Cummins - Allocation of Capital in the Insurance Industry

Question 1

Why allocate capital?

Answer 1

Motivation: to maximize shareholder value, that is, to increase the market value of equity capital.

Question 2

How can these line allocations be used to maximize firm value:

One approach is to calculate RAROC

Answer 2

RAROC_i = Net Income/Ci, Ci is the capital allocated to the line.

Net Income should be after taxes, and interest expense. Interest expense comes in the form of underwriting loss for insurers.

The negative underwriting return, which is analogous to interest expense, needs to be taken out when calculating the return from a line of business.

Determining whether a line’s current risk-adjusted return is adequate:

Compare the risk-adjusted return with the cost of capital for business i, where the cost of capital is obtained using an appropriate asset pricing model.

If the risk-adjusted return is below the cost of capital, the line of business is reducing the firm’s market value. Re-price the insurance, tightening underwriting standards, or withdrawing from the line of business.

Question 3

How can these line allocations be used to maximize firm value:

Another Approach: Economic Value Added

Answer 3

EVA_i = Net Income_i - r_iC_i; where r_i is the cost of capital

EVAOC_i = (Net Income_i/C_i)-r_i

Question 4

How to determine the cost of capital for business i?

Answer 4

1. “pure play” technique.

• Estimate the cost of capital by finding other firms that offer only one line of business.
• The cost of capital for a business in the multiple-line business can then be based on the cost of capital of mono-line firms.
• Problematic in the insurance industry because
  
  • it is difficult to find firms that write only one line of business.
  • the underwriting risk characteristics could differ significantly.

2.”full-information betas”.

• use data to conduct regressions that permit the estimation of cost of capital by line.
• problem: lack of quality data

Question 5

Capital Allocation Methods

Answer 5

1. Regulatory Risk-based Capital
2. CAPM model
3. VaR (not sufficient data)
4. Marginal Capital Allocation

Question 6

Why is it unwise to use regulatory risk-based capital in allocating capital for the purpose of managing the firm?

And list one advantage.

Answer 6

It is unwise to use regulatory risk-based capital in allocating capital for the purpose of managing the firm:

1. regulatory charges are of questionable accuracy and are based on book rather than market values
2. regulatory charges ignore important sources of risk such as interest rate risk, as well as insurer’s transaction in the derivative market.
3. They would be accurate only for the average firm in the industry. In the case of firm with books of business having above or below average risk, it would produce inappropriate allocations of capital.

Advantage: captures most of the elemenets of risk

Question 7

What are the problem with using CAPM model?

Answer 7

1. The CAPM only rewards the firm for bearing systematic underwriting risk; that is, the underwriting risk that is correlated with the market portfolio. However, insurer also need to be concerned about extreme events (e.g. tail risk)
2. LOB underwriting betas are difficult to estimate given the data currently available.
3. Research has shown that rates of return are driven by other economic factors besides beta coefficients. Sole reliance on the CAPM would ignore important determinants of cost of capital.

CAPM can serve as a benchmark to compare with other estimations.

Question 8

Difine exceedence probability.

Discuss three issues with using exceedence probability with VaR for Capital Allocation.

List one advantage

Answer 8

Exceedence Probablity: P(Li> E(Li) + Ci). The probability that a line of business’ losses will be greater than then expected loss and the allocated capital to absorb shocks.

1. The firm may not have enough capital to attain a given exceedence probability for all of its business. => It can either raise the exceedence probability or raise more capital.
2. The exceedence probability approach as outlined here does not consider the diversification effect across lines.
3. The exceedence probablity does not tell managers anything about the amount by which losses are likely to exceed the available resources.

Advantage: based upon traditional actuarial theories, such as probability of ruin.

Question 9

The insolvency put option - advantages and disadvantages

Answer 9

Advantages of EPD vs. VaR:

1. more useful to know that the expected loss in excess of some asset-to-liability ratio will be 5M rather than just know the prob. of exceeding the ratio.
2. consistent with the financial theory of pricing risky debt contract

Disadvantage of EPD:

does not take into account the benefits of diversification

Note from Goldfarb manual: in Cummins, the EPD Ratio is a standard put option on the ratio of the assets to the liabilities with a strike price equal to 1.0. If the ratio of assets to liabilities is less than 1.0, then the firm is insolvent and the deficit (as a percent of the liabilities) is the amount by which the ratio is below 1.0. The volatility parameter in the Cummins examples is therefore the volatility of the asset-to-liability ratio. It reflects not just the separate asset and liability standard deviations but also their correlations.

Question 10

How is capital allocated by the M-P method?

Answer 10

1. Calculate the risk capital required by firms that combine two of the business.
2. Calculate the marginal capital required when the excluded business is added to the two-business firms.

The capital allocated to a given business is equal to the marginal capital required when it is added to the appropriate two-business firm.

Question 11

How does the M-R approach allocate capital

Answer 11

It allocates capital by determining the effect of very small changes in loss liabilities for each line of business

Question 12

Which one of the M-R & M-P method is correct?

Answer 12

M-P method is appropriate when adding entire business to the firm; M-R method is appropriate for the firm’s normal operations. It avoids the problem of how to deal with the allocated capital under the M-P approach. In addition, most decision making regarding pricing and underwriting typically involves small changes to an existing portfolio.

Question 13

What are the three most important sources of costly capital to insurers?

Answer 13

1. Agency and informational costs. Examples:

Managers not acting in the best interest of shareholders.

2. double taxation of investment income
3. Regulatory costs

• regulator has the legal right to seize control of the insurer when its assets still exceed its liabilities.
• Investment restriction