05_Mildenhall_pt2 Flashcards
Three Types of Insurance Demand
- Risk transfer – the insured purchases insurance to shift their risk to insurers. They do this by pooling their risks with other insureds
- Satisfying demand – the insured purchases insurance to satisfy statutory, regulatory, or contractual requirements
- Risk financing – the insured purchases insurance to finance uncertain future contingencies in an efficient manner
Identify five forms of insurance services an insurer supplies.
- Sales
- Marketing
- Risk surveys
- Loss control
- Risk bearing
- Pricing
- Underwriting
- Customer billing and support
- Investment Management services
Briefly describe two critical functions when managing a risk pool.
- Controlling access to the pool through UW and pricing
- Ensuring the pool is solvent by funding risk-bearing assets through the sales of liabilities
Briefly describe three ways in insurers bundle UW, pricing, risk-bearing, claims handling, and customer service when managing a risk pool.
- Some companies offer all of these services in-house
- Customer-facing functions are included with a direct writer, but farmed out to independent agents or brokers for other types of writers
- Managing general agents (MGAs) might only provide UW and pricing services
Parametric Insurance Contracts
- Policies pay based on an objective event outcome, such as hurricane intensity and landfall
- These policies are easy to underwrite since they do not depend on the characteristics of the insured
- These policies are difficult to design in such a way that they eliminate the potential for an insured to profit from a claim
- Under these policies, the insured is exposed to basis risk, which is the mismatch between the insured’s subject loss and the insurance recovery
Dual-Trigger Insurance Contracts
- Policies pay based on an objective event outcome AND the event causes an economic loss to the insured
- The indemnity payment is a function of the underlying subject loss suffered by the insured
- These policies apply an indemnity function 𝑓() to the subject loss 𝐿 that combines limits, deductibles, etc
Explain why franchise deductibles fail to meet the indemnity function requirements underlying a dual-trigger contract.
The indemnity function 𝑓() has the following conditions:
* 0 ≤ 𝑓(𝐿) ≤ 𝐿
* 𝑓(𝐿) is a monotonic function of 𝐿
* 𝐿 − 𝑓(𝐿) is a monotonic function of 𝐿
* 𝑓 is continuous
Under a franchise deductible 𝑑, if 𝐿 < 𝑑, then 𝑓(𝐿) = 0. But, if 𝐿 > 𝑑, then 𝑓(𝐿) = 𝐿 instead of 𝐿 − 𝑑. Thus, 𝑓 is not continuous (jump at 𝑑) and 𝐿 − 𝑓(𝐿) is not monotone (increases until it hits 𝑑, then drops to zero).
Explain why excess of loss covers meet the indemnity function requirements underlying a dual-trigger contract.
The excess of loss indemnity function is 𝑓(𝐿) = (𝐿 − 𝑎)! for some threshold 𝑎.
Clearly, 0 ≤ 𝑓(𝐿) ≤ 𝐿. Also, 𝑓 is continuous and monotonic since it is zero before 𝑎, and then increases from zero after 𝑎. Finally, 𝐿 − 𝑓(𝐿) is monotone since it increases to 𝑎 before 𝑎 and says there after 𝑎.
Describe the general payment order upon liquidation of an insurer.
From highest (i.e., senior) to lowest priority:
1. Receiver expenses
2. Insurance claims from policyholders
3. Debtholders
4. Shareholders
Capital vs. Equity
Capital (i.e., policyholder surplus) equals assets net of liabilities owed to policyholders.
this is the portion of money set aside on top of the loss reserves to fund the losses.
Equity equals assets net of liabilities owed to all parties EXCEPT owners.
Equity is also defined as the owner’s residual value or value of the owner’s interest in the company
Equity is usually lower than capital as capital would include the impact of any debt (which is excluded from equity)
Four Types of Insurer Capital
- Common equity – comprised of capital stock (par value of shares issued), additional paid-in capital (excess of amounts paid-in over par value), and retained earnings. Note that capital stock and additional paid-in capital only apply to stock companies
- Reinsurance capital – a reinsurance transaction can be thought of as the sale of the residual value for a specific portion of the business
- Debt capital – when an insurer cannot issue shares (ex. mutual), it can use surplus notes to raise capital
- Preferred equity – blends characteristics of debt and equity
Six Reasons Why Equity Capital is Expensive
- Principal-agent problem – investors and management do not have perfectly aligned incentives
- No independent validation of insurance pricing
- Equity requires a long-term commitment to a cyclical business
- Returns are left-skewed (investors prefer right-skewed returns)
- Regulatory minimum capital standards can force an insurer into supervision before it is technically insolvent (could lead to dividend restrictions)
- Double taxation – insurers’ corporate profits and dividend distributions are taxed (essentially taxes investors twice)
Four Ways in Which CAT Bonds Address the High Cost of Equity Capital
- CAT bonds are not equity and do not have market risk
- CAT bonds are a diversifying, zero-beta (i.e., independent of the financial market) asset class
- Catastrophe pricing can be validated
- There are no principal-agent problems since CAT bond cash flows are contractually defined
Provide a major disadvantage of CAT bonds.
CAT bonds are illiquid and trade in a thin market.
Weighted Average Cost of Capital (WACC)
The WACC combines the cost of all forms of capital into a single figure. It is the weighted average of the various forms of capital.
Briefly describe two theories of capital structures.
- Trade-off theory – the debt and equity mix trades off the costs and benefits of each capital type. It compares the expense of equity and the right of debt holders to force bankruptcy
- Pecking order theory – informational asymmetries between management and owners makes equity more expensive, in which case retained earnings are the favorable form of financing
Notes: The Trade-Off Theory suggests that a company balances the tax benefits of debt (since interest is tax-deductible) against the costs of potential financial distress (such as bankruptcy costs). This theory proposes that there’s an optimal capital structure where the marginal benefit of debt equals the marginal cost of financial distress.
Notes: The Pecking Order Theory is a financial theory that explains how companies prioritize their sources of financing when they need capital. It suggests that firms prefer to use internal funds (like retained earnings) first, and only turn to external sources of capital if necessary.
Regulatory Regimes Around the World
- Solvency II – used in the EU; assets are based on market value and liabilities consist of a best estimate plus a risk margin
- NAIC SAP – used in the US; focuses on the balance sheet; assets that cannot be readily converted to cash are considered non-admitted on the balance sheet
- GAAP – used in multiple jurisdictions; loss reserves are booked at the undiscounted best estimate; allows deferral of acquisition expenses
- IFRS – focuses on market value; loss reserves are valued on a discounted basis and include a risk adjustment
- Rating agency evaluations – rating agencies typically use adjusted statutory or GAAP financials in their internal capital models
Top-Down Pricing
This textbook follows top-down pricing. This means that it begins by pricing an insurer’s total portfolio such that aggregate premium satisfies a stability criterion. A stability criterion essentially establishes a constraint.
For example, we may want to price the total portfolio such that the probability of ruin is at most 5%. A bottom-up pricing approach would focus on pricing individual risks rather than the portfolio in total.
Timing Risk and Amount Risk
Insurance loss payments have both timing risk and amount risk, which may be dependent risks since larger claims often take longer to settle.
Timing risk refers to uncertainty in how and when a claim will be paid out.
Amount risk refers to uncertainty in the amount of the claim.
Assumptions Underlying CAPM and Black-Scholes Financial Models
- Competitive – there are many small sellers and buyers and undifferentiated products
- Perfect – there are no information or transaction costs, and no bid-ask spread. In addition, everyone can borrow or lend at the same risk-free rate, there are no restrictions on short sales, and there are no taxes
- Complete – there are enough securities to replicate any set of future period cash flows by securities trading
- Arbitrage-free – there is no potential for a risk-free gain on an initial investment of zero
- General Equilibrium – supply equals demand, no trader has an incentive to trade to improve their position, and everyone agrees all products are fairly priced. There is no arbitrage in when prices are in general equilibrium
Myers-Cohn Fair Premium Condition
A premium is fair if “whenever a policy is issued, the resulting equity value equals the equity invested in support of that policy.”
If premium increases equity, it is unfair to the policyholder because it transfers wealth from them to investors.
If premium decreases equity, it is unfair to investors because it transfers wealth from them to the policyholder.
Fair rates mean that prices are in equilibrium. Otherwise, investors would have an incentive to write more or less insurance.
Discuss an argument for using the risk-free rate for investment income in the DCF model.
Discuss an argument for using the anticipated market return for investment income in the DCF model.
Proponents of the risk-free rate argue that premium profit margins should not depend on actual investment portfolios, but only on the risk-free rate and systematic underwriting risk. Since policyholders do not share in the investment risks of the insurer, they should pay the same premium regardless of the firm’s investment strategy.
Proponents of the anticipated market return argue that adding investment risk increases the probability of default for policyholders and changes their expected loss recoveries. Hence, policyholder premiums should reflect the anticipated market return.
Describe the IRR model.
Provide one advantage and one disadvantage of the IRR model.
The IRR model is from the investor’s viewpoint. It estimates all cash flows to or from the investor (called “equity flows”) and then computes the discount rate (i.e., the IRR) required to produce a present value of zero. If the IRR ≥ the investor’s hurdle rate, then the project should be undertaken.
An advantage of the IRR model is that it doesn’t require us to determine discount rates for each cash flow.
A disadvantage of the IRR model is that it requires a hurdle rate (i.e., required rate of return) to make the final decision.
Describe the DCF Model.
The DCF model discounts each cash flow in a project at an appropriate risk-adjusted interest rate. Some cash flows are positive (ex. recurring revenue) while others are negative (ex. initial investment). If the total DCF is positive, then the project should be undertaken.
