ACSG1614 Introduction to Actuarial Science - Risk - PDF

ACSG1614 – Introductio n to Actuarial Science Disclaimer These notes are for registered students of module ACSG1614 at the University of the Free State for Academic Year 2023 only and may not be distributed to any other person or entity. The intention of these notes are only to give a b...

ACSG1614 – Introductio n to Actuarial Science Disclaimer These notes are for registered students of module ACSG1614 at the University of the Free State for Academic Year 2023 only and may not be distributed to any other person or entity. The intention of these notes are only to give a brief introduction to the world of Actuarial Science and related fields, as such, concepts might be over-simplified and simple language will be utilized to make it palatable for first time readers. These notes have not been reviewed by anyone, and as such the quality or correctness cannot be guaranteed to any degree. No opinion, example or statement given in these notes or made in class should be seen as advice of any kind or in any way. 2 1 RISK What is a risk??? In Actuarial terms: o Uncertainty o Potential downside A risk or risk event is sometimes referred to as a Peril. 4 Forms of risk ￮ Pure risk ￮ Speculative risk ￮ Particular risk ￮ Fundamental risk 5 Pure risk This is a risk that: o Has a potential downside o Or nothing happens No upside is possible Example - car ownership State 1 State 2 No Damage occurs Damage/theft 6 Speculative risk This is a risk that either: o Has a potential downside o No loss occurs o Has a potential upside Example - Investing State 1 State 2 State 3 Profits Break Even Losses 7 Particular risk A risk that pertains to an individual or a particular group: o Life o Property o Income o Health o Wealth Particular risk Pure Speculative 8 Fundamental risk A risk that pertains to an entire group or population: o Natural phenomenon o Social Problems o Economic disasters Fundamental Natural Social Economic Fundamental risks are almost always Pure risks. 9 When defining a risk Be clear Weather is not a risk. A risk is: o Raining more than 100mm in a day. o Hailstorm o Wind of 50 km/h + o Not raining at least 300 mm in a year Almost anything can be worded as a risk – in this course please try and focus on the main risks. 10 Lets try identiying some risks What major risks are you exposed to: o Death - Pure risk (no upside) – Particular risk (only you) o Disability - Pure risk (no upside) – Particular risk (only you) o Cellphone lost/stolen/damaged - Pure risk (no upside) – Particular risk (only you) o Similarly – laptop/car/any property o Failing - Pure risk – Particular risk o Falling ill - Pure risk – Particular risk o o Death of provider - Pure risk – Particular risk 11 Other (non-particular) risks What major risks are you exposed to: o Economic downturn – Employability o AI – Employability (possibly Terminator) o War - Everything o Extreme weather - Everything Fundamental risks more easily overlooked, possibly the most consequential. 12 What risks can you insure What major risks are you exposed to: o Death - Life insurance o Disability - Income protectors and Critical illness o Property - Property insurance with the aim of replacing o Failing - No insurance possible – you are in control o Falling ill - Medical scheme or health insurance o Death of provider o - Life cover o Economic downturn - Uninsurable o AI - Uninsurable o War -Some consequences insurable – Life, property o Extreme weather -Some consequences insurable – Life, property 13 Why are some risks insurable Desired properties of insurance: o Pooling Many similar risks should exist = statistical clarity and profit o Uncorrelated Risks should be independent = one risk does not cause the othe o Insurable interest Risk event should equal some loss, not for profit o Quantifiable Sufficent Info to price o Measburable Measure when risk occurs, and the amount of loss o Limited liability Ultimate upper limit to insurance pay-out o Small likelihood Probability of risk event should be relatively small o Limiting moral hazzard and anti-selection Moral Hazzard = Policyholder behavior changes as a result of insurance Anti-selection = Policyholder that are bad risk gets insurance 14 And those that are good risks do not. Why not insurable? o Failing - Moral hazard, anti-selection?, measurable o Economic- downturn -Correlation, measurable and quantifiable o AI - Correlation, measurable and quantifiable - o War (General cover) - Correlation, measurable and quantifiable 15 Desirable but not Mandatory Hail storm: o Problems - correlated (effects all in area) Resolved by: o Insuring many geographical areas o Reinsurance 16 2 Risk managment Risk management steps Identify Quantif y Manage 18 1. Identify Identify all risks. Not identified ≠ does not exist Some basic considerations: o Property o Health o Income o Liability 19 2. Quantify Basic concept: Probability x consequence (Cost) The chance of something happening to your car is 30% this year, and the average cost is R50 000. Expected loss = 0.3 x 50 000 = R15 000 20 More detail Likelihood Loss Risk event(s) 50% R0 to R3 000 Small scratches and bumps Minor accidents which requires 30% R3 000 to R15 000 some part replacement Major accidents which requires 15% R15 000 to R100 000 extensive repairs Theft or damage to such an 5% R100 000 to R150 000 extent that the car needs to be written off. 21 Risk Matrix Used to identify which risks are most consequential. Target investigation/quantification. High probability, low consequence High probability, high consequence Such as: Such as:  Minor damage to your car  Hospitalization when you are older  Minor injuries to yourself  Raining during a music festival in  Cell phone getting lost, stolen, the summer damaged Low probability, low consequence Low probability, high consequence Such as: Such as:  Cell phone blowing up whilst charging  Damage due to severe earthquake  Meteorite strike  Political unrest and economic meltdown 22 3. Manage Options available: o Avoid o Reduce o Share o Transfer o Finance o Postpone/Defer/Delay o Insure o Retain Retain not really an option for most common risks, and as such will not earn marks in most commercial scenarios. 23  Risk Factor 3 vs Rating Factor Risk Factor vs Rating Factor: Risk factors are factors that directly impact on the probability or consequence of a risk event occurring. Rating factors are the factors used to quantify the risk by an insurer (predict either probability or size). Most risk factors are ratings factors, but some rating factors are a proxy for the risk factor (i.e. a measurable factor). 25 Risk Factors Let us consider car insurance again. The following risk factors would influence likelihood or size of a claim: ￮ Driving ability ￮ Time spent on the road ￮ Safety features of the car ￮ Price of the car ￮ Road conditions (traffic, state of the roads) the individual is traveling in It might however not be possible to measure these factors directly 26 Rating factor ￮ Driving ability ￮ Age ￮ Claims Record ￮ Time spent on the road ￮ Occupation ￮ Distances travelled ￮ Safety features ￮ Colour of the car ￮ Make and model ￮ Price of the car ￮ Price of the car should be easily verifiable ￮ Road conditions can be estimated by ￮ Home address ￮ Business address 27 Life insurance Risk Factors (influences probability of death) o Health o Blood pressure o Diabetes o Other diseases o Gender o Lifestyle o Smoking, drinking o Occupation o Hobbies o Diet o Spend on junk food 28 3 Role of insurance Role of insurers Insurers trade uncertainty for certainty in exchange for a premium. You are certain that your R100 000 car will continue to contribute to your wealth at least to some extent (Say R80 000), in exchange for a premium. The premium ≈ the risk you pose. If the probability of you crashing your car is 10% this year. The premium will be roughly R10 000. This is known as the risk premium 30 Risk premium vs Office premium So the Risk Premium is the part of the total premium that you pay to compensate the insurer for the actual risk that you pose. The insurer will also have the following (among other) costs: o Design o Marketing o Administrative o Commission As well as a profit motive. These will be added onto your total premium being paid. The total premium is known as the Office premium. 31 Risk premium vs Office premium Office premium = Risk Premium + Costs + Profit loading So insurers charge more for insurance than what the true expected costs of the underlying risk is. Risk premium = R10 000 Commission = R500 Admin = R500 Recoup of Design = R800 Profit = R200 Office Premium = R12 000 32 Advantages of insurance ￮ Capital efficiencies ￮ Relieving the burden on the state ￮ Limiting destitution ￮ Job creation ￮ Financial stability ￮ Reduces risk aversity/increases willingness to take risks 33 4 Type of losses Types of losses ￮ Financial – Direct Costs and Losses ￮ Property ￮ Income ￮ Most other risks have a financial component ￮ Physical - Indirect losses (Future income and Quality of life) ￮ Health ￮ Limbs ￮ Life ￮ Emotional – Indirect losses (Quality of life) ￮ PTSD ￮ Trauma associated with health ￮ Sentimental value 35 Forms of insurance benefit: o Reinstatement Brings you back into the same financial position that you were before/prior to the event. Also known as Indemnity. o Indemnity minus excess Fixed/percentage charge that you will always need to pay. o Pre-determined Lump sum/income Benefit is pre-determined in contract o Externally determined Court determines the benefit 36 Benefit ￮ for type of loss Financial ￮ Property ￮ Property can be replaced, damage repaired or value refunded – Indemnity possible ￮ Income ￮ Lost income can be paid – indemnity possible ￮ Most other risks have a financial component – see below ￮ Physical ￮ Health ￮ Medical Bills can be paid, but insurer cannot bring you back to health, value of critical illness needs to be pre-determined. ￮ Limbs – Same as above ￮ Life ￮ Indemnity not possible, some pre-determined benefit ￮ Emotional PTSD , Trauma associated with health, sentimental losses ￮ Indemnity not possible, pre-determined benefit? Measurable? Might be difficult to measure and confirm emotional losses and provide insurance. 37 What did we learn? ￮ Forms of risks ￮ Risk Management Process ￮ Identification ￮ Quantification ￮ Management ￮ Desirable features for Insurance ￮ Risk and Ratings factors ￮ Risk vs Office Premium ￮ Societal benefits of insurance ￮ Types of Insurance pay-outs 38 5 Basic Cacluations Simple example How much should I pay for my cellphone insurance. Value: R5 000 Probability of theft p.a.: 10% Annual premium: R500 This is known as the risk premium 40 Simple example Lets say there are 100 insured cellphones: X X X X X X X X X X If 10% of them were stolen, a total of 10 would be stolen. As such, the insurer will need to pay 10 x R5 000 = R50 000 out. Which means that it will need to charge R50 000 in total As such, per cell phone the insurer will need to charge: R50 000/100 = R500 per policy Or using our basic formula: 41 Value = probability of cash flow x size of cash flow = 10% x 5000 = R500 Remember Value = Probability of cashflow x size of cashflow. We can use this to fairly easily calculate the risk premium. But we would also like to calculate how much the total premium charged by the insurer will be, given all the other costs and profit requirement of the insurer. Office premium = Risk Premium + Costs + Profit loading So for our cellphone insurance, we had a risk premium of R500 per policy. If we were to assume that administration of the policy would be R10 per policy, and the sales person will get 10% of each premium as commission. How much should the insurer charge for the policy in total if a R15 per policy profit is required? 42 Remember So we have: Risk Premium = R500 per policy Admin Expenses = R10 per policy Commission = 10% x P = 0.1P Profit = R15 per policy Office premium = P So: Office premium = Risk Premium + Costs + Profit loading P = 500 + 10 + 0.1P + 15 0.9P = 525 P = R583.33 = Office premium 43 Risk Premium Likelihood Loss Risk event(s) 50% R0 to R3 000 Small scratches and bumps Minor accidents which requires 30% R3 000 to R15 000 some part replacement Major accidents which requires 15% R15 000 to R100 000 extensive repairs Theft or damage to such an 5% R100 000 to R150 000 extent that the car needs to be written off. *Using the average loss to quantify Expected Loss: 0.5 x R1 500 + 0.3 x R9 000 + 0.15 x R57 500+ 0.05 x R125 000 = R18 325 A risk premium of R18 325 might be suitable given the above scenario. 44 From Notes We know that 300 cars out of every 100 000 cars crash annually. The average value of a car is R250 000 and the average value of a claim is R150 000. The administration fee on a policy is R50 per policy per annum. The general expenses of a company is R80 000 which pays for water and electricity, rent, salaries and other office expenses. The company expects to sell 10 000 policies, want to make 10% profit on each premium and has to pay 5% commission per premium. Calculate the annual premium? Probability of Crash = 300/100 000 = 0.003 The claims we expect to pay in a year is R150 000 x 0.003 = R450 per policy Admin fee is R50 per policy Other expenses are R80 000 for the whole company, but could be distributed over all policies, thus R80 000/10 000 = R8 per policy. P = R450 + R50 + R8 + 0.05P + 0.10P 45 You try An average cellphone costs R5 000. We know that last year 5 million of the estimated 70 million cellphones were stolen. An insurer has brought a cellphone insurance product to market that will make a payment if a cellphone is stolen. The insurer expects to sell 100 000 policies. Insurer costs: o Design: R500 000 ￮ Administration: R10 per policy Profit requirement: 10% of premium Solution: P = 5/70 x 5000 + 500 000/100 000 + 10 +0.1P P = 413.49 46  2020 Semester Test ￮ The average value of a coin collection is R50 000. The Payment per Claim = insurance company is willing to protect 90% of the 0.9 x 50 000 =R45 000 value of the coin collection. It has been estimated that there is a 10% chance of theft of such coin collections 10% chance in a year. RP = 4500 ￮ The insurer expects to sell 2000 such coin collection policies in the next year. The insurer expects to incur the following expenses: R500 000/2000 = R250 ￮ R500 000 total design and marketing expenses 0.05P ￮ 5% of premium commission payable to the sales person ￮ R50 R50 administration expense per policy per year ￮ R100 000/2000 =R50 The insurer want to make R100 000 profit in total on this product. P = 4500 + 250 +0.05P + 50 +50 47 P= R5105.26  2019 Semester Test ￮ Property insurance policy that will compensate policyholders for the $200k x 1.1 damage suffered as a result of a category 5 hurricane. If a category 5 = 220 000 hurricane were to hit, the damage to any individual property is expected to be 110% of the property value. 1/10 = 10% ￮ The average value of a property on the island is $200 000. Historically there have been a category 5 hurricane once every 10 years. RP = $22 000 ￮ Insurer will sell contracts at the start of the year that will provide cover for the full year. They have or will incur the following costs: 5m/5k ￮ $5 million to develop and market this product = $1000 ￮ Pay 2% of premium as commission to their sales agents 0.02P ￮ Pay $50 dollars to an administrator for each policyholder’s information 50 that they capture on the system ￮ Class19 requires a profit margin of 10% of premiums and expect to 0.1P sell 5000 policies. P = 22 000 + 1000 +0.02P+50+0.1P 48 P=26193.18 Thanks ! Any Questions? 49