical foundation

18

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Expected ROE (aka cost of capital or required return) using the CAPM

(Cummins - Capital)

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Expected ROE = cost of capital = required return =

risk-free rate + firm equity beta * (market return - risk-free rate)

19

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Firm's equity beta coefficient for CAPM (2)

(Cummins - Capital)

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beta = covariance(firm return, market return) / variance(market return)

beta = beta(assets) * (1 + sum of LOB liability leverage ratio) + sumproduct(LOB beta * LOB premium leverage ratio)

where

liability leverage ratio = liability / total equity and

premium leverage ratio = premium / total equity

20

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LOB required UW return under CAPM (r(i))

(Cummins - Capital)

### r = -LOB liability leverage ratio * risk-free rate + LOB beta * market risk premium

21

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TCR under CAPM

(Cummins - Capital)

### TCR = 1 - required UW return

22

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Components of the LOB required UW return under CAPM (2)

(Cummins - Capital)

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1. -k(i) * risk-free rate = interest paid by LOB for use of policyholder funds

2. LOB beta * (market return - risk-free rate) = LOB rate of return based on its systematic risk

23

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Implication of CAPM

(Cummins - Capital)

### not necessary to allocate capital by LOB, instead charge each LOB for the CAPM cost of capital, which reflects the LOB beta and leverage ratio

24

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Problems with the CAPM approach to capital allocation (3)

(Cummins - Capital)

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1. reflects systematic UW risk but does not capture risk of extreme events

2. LOB betas are difficult to estimate

3. rates of return are driven by factors other than beta, which are ignored by CAPM

25

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Value at risk (VaR)

(Cummins - Capital)

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max amount a firm could lose with a specified probability

use w/exceedance probabilities for capital allocation

26

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Exceedance probability

(Cummins - Capital)

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probability losses from a LOB will exceed the expected losses + allocated capital

epsilon(i) = Pr(Loss(i) > E[Loss(i)] + allocated capital(i))

27

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Using exceedance probabilities to allocate capital

(Cummins - Capital)

### solve for the amount of capital needed for each LOB such that each LOB exceedance probability = target exceedance probability

28

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Exceedance probability curve

(Cummins - Capital)

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plots probability (y-axis) against (E[L] + C) / E[L] on the x-axis - curve slopes down & right

more risky LOB have a higher x-axis ratio for a given probability level

29

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Interpretation of required capital to expected loss ratio

(Cummins - Capital)

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$ amount the insurer would need to commit in capital for each dollar of expected losses to achieve the given exceedance probability

= 1 - asset-to-liability ratio

30