Cummins Capital

Question 1

Briefly describe the uniqueness of debt capital for insurance companies

Answer 1

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.

Question 2

Briefly describe a firm’s true mission

Answer 2

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.

Question 3

Calculate RAROC and use it to make decisions.

Answer 3

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.

Question 4

Identify 3 potential solutions when RAROC smaller than hurdle rate.

Answer 4

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

Question 5

Calculate EVA and use it to make decisions.

Answer 5

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

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

Question 6

Calculate EVAOC and use it to make decisions.

Answer 6

EVAOC = EVA/Capital

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

Question 7

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

Answer 7

1. Pure Play Technique
2. Full Information Betas Technique

Question 8

Describe the Pure Play Technique to determine CoC

Answer 8

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

Question 9

List 2 issues with the Pure Play Technique.

Answer 9

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.

Question 10

Describe the Full Information Betas Technique to determine CoC.

Answer 10

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

Question 11

Name an issue with Full Information Betas Technique.

Answer 11

Lack of quality data.

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

Question 12

Describe RBC technique to allocate capital.

Answer 12

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

Question 13

Describe the investment RBC

Answer 13

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

Question 14

Describe the loss reserve RBC.

Answer 14

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

Question 15

Describe the Written P RBC

Answer 15

Accounts for possibility that LR on NB greater than expected.

Question 16

Describe the Credit RBC

Answer 16

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

Question 17

Describe the Off-Balance Sheet RBC

Answer 17

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

Question 18

When does RBC trigger regulatory actions.

Answer 18

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.

Question 19

List 4 reasons why using RBC is unwise

Answer 19

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.

Question 20

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

Answer 20

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.

Question 21

Describe the Capital Asset Pricing Model (CAPM)

Answer 21

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

Question 22

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

Answer 22

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

Question 23

Calculate Net Income under CAPM for 2 LOBs

Answer 23

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

Question 24

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

Answer 24

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))

Question 25

List 2 advantages of CAPM

Answer 25

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.

Question 26

Describe 3 issues with CAPM approach

Answer 26

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.

Question 27

Describe how capital is allocated using VaR allocation approach.

Answer 27

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.

Question 28

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

Answer 28

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.

Question 29

Describe the Insolvency Put Option

Answer 29

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.

Question 30

Explain how capital is allocated to LOB under Insolvency Put Option

Answer 30

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.

Question 31

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

Answer 31

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.

Question 32

Provide a disadvantage of EPD approach.

Answer 32

EPD approach is problematic because it does not reflect diversification across LOBs. It considers each LOB separately.

Question 33

Identify an allocation method that account for diversification benefits.

Answer 33

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.

Question 34

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

Answer 34

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).

Question 35

Explain how the source of capital depends on default risk.

Answer 35

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.

Question 36

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

Answer 36

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.

Question 37

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

Answer 37

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.

Question 38

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

Answer 38

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).

Question 39

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

Answer 39

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.

Question 40

Does M-R approach has corporate capital?

Answer 40

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

Question 41

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

Answer 41

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

Question 42

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

Answer 42

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

Question 43

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

Answer 43

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.

Question 44

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

Answer 44

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

Question 45

Describe the spread cost.

Answer 45

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.

Question 46

List 7 conclusions of Cummins Capital paper

Answer 46

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.