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Risk measurement
MODULE 3
Frequency and severity of losses.
Frequency of loss refers to number of times in a given period a loss is likely to happen.
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Historical data will provide this info. (Eg: frequency of injuries in the past/no of worker-years) in the absence of historical data, industry data can be used. Informed judgement can be used as well.
Severity of loss measures the magnitude of loss per occurrence. One way to estimate is from historical data. (average severity/occurrence)
Expected loss = frequency of loss*severity of loss. Expected loss affects business value and insurance pricing.
3.6
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Property Exposures Frequency Severity Range Average Severity Expected Loss
Damage to automobiles Medium $0-$20,000 Low Medium
Stolen property High 0-2,000 Low Low
Small fires Low 100,000-500,000 Medium Low
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Major fires Low 500,000-10,000,000 High Low
Note:
Std deviation for high frequency low severity is low while std deviation for low frequency severity is high
Infrequent but potentially large losses are less predictable and pose greater risk than more frequent smaller losses.
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Risk control
Risk control is the process of implementing measures to reduce risk associated with a hazard.
Benefits of risk/loss control:
Elimination of expenses associated with
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Repair or replacement of damaged property
Income losses due to destruction of property
Extra costs associated with maintaining operations
Adverse liability judgements
Medical costs to treat injuries
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Income losses due to death/disabilities
Cost of risk control
Installation and maintenance expenses eg sprinkler system
There are associated costs involved like employee benefits apart from salary
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Some measures push up utility bills eg power bill
Risk control techniques
• Risk avoidance
• Risk prevention
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• Risk reduction
Risk avoidance
Risk avoidance involves not performing an activity that carries risk. Eg: not buying a property, not flying, not travelling. There is loss of opportunities arising out of performing such activities. Not doing a business will avoid risk but one loses on opportunity and profits.
Advantages:
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Chances of risk is reduced to zero in case where loss exposure is not started. In situations where exposure has already started, we can reduce to zero for future activities. Residual risks may still persist.
Disadvantages:
A firm cannot avoid all losses like premature death of an employee.
It is not feasible/practical to avoid all losses without shutting down the business eg car factory cannot avoid all risks if it has to continue producing cars
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Risk control techniques- Risk prevention
It refers to measures that reduce the frequency of a particular loss. This focuses on stopping losses from happening. Important to prevent death/injury to people.
Businesses employ loss control engineers - to identify sources of risks and institute corrective actions. Like poor lighting, poor maintenance, improper security, etc. training is given on operating aspects
Eg: changing slippery floor, building safety enclosures to dangerous machinery etc
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Risk control techniques- Risk reduction
Risk financing techniques- risk retention.
Risk financing techniques- risk transfers.
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Risk management decision methods
Risk avoidance
Loss control
Risk retention
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Non-insurance transfers
insurance
Pooling arrangements and diversification of risk
Most popular risk management tool is diversification. Essential part of insurance/financial markets
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Simple methods like pooling between two to diversification amongst many
Pooling arrangement reduces risk when losses are independent (uncorrelated)
Pooling refers to spreading losses incurred by a few over the entire group so that everyone bears average loss instead of actual loss.
2-person pooling arrangement
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Shahrukh and Salman have a possibility of an accident in the coming year,
20% chance of an accident with a loss of 2500
Probability distribution of accident loss is highly skewed. (0 – 0.8; 2500 – 0.2)
Their losses are uncorrelated.
What is the expected loss and standard deviation for each one of them?
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Expected loss = 0.8*0 + 0.2*2500 = 500
Standard deviation = Root 0.8(0-500)² + 0.2(2500-500)² = 1000
Pooling arrangement...
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Pooling allows them to pool their risk and split losses equally
What is the expected loss and standard deviation for each one of them?
Pooling arrangement..
Possible outcome Total cost Cost paid by each person Probability
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Neither Shahrukh nor salman 0 0 0.8*0.8=0.64
Only Shahrukh 2500 1250 0.2*0.8=0.16
Only salman 2500 1250 0.2*0.8=0.16
Both of them 5000 2500 0.2*0.2=0.04
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Expected cost = 0.64*0+0.32*1250+0.04*2500 = 500
Standard Deviation = Root of 0.64*(0-500)² + 0.32*(1250-500)² + (2500-500)² = 707
Pooling arrangement doesn't change either person's expected cost but it reduces the standard deviation. (1000 to 707)
This is how risk gets reduced by diversification. Loss has become more predictable.
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Many-people pooling
Assume that now Amir khan who has the same probability of risk also joins the pooling arrangement. If anyone meets with an accident, each will share one-thirds of the average loss or expected loss
As more and more people join the pool, the mean loss remains the same but standard deviation goes down hereby reducing the risk for each participant
Expected loss or mean remains the same but the standard deviation further decreases making it more normal distribution less skewed and more bell shaped
Note that here the risk is not transferred to anyone else, but it is reduced as a whole for each pooling participant.
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Fig 4.2 page 59
Graph with pooling
Graph without pooling
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summary
As the number of participants in a pooling arrangement goes up, the standard deviation is coming down as near to zero as possible for each participant. Probability of extreme high or low outcome is reduced. This leads to the law of large numbers.
Law of large numbers states that “The greater the number of exposures, the more closely will actual results approach the probable result that are expected from an infinite number of exposures (tossing a coin a million times)
Also, as the number increases the probability distribution curve of average loss tends to become more and more bell shaped tending towards a Normal distribution. This reflects central limit theorem.
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Solve
Suppose each participant in a pooling arrangement has USD 0 to 4000 loss with each participants expected loss usd 1000, sketch the probability distribution of average losses if the losses across the participants are independent and if
1. there is 1 participant (no pooling)
2. there are 100 participants
3. there are 1000 participants.
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Pooling with correlated loss
Positive correlation because of:
Catastrophe and epidemic hit a large population at the same time
When losses are correlated then increase/decrease in one leads to increase/decrease in another.
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Therefore, Pooling arrangement reduces risk for each participant even when the losses are positively correlated but to a lesser degree.
Assuming Shah Ruk and Salman's accidents are correlated, then probability of shah Ruk having an accident knowing that Salman has had an accident > 0.04
Changing scope of financial management
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Changing scope of risk management
Traditionally risk management focused on pure loss exposures including property risks, liability risks and personal risks.
In 1990s new trend emerged where risk management included speculative financial risks.
Recently some businesses have expanded the scope to include all risks.
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Financial risk management
Financial risk management refers to identification, analysis and treatment of speculative financial risks which includes
- commodity price risk
- interest rate risk
- currency exchange rate risk
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Commodity price risk: it is the risk of losing money if the price of a commodity changes. Both producers/sellers and users have this risk. Eg: agri grains
Futures&options can be used to hedge this risk
Financial risk management
Interest rate risk:
Risk of loss caused by averse interest rate movements. Eg: a bank has loaned housing loan for 20-30 years at a particular interest rate. If rates go up, they have to borrow deposits at a higher rate. Similarly a corporate may have issued bond o public at a rate, they have to pay the coupon rate
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Currency exchange rate:
Exchange rate is the value at which one country's currency is converted to another Nation's currency. This affects both imports and exports.
History of Managing financial risk
Traditionally pure risk and speculative risk were different and handled by separate departments
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Pure risk by risk retention, risk transfer and risk control.
Speculative risk handled by finance department through contractual provisions and capital market instruments.
- contractual provisions include call features on bonds and adjustable interest rate provisions on mortgages
- capital market approaches include forward, futures options and swaps
History
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In the 1990s some companies started taking a holistic view of pure and speculative risk to achieve advantage by combining both the risk coverages
In 1997, Honeywell became the first company to go into an “integrated risk program" with AIG.
An integrated risk program is a risk treatment technique that combines coverage for pure and speculative risks in the same contract. Honeywell covered traditional property and casualty insurance as well as coverage for currency exchange rate risk.
Some companies created a new position called chief risk officer(CRO) who is responsible for treating pure and speculative risks in the organization.
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History
Combining two risks in the same contract makes it cheaper. Companies who can afford a certain level of loss can go for trigger option where the insurance company pays only if two specified losses occur like one property claim and another exchange rate claim. Such contracts are cheaper.
Enterprise risk management
some companies went a step further and covered pure risk, speculative risk, strategic risks and operational risks.
Strategic risk refers to uncertainty regarding the organization's goals and objectives and the organization's strengths, weaknesses, opportunities and threats.
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Operational risk refers to risks that develop out of business operations like manufacturing products and providing service to customers
Combining all these risks in one package reduces risk as long as they are not positively correlated. If they are negatively correlated risk can be reduced significantly.
History
Advantages of ERM:
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Holistic treatment of risks
Advantages over competing businesses.
Positive impact upon revenues
Reduction in earnings volatility
Compliance with corporate governance guidelines
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Barriers to ERP:
Organisation culture
Turf battles
Perception of not a priority
Lack of formal process
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Deficiencies in intellectual capital and technology
Futures and option basics
Spot market: delivery based
Example- buy wheat at 30,000/ton, sell sugar at 45000/ton Derivative contracts
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Futures market: right to buy/sell, usually no delivery, square up position.
Eg: as a buyer buy wheat futures for june at Rs 25,000/ton market price is 30,000. you square up position by selling square up make Rs 5000. buy physical wheat at Rs 30,000 from spot market. Effective price is Rs 25000 which is futures contracted price
As a seller, sell wheat at Rs 40,000 in the june futures market price crashes to Rs 20,000. you square up your position by buying spot. You make Rs 20,000. sell physical wheat at Rs 20,000 in spot market. Effective price is Rs 40,000
Options contract
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Options contract can be used to protect against adverse price movements.
Call option – option to buy at a specified price during a specified period
Put option – option to sell at a specified price during a specified period
Both call and put have buyers/writers and sellers (4 legs)
Many strategies like straddle, strangle, butterfly,...
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Simple option to protect a price drop is “covered put option"
Eg: someone has 100 HUL shares at current market price of Rs 900 fears a price drop but feels it may also increase.
He buys a put option for a strike price of 900 paying a premium of Rs 5
If market drops to 800, then he exercise his 'in the money' option makes 900-800-5 = Rs 95
If market moves up to 1000, then the option is out-of-money and wishes not to exercise the option and loses only Rs 5 of premium
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Hedging with Futures
Hedging a commodity risk using futures contract:
A corn grower estimates in May about 20,000 bushels of December. He notices a price of $2.90/bushel of futures in December. He fears that the actual spot price in December will be lower. So he books 4 contracts of size 4000 bushels each at $2.90/bushel. He will buy back 4 contracts to offset his position
If market price is 2.5/bushel in December.
Sale of 4 contracts at 2.90 in may .... 4*5000*2.90 = 58000
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Buy-back at 2.50 in December .... 4*5000*2.50 = 50000
Gain on futures contract = 58000-50000 = 8000
Sale of physical stock in December = 4*5000*2.50 = 50000
Total revenue = 50,000+8000 = 58000
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Hedging with futures
If market price is 3.00/bushel in December.
Sale of 4 contracts at 2.90 in may .... 4*5000*2.90 = 58000
Buy-back at 3 in December .... 4*5000*3 = 60000
Gain on futures contract = 58000-60000 = (2000)
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Sale of physical stock in December = 4*5000*3 = 60000
Total revenue = 60,000-2000 = 58000
So, no matter what the price is in December the farmer gets contracted price of may of $ 58,000.
Solve,
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1. You are having 100 shares of HUL and the current market price is Rs 900. you fear that the market will crash and sell it in the june futures market at Rs 950. in june the price of HUL comes to Rs 920
Calculate your realisation
What is your realisation if the price comes down to Rs 900 your gain in the whole transaction?
2. Colgate palmolive is quoting at Rs 1000/share. You expect market to go up. So you buy futures at Rs 1050 for June. If market goes to Rs 1250. what is your profit? What would have happened if you had bought spot?
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Insurance market dynamics
Risk control, risk retention and risk transfer are the methods of risk management
Risk retention by current earnings, loss reserves, borrowings or captive insurance
Risk transfer by a property and liability insurance company.
Decision needs to be taken about risk retention or risk transfer. It depends upon conditions in the insurance market-place.
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3 imp factors influencing insurance market are:
- underwriting cycle
- consolidation in the insurance industry
- securitisation of risk
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1. Underwriting cycle
Underwriting means “sign and accept liability under insurance policy), thus guaranteeing payment in case of loss or damage occurs"
Underwriting cycle – property and liability insurance rates fluctuate between periods of tight underwriting standards and high premiums called 'hard' insurance market and periods of loose underwriting standards called 'soft' insurance market.
This is measured in terms of combined ratio which is equal to paid losses and loss adjustment expenses plus underwriting expenses to premiums
If combined ratio is more than 1 (100%) then underwriting operation is profitable. Less than 1 is loss making.
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Risk managers must study current status of the cycle for making retention transfer decisions. Buy when market is soft and retain when the market is hard
Y underwriting cycle fluctuates
1. Insurance industry capacity - capacity refers to relative level of surplus which is assets less liabilities. They reduce premium and go soft when they have surplus and increase premium and go hard when they are deficit. Competition hastens this process.
External factors like earthquake, 9/11, katrina can increase claims and reduce surplus and harden the market.
2. Investment returns- insurance business also is an investor generating revenues from premium collections. They sell insurance at lower premiums expecting higher investment returns. this is called 'cashflow underwriting'
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2. Consolidation in industry
Consolidation means combining of business organisations through mergers and acquisitions.
A number of trends have changed the insurance market like
- insurance company mergers and acquisitions
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- insurance brokerage mergers and acquisitions
- cross-industry consolidations
(Read george rejda page 68 for examples)
Securitisation of risk
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Securitisation of risk means that insurance risk is transferred to the capital market through creation of financial instruments such as catastrophe bond, futures contract, options contract and other financial instruments.
This increases capacity for insurers and provides access to capital of many investors.
Weather is another factor that determines risk in insurance. weather bonds are floated to securitise it. A weather option provides a payment if a specified weather contingency
Loss forecasting
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Done on the basis of statistical analysis of past losses.
Risk profiling or risk mapping refers to analyzing the severity frequency of various risks involved in the business.
Based on loss forecasting the manager is able to decide on control measures.
Loss forecasting is done on the basis of
Probability analysis:
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Probability or chance of loss of an event refers to the long run frequency of occurrence. Probability distribution is mutually exclusive and collectively exhaustible list of all outcomes arising out of an event along with probability associated with each outcome.
Statistical analysis:
It talks about a distribution of losses and parameters associated with it like mean mode median regression analysis and mortality tables.
Regression talks about relationship between one or more dependent variables and an independent variable. Eg
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Mortality table indicates probability of death at a particular age. mortality rate of 0.001at an age of 25 indicates that 1 out of 1000 insured will die during that year. If all the 1000 are insured for 1 lakh each then the company has to pay 1 lakh. In order to do this the company has to collect Rs 1 lakh from 1000 insured which amounts to 100 per lakh of sum assured or 1 per 1000 sum assured
Law of large numbers:
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This download link is referred from the post: VTU MBA Lecture Notes - 1st Sem, 2nd Sem, 3rd Sem and 4th Sem || Visvesvaraya Technological University