Cummins - Capital Flashcards by Kate Vista

Capital allocation

Cummins - Capital

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

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Firm mission

Cummins - Capital

maximize market value

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Uses for capital allocation (2)

Cummins - Capital

measure performance by LOB by ensuring each LOB is making adequate profit to cover its cost of capital
making LOB pricing and UW decisions

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Measures of return (3)

Cummins - Capital

risk-adjusted return on capital (RAROC)
economic value added (EVA)
economic value added on capital (EVAOC)

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

Cummins - Capital

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

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Measuring return adequacy using RAROC

Cummins - Capital

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

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

Cummins - Capital

re-pricing the LOB
tightening UW standards
withdrawing from the LOB

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Economic value added (EVA) - definition and formula

Cummins - Capital

measure of return on investment in excess of its required return

EVA = net income - required return * allocated capital

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Measuring return adequacy using EVA

Cummins - Capital

EVA >= 0 means LOB adds value to the firm

EVA < 0 means LOB is reducing firm value

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Economic value added on capital (EVAOC)

Cummins - Capital

rate of return form of EVA

EVAOC = EVA / allocated capital

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

Cummins - Capital

pure play approach

2. full information betas

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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

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Reasons the pure play approach is difficult (2)

Cummins - Capital

few mono-line firms exist

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

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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

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Reason the full information betas approach is difficult

Cummins - Capital

often lack data needed

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Capital allocation techniques (5)

Cummins - Capital

risk-based capital (RBC)
capital asset pricing model (CAPM)
value at risk (VaR)
insolvency put option/expected policyholder deficit (EPD)
marginal allocation methods

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

Cummins - Capital

based on worst-case scenario instead of statistical concepts
ignores correlations
based on book value (vs. market value)
ignores important sources of risk such as interest rate risk
has no theoretical foundation

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Firm’s equity beta coefficient for CAPM and formulas (2)

Cummins - Capital

equity beta = normal CAPM beta&raquo_space; used to estimate the firm’s cost of capital

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

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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

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TCR under CAPM

Cummins - Capital

TCR = 1 - required UW return

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

Cummins - Capital

-k(i) * risk-free rate = interest paid by LOB for use of policyholder funds
LOB beta * (market return - risk-free rate) = LOB rate of return based on its systematic risk

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

Problems with the CAPM approach to capital allocation (3)

Cummins - Capital

reflects systematic UW risk but does not capture risk of extreme events
LOB betas are difficult to estimate
rates of return are driven by factors other than beta, which are ignored by CAPM

Value at risk (VaR)

Cummins - Capital

max amount a firm could lose with a specified probability

use w/exceedance probabilities for capital allocation

Exceedance probability | Cummins - Capital

probability losses from a LOB will exceed the expected losses + allocated capital epsilon(i) = Pr(Loss(i) > E[Loss(i)] + allocated capital(i))

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

Exceedance probability curve and relative risk | Cummins - Capital

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

Interpretation of required capital to expected loss ratio | Cummins - Capital

$ 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

Problems with the VaR approach to capital allocation (3) | Cummins - Capital

1. firm may not have enough total capital to meet the specified exceedance probability 2. does not reflect diversification benefit (b/c uses stand-alone exceedance probabilities) 3. does not reflect the amount by which losses will exceed the exceedance probability

Insolvency put option (aka expected policyholder deficit (EPD)) (Cummins - Capital)

considers the policyholders' claim on the firm a put option on the firm's assets (A) with strike price = firm's liabilities (L) at maturity: if A >= L, policyholders receive L if A < L, policyholders receive A

Value of the policyholders' claim under the insolvency put option/expected policyholder deficit (EPD) (Cummins - Capital)

value of policyholders' claim = PV(losses) - value of the insolvency put option = Le^-rt - value of put option

Reason the insolvency put option/expected policyholder deficit approach is superior to VaR for capital allocation (Cummins - Capital)

it considers the expected value of loss (vs. the probability of losses exceeding a specific amount)

Advantage of the insolvency put option/expected policyholder deficit approach to capital allocation (Cummins - Capital)

consistent with the theory of pricing risky debt contracts

Disadvantage of the insolvency put option/expected policyholder deficit approach to capital allocation (Cummins - Capital)

does not consider diversification

EPD ratio | Cummins - Capital

EPD ratio = EPD / Liabilities

Asset-to-liability ratio | Cummins - Capital

A / L = 1 + C / L

Marginal capital allocation methods (2) | Cummins - Capital

1. Merton-Perold (M-P) | 2. Myers-Read (M-R)

Risk capital | Cummins - Capital

smallest amount that can be invested to insure value of firm's net assets

Sources of risk capital (2) | Cummins - Capital

1. if no default risk, risk capital is supplied by the firm | 2. if default risk, risk capital is partially supplied by liability holders

Merton-Perold (M-P) method for capital allocation | Cummins - Capital

extension of the insolvency put option/expected policyholder deficit method that accounts for diversification M-P allocated capital(i) = total capital - capital (all LOB except i) where the total capital and joint capital are estimated using EPD

Merton-Perold (M-P) method vs. Myers-Read (M-R) method total % of firm's capital allocated (Cummins - Capital)

M-P will allocate < 100% - unallocated capital = "corporate" level capital M-R will allocate 100%

Best use for the Merton-Perold (M-P) method for capital allocation (Cummins - Capital)

decision-making when adding entire LOB to the firm

EVA and RAROC metrics in Merton-Perold (M-P) method vs. Myers-Read (M-R) method (Cummins - Capital)

M-P produces higher EVA and RAROC b/c of unallocated capital

Myers-Read (M-R) method for capital allocation | Cummins - Capital

allocates capital by determining the effect of very small changes in loss liabilities for each LOB allocated capital = s(i) * L(i) s(i) = s - (dp/dsigma) / (dp/ds) * [(sigma(i,L) - sigma(L)^2) - (sigma(i,V) - sigma(L,V))] / sigma ``` s = surplus-to-liability ratio p = insolvency put option per $ of liabilities sigma(i,L) = covariance parameter b/w losses in LOB & firm's losses sigma(i,V) = covariance parameter b/w losses in LOB & firm's assets sigma(L,V) = covariance parameter b/w firm's losses & assets ```

Main difference between Merton-Perold (M-P) method and Myers-Read (M-R) method for capital allocation (Cummins - Capital)

M-P uses a macro marginal allocation | M-R uses a micro marginal allocation

Best use for the Myers-Read (M-R) method for capital allocations (Cummins - Capital)

decision-making for firm's normal operations

Allocated capital under the M-R method when a LOB has a large covariance with total assets (Cummins - Capital)

receives less allocated capital b/c the large correlation reduces risk (acts as a natural hedge)

Allocated capital under the M-R method when a LOB has a large covariance with total losses (Cummins - Capital)

receives more allocated capital b/c of increased risk

Agency costs (frictional costs) | Cummins - Capital

costs incurred when managers behave opportunistically in a way that fails to maximize firm value

Informational costs (frictional costs) | Cummins - Capital

costs incurred through adverse selection & morale hazard

Sources of costly capital/market frictions/frictional costs (3) (Cummins - Capital)

1. agency & information costs 2. double taxation of investment income 3. regulatory costs/restrictions leading to insurer's holding inefficient portfolios

Reason a spread (aka cost of capital) develops b/w returns that could be earned by investing directly in capital markets and actual returns earned on capital for insurers (Cummins - Capital)

existence of market frictions/frictional costs