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CAS Exam 9 > Cummins Capital > Flashcards

Cummins Capital Flashcards

1
Q

Briefly describe the uniqueness of debt capital for insurance companies

A

An insurer’s deb capital is provided by its customers (policyholders) in form of premiums.

Unlike bondholders, insurance policyholders are unable to protect themselves against insolvency through diversification. In most cases, policyholders buy insurance through a single insurer.

Capital is extremely important in insurance industry as it assures policyholders that their losses will be covered even if claim amounts are larger than expected.

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2
Q

Briefly describe a firm’s true mission

A

Maximize its market value.

Firms do this by using capital allocation to measure performance by LOB and ensuring each line is making an adequate profit to cover its cost of capital and add value to the firm.

If a LOB is found to make inadequate profit, firm can maximize firm value by withdrawing that LOB. Even if this leads to decline in revenue, it may actually increase firm value.

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3
Q

Calculate RAROC and use it to make decisions.

A

RAROC = Net Income / Capital

Net income is after taxes and interest expenses.

If RAROC higher than LOB CoC, writing LOB is consistent with firm value maximization.

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4
Q

Identify 3 potential solutions when RAROC smaller than hurdle rate.

A
  1. Reprice LOB
  2. Tightening underwriting standards (shrink)
  3. Withdraw from LOB
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5
Q

Calculate EVA and use it to make decisions.

A

EVA = Net income - r*C
r is LOB CoC

If EVA positive, writing the LOB is consistent with firm value maximization.

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6
Q

Calculate EVAOC and use it to make decisions.

A

EVAOC = EVA/Capital

If EVAOC is positive, writing the LOB is consistent with firm value maximization.

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7
Q

List 2 methods for determining CoC for a LOB when firm writes multiple LOBs

A
  1. Pure Play Technique
  2. Full Information Betas Technique
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8
Q

Describe the Pure Play Technique to determine CoC

A

Estimates CoC by examining mono line pure play firms that only write that LOB.

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9
Q

List 2 issues with the Pure Play Technique.

A
  1. It’s difficult to find mono-lines firms
  2. Even if we do find such firm, the uw risk characteristics may differ significantly from multi-lines firm.
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10
Q

Describe the Full Information Betas Technique to determine CoC.

A

Estimates CoC by running regressions on data from other multi-lines firms.

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11
Q

Name an issue with Full Information Betas Technique.

A

Lack of quality data.

Many insures do not capture the data needed to implement these types of methodologies.

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12
Q

Describe RBC technique to allocate capital.

A

Regulatory risk-based capital (RBC) is the minimum capital required to avoid regulatory intervention.

Rt = R0 + (R1^2 + R2^2 + R3^2 + R4^2 + R5^2)^0.5

The square root is a covariance adjustment implicitly assuming zero correlation between risks 1 to 5.

R0: RBC for holding of stocks of firm’s subsidiaries
R1: investment RBC
R2: Loss reserves RBC
R3: Written P RBC
R4: Credit RBC
R5: Off-balance Sheet RBC

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13
Q

Describe the investment RBC

A

Accounts for various charges of bonds, stocks and other investments.

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14
Q

Describe the loss reserve RBC.

A

Allows for risk of adverse development in reserves (unfavourable PYD)

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15
Q

Describe the Written P RBC

A

Accounts for possibility that LR on NB greater than expected.

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16
Q

Describe the Credit RBC

A

Allows for possibility that agents and reinsurers will default on obligations.

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17
Q

Describe the Off-Balance Sheet RBC

A

Allows for unexpected payments from contracts that do not show up on BS such as loan guarantees for subsidiaries.

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18
Q

When does RBC trigger regulatory actions.

A

If insurer total capital below 200% of RBC, regulatory actions might be taken.

Even if LOB capital below LOB required capital, if firm total capital greater than required capital, there will be no regulatory actions.

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19
Q

List 4 reasons why using RBC is unwise

A
  1. Regulatory risk charges may not be accurate.
    For example: some charges are based on worst case scenarios rather than statistical concepts such as variance and covariance.
    The formula ignores correlation among businesses.
  2. Regulatory risk charges are based on book value rather than market value.
  3. Regulatory risk charges ignore important sources of risk such as interest rate risk.
    Even if charges were accurate, they would be only for average firm in industry.
  4. There is no theoretical foundation for RBC formula.
    Business may be charges for too much or too little capital leading to suboptimal decisions.
20
Q

List 2 reasons why RBC is still important despite its limitations.

A
  1. RBC identifies most of the important risks faced by insurer.
  2. Regulatory capital may serve as constraint on some firm’s activities due to RBC solvency thresholds.
21
Q

Describe the Capital Asset Pricing Model (CAPM)

A

CAPM allows managers to compare preferred method to results generated by classic techniques.

22
Q

Calculate expected return on equity (CoC) under CAPM for:
1. Single LOB
2. 2 LOBs firm

A

r_E = r_f + b_E*(r_M - r_f)
b_E = Cov(r_E, r_M)/Var(r_M)

r_E = I/E = r_A(E+L1+L2)/E + r1(P1/E) + r2(P2/E)
b_E = b_A(1+k1+k2) + b1s1 + b2s2
ki = Li/E
si = Pi/E

23
Q

Calculate Net Income under CAPM for 2 LOBs

A

I = r_AA + r1P1 + r2*P2
A = E + L1 + L2

24
Q

Calculate the Required UW Return under CAPM and explain it in words.

A

ri = -kir_f + bi(r_M - r_f)

Each LOB pays interest for use of policyholders funds (-kir_f) and receives a rate of return based on systematic risk of LOB (bi(r_M - r_f))

25
Q

List 2 advantages of CAPM

A
  1. Provides useful way of conceptualizing contributions of firm’s LOBs to return on equity.
  2. We do not allocate capital by LOB. Instead, we charge each LOB for at least the CAPM CoC, which reflects the LOB’s beta coefficient and leverage ratio.
26
Q

Describe 3 issues with CAPM approach

A
  1. CAPM reflects systematic UW risk which is the correlation of UW performance with market portfolio. However, insurers are also concerned about risk of extreme events which is not captured in CAPM return.
  2. LOB UE betas are difficult to estimate.
  3. Rates of return are driven by factors other than beta, but CAPM fails to capture these other factors.
27
Q

Describe how capital is allocated using VaR allocation approach.

A

Value at Risk (VaR) is the max amount a firm could lose over specified time period with specified probability.

To implement VaR, we focus on exceedance probabilities:
ei = P(Loss i greater than E(Loss i) + Ci) = P(Loss i / E(Loss i) greater than 1 + Ci/E(Loss i))

Under VaR approach, higher risk LOBs require more capital relative to expected losses in order to attain specified exceedance probability.

28
Q

Describe 3 problems with using VaR for capital allocation. List a solution for each problem.

A
  1. A firm may not have enough capital to ensure all LOBs meet specified exceedance probability.
    If this occurs, firm can raise probability level or raise more capital.
  2. The standalone exceedance probabilities do not reflect diversification across LOBs.
  3. VaR does not reflect the amount by which losses might exceed the exceedance probability level.

Problems 2 and 3 can be solved by the insolvency put option.

29
Q

Describe the Insolvency Put Option

A

The insolvency put option draws upon option pricing theory.

Consider a firm with random assets A and liabilities L that is subject to default risk.

If A greater than L at liability maturity date, then policyholders receive the value of the liabilities.

If A smaller than L, owners of firm default on liability payments and policyholders receive assets of firm.

This is equivalent to a put option.

30
Q

Explain how capital is allocated to LOB under Insolvency Put Option

A

Capital is allocated to LOB such that LOB achieves EPD ratio equal to target EPD ratio.

Riskier line would require more allocated capital to produce same EPD compared to less risky line.

Value of policyholders claims = L*e^-rt - P(A,L,r,tau,sigma)
P(A,L,r,tau,sigma) is the value of the put option on A with strike price of L
tau is the time to maturity
sigma is the risk parameter reflecting volatility of assets

Insolvency Put Option is also known as EPD allocation.

31
Q

Describe 2 advantages of EPD approach to capital allocation (insolvency put option)

A

EPD is preferable to VaR because:

  1. It considers expected value of the amount that can be lost rather than just providing the probability of exceeding a specific loss amount.
  2. It is consistent with the theory around pricing risky debt contracts.
    This is important because financial theory tells us how to maximize value or add value to a firm.
32
Q

Provide a disadvantage of EPD approach.

A

EPD approach is problematic because it does not reflect diversification across LOBs.

It considers each LOB separately.

33
Q

Identify an allocation method that account for diversification benefits.

A

Assuming LOBs are not perfectly correlated, multi-lines firms should require less capital than one would obtain by simply adding up the standalone capital figures for each individual LOB.

The Merton-Perold (M-P) method is an extension of the EPD method that accounts for diversification.

34
Q

What is the main concept behind Merton-Perold (M-P) allocation method.

A

M-P rely on risk capital (value of an option that guarantees firm will receive no less than its net assets at the option maturity date).

35
Q

Explain how the source of capital depends on default risk.

A
  1. If there is no default risk, risk capital is supplied entirely by the firm
  2. If there is default risk, risk capital is partially supplied by liability holders.
36
Q

Describe the steps used to allocate capital under M-P allocation method.

A
  1. Calculate risk capital for each LOB combination excluding 1 entity.
  2. Calculate risk capital for firm in total
  3. Subtract each combination to total to calculate marginal capital required to add LOB the firm.
37
Q

Define corporate capital under M-P method. What is the thinking behind?

A

The unallocated capital is considered corporate level capital and is due to:
1. Diversification benefits
2. Imperfect correlation leading to lower capital when adding LOBs

This leads to higher EVA and RAROC metrics under M-P method since less capital is being allocated.

Thus, profitable projects or LOBs that may have been rejected under other methods may be accepted under M-P method.

38
Q

Describe the main difference between M-P method and Myers-Read method.

A

M-P allocates capital at the margin by adding entire LOBs to the firm (macro marginal allocation).

M-R allocates capital at the margin by determining the effects of extremely small changes in loss liabilities for each LOB (micro marginal allocation).

39
Q

Calculate the surplus required in LOB i under M-R approach

A

si = S - (dp/dsigma)/(dp/dS) * ((sigma_iL - sigma_L^2)^2 - (sigma_iV - sigma_LV))/sigma

S = surplus to liability ratio = sum of Ci/Li
sigma = overall volatility parameter
p = P / sum of Li
dp/dS is the rate of change in p with respect to S
dp/dsigma is the rate of change in p with respect to sigma
sigma_iL is the covariance parameter between LOB losses and portfolio losses
sigma_L^2 is the volatility parameter for total losses L
sigma_iV is the covariance parameter between LOB losses and firm’s assets
sigma_LV is the covariance parameter between firm’s assets and losses.

The formula is intended to equalize marginal default values across LOBs.

40
Q

Does M-R approach has corporate capital?

A

No, M-R method provides a full allocation of capital.

41
Q

Complete the sentence:
LOBs with large covariance with insurer total losses (sigma_iL) should receive _____ capital allocation.

A

Larger

This is because a larger covariance with portfolio losses increases firm overall risk.

42
Q

Complete the sentence:
LOBs with large covariance with insurer total assets (sigma_iV) should receive _____ capital allocation.

A

Smaller

This is because large covariance with insurer assets decrease firm overall risk (natural hedge).

43
Q

When is M-R method preferable over M-P?

A

M-R allocates full capital of the firm.

Since M-R is a micro allocation method, it aligns more closely with normal operations of a firm. Firm typically make small changes to an existing portfolio (ex: pricing and uw changes) rather than adding and/or removing entire LOBs.

44
Q

When is M-P method preferable over M-R?

A

M-P might be preferable when a firm is adding entire businesses to the firm.

45
Q

Describe the spread cost.

A

Due to frictional costs, a spread develops between fair market returns and insurer investment returns.

This spread cost should be taken into account in determining whether LOBs are earning appropriate rates of return.

46
Q

List 7 conclusions of Cummins Capital paper

A
  1. EPD provides more information than VaR
  2. Using an option model that reflects diversification leads to better decision making regarding pursuit of projects or LOBs.
  3. The CoC allocated to a line is the spread cost (cost above and beyond CoC caused by frictional costs)
  4. Capital allocation should consider both asset and liability risk and allow for covariability between assets and liabilities.
  5. Capital allocation should consider the duration and maturity of liabilities.
  6. Decision-making system should inform the design of data system.
    We start by figuring out which methods we want to use to make decisions. Then, we design our data system such that we have required information to be implemented.
  7. Successful firms will be those implementing capital allocation and other financial decision making techniques.

CAS Exam 9 (24 decks)

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