Risk Management for Financial Institutions Assignment 1: Risk and Capital Management at an insurer Introduction Learning objectives • You will learn how a typical insurance balance sheet translates to a risk and capital position, the latter being expressed in the Solvency II SCR ratio • You will learn what material risk exposures are for a simple insurer’s balance sheet • You will learn how to optimize the balance sheet by changing the asset allocation on the balance sheet Way of working • In groups of 5, construct the SCR calculation tool to determine the required capital for the insurer presented. • Identify possible risks and quantify the amounts per risk type using the SCR calculation tool you have built. • Write the results in a report. Deliverables • SCR calculation tool • A report with the results of the SCR tool and analysis of the risk profile of the insurer Phasing and deadlines • The insurance assignment is split into three phases of each 1 week: 1. Week 1: Construction of best estimate balance sheet 2. Week 2: Quantification of applicable Standard Formula capital requirements 3. Week 3: Explanation on risk profile and manual on SCR calculation tool. • The deadline for the assignment is Friday, September 29th at 23:59 • Students will receive their grade and feedback 1-2 weeks after their submission. General feedback will be shared during the tutorials. General Remarks • Enter the names and student numbers on the front page • Try to make each function in Excel as dynamic as possible • Check sheets on #REF!, #N/A other error messages Case description Insurance companies report and manage their capital and risk profile using the Solvency II Framework. In this case we will calculate the SCR ratio of a hypothetical insurance company using the Standard Formula approach as given in the Solvency II Delegated Regulation (EU) 2015/35, articles 136-138, 142, 164-169 It is noted that in practice most insurance companies have internally developed capital and risk models as the Solvency II standard formula is not always a good reflection of the actual risk profile of the insurance company. The large companies also have so-called Solvency II internal models. These models are used to calculate and report the SCR ratio based on an internal model that must be approved by the supervisory authority (e.g., DNB in The Netherlands). In the literature you can also find information on risk return measurement tools (for example RaRoC) that are internally developed by insurance companies. A good reference is Tom Wilsons’ book on Value and Capital Management. In this assignment we implicitly assume that the standard formula gives a good refection of the risk profile of this insurer. Below we give a high-level description of the products of the insurance company and of the investment portfolio that the company holds to meet its future liabilities. Assets (investments) • • • • The assets of the insurance company consist of investments in the equity market and fixed income (bonds). For the equity investments the current market values are readily available. For most (public) fixed income investment this is in practice also the case, but for the purpose of this case you will determine the value yourself by projecting the cash flows and discounting these, using some simplifying assumptions, to derive the present value. This will also enable you to determine the value under different (shocked) interest rate circumstances. Liabilities • • • • The liabilities of the insurance company consist of two insurance products which are described in more detail below. The cash flows of these liabilities bear a lot of uncertainty, and you must make assumptions, for example about expected mortality and lapse rates. Lapse means that a policyholder stops the insurance. In Solvency II we use our best estimate of parameters such as mortality, lapse, and expenses to calculate the value of liabilities. The term Best Estimate Liabilities (BEL) is introduced for the present value of the liabilities in Solvency II. Examples Product 1: Annuity • • • • • • The purpose of this product is to provide for a lifetime income at retirement. This annuity has a yearly premium paid until (and including) a cut-off date (here 67) and pays out the insured sum (claim) every year a policyholder is still alive after the cut-off date. The insurance pays out an amount when a person lapses. The amount is equal to 100% of the historically paid premiums. Note that the first product incepted several years ago, so premiums have been paid for a longer time already. The relevant cash flows for the BEL are the claims + lapses + expenses – premiums paid. Only a fixed amount of cost per policy is assumed in this example. Annuity Cash Flows Illustration • • • • Premiums paid are 25 per annum until and including the cut-off age of 67 Expenses are 10 per annum for the entire length of the contract Lapses are 80% of premiums paid so far The insured sum (claim) of 100 is paid out every year the policyholder is still alive after the cut- off date See below two example cash flow projections for this product in Example 1, the premiums paid are negative as it is a liability perspective. Hence, the liability is being reduced. In Example 2, the premiums are positive because the person lapses before the age of 65. Product 2: Term life insurance • • • • • The purpose of this product is to provide a benefit for relatives or to pay off debt (like a mortgage) at the time of death of a policyholder This term life insurance has a yearly premium paid until (and including) the cut-off date (65) and it pays out the insured sum (claim) at time of death of the policyholder The insurance pays out an amount when a person lapses. The amount is equal to 100% of the historically paid premiums The relevant cash flows for the BEL are the (claims + lapses + expenses - premiums) paid Only a fixed amount of cost per policy is assumed in this example Theoretically, the insurer would earn interest rates although they are giving 100% of the paid premiums when someone lapses. Term Life Cash Flows Illustration • • • • Premiums paid are 25 per annum until and including the cut-off age of 65 Expenses are 10 per annum for the entire length of the contract Lapses are 80% of premiums paid so far The insured sum (claim) of 1000 is paid out at death See below two example cash flow projections for this product Policyholder Flow Illustration • • • We assume we start with 1000 policyholders. They are all 25 years old and in 2020Q4. Every year a proportion of the population dies, for this illustration we assume the probability of death is equal to the age/500 (25-year-old has 5% mortality probability) Every year a proportion of the population lapses (3%) • • In our example the lapse and mortality probabilities are applied to the starting number of policies, such that they can be summed The illustration below shows the flow of policyholders due to deaths and lapses for a selected range of age *Note: this example is not realistic but assume it for easiness. Week 1 → Basics of the balance sheet are calculated The balance sheet consists of both assets and liabilities, discounted to obtain the present value of each item. A simplified balance sheet is provided in the Excel file, under the sheet ‘Market Value Balance Sheet’. Please follow the following steps to calculate the basics of the balance sheet of this insurance company. The risk margin is out of scope for week 1, as we need the Solvency Capital Requirement (SCR) to obtain the risk margin. Step 1 – Sheet ‘RF Curve’ • • • • • • We will discount the cash flows of both assets and liabilities with the Solvency II (SII) risk free interest rate curve. This is a simplification as assets are normally discounted with a market interest rate curve plus asset spread. The asset spread represent the premium an investor requires to be compensated for the credit risk. The lower the credit worthiness of the issuer of the bond, the higher the asset spread. An indication of the credit worthiness is the rating of an issuer assigned by credit rating agencies. The SII risk free rate can be obtained from the EIOPA website https://eiopa.europa.eu/regulation-supervision/insurance/solvency-iitechnicalinformation/risk-free-interest-rate-term-structures We calculate the value per end of the year 2020, pick the appropriate folder of Monthly Technical Information. The base risk-free interest rate curve can be found in the Term Structure excel, take the spot rate Euro curve including VA (Volatility Adjustment). Step 2 – Sheet ‘FI Assets’ • Refer to the risk-free interest rate curve of step 1 in column D o Note that we use the liability discount curve in this case and no spread is assumed. • • • • Project the cash flows of Bond 1 in column F. Remember that these are yearly coupon paying bullet bonds, i.e., at maturity the cash flow is coupon plus notional. Calculate the discount factor in column G. Calculate the present value of cash flows in column H, by multiplying the cash flows with the discount factors. Repeat this process for Bond 2. Step 3 – Sheet ‘Mortality Table’ • • For the BEL we need a mortality rate assumption. Every two years The Royal Dutch Actuarial Association (Koninklijk Actuarieel Genootschap or ‘AG’) publishes a new Projections table, providing an insight into the expected development of life expectancy in The Netherlands, based on the most recent information at the time. The relevant website is https://www.ag-ai.nl/view.php?action=view&Pagina_Id=1007 ▪ Download the excel sheet titled “Parameters and best estimate mortality rates Projections Life Table AG2020 (Excel)” which contains the estimated mortality probabilities o Note that our example policyholders are both males o Qx is the actuarial notation for the probability that a person of a certain age and gender will die in certain year ▪ For example, Sheet ‘qx vrouwen’ cell F34 (0.02863931%) is the probability of a female person age 32 dying for the projection year 2024 ▪ Note that we valuate at end of year 2020, so the 2021 probability gives us the expected mortality rate for the first year ▪ Hint: Which probabilities should be used when considering the same female one year from now? Two years from now? Step 4 – Sheet ‘BEL’ • • • • • • • Refer to the risk-free interest rate curve found in step 1 in column D. Provide the mortality probability Qx in column G o The age and year(t) are already provided o A function could be useful to match the correct mortality probabilities with the corresponding year and age. Calculate the survival probability in column H (Px in actuarial terms), which is 1 – Qx. Do the first row now for columns J:T Calculate the expected number of deaths in column K o This is the starting number of policies times the mortality probability. Calculate the expected number of lapses in column o This is the starting number of policies times the lapse probability (conditional on that the cut-off age has not yet been reached, otherwise 0) Calculate the expected number of ending policies in column o This is the starting number of policies minus expected deaths and lapses. • • • • • • • • • Calculate the annuity payout in column o This is the starting number of policies times the insured amount times a dummy to cope with the cut-off date Calculate the expense payout in column O o This is the ending number of policies times the yearly expenses, corrected for inflation o The base expenses in the first year are given o The yearly expenses corrected for inflation are calculated with use the following formula: Corrected ExpensesT = Base Expenses * (1 + InflationT )(T-1) , o The inflation curve can be found in the Inflation Curve tab Calculate the premium income in column P o If the cut-off date has not been exceeded, this is the ending number of policies times the yearly premium. Calculate the lapse pay-out in column Q o Multiply the expected lapses with the lapse pay-out, as explained before. Calculate the total cash flow in column R o What are the relevant cash flows and are these in- or outflows for the insurer? Calculate the discount factor in column S The number of policies at year start in the second year of projection is equal to the number of policies at the end of the year of the first year of projection Calculate the BEL (present value of Best Estimate Liabilities) at t-1 in cell T18, that is in cell T18 the BEL at t=0 should be calculated Repeat these steps for product 2 o Note that the annuity payment is a mortality pay-out here Week 2 → Solvency capital requirements In this phase you will calculate the amount of capital the insurance company should hold given the risks it runs, based on the Solvency II standard formula. Please follow the following steps. Step 5 – Sheet ‘RF Curve’ • Fill in the shocked (up and down) risk free interest rates in column F and L o Use the same source as Step1 o Obtain the spot rates for the up and down shock, including VA Step 6 – Sheet ‘FI Assets’ • Fill in the counterparty credit rating of the two bonds in row 12 o You can look these up, pick a rating of either one of the large credit rating agencies (e.g. Moody’s, S&P and Fitch). Use a format of similar letters only, that is AA+ or AA1 is all AA and BAA is BBB Step 7 – Sheet ‘Mortality Risk’ • • • Fill in the SCR mortality shock in cell B15, this can be obtained from the SII delegated acts (the delegated acts will be provided) Calculate the value of liabilities similar to step 4 but adjust (columns G and W) for the mortality shock Note that a mortality shock will increase mortality probabilities Step 8 – Sheet ‘Longevity Risk’ • • • Fill in the SCR longevity shock in cell B15, this can be obtained from the SII delegated acts (the delegated acts will be provided) Calculate the value of liabilities similar to step 4 but adjust (columns H and W) for the longevity shock Note that a longevity shock will decrease mortality probabilities Step 9 – Sheet ‘Life Risk Total’ • • • • The SCRs are already calculated in the previous two steps and show up in cells C20 and C21 Insert the correlation matrix in cells C10:I16, from the SII Delegated Acts Calculate the SCR (after diversification) in Cell C5, this is similar to calculating the total variance of a portfolio with multiple assets. The MMULT formula in excel might be convenient, be sure to hold ctrl+shift+enter when using the formula Step 10 – Sheet ‘Interest Rate Risk’ • • • • • • • • • Shocked interest rates are already obtained in step 5 Refer to the asset cash flows in columns D:E Refer to the BE cash flows in columns F:G Calculate the surplus cash flows (assets minus liabilities) in column H o We can work with the surplus as we use the same discount curve for assets and liabilities Refer to the risk-free interest rate in column J Calculate the discount factors in column K, in line with previous steps Discount the cash flows, by multiplying them with the discount factor Repeat these steps for the interest up shock in columns R:X Repeat these steps for the interest down shock in columns Z:AF Step 11 – Sheet ‘Spread Risk’ • • • • • • • • • • • • • Obtain the capital requirement tables per rating and duration from the SII delegate acts. Use the formula SCR % = 𝑎𝑖 + 𝑏𝑖 ∗ 𝑐𝑜𝑟𝑟𝑒𝑐𝑡𝑒𝑑 𝑑𝑢𝑟𝑎𝑡𝑖𝑜𝑛. Where corrected duration is the duration in years exceeding a multiple of 5 years o Rows 24:28 represent 𝑎𝑖 o Rows 31:35 represent 𝑏𝑖 We derive the duration of the bonds by calculating the value of the bonds after a shock has occurred to the interest rate curve Refer to the base risk-free rate in cell E48 and below Calculate the up and down shocked curve in cell F49:G49 and below, simply add the shocksize to the base spot rate Refer to the base cashflow in cell I48 and below Calculate the three discount factors in cells J48:L48 and below Calculate the present value for the base scenario in cell M48 and below Calculate the shocked values in cells N48:O48 and below Calculate the duration in cell O101, use the following formula: o (𝑃𝑉down−𝑃𝑉up)/2∗100∗(1%/𝑎𝑏𝑠(𝑠h𝑜𝑐𝑘𝑠𝑖𝑧𝑒))/𝑃𝑉base Repeat these steps for bond 2 in columns T:AF Refer to the correct values in cells C7:H8 Calculate the capital requirement (%) for the bonds in cells I7:I8 Calculate the capital requirement (€) for the bonds in cells J7:J8 Step 12 – Sheet ‘Equity Risk’ • • Map the equity exposure in cells C8:D9, in line with the delegated acts Fill in the Symmetric Adjustment in cells F14:F15, if applicable (note that there is only one Symmetric Adjustment) o This can be obtained at https://www.eiopa.europa.eu/tools-anddata/symmetric-adjustment-equity-capitalcharge_en o Remember to use the correct reference date • Fill in the capital charges in cells I14:J15 o This can be obtained from the SII Delegated Acts o Calculate the total equity SCR in cell C20 o The formula can be found in the SII Delegated Acts Step 13 – Sheet ‘Market Risk Total’ • • Fill in the correlation matrix in columns F:K o Note that for some cells you can use a formula. The ‘A’ here is a helper cell, as there is some dependence in the correlation matrix Calculate the total market risk SCR in cell N8, you can use the matrix formula again Step 14 – Sheet ‘BSCR’ • • • Refer to the market and life SCR in column C Insert the correlation matrix for the Basic SCR in columns F:J Calculate the Basic SCR in column M o Cell M9 is the sum of column C o Cell M7 is the Basic SCR, including diversification (matrix multiplication with the correlation matrix) o Cell M8 is the difference between the two cells Step 15 – Sheet ‘Overall Results’ • • • Aggregate all results in column E Remember that pre-diversified is simply the sum of standalone SCRs, where postdiversified takes into account diversification trough the correlation matrix For simplicity we assume in this case that the amount of capital for operational risk is 0 Step 16 – Sheet ‘RM’ • • • • Refer to the relevant SCR for the risk margin in cell C6 o For this example, that is the life risk SCR Fill in the Cost of Capital (CoC) in cell C7 o This can be obtained from the SII Delegated Acts Refer to the risk-free interest rate in column D o Note that, for simplicity, we use the curve including VA in this example, while the Solvency II rules stipulate that the Risk Margin should be discounted without VA. The Risk Margin can be calculated with several methods. We use the risk driver method and we only use the BEL run-off pattern as a risk driver in this example. This will result in a Risk Margin with a similar runoff pattern as the BEL • In column F the sum of the two products’ BEL at t-1 can be referred to • Produce the Risk Margin cash flows in column H o Use the formula SCR*CoC*Riskdriver • Calculate the discount factor in column I • Calculate the present value of the Risk Margin in column J You now have completed all the steps needed to derive the Market Value Balance Sheet of the insurance company and the Solvency Capital Required. Please refer to the sheet Market value balance sheet (2) to see the results. Week 3 – Analysis Write an analysis of the balance sheet and SCR of this company. Address at least the following questions: • • • • • • • What is underlying business model for this insurance company? What are the risk exposures ranked from largest to smallest? Can this be explained from the business model? How large is the diversification benefit for this insurance company? For simplicity you assumed that operational risk is zero. Please describe (qualitatively) the type of risks that an insurance company runs from running its operations for which it should hold capital In the case the standard formula was used to derive the Solvency Capital Required. What is your view on the representativeness of the standard formula for this company? In your view, can the risk-return profile of the insurance company be improved, from a shareholder perspective, by changing the investment portfolio? Please feel invited to demonstrate this by calculating through a different asset mix. Please make explicit any return assumptions you use.
