Risk Management & Insurance

• Rapid Settlement
• Objectivity
• Standardization
• Simplicity
• Transparency

Definition: Indices for ILS and derivatives

• Objectively-defined and quantifiable measures; readily observable
• Differentiated into industry loss indices and parametric indices (aggregate physical parameter values, e.g. wind speeds for hurricanes)

Quality Dimensions

• Accuracy: index values should be reliable and subject to as little revision as possible
• Granularity: high geographic and business line resolution to minimize basic risk
• Timeliness/frequency: responsive and published without great delays
• Index history: the more data available, the better possibilities for risk assessment

Definition: Cat Bonds

• Financial instrument (securitization) whole values are mainly driven by catastrophe risks
• Designed to HEDGE SPONSORS against losses caused by (natural) disasters
• Covered Terriroy: Geographic area in which cat need to occur
• Reference Peril: Type of disaster covered by transaction

Functions

• Direct transfer of natural catastrophe risk to the capital markets (like reinsurance; you get reimbursed for what you have to pay to your customers)
• Liability-hedge: ex-ante supply of debt capital to (re) insurer through SPV

• US Wind (95% of all; ususally Florida and Gulf Coast with severe windstorms)
• US Earthquake (California)
• Europe Wind (North Atlantic regions, i.e. northern and western Europe with cyclones)
• Japan Earthquake

• Insurance loss potentials from natural catastrophes are on the rise globally (more values in disaster-prone areas such as the Gulf Coast , and climate change)
• Size of global capital markets can absorb losses from mega-events (huge market compared to equity capital concentrated in insurances) -> transfer from insurance to capital markets
• Reliable scientific models and measurements for meteorological and seismic events
• Modern pricing approaches compatible with financial theory
• Attractive security format for fixed income investors
• Minimal credit risk since cat bonds are fully collateralized transactions

1. SPV gains cat risk exposure via reinsurance contract/cat swap with sponsor
2. SPV issues a bond
3. SPV uses investor money to purchase highly-rated collateral (MMF in T-Bills)
   • Trigger-Event: Sponsor is repaid from collateral , investors use all/part of their principal
   • If nothing happens, investors get their whole principal plus MMF +S_cat back

Tenor is usually around three years and cat bonds can feature a variety of trigger types

• Property Catastrophe Risk (almost "pure play")!!!
• Liquidity Risk (however, there's a fairly active secondary market nowadays)
• Credit Risk (minimized due to tight collateral provisions, very secure!)
• Interest Rate Risk (minimized due to floating rate coupons)

Indemnity

• Bond pays if ACTUAL INSURANCE LOSSES suffered by the sponsor exceed a threshold
• Like traditional reinsurance: perfect hedge against catastrophe (not basic!) risk!

Industry Loss

• Industry-wide losses are aggregated into an index by providers
• They are modified with index weights for geographical locations to match exposure

Modeled Loss

• Model insurance portfolio and modeling software
• If disaster occurs, losses are modeled based on corresponding physical parameters (model shows how damatic losses are and if money is paid out)

Parametric (pure and index)

• Pure parametric: based on values of physical parameters such as wind speed
• Parametric index: weighted and aggregated data from different weather stations

Transparency for investors

• Asymmetric information: sponsors have better portfolio information than investors
• Moral Hazard: underwriting standards and claim-settlement practices may be relaxed

Basic risk for sponsor

• Possibility that sponsor is not perfectly indemnified for his losses
• So, if basic risk is high, cat bond is NOT A GOOD HEDGE to the sponsor

Settlement time (!)

• Time needed to determine payout after event has occured

Accounting and regulatory acceptance

• Trigger determines if the cat bond receives a quasi-reinsurance status for sponsor

Proportional payout and binary payout ("all or nothing")

Critical Role:

• Provide a comprehensive probabilistic risk analysis because of a lack of historical data, natural science expertise, and exposure information
• Firms: e.g. RMS, AIR worldwide, EQECAT

Main Output

• Probability distribution of insurance losses
• Crucial input for selection of the trigger thresholds and the pricing of the cat bond

Four major components:

• Hazard module (only sufficient alone if you have parametric trigger)
• Inventory module (database of properties in the area)
• Damage module (material, age, size etc.)
• Financial module

s.picture

Reinsurance is a catalyst for economic growth

Insured Risks -> Primary Insurance -> Reinsurance -> Retrocession & Capital Markets

Insured risks: very uncertain about their individual risk
Primary Insurance: as much market and pricing power as possible, diversification irrelevant
Reinsurance: replication of theoretical diversified portfolio (risk profiles become much more predictable)

Functions:

1. Risk Transfer (diversify risks on global basis) - mobility of capital & premiums
2. Capital Market (invest premium income) - ability to invest in real economy
3. Information (put price tag on risks) - market- and risk-based pricing

• geographical (culture, society...)
• lines of business (life, car, mortality...)
• number of independent risks

The better the diversification, the less capital is needed to meet claims

• Underwriting (assessment, pricing, capacity allocation and assuming risk)
• Capital Management (adequate for 100 and 200 year events)
• Asset Management (assets need to be there when claims are made)

• Economic growth
• Urbanization trends and infrastructure growth (>50% world population lives in urban areas now)
• Natural catastrophe protection gap
• Large mortality protection gap

Economic

•  Higher income and wealth drives demand for motor, home and savings products

Social

• Longevity and reduced inter-generational support will create opportunities for old-age health and pension products 

Infrastructure

• New opportunity for commercial insurance during the 
  construction phase of infrastructure projects
  

Environment

• Many large cities located in areas exposed to multi-natural disasters to create higher demand for nat cat re/insurance

s. picture

• Regulatory environment
• Financial markets, sovereign debt
• mature markets, high growth markets
• low interest rates, inflation, price pressure
• Weak growth
• Changing risk landscape

1. Speculative Risks: with positive probabilities for loss AND gain (gambling etc.)
2. Pure Risks: only a chance of loss OR no loss (e.g. owner of a house might lose it due to an earthquake) -> only pure risk are really insurable
3. Dynamic Risks: Speculative risks resulting from changes in the ECONOMY (e.g. change in price level, consumer tastes, technology...)
4. Statis Risks: Risk occuring even WITHOUT economic change. Tends to occur with a regularity over time (e.g. natural catastrophes) -> more insurable than dynamic risks

Minimization of loss frequency and/or the magnitude of the losses that occur

Scientific approach that deals with PURE RISKS to develop procedures for:

1. Identification
2. Measurement
3. Valuation and Treatment

of risks

• Develop and exploit exposure checklists and risk questionnaires
• Implement risk models
• Implement measures for risk cntrol (risk avoidance tools and risk reduction)
• Develop or apply risk financing tools (e.g. hedging with derivatives or contingent capital, insurance...)

• Ex-post premia (after occurence; not all mebers were liquid)
• Adverse Selection (asymmetric information; before signing of contract: maybe price for premium set too low because of lack of information about the insured individual)
• Moral hazard (asymmetric information; after signing of contract: insured individual might take on higher risk)

A: Car is NOT behind first choice (P=0,5)

B: Showmaster opens particular gate (P=2/3)

(0.5*2/3)/0.5= 2/3

• Risk measurement is not sufficient: individual risk preferences play a role in decision making processes
• Game of chance for 1 player: coin toss as long as head appears, game stops when tail appears
• Amount of money for head is doubled each round

-> Paradox: expected value of game would go to infinity but  people wouldn't be willing to pay a high price to enter such a game!

Assumptions:

• Rationality and risk aversion of investors
• Jointly normally distributed random asset returns
• Complete capital markets

Goal:

Choose asset proportions in portfolio such that, given a certain amount of risk, the expected portfolio return is maximized, or given a certain expected return, risk is minimized

Expected portfolio return: weighted combination of expected returns of individual assets

Risk: Standard deviation of portfolio return

Explanations of the picture:

• Upper part of the hyperbola: efficient frontier (highest expected return for a given level of risk)
• Two Mutual Funds Theorem: Any risky portfolio on frontier can be generated by two other efficient funds (here: go short on MF1 and long on MF2)
• There's a risk free asset which is uncorrelated with the others because its variance is zero 
• Capital Allocation Line is the tangent line to the efficient frontier with intercept R_{f (it shows the possible combinations of risk-free asset and risky portfolio)}
• The point where the CAL and the EF touch shows the highest possible return you can get (if there is a risk free asset)
• In order to move up the line, borrowing is needed (higher risk but higher return)
• One Mutual Fund Separation Theorem: Separation of individual risk preferences from portfolio choice (different investors hold different amouts of R_f asset and tangency assets)

Main assumptions:

• All investors have access to the same universe of securities
• Expectations are homogeneous
• Investors are rational, risk-averse mean-variance optimizers
• Market of perfect competition
• No market frictions
• One period planning horizon
• Unlimited risk-free borrowing and lending possible (with same rates)
• Divisible assets (it can be traded in very small stacks/proportions)
• Investors remove all idiosyncratic (specific) risk by diversification
• Market risk cannot be diversified away and investors want to be rewarded for that
• Optimal risky porfolio is tangency portfolio (s. Markowitz) -> benchmark portfolio for asset valuation
• Expected "return-beta"-relationship: Security Market Line (contains not only portfolios but also single assets; all fairly priced securities lie on the SML)
• Assets above the SML are underpriced and beneath overpriced (difference: alpha)
• Slope of the SML: market risk premium

Variables:

E(R_m)-R_f = Risk premium of the market portfolio (slope of the SML)

ß = sensitivity of an asset within a portfolio with respect to market movements (market porfolio's beta=1)

-> Thus, the risk premium varies in direct proportion with ß

Formula: s. Picture

Capital Market Line

The CML is a line that is used to show the rates of return, which depends on risk-free rates of return and levels of risk for a specific portfolio.

Security Market Line

SML, which is also called a Characteristic Line, is a graphical representation of the market’s risk and return at a given time.
 

Differences:

One of the differences between CML and SML, is how the risk factors are measured. While standard deviation is the measure of risk for CML, Beta coefficient determines the risk factors of the SML.
 

While the Capital Market Line graphs define efficient portfolios, the Security Market Line graphs define both efficient and non-efficient portfolios.
 

While calculating the returns, the expected return of the portfolio for CML is shown along the Y- axis. On the contrary, for SML, the return of the securities is shown along the Y-axis. 
 

The standard deviation of the portfolio is shown along the X-axis for CML, whereas, the Beta of security is shown along the X-axis for SML

The CML determines the risk or return for efficient portfolios, and the SML demonstrates the risk or return for individual stocks.

Beta is the sensitivity of an asset within a portfolio with respect to market movements

Normative Economics:

How SHOULD we act in risky situations?

Behavioral Economics:

How DO people behave in reality?

-> Both are important!! Normative Economics is not going to be replaced by Behavioral Economics but rather complemented

Random Risk (risk in the narrower sense):

Exists even with full knowledge of the true characteristics of the randomness (e.g. fair dice game)

Tool: Probability Theory

Model Risk (model misspecification risk):

Does the chosen model sufficiently well in describing the data set or the relevant issue under consideration? One might choose the wrong model to explain the phenomena in reality.

Tool: Statistical inference (process of drawing conclusions from sampling etc. WARNING: psychological issue: people become too dependent on the outcomes of these models)

Parameter Risk (calibration risk):

It's uncertain if parameter values estimated from historical data remain valid in the future ("stationarity"), data ight be outdated (mortality tables, calculations of probabilities of occurence of floods etc.)

Tool: forecasting

-> This is often the most dangerous component!

Physical Risk Sources (earthquakes, storms, floods)

Social Risk Sources (social structures, longevity, mortality)

Political Risk Sources (unstable political conditions)

Legal Risk Sources (new regulations)

Operational Risk Sources (errors by insurance staff, inefficient coporate processes)

Macroeconomic Risk Sources (changes in asset prices, interest rates, exchange rates)

Market Risk: Change in interest rates, asset prices etc. Relevant for asset management. Frequently expressed in terms of return volatility (real, estate, stocks etc.)

Credit Risk: Counterparty risk (default risk) of contracting partner (including reinsurer). Affected: corporate bonds, derivatives...

Operational Risk: Risk of loss from inadequate or failed internal processes, people and systems, or from external events. It includes legal risk but excludes strategic and reputational risk.

General Underwriting Risk: Insufficient premium calculation (Premiums < E(claims))

• Large and/or many claims: "random risk" (pure risks)
• Change in probability distribution of claims - "change risk"
• Insufficient reserving regarding belated claims (see 4.2)
• Example of modelling underwriting risk s. picture

s. picture

Policy holders have similar risks with relatively low occurence probability

Reinsurers pool already diversified risks and attain even more diversification

Criteria for insurability of risks:

• Loss definition (exact! No correlation between different risks)
• Stochasticity of loss (pure risks)
• Diversification principle (collection of risks needed, i.e. a critical number of people)
• Measurability of loss severity and probability

Examples for limits of insurability:

• General business risk, i.e. insurance  of "whole business" (obscure risk porfolios, i.e. risks might be correlated and can't be defined clearly)
• Deterministic losses (e.g. corporate taxes can't be insured)
• Nuclear risks (diversification not possible/difficult, probability can't be calculated but losses would be so high that the insurer might go bankrupt)

Mannheimer Lebensversicherung:

• Very large stock portfolio of 13-45%
• Insufficient management of market risks
• In 2003 DAX fell to 2200 points
• Led to excessive leverage
• Bail-out by "Protektor-AG" (guarantee fund financed by German life insurance industry)

Equitable Life:

• Pension guarantees promised to policyholders were too high and insufficiently hedged
• In 2000, company had to suspend underwriting of new contracts for life-insurance business; it went on sale with huge losses!

AIG:

• September 08: Liquidity crisis and downgrading led to collapse of stock price by 95%
• Bail Out Package ($182bn) by Federal Reserve Bank (largest bail out in US-history)
• Losses in 08: more than $100bn
• As opposed to other two examples: Repayment in 2012/13: government could sell shares with a plus of $22bn

Risk Identification:

Process of systematically and continuously monitoring the risks of a firm, both before and after their realization

First step of risk management is risk awareness and major issue are undetected risks, thus permanent risk monitoring is required

Problem in practice: "Distance" (geographical, organizational, expertise) between risk manager and particular risks