vAR problem, option class

Insurance and Risk Management (FINA 467)

 Instructor: Leon Chen, Ph.D., FRM

 Email: [email protected]

 Office Hours (see syllabus)

Sample of RMI Job Positions

 Risk Analyst/Manager ($60k+ ~ $160k+)  Credit Risk Analyst/Manager ($60k+ ~ $160k+)  Portfolio Analyst/Manager ($70k+ ~ $180k+)  Insurance Agent and Broker ($40k+ ~ $60k+)  Actuary ($70k+ ~ $200k+)  Claims Adjuster ($50k+ ~ $70k+)  Loss Control Specialist ($40k+ ~ $70k+)  Insurance Underwriter ($50k+ ~ $80k+)  Employee Benefits Analyst/Manager ($50k+ ~ $130k+)

(HR data as of July 2020, salary.com)

Understanding Risk

Chapter 1

Instructor: Leon Chen

What is Risk

As we know, there are known knowns. There are things we know we know.

We also know there are known unknowns. That is to say, we know there are some things we do not know.

But there are also unknown unknowns, The ones we don't know we don't know.

—Donald Rumsfeld, U.S. Former Defense Secretary Feb. 12, 2002, Department of Defense news briefing

Meaning of Risk

 Risk: consequence of uncertainty about a future outcome, particularly the consequences of a negative outcome.  Why do we care about risk? (more discussions on this later)  What are some of examples of risks?  Any example of risky activities an undergraduate at MNSU

faces?

 Loss Exposure: Any situation or circumstance in which a loss is possible, regardless of whether a loss occurs.

 Chance of loss: the probability that an event will occur.

Attitudes Toward Risks

 Risk averse  Low tolerance of risk; willing to pay extra to avoid the risk,

even if the expected return E(r) is positive

 Risk seeker  High tolerance of risk; willing to pay to gamble even if the

expected return E(r) is negative

 Risk neutral  Seeking highest expected return; i.e., will not pay extra to

avoid the risk if E(r)>0; will not pay to gamble if E(r)<0.

Basic Categories of Risk

 Objective vs. Subjective Risk

 Good vs. Bad Risk (risk vs. return)

 Pure vs. Speculative Risk  pure risk: only the possibilities of loss or no loss  speculative risk: possibilities of both loss and profit

 Fundamental/Systemic (non-diversifiable) vs. Particular/Idiosyncratic (diversifiable) Risk  A fundamental risk affects the entire economy or large numbers

of persons or groups (hurricane)  An particular risk affects only the individual (car theft)

 Enterprise (Holistic) Risk: a term that encompasses all major risks faced by a business firm. What are some major risks faced by a business firm?

Types of Pure Risks  Personal Risks

 Premature death of family head  Insufficient income during retirement  Poor health  Involuntary unemployment

 Property Risks  Physical damage to home due to fire, tornado, vandalism, etc.

 Liability risks  No maximum upper limit of loss  A lien can be placed on your income and financial assets  Defense costs can be enormous

Examples of Risk Exposures by the Pure Risk and Speculative Risk

Pure Risk Speculative Risk Property damage risk Market risks: interest risk, foreign

exchange risk, stock market risk

Natural disaster risk Investment risk

Longevity risk Regulatory risk

Mortality and morbidity risk Credit risk

Accident risk Reputational risk

Liability risk Strategic Risk

Environmental risk Operational risk Technological innovation risks

Cyber risk Political risk

Examples of Risk Exposures by the Diversifiable and Non-diversifiable

Peril and Hazard

 A peril is defined as the cause of the loss (in an auto accident, the collision is the peril) – natural, human and economic perils

 A hazard is a condition that increases the chance/severity of loss  Physical hazards are physical conditions that increase the

chance of loss  Moral hazard is dishonesty or character defects in an individual,

that increase the chance of loss.  Morale Hazard is carelessness or indifference to a loss because

of the existence of insurance.

Types of Perils by Ability to Insure

Measuring Risk

Chapter 2

Instructor: Leon Chen

Probability Distribution

 The probability of an event is the long-run relative frequency of the event, given an infinite number of trials with no changes in the underlying conditions.

 Events and possible outcomes can be collected and summarized through a probability distribution.  discrete distribution vs. continuous distribution

Example – construct a probability (discrete) distribution of the sum of dots for a roll of two fair dices

Example of a Normal (Continuous) Distribution of Corporate Profit

Comparing Three Distributions 1

Comparing Three Distributions 2

19

Normal Distribution Features  About 68% of all observations will be within 1 standard

deviation from the mean; about 95% of all observations occur within 2 standard deviations from the mean; about 99% of all observations should be within 3 standard deviations from the mean. Cumulative probability can be obtained using Excel function NORMDIST().

Normal Distribution Example

 Assume:  Large number of independent loss exposure units  Expected total loss = $1,000,000  Standard deviation of total losses = $200,000

 What is the probability that losses will exceed $1,400,000?  Use rule of thumbs: (1 – 95%)/2 = 2.5%  Use Excel function (more precise):

• 1 – NORMDIST(1.4, 1, 0.2, TRUE) = 2.28%

Common Measures of Risk

 Consider a certain loss L with n possible loss outcome Li (i=1,2,…,n). Distributions are normally characterized by:  Mean – a measure of central tendency

 Standard deviation or Variance – a measure of dispersion

 Coefficient of Variation is a normalized measure of dispersion.

( )L i ior E L P Lµ = ∑

[ ]22 ( )L i iP L E Lσ = −∑

L L Lcv σ µ=

Example

 Calculate mean (expected loss), standard deviation, and coefficient of variation for the following (simplified) loss distribution of a person’s monthly healthcare cost:

Outcome Probability Loss

1 70% 0

2 20% $200

3 8% $5,000

4 2% $20,000

Another Example

 Calculate the expected value of this corporate product strategy:

Other Measures of Risk

 Value at Risk (VaR): the worst-case scenario dollar value loss (up to a specified probability level) that could occur for a company exposed to a specific set of risks  Also referred to as tail risk; can be used to determine level of

reserves  VaR (e.g., of a stock portfolio) can be obtained using

simulations

 Maximum Probable Loss vs. Maximum Possible Loss  Maximum probable loss: a type of VaR in the context of

pure risk exposures; the worst loss that is likely to happen.  Maximum possible loss: the worst loss that could happen.

CAPM Measure of Portfolio Risk

 The Capital Asset Pricing Model (CAPM) provides a Beta measure of how the return on an asset systematically varies with the variations in the market.

 The general (1-factor) CAPM framework is expressed as E(Rp)= Rf + βp* [ E(Rm) – Rf ] (Q: what is the factor here?)

 We can expand CAPM to multi-factor asset pricing model – the key is to find useful factors (such as macroeconomic factors, factors based on firm fundamental characteristics).

In-class Exercise 1

 Name 3 fundamental risks and explain why each of them is non-diversifiable. How do we address these risks in our society?

 Name 3 particular risks and explain why each of them is diversifiable. How do we address these risks in our society?

In-class Exercise 2

 Let’s get back to our previous example of rolling 2 fair dices.

 Calculate the expected value, the standard deviation, coefficient of variation of the outcome (sum of dots). You may use Excel.

In-class Exercise 3

 Assume:  Large number of independent loss exposure units  Expected average loss = $1,000  Standard deviation of the average loss = $300

 What is the probability that the average losses will exceed $1,500? (hint: use normdist() function in Excel)

In-class Exercise 4

 You are appointed as Risk Manager of a local company. The company has established a fund with which to finance losses to the company’s motor vehicle fleet. The Board wants you to have 99.5% certainty that annual losses will NOT be greater than the amount money held in the fund.

 You analyze past loss data and find that mean (average) losses equal to $3 million per year with a standard deviation of $250,000. The data follow the normal distribution.

 How much would you recommend to be held in the fund?

In-class Exercise 5

 A company has 3 (independent) manufacturing plants, and each has $1 million in value. Simplistically, let us assume that the chance of a single fire destroying the whole plant in each year is 5%.

 What is the maximum possible loss?

 What is the maximum probable loss given 99% confidence level?

In-class Exercise 6

 Now let’s have some fun running a simple simulation in Excel to determine a portfolio VaR.

 Assume that you manage a large portfolio with the current value of $1 million, and assume the monthly return follow a normal distribution with mean of 1% and standard deviation of 5%.

 Run 1000 instances and determine the portfolio VaR for the following 1-month period, given 95% confidence level. (hint: use Norminv(Rand()) functions in Excel). How about VaR for 1-year period?