PART I
Lecture 1: Overview of the Banking Industry and Main Trends
The Banking Sector: an Overview
- Banks are nancial institutions that provide various services to individuals, businesses, and governments.
- Main trends in banking can be categorized based on the business mix and types of clients.
- Examples of banking de nitions include commercial vs. investment banking, retail, corporate, and private
banking, and wholesale vs. retail banking.
What Do Banks Do?
- Banks generate income through various sources:
- Interest revenues: Earned from lending and investment portfolios.
- Interest expenses: Associated with funding.
- Fees and commissions: Generated from deposit service charges, trading revenue, advisory services,
brokerage, underwriting, mortgage servicing, and credit card services.
- Non-interest expenses: Include rent, wages, and other operating costs.
- Banks face di erent types of risks, such as credit (default) risk, liquidity risk, interest rate risk, market risks,
and operational risk.
- E ective risk management is essential for banks and involves credit risk management, liquidity
management, investment portfolio management, asset liability management, and capital management.
- Net Interest income and Net Non-interest income are important metrics for measuring a bank's pro tability.
Business Models and Products/Services
- Banks o er a range of products and services, including payment services, saving products (deposits),
lending, underwriting services, asset management services, advisory services, and risk management
products.
- Universal banking involves o ering a broad range of nancial products and services.
- Commercial banking serves businesses and individuals, while investment banking caters to large
corporations, governments, nancial institutions, and non- nancial institutions.
How Banks Di er
- Banks can di er based on their organizational structure, such as being a unit bank or a branching bank, or
being part of a Bank/Financial Holding Company (BHC/FHC).
- Delivery channels for banking services include traditional bricks-and-mortar branch networks as well as
internet and mobile banking.
- The size of a bank plays a signi cant role in its operations, with larger banks o ering a variety of nancial
services and having di erent internal organizational structures.
- The trend in the banking industry is towards consolidation and concentration, resulting in larger banks and
fewer institutions.
Main Trends
- In Europe, there has been a consolidation process, with a decrease in the number of banks through
mergers. The largest banks are subject to stricter supervision.
- In the United States, the banking system is multi-tiered, with community banks, regional banks, and
national/global banks o ering di erent services based on their size and area of operation.
- Banks have grown bigger and become more universal due to factors such as deregulation, cost savings,
economies of scale and scope, risk reduction through diversi cation, and widening sources of revenue.
- However, large banks may face challenges such as complexity, agency problems, moral hazard, and
empire-building incentives.
Additional Trends
- The number of branches in US banks has increased over time, although there has been a recent decline.
- Commercial banks primarily rely on loans nanced by deposits.
- Banking trends have been in uenced by deregulation, which loosened regulations in the pre-crisis years.
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Lecture 2: Funding, products and strategies (Deposit liabilities)
Background
- Deposit runs - Banking theories:
- Deposits are demandable, meaning depositors can request their funds back at any time.
- Banks face the risk of runs on their liabilities.
- Liquidity risk can be managed by holding cash and other liquid assets.
- Banks have a maturity mismatch between long-term assets and short-term liabilities.
- The threat of runs acts as a discipline device to limit risk-taking by bank managers.
- Deposits are covered by government guarantees (deposit insurance) for stable funding.
- Importance of funding structure:
- Determines the development of business and impacts bank pro tability and risks.
- A ects pro tability through interest expenses, operating costs, and income from payment services.
- In uences risk factors such as interest rate risk and liquidity risk.
Funding structure
- Flexibility vs. stability:
- Commercial banks fund their balance sheets in layers from most stable to most volatile.
- Equity-related instruments, such as stocks and subordinated debt, also contribute to funding.
- Funding types:
- Retail deposit funding / Customer deposits:
- Considered stable due to customer loyalty and deposit insurance, even though they can be
requested with short notice.
- Low sensitivity to changes in credit risk.
- Less exible to raise funds on short notice.
- Wholesale funding:
- Short-term liabilities like Fed Funds, Repos, Large CDs, and Commercial Paper.
- Less stable than retail funding.
- Short-term maturity, large amounts, and unsecured.
- Sensitive to changes in market interest rates.
- More exible during favorable market conditions.
- Volatility of wholesale funding:
- During the 2007-08 nancial crisis, wholesale funding sources became scarce.
- Banks had to sell securities at a loss or nd expensive sources of credit.
- Basel III regulations assign higher stability factor to retail deposits.
- Wholesale short-term funding has lower stability factor.
- Equity-related instruments, such as stocks and subordinated debt, also contribute to funding.
Main types of retail deposits (US):
- Checking accounts: Demand deposits that can be withdrawn at any time.
- Saving deposits: Flexible accounts with modest interest rates and withdrawal limitations.
- Time deposits: Certi cates of deposits with di erent maturities, o ering market interest rates.
Deposit rates and Monetary Policy:
- Deposit rates generally move in line with the Fed Funds rate.
- Deposit rates are typically below the Fed Funds rate, with upward stickiness and downward exibility.
- Interest-rate sensitivity varies across deposit types, with time deposits tracking the Fed Funds rate closely.
Pricing deposits:
- Deposits are a low-cost funding source due to deposit insurance and customer loyalty.
- Operating costs and fees associated with payment services contribute to pricing.
- Pricing strategies are important for client segmentation.
- Pricing can be based on cost-plus pro t margin, marginal cost, or conditional and relationship pricing.
- Regulation Q imposed limits on deposit rates, leading to the introduction of money market mutual funds.
- Deposits are usually priced separately from other services.
- Cost-plus pricing formula:
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- Pricing at Marginal Cost
- When pricing deposits at marginal cost, banks consider the cost of acquiring new funds rather than the
historical average cost. This approach helps manage interest rate risk.
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Segment-based Deposit Pricing:
- Factors in uencing deposit pricing:
- Types of customers: Di erent depository institutions have varying customer segments they aim to serve.
- Cost of serving customers: The cost associated with serving di erent types of depositors a ects pricing
decisions.
- Deposit pricing considerations:
- Interest rates and fees: Depositors receive an interest rate on their deposits but may also have to pay
fees to maintain the deposit account.
- Detailed client segmentation: Deposit pricing requires a thorough understanding of customer segments
to target high-quality customer relationships.
- Conditional and relationship pricing: Pricing strategies that depend on speci c conditions and customer
relationships.
- Relationship Pricing:
- De nition: Special treatment given to customers based on the number of services they use.
- Customers who utilize additional services may receive lower deposit fees.
- Relationship pricing aims to foster customer loyalty and reduce sensitivity to competitors' prices.
Conditional Pricing:
- De nition: A deposit structure where customers pay low or no fees if their account balance remains above
certain thresholds. Higher fees may be charged if the balance falls below the thresholds.
- Example of the Use of Conditional Deposit Pricing by Two Banks Serving the Same Market Area:
- Examples of conditions for conditional pricing:
- Number of transactions: The more transactions (checks written, deposits made, wire transfers), the lower
the fees.
- Average balance: The higher the average balance over a designated period, the lower the fees.
- Deposit maturity: The length of time the deposit is held can impact the fees.
- Cost-plus pro t & Conditional pricing: Example:
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Lecture 3: Funding, products and strategies (Non-deposit liabilities)
Background:
- The Customer Relationship Doctrine: Lenders prioritize making loans to customers who are expected to
generate positive net earnings (NPV>0).
- Loans "make" deposits: Lending decisions often precede funding decisions, as loans result in deposits.
- Liability Management: Banks seek the lowest-cost source of borrowed funds to meet customers' credit
needs.
Alternative Non-deposit Sources of Funds:
- Federal Funds Market / The interbank market:
- Banks borrow immediately available reserves from other nancial institutions and typically return them
within 24 hours.
- Types of Fed Funds Loan Agreements:
- Overnight Loans: negotiated electronically (Fedwire), returned the next day, normally not secured by
speci c collateral.
- Continuing Contracts: automatically renewed each day, normally between smaller respondent
institutions and their larger correspondents.
- The Eurosystem's equivalent is the TARGET2 system, which processes large-value payments in realtime.
- Bank A and Bank B both have accounts with a central bank. When Bank A submits a payment
instruction to TARGET2, the central bank debits Bank A's account and credits Bank B's account,
thereby settling the payment. TARGET2 then transfers the payment information to Bank B.
- Repurchase Agreements (Repos):
- Collateralized transactions where the purchaser provides marketable securities as collateral to reduce
credit risk.
- Repos in the US are often triparty and overnight.
- Haircuts: The di erence between the market value of collateral and the borrowed amount. Haircuts
depend on issuer quality, security type, and residual maturity.
- Borrowing from the Central Bank:
- Borrowing from the Federal Reserve (discount window): Loans made by the Fed must be backed by
acceptable collateral.
- Three main lending programs:
- Primary Credit: available to institutions in sound nancial condition, rate is slightly higher than the
federal funds rate.
- Secondary Credit: available at a higher interest rate and haircuts on collateral, made to institutions not
qualifying for primary credit.
- Seasonal Credit: cover longer periods than primary credit, addressed to small and medium institutions
(e.g., Deposits < $ 500 mill) experiencing seasonal swings in-deposits and loans, lowest interest rate.
- Borrowing from the European Central Bank (ECB): MRO rate (1 week), LTRO rate (1-3 month) and MLF
rate (overnight). The ECB sets these rates as part of its monetary policy.
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- Nowadays, all borrowing from the ECB is composed of funds borrowed at negative rates (deposit facility)
for three years, with the agreement that funds have to be used for new loans (TLTRO III)
- Borrowing from the Central Bank (Lender of Last Resort):
- Central banks are the Lenders of Last Resort (LOLR) and provide credit to banks during crises.
- Bagehot's principle suggests that central banks should lend freely against good collateral at a penalty
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rate during nancial crises.
The determination of what constitutes good collateral is made by the LOLR.
A collateral framework is established, which is a list of eligible securities.
Typically, government bonds are included in the list of eligible securities, but it can change over time.
During crises, the LOLR may accept lower-quality collateral, such as asset-backed securities (ABS).
In the Euro-area, bank bonds and non-marketable assets like loans can be considered eligible
collateral.
Large Negotiable Certi cates of Deposits (CD):
- Interest-bearing receipts for deposited funds with a speci ed period and interest rate.
- Di erent types: Fixed-rate CDs, Variable-rate CDs, etc.
- Important market for US and European banks.
Long-term Non-deposit Sources of Funds:
- European banks tap longer-term non-deposit funds.
- Examples: Covered bonds backed by high-grade mortgages or loans to the public sector.
- Covered bonds reached €2.7tn by the end of 2019, comprising a signi cant portion of European bank debt
securities.
Choosing among Alternative Nondeposit Sources
- Factors to Consider for Nondeposit Funding Sources:
- Relative costs of raising funds from each source, which can vary due to di erences in maturities and the
presence of collateral.
- Risk associated with each funding source:
- Interest rate risk: Fluctuations in interest rates, which increase with the duration of funding.
- Rollover risk: The inability to issue new debt to pay o existing debt. More relevant for short-term
debt, higher market rates, and weaker banks.
- Maturity for which funds are needed, considering the asset-liability maturity mismatch that banks
typically maintain.
- Size of the borrowing bank: Money market securities often have large denominations, which may not
align with the borrowing requirements of smaller nancial institutions.
- Regulatory limitations on the use of alternative funding sources: Basel III liquidity ratios (e.g., NSFR)
penalize the use of wholesale funding after the 2007-08 nancial crisis, favoring more stable retail
deposits.
Shadow Banks
- Buyers of non-deposit liabilities issued by banks are commonly referred to as shadow banks.
- Shadow banks are entities and activities outside the regular banking system involved in credit
intermediation.
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- Examples of shadow banks: Money market mutual funds, Finance and mortgage companies, Asset-backed
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commercial paper (ABCP) and Special Purpose Vehicles (SPV), and Government-sponsored enterprises
(GSEs).
Some shadow banks, like hedge funds and nance companies, issue non-deposit liabilities (such as repos)
to fund their assets.
Mutual funds issue liabilities in the form of redeemable shares, similar to bank deposits but without
insurance.
Mutual funds hold securities as assets, including potentially long-term investments like treasury bonds.
Shadow banks engage in maturity/liquidity transformation, similar to banks, but with less regulation (no
capital requirements) and without bene ts like deposit insurance and central bank liquidity support.
Mutual funds, despite their similarities to banks, can also be exposed to runs and liquidity crises.
Lecture 4: The Role of Capital
Function of Capital
- Equity capital acts as a cushion that protects the bank's liability holders from unexpected losses a ecting
the bank's assets.
- Banks require adequate capital for several reasons:
- Banks inherently take on various risks, including credit, liquidity, and interest rate risk.
- Bank funding is fragile due to the unique nature of liability holders, such as depositors.
- Bank failures can have a signi cant impact on nancial system stability and the real economy.
- Moral hazard creates a tendency for banks to hold low levels of capital, as they may expect bailouts in
case of failure. This is often referred to as the "too-big-to-fail" problem.
- Regulations are necessary to establish a link between the capital held by a bank and the risks it assumes.
- Bank capital serves other purposes:
- It acts as a long-term source of funds and provides the necessary capital for starting the business.
- It promotes public con dence among debt holders.
- It reduces con icts of interest between shareholders and liability holders by requiring shareholders to
have "skin in the game."
Determining the Amount of Capital to Hold
- Regulators prefer banks to hold higher levels of capital:
- Higher capital reduces the likelihood of bank failures.
- Riskier banks should hold more capital, while lower-risk banks may be allowed to increase nancial
leverage.
- Banks may prefer to operate with lower levels of capital than what is socially optimal:
- Lower capital increases return on equity (ROE) when all other factors remain the same.
- Banks often aim to meet the minimum capital requirements.
- Banks have a higher book debt to asset ratio (around 90%) compared to non- nancial companies
(around 25%).
- Government safety nets, such as deposit insurance, may contribute to moral hazard and lower capital
levels.
Regulatory Capital
- Regulators require banks to meet minimum capital requirements.
- The Basel Agreements (Basel I, II, and III) are a set of agreements prepared by the Basel Committee on
Banking Supervision.
- The main purpose of these agreements is to ensure that nancial institutions have su cient capital to meet
obligations and absorb unexpected losses related to i) credit risk, ii) market risk, and iii) operational risk.
- The broader capital requirement is the "Total risk-based capital ratio," which considers all three categories
of risk.
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- What Constitutes Regulatory Capital?
- Total Regulatory Capital (RC) = Tier 1 + Tier 2
- Tier 1 Capital = Common Equity Tier 1 (CET1) + Additional Tier 1 Capital (AT1)
- CET1 = Common equity - deductions
- CET1 represents the highest quality capital with the best loss absorption capacity.
- Common equity includes common shares, retained earnings, the eligible portion of minority
interests, and stock surplus (share premium).
- Deductions from CET1 capital include: Goodwill and intangible assets, Unrealized gains, Deferred
tax assets
- AT1 consists of capital instruments with no xed maturity and no incentives to redeem.
- Tier 2 Capital comprises long-term subordinated debt with a minimum maturity of ve years
- It is capable of absorbing losses in the event of a crisis (referred to as "gone-concern capital").
Basel
- Basel I (1988):
- Basel I introduced the concept of Risk-Weighted Assets (RWA) for the rst time.
- Bank assets were categorized into di erent risk groups with preassigned risk weights (0%, 10%, 20%,
50%, or 100%).
- The assigned risk weights were based on the perceived level of risk associated with each asset category.
- This approach created incentives for risk shifting, as riskier assets within the same risk group provided
higher returns while requiring the same amount of equity nancing.
- Basel II (2004):
- Basel II provided banks with two methods for determining capital requirements.
- Standard Approach (SA):
- This method is similar to Basel I, where external ratings from credit agencies are used to determine
risk weights for assets.
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- Internal Ratings-Based (IRB) Approach:
- Banks can use an internal process to assess the creditworthiness of borrowers.
- The IRB approach allows for a more accurate measurement of risk, o ering a greater number of risk
weights.
- Banks need approval from their supervisors to use the IRB approach.
- Basel III (2010):
- Basel III introduced updates to the Standard Approach.
- The bank's asset portfolio is classi ed based on the type of counter-party and type of assets.
- Within each class, the risk weights vary based on the credit rating of the counter-party.
- This approach aims to provide a more nuanced assessment of risk by considering speci c
characteristics of counter-parties.
- The objectives of Basel III include promoting a more resilient banking sector, reducing the risk of spillover to
the real economy during nancial and economic stress, strengthening transparency and disclosures, and
improving the resolution of systemically signi cant cross-border banks.
- The main measures of Basel III include signi cantly increasing the quality and level of banks' capital,
providing stricter and common guidance on risk-weighted assets (RWAs), reducing systemic risk,
increasing risk coverage, and introducing liquidity requirements.
Internal Ratings-Based
- IRB Approach
- The IRB approach is a method used by banks to assess credit risk.
- It involves using internal credit risk parameters to calculate the borrower's probability of default (PD).
- The PD is then mapped into risk weights (RW) that determine the amount of capital required to cover the
risk.
- Implementing the IRB approach requires a costly and extensive risk management system that needs to
be certi ed by regulators.
- Some banks have more than 100 di erent risk models with thousands of parameters in place.
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- Constant validation and recalibration of these models are necessary tasks for the bank's risk
management team.
- Initially, the IRB approach was introduced only by the largest banks, while smaller banks remained under
the Standard Approach (SA).
- Criticism of IRB:
- The IRB approach has faced criticism due to its high complexity and the possibility of manipulating the
system to reduce capital requirements, especially with the IRB approach.
- Evidence from German banks during the introduction of Basel II suggests that banks using IRB models
consistently underestimated risk.
- Some banks took advantage of the time taken by regulators to validate models, allowing them to have
both IRB and SA loans in their portfolio, which resulted in lower capital charges.
- Interestingly, despite having lower probabilities of default (PD), loans assessed using IRB often have
higher interest rates because the actual default rates tend to be higher.
- This indicates that banks are aware that IRB loans are riskier but keep risk weights low to lower the
capital charge, disproportionately bene ting large banks that use the IRB approach.
RWA - risks explained
- Market Risk:
- Market risk refers to the potential losses that banks may incur due to changes in market conditions, such
as stock prices, interest rates, exchange rates, and volatility.
- Examples of market risk include interest rate risk and exchange risk.
- The amount of capital required to cover unexpected losses resulting from market risk is measured using
VaR (Value at Risk) models.
- VaR represents the maximum amount a bank might lose over a speci c time period with a certain
con dence interval.
- The time horizon and con dence interval for VaR are established by supervisors.
- Operational Risk:
- Operational risk refers to the risk of loss resulting from inadequate human resources, failures of
processes and systems, or external events.
- It is the second most important risk after credit risk in the banking sector.
- Examples of operational risk include internal or external fraud, damage, aging or faulty computer
systems, and natural disasters.
- The capital requirement to protect against operational risk can be determined using the Basic Indicator
Approach (a xed percentage of gross income) or more advanced approaches based on internal models.
Lecture 5: Lending, Relevance, Policies, and Products.
Background
- Why lending is important?
- Banks’ dominant assets because they are highly pro table through interests and fees.
- Lending helps support the growth of new businesses and job creation.
- Banks act as intermediaries, reducing information asymmetry between borrowers and lenders.
- Asymmetric information
- Banks reduce information asymmetry through adverse selection (lending to low-quality clients at higher
rates) and moral hazard (ensuring borrowers ful ll loan obligations).
- Banks serve as information providers, especially for small and opaque borrowers.
- European countries rely more on bank-based systems, while the US relies on bond markets for nancing.
Types of loans
- Designing the loan agreement
- Loan agreement includes the purpose, loan terms (amount, maturity, repayment schedule), collateral,
and loan covenants.
- Loan Purpose, examples
- Working capital loans: Short-term loans for immediate business needs.
- Capital projects: Long-term investments in xed assets.
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- Mergers and acquisitions (M&A) or leveraged buyouts (LBO).
- Types of loans to businesses
- Revolving Credit/Credit lines: On-demand funding with predetermined terms, similar to a credit card.
- Term loans: Long-term loans with funds disbursed upfront and various payment structures.
- Syndicated loan: large corporate loan made a group of lenders, participants are often non-banks, such
as hedge funds.
- Types of loans to households
- Real estate loans: Used to purchase property and land, heavily securitized.
- Consumer loans: Individual loans for durable goods, education, medical care, etc., usually unsecured
and short to medium-term, highly standardized (credit analysis carried out through credit scoring system)
Caveat: Lending is pro table but costly and risky too
- Credit risk is the main source of risk in lending, referring to the borrower's inability or unwillingness to repay
the loan.
- Non-payment leads to solvency problems and liquidity risks associated with delayed payments.
Managing credit risk
- How do banks manage credit risk?
- Individual level: Evaluate borrower's creditworthiness (willingness to repay the loan) through credit
analysis, credit review, and credit workouts.
- Portfolio level: Manage loan portfolio volume and quality through origination, replacement, and credit risk
transfer tools.
- Credit analysis (the screening phase)
- Assess borrower's creditworthiness using quantitative and qualitative information.
- Consider nancial statements, credit history, management quality, and personal knowledge.
- Hard and Soft Information
- Quantitative information includes nancial statements, cash ow analysis, and credit history.
- Qualitative information focuses on management quality and personal judgments.
- Example of credit scoring: the FICO System
- FICO scores range from 300 to 850, indicating credit risk to lenders.
- Factors considered: payment history (35%), amount owed (30%), credit history length (15%), new credit
requests (10%), and types of credit used (10%).
- Why do we need risk classi cation?
- Helps with loan pricing, setting loan loss provisions, and calculating regulatory risk weights for capital
requirements.
- Role of collateral and loan covenants
- Collateral reduces adverse selection and moral hazard, providing security for loans, it includes:
- Real guarantees/assets: physical and nancial.
- Personal guarantees: owner pledges personal assets (both real or nancial).
- Loan covenants protect against changes in the borrower's operating environment, they can be:
- Positive (A rmative): indicate speci c provisions to which the borrower must adhere to and take
actions to ful ll requirement.
- Negative: indicate nancial limitations and prohibited events.
- Monitoring
- Monitoring is the process of overseeing the performance of existing loans in order to reduce moral
hazard. It involves regularly assessing various aspects of the loan and borrower's conditions, examples:
- Use of Loan Proceeds: Monitoring how the loan proceeds are being used by the borrower.
- Borrower's Condition: Assessing if there have been any changes in the borrower's nancial condition
or overall situation.
- Loan Repayment Schedule: Checking if the borrower is making timely payments or if there are delays.
- Covenant Compliance: Monitoring if the borrower has violated any loan covenants, which are speci c
requirements outlined in the loan agreement.
- Collateral Quality: Evaluating the quality and condition of the collateral provided by the borrower. This
includes ensuring it is being maintained properly and if its market value has decreased.
- Evaluation of Financial Conditions: Assessing any major events that may impact the borrower or the
industry they operate in.
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- Loan Downgrading: If problems arise, the loan may be downgraded according to the risk classi cation
scheme, and higher provisions may be required.
Non-Performing Loans (NPLs)
- Non-Performing Loans (NPLs) refer to loans that are either more than 90 days past due or unlikely to be
fully repaid. NPLs are categorized into three subcategories based on the severity of the situation:
- Bad Loans: Loans where the debtors are insolvent or in substantially similar circumstances.
- Unlikely-to-Pay (UTP): Loans where the banks believe the debtors are unlikely to ful ll their contractual
obligations unless certain actions, such as the enforcement of guarantees, are taken.
- Past-Due Exposures: Loans where interest payments are more than 90 days late but are not classi ed as
bad loans or unlikely-to-pay exposures.
- Net Non-Performing Loans (Net NPLs) = Gross Non-Performing Loans (Gross NPLs) - Loan Loss Reserve
- Loan Workouts
- Loan workouts refer to the process of recovering funds from problem loan situations, particularly NPLs.
The goal of loan workouts is to maximize the full recovery of funds. Here are the steps lenders typically
take in troubled loan situations:
- Loan Restructuring: Modifying the terms of the loan agreement to increase the probability of full
repayment. This may involve deferring interest and principal payments, extending the maturity of the
loan, liquidating unnecessary assets, or providing new funds to support the borrower.
- Procedures for Loan Recovery: Implementing strategies to recover the loan funds. This can be done
through:
- Judicial Enforcement: Seeking legal remedies through court proceedings.
- Extra-judicial Proceedings: Resolving the loan situation through negotiations between the debtor
and creditor outside of the court system.
Lecture 6: Monetary Policy. Transmission through the banking system.
Central Bank Balance Sheets
- Asset Classes:
- Securities:
- Before 2008: Mostly short-term government bonds.
- After 2008: Long-term government bonds and other asset-backed securities (e.g., mortgage-backed
securities) through Quantitative Easing (QE).
- Loans to Financial Institutions or other liquidity facilities:
- Credit provision to assist nancial institutions and stabilize markets during times of crisis.
- Liabilities Classes:
- Currency in circulation: these are banknotes and coins, that grow at constant rate with economy.
- Reserves/Deposits from banks: banks hold an account with the central bank (just like retail deposits with
banks themselves).
- There are required reserves (% of transaction-checking deposits) and excess reserves.
- There are other liabilities: reverse repos and other short-term funds (more technical adjustments).
Normal Times (US Fed): Open Market Operations
- Open market operations involve:
- Purchase/sale of securities by the Fed from a set of banks (primary dealers).
- Loans to nancial institutions through the discount window.
- Objective of Open MarThe ket Operations: In uence the money supply (bank reserves).
- Banks can exchange reserves in the Federal Funds market (a money market).
- Federal Funds market o ers safe, short-term (overnight) instruments.
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The
Federal Reserve Balance Sheet
What happens to interest rates?
Transmission of Monetary Policy
- Monetary policy a ects bank credit by providing money to banks, which they can then lend to rms and
households.
- This leads to a decrease in short-term policy rates and loan interest rates.
- Contractionary monetary policy reduces the quantity of reserves, leading to a contraction in lending and a
cooling down of the economy.
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- Unconventional monetary policy, such as Quantitative Easing (QE), involves buying di erent types of
securities (e.g., mortgage-backed securities, long-term Treasury bonds), but the principle remains the
same.
- The bank lending channel of monetary policy refers to the e ects of monetary policy on the supply of bank
credit.
- Monetary policy shocks can also in uence credit demand by a ecting aggregate demand.
Is there a bank lending channel?
- The presence of a bank lending channel of monetary policy is widely accepted.
- Traditional macroeconomic models did not incorporate bank lending, focusing on money and bonds
(monetarist view).
- Models like the IS-LM framework recognized the in uence of interest rates (i) on investment and
aggregate demand.
- Before the nancial crisis of 2007-08, standard macro-models used by central banks did not consider the
role of banks or nance. However, the crisis demonstrated the signi cance of nancial intermediation for
the real economy.
The Bank Lending Channel
- Three main theories explain the existence of the bank lending channel:
- Bank Reserve Channel:
- Traditional view of how monetary policy a ects bank credit through required reserves.
- When reserves are reduced, banks must decrease reservable deposits (checking accounts), limiting
their ability to provide credit.
- Banks can borrow other funds, but this may be more expensive and can constrain loan supply.
- This channel has been less active since the 2008 nancial crisis due to ample excess reserves.
- Bank Pro ts/Capital Channel:
- Banks earn money from the interest rate di erence between assets (loans) and liabilities (deposits).
- Positive net interest margin (NIM) results from maturity mismatch.
- NIMs are quite stable compared to a much more volatile Fed Funds rate. Stability comes from the fact
that in fact both assets and liabilities are rate sensitive (matching interest rate sensitivity with maturity
mismatch).
- Monetary policy rates a ect interest income and expenses.
- The mix of xed-rate and variable-rate assets determines the impact on net interest income.
- Decreased pro ts lead to a reduced willingness to provide new loans and a decrease in book equity or
capital, a ecting credit supply.
- Bank capital a ects the transmission channel of monetary policy.
- Banks with low capital expand credit supply (relatively more than other banks) when monetary policy
is expansionary especially to high-risk rms.
- Market Power:
- Market power refers to the ability of banks to exert in uence over interest rates and funding conditions
in the market.
- When interest rates rise, banks face certain e ects on their operations and credit supply, namely:
- Loss of Deposits and Widening Deposit Spread (the di erence between the deposit rate o ered by
banks and the Fed Funds rate).
- Decrease in Credit Supply.
- Banks with a strong branch network have market power over retail deposits. They can keep their
deposit rates relatively insensitive to market rates, leading to lower overall deposit levels.
- Recent research suggests that banks strategically reduce credit and deposits, particularly in areas with
fewer competing banks (low HHI - index that measures market concentration).
- Market power also exists in the loan market, where banks can in uence loan rates and conditions,
impacting borrowing costs and access to credit.
Unconventional Monetary Policy:
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- In the past, monetary policy mainly relied on adjusting short-term interest rates to in uence lending and
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stimulate the economy. Banks would respond to changes in interest rates by adjusting their lending
activities.
Since the 2008 nancial crisis, central banks have employed unconventional monetary policy measures
such as quantitative easing (QE) and other asset purchases.These measures involve the central bank
buying assets, such as government bonds or mortgage-backed securities (MBS), from nancial institutions.
The e ectiveness of unconventional monetary policy in stimulating lending is di erent from conventional
measures.
The type of assets purchased through unconventional monetary policy matters.
- For example, during QE1 and QE3, there was an increase in MBS purchases, which are commonly held
by banks. Banks with higher holdings of MBS tend to increase lending more, but their focus is primarily
on mortgage loans rather than corporate loans.
Increased lending driven by unconventional monetary policy may be skewed towards mortgage loans,
reducing the availability of credit for businesses.
PART II
Lecture 7&8: Banks’ Asset Quality
Classi cation and Measures
- New Classi cation since 2015 (following the completion of the Comprehensive Assessment):
- Bad Loans (Highest risk for the bank): exposures to insolvent debtors (even when the insolvency has not
been declared by a court), or in essentially similar situations, regardless of any expected loss calculation
made by the ban
- Unlikely to Pay: exposures, other than Bad loans, where according to the bank the debtor is unlikely to
pay its credit obligation in full (principal and interest), without embarking on actions such as the
realization of collateral.
- Past Due (lowest risk for the bank): exposures, other than Bad loans and Unlikely to pay, which at the
reference date are more than 90 days past-due and exceed a given materiality threshold.
- Asset Quality has impact on Loan Loss Provisions, which in turn has impact on Net Income and Capital.
Current Banking Sector Challenges
- Low interest rate environment and high competition on commission income:
- Banks face challenges due to a low interest rate environment, which reduces their interest income
contribution to revenues.
- Net interest income, representing a signi cant portion of total revenues for traditional banks, is
decreasing.
- To sustain pro tability, banks have advised clients to invest in fee-based products like asset
management and insurance, leading to aggressive growth in commission income.
- However, increased competition in fee-based products poses long-term sustainability concerns.
- Heavy cost structures:
- Banks have high xed costs and a widespread branch presence, especially in Southern Europe.
- New technologies and digital platforms require substantial investments while reducing the need for
physical branches and employees.
- Fintech incumbents present both threats and opportunities for traditional banks, requiring them to adapt
to changing customer preferences and technological advancements.
- Asset quality:
- Asset quality issues have a ected EU banks in recent years.
- Provisions on bad loans have negatively impacted banks' core pro tability.
- Non-performing loan coverage levels have reached approximately 45%.
- Resolving asset quality issues is crucial to restore con dence in the banking sector and potentially
improve its valuation.
- Capital:
- Capital ratios have improved due to extraordinary actions taken by EU banks, such as rights issues and
asset disposals.
- Stricter requirements for capital are being and will be applied to banks.
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- Asset quality and capital are interconnected, and addressing asset quality concerns is important for
maintaining su cient capital levels.
- Regulatory uncertainty and cost of regulation:
- The regulatory environment for banks is evolving rapidly, leading to increasing regulatory costs.
- National or cross-border mergers and acquisitions can be a way to address challenges, but regulatory
certainty is essential for such transactions.
- Banking sector stock re-rating requires addressing asset quality and pro tability issues.
Key Relationships
Valuation matrix
Selling non-performing loans (NPLs) from banks' balance sheets
- Bene ts:
- RWAs release: Selling NPLs reduces the amount of risky assets on the balance sheet, leading to a
release of RWAs.This release allows banks to free up capital that can be utilized for other purposes.
- Improvement of capital ratios.
- Improvement of asset quality indicators / market perception.
- Remove the risk of further credit deterioration / increase of coverage: NPLs pose the risk of credit
deterioration, resulting in potential loan losses. Selling NPLs removes the risk associated with these
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loans, it also reduces the need for additional provisions against potential losses, which can positively
impact pro ts and return on equity (RoE).
- Room for capital re-deployment on more pro table business.
- Example 1 - NPE are sold at carrying value:
-RWA = 300 (Net NPLs) * 100% (risk weight)
-Bank wants to sell NPL = 300
-P&L impact = 300 - 300 = 0
-Impact on CET 1 = 0 (no tax assumed)
-Impact on RWA = -300 (carrying value = 300)
- Example 2 - NPE are not sold at carrying value:
- If sale price is lower than the carrying value, then Carrying Value = Gross Non Performing Exposures
(Gross NPEs) * (1 – Cash Coverage) = Net Non Performing Exposure (Net NPEs).
- Sale price lower than carrying value results in the P&L loss.
-RWA = 300 (Net NPLs) * 100% (risk weight)
-Bank wants to sell NPL = 280
-P&L impact = 280 - 300 = -20
-Impact on CET 1 = -20 (no tax assumed)
-Impact on RWA = -300 (carrying value = 300)
- Example 3 - NPE are not sold at carrying value, tax = 10%:
-RWA = 300 (Net NPLs) * 100% (risk weight)
-Bank wants to sell NPL = 280 (tax = 10%)
-P&L impact pre tax = 280 - 300 = -20
-P&L impact post tax = -20 * 90% = -18
-Impact on CET 1 = -18 (no tax assumed)
-Impact on RWA = -300 (carrying value = 300)
Lecture 9: The Investment Function in Financial-Services Management
Investment Function and its Importance
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- Most banks have a primary function of providing loans, but they also allocate funds to investments in
securities.
- Reasons why banks allocate funds to investments in addition to loans:
- Liquidity: Investments in securities provide banks with assets that can be easily converted into cash if
needed.
- Risk: Diversifying the investment portfolio helps banks manage risk and reduce potential losses.
- Diversi cation: Banks allocate funds to investments in di erent geographical areas or sectors to spread
risk and avoid overexposure to a speci c market.
- Tax e ciency: Certain investments o er tax advantages, allowing banks to optimize their tax obligations.
- Stabilize income: Investments can help banks generate steady income, especially during periods of low
interest rates.
- Typically, 1/5 to 1/3 of a bank's assets are allocated to investments in securities, managed by investment
o cers.
- Common types of investment instruments held by banks include government bonds and notes, corporate
bonds, asset-backed securities (ABS), and more.
Available Investment Instruments
- Money Market Instruments
- Money market instruments have a maturity of up to one year.
- They are considered low risk but also o er low returns.
- These instruments are highly liquid and easily tradable in the market.
- Capital Market Instruments
- Capital market instruments have a maturity beyond one year.
- They are expected to provide higher returns but also come with higher risk.
- Liquidity of capital market instruments may vary depending on market volatility.
Money Market Investment Instruments
- Treasury Bills (T-bills): Short-term government bonds with high safety and liquidity. They are issued at a
discount to par value and have a xed maturity date.
- Short-Term Treasury Notes and Bonds: These instruments have longer original maturities, but when they
approach one year to maturity, they are considered money market instruments. They o er higher returns
but are also more sensitive to interest rate movements.
- Federal Agency Securities: Marketable notes and bonds sold by agencies owned or sponsored by the
federal government, such as Fannie Mae and Freddie Mac. While not always explicitly governmentguaranteed, investors believe these agencies would be rescued by Congress if in trouble.
- Other: Certi cates of Deposit, Eurocurrency Deposits, Banker’s Acceptances, Commercial Paper, and
Short-Term Municipal Obligations.
Popular Capital Market Investment Instruments
- Corporate Notes and Bonds: Corporate notes have a maturity within ve years, while corporate bonds have
maturities longer than ve years. They o er higher pre-tax yields compared to government securities but
come with higher risks. They help sustain banks' interest income, especially during periods of low interest
rates.
- Treasury Notes and Bonds: These are longer-term government securities with original maturities beyond
one year. They are issued to nance government projects and operations, and their yields are closely
monitored as indicators of market and economic conditions.
Maturity Distribution Strategies in Investment
- Once the investment o cer determines the type of securities a nancial rm should hold, the next
consideration is how to distribute those securities over di erent maturities. This decision impacts the risk
and return pro le of the investment portfolio. Here are some commonly used maturity distribution
strategies:
- The Ladder or Spaced-Maturity Policy:
- Strategy: Equally divide the investment portfolio among di erent acceptable maturities. Choose a
maximum acceptable maturity for the portfolio.
- Advantages: Simple to implement, reduces investment income uctuations, provides exibility to take
advantage of other investment opportunities.
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- The Front-End Load Maturity Policy:
- Strategy: Focus on shorter-term securities, emphasizing liquidity. Mainly a "liquidity strategy" to ensure
funds are readily available.
- Advantages: Simple strategy with strong liquidity. Limited exposure to interest rate uctuations,
minimizing potential capital losses and maximizing reinvestment opportunities.
- The Back-End Load Maturity Policy:
- Strategy: Concentrate on longer-term securities, aiming for income generation. Consider the investment
portfolio as a "source of income."
- Advantages: Maximizes income potential, especially when expectations are of falling interest rates.
- Important: Availability of alternative funding sources to meet short-term liquidity needs.
- The Barbell Strategy:
- Strategy: Combines long-term and short-term strategies while avoiding intermediate maturities. No
holdings at intermediate maturities.
- Advantages: Provides coverage in case short-term liquidity needs arise. Allows exposure to some
income potential.
- The Rate Expectation Approach:
- Strategy: Decide and adapt the investment strategy based on expectations and forecasts of interest rate
movements.
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- Advantages: Maximizes returns and opportunities based on anticipated interest rate changes.
- Point of attention: High risk and reliance on forecasts, making it a complex strategy. High transaction costs
involved in switching the investment portfolio.
Lecture 10: Liquidity and Reserves Management. Strategies and Policies
Liquidity
- Why nancial institutions care about liquidity? Financial rms strive to maintain liquidity, which refers to
their ability to access readily spendable funds at a reasonable cost when needed.
- Why does this happen? Maturity mismatch: Financial institutions often face maturity mismatch, where the
maturity of their assets (loans and investments) di ers from the maturity of their liabilities (deposits and
borrowings).
Financial Institutions' Treasury Function
- Market/funding liquidity risk: Financial rms need to manage the risk associated with market liquidity and
their ability to fund their operations.
- Regulatory Framework: Financial institutions adhere to regulatory requirements, such as maintaining a
liquidity bu er, to ensure they can meet their liquidity needs.
- Forecasts: Financial institutions make forecasts to predict their future liquidity requirements and take
proactive measures to prevent liquidity risks.
- Liquidity rescue plan: Financial institutions develop contingency plans to address liquidity shortages, such
as selling assets or borrowing from central banks, while maintaining a pro t-oriented approach.
Net Liquidity Position
- The treasurer of a nancial institution must monitor the net liquidity position, which is in uenced by various
factors.
- Supplies of Liquidity Flowing into the Financial Firm:
- Positive changes in liabilities: In ows of deposits, issuance of bonds, etc.
- Negative changes in nancial assets: Loan repayments by customers, sale of securities, etc.
- Sale of real assets: Disposal of real estate.
- Borrowings from the money market/capital increases: Accessing short-term borrowings or raising
capital.
- Revenues from non-deposit services: Commissions, dividends, etc.
- Demands on the Financial Firm for Liquidity:
- Negative changes in liabilities: Withdrawals of deposits, repayment of bonds, etc.
- Positive changes in nancial assets: Granting loans, acquisition of securities, etc.
- Acquisition of real assets: Purchase of real estate.
- Financial costs: Payment of dividends to stockholders, interest expenses.
- Non- nancial costs/operating expenses: Salaries, rent, etc.
- Taxes: Payment of taxes.
- These various sources of liquidity demand and supply come together to determine each nancial rm’s net
liquidity position at any moment in time.
-Liquidity De cit: Lt < 0
-Liquidity Surplus is Lt > 0
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Liquidity Management Strategies
- Strategy #1: Asset Liquidity Management (or Asset Conversion)
- Liquidity is stored in assets, primarily cash and marketable securities.
- When liquidity is needed, selected assets are converted into cash to meet the cash demands.
- Liquid assets should have three key features: ready marketability, stable prices, and reversibility.
- Transaction costs, low returns, and foregone income from selling assets are associated with this strategy.
- Strategy #2: Borrowed Liquidity (Liability) Management
- Funds are borrowed to cover anticipated liquidity needs.
- Advantages include borrowing only when needed, no need to change asset composition, and exibility
to borrow more as needed.
- This strategy carries risks due to volatile interest rates and changes in credit availability.
- Lehman Brothers' collapse serves as an example of the challenges faced when purchasing liquidity.
- Strategy #3: Balanced Liquidity Management
- This strategy combines elements of Strategy #1 and Strategy #2.
- Some liquidity needs are met by holding liquid assets, while others are addressed through borrowings.
- Short-term borrowing addresses unexpected liquidity needs, while planned and forecasted liquidity
needs are speci cally addressed.
Estimating Liquidity Needs
- Methodology #1: Sources and Uses of Funds Approach
- Forecasts loans demand and deposit availability for a given time period.
- Step 1: Loans and deposits must be forecasted
for a given time period. Common
methodologies consider trend, seasonality, and
cyclicality in forecasting.
- Step 2: The estimated change in loans and
deposits must be calculated.
- Methodology #2: Structure of Funds Approach
- Step 1: Classi cation of the banks’ liabilities
based on liquidity.
- Step 2: Setting up liquidity reserves against
those liabilities.
- How to estimate liquidity needs? By calculating
weighted probabilities, as showed on the right:
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- Methodology #3: Liquidity Indicator Approach
- Estimating liquidity needs based upon experience and industry averages by adopting certain liquidity
indicators, such as cash position indicator: cash / total assets, liquid securities indicator: cash and cashlike securities / total assets.
Lecture 11: Analysis of Banks’ Financial Statements (1/2)
Key Stakeholders
- Various stakeholders are interested in analyzing banks' nancial statements, including:
- Regulators
- Investors (debt and equity)
- Auditors
- Equity Research Analysts
- Corporate Finance Advisors / Investment Banks
- Competitors
- Clients (potentially)
Analyzing Financial Statements and RoE Limitations
- Return on Equity (RoE) is a commonly used measure to assess a bank's performance and returns for
shareholders.
- RoE = Net Income / Shareholder's Equity
- However, relying solely on RoE to evaluate a bank's performance may lead to a limited assessment. RoE is
in uenced by other factors and should be seen more as an immediate benchmark communication tool
between banks and markets rather than a meaningful assessment tool of the quality, soundness, and
performance of a bank.
- Limitations:
- It doesn't consider the bank's riskiness in terms of capital and leverage.
- It may include extraordinary and non-recurring items that distort the true performance.
- It depends on the bank's assessment of credit quality, which may not accurately re ect the asset quality.
- It has a limited time horizon and may not re ect sustainable pro tability.
Which Financial Statements Need to Be Analyzed?
- The choice between consolidated and parent company accounts depends on the objectives of the
analysis.
- Generally, to gain a comprehensive understanding of a banking group's nancial performance and
situation, consolidated accounts should be used as a basis for the analysis.
Banks' Financial Statements: What to Expect
- Funding: Information about the sources of funding for the bank, including deposits, borrowings, and
capital.
- Lending: Details about the bank's loan portfolio, including loan quality, provisions for loan losses, and
interest income.
- Finance/Investment Function: Information about the bank's investment activities, including securities
holdings, interest income, and gains/losses on investments.
- Financial Services: Insights into additional services provided by the bank, such as payment services,
advisory services, and other fee-based activities.
- Stakes: Disclosure of any signi cant ownership stakes or investments held by the bank.
Key Principles for Preparing Financial Statements
- The International Accounting Standards Board (IASB) is responsible for developing and updating
international accounting principles known as IAS/IFRS.
- In Europe, the implementation of IAS/IFRS is governed by Regulation (EC) 1606/2002, although member
states may apply di erent accounting principles under certain circumstances.
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- In Italy, the adoption of IAS/IFRS is required for publicly traded companies, companies issuing nancial
instruments to the public, banks, nancial intermediaries, and insurance companies.
- Smaller companies may be exempt from full IAS/IFRS adoption.
- The Bank of Italy provides instructions for the preparation of consolidated nancial statements, including
mandatory forms and contents of the nancial statement notes.
- The nancial statement items are assigned speci c codes for reporting purposes.
Key Components of Banks’ Financial Statements
Balance Sheet Reclassi cation Methodology
- The balance sheet can be reclassi ed in di erent ways to cater to the objectives and perspectives of
stakeholders analyzing the document.
- One common methodology is the reclassi cation based on Interest Earning Assets (IEA) and Interest
Bearing Liabilities (IBL).
- This approach separates assets that generate income from those that do not and separates liabilities that
do not have a nancial cost from those that do.
- Interest Earning Assets (IEA): Key Components
- The majority of a bank's IEA consists of loans to customers, nancial assets, and equity investments.
- The bank is likely active in the traditional banking sector, and the credit function and nance are
important areas to scrutinize when assessing the bank.
- Interest Bearing Liabilities (IBL): Key Components
- Banks typically nance their activities through three funding channels.
- From retail customers: Re ected as "Due to Customers" or "Customer Deposits."
- From other banks: Re ected as "Due to Banks" or "Interbank Funding."
- From the wholesale market: Re ected as "Securities Issued."
Loans to Customers
- Loans to customers on the balance sheet are presented on a "net" basis, which means they are shown
after deducting the loan loss reserve.
- Analyzing the loan book can provide further details about the bank's activities, such as:
- Geographical breakdown of loans: Helps understand the bank's presence in di erent regions and the local
economies in those areas.
- Breakdown of loans by clients: Di erentiates between retail customers, large corporates, SMEs, etc.
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- Breakdown of loans by product: Highlights the types of loans o ered, such as mortgages, consumer credit,
etc.
- Breakdown of loans by sector: Shows the distribution of loans across sectors like manufacturing, travel
industry, etc.
- Customer loans reported on the balance sheet do not include any o -balance sheet exposures the bank
might have. Analyzing o -balance sheet exposures is relevant once the bank's business model is identi ed.
Funding
- Customer Deposits / Due to Customers:
- An important indicator of the bank's funding strategy.
- Mainly includes current accounts and time deposits.
- Generally stable compared to wholesale funding.
- Di erent types of deposits have varying costs of funding.
- Changes in customer deposits indicate the bank's reputation and reliance on the retail market.
Signi cant deposit out ows can occur during nancial crises, leading to a "bank run" scenario.
- Due to Banks / Interbank Funding:
- Indicates the extent to which the bank relies on funding from other banks.
- Less stable source of funding compared to customer deposits.
- Con dence among nancial institutions can impact interbank funding availability.
- Securities Issued:
- Debt issued by the bank in the market and subscribed by investors.
- Usually carries a higher cost of funding compared to other sources.
- Medium-term source of funding for the bank.
Lecture 12: Analysis of Banks’ Financial Statements (2/2)
Business Model & Pro tability
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Capital & Leverage
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Asset quality
PART III
Lecture 13: Interest rate risk (1/2)
Straight Bond Overview
- A straight bond, also known as a plain vanilla or bullet bond, represents a borrowing agreement between an
issuer (borrower) and a holder (lender).
- The issuer sells the bond to the holder in exchange for cash.
- The bond agreement includes speci c payment obligations and terms.
- Payments, known as coupon payments, are made by the issuer to the holder at speci ed dates according
to a coupon payment schedule.
- The bond has a maturity date, at which the issuer pays the holder the bond's par value (or face value) to
extinguish the debt.
- If the bond does not have coupon payments, it is called a zero-coupon bond.
- The bond can be classi ed as either xed rate/income or variable rate/income, depending on whether the
payments are xed or dependent on factors like interest rates or economic variables.
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Notation Used
- R > 0: Annual interest rate assumed to be constant.
- Semiannual interest rate: R/2
- Quarterly interest rate: R/4
- N: Bond maturity, indicating the number of years until the bond expires.
- F: Face value of the bond, which is paid at maturity. Typically normalized to $100 or $1,000.
- c: Annual coupon rate that determines the coupon payment at the end of each period, based on the
payment frequency.
- Yearly payment frequency (e.g., Bund, OAT): cF
- Semiannual payment frequency (e.g., US Treasuries, BTP): cF/2
- Quarterly payment frequency (e.g., US corporate bonds): cF/4
- P: Bond price, representing the current market value of the bond.
- The relation between a bond’s price P and interest rate R is negative.
Bond pricing (annual coupons)
- Discount factor:
- Cash ow received at the end of time t:
- Present value of CFt: (
- Bond price:
- Bond price with m payments per year:
Amortization
- For bonds, the principal/face value is re-paid (in full) at maturity.
- A handful of bonds (usually, emerging markets sovereigns/corporates, called amortizing/sinkable bonds)
gradually repay the principal over time according to a pre-speci ed amortization schedule.
- Provided the coupon is xed, these continue to be xed-income securities, although cash ows re ects
coupon payments (on a decreasing face value) as well as principal repayments.
- Amortizing loans:
- Bullet loans require principal amount repayment at maturity (zero-coupon bonds).
- Interest-only loans require principal amount repayment at maturity plus interest payments during the
life of the loan (Fixed-coupon bonds).
- It is most typical that loans are amortizing in that the principal amount is gradually repaid during the life
of the loan.
- Often used amortizing schemes prescribe either equal installments (French-type) or equal principal
repayments (Italian-type).
Relationships
- Inverse relationship: as rates increases, price falls;
- Convexity: an increase in R results in smaller price decline than the price gain associated with a decrease
of equal magnitude in R.
- Maturity: prices for long maturities bonds are more sensitive to interest rate changes than those of short
maturities.
- Coupon: prices for high coupon bonds are less sensitive to interest rate changes than those of low coupon.
- Interest rate R: prices for high R bonds are less sensitive to interest rate changes than those of low R
bonds.
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Duration (D)
- Macaulay duration: The duration for a bond with c coupon payments, N years to maturity and price P
(equivalently, interest rate R) is:
- for annual coupon payments:
- for m coupon payments per year:
- Duration measures the e ective maturity of a bond.
- The duration of a zero-coupon bond equals its maturity: D = M.
- Properties of a duration:
- duration decreases with R
- duration decreases with coupon
- duration usually (except for deep discount bonds, c << R) increases with maturity but at a decreasing
rate
Duration and maturity for m = 1 and R = 10%.
-black: zero-coupon bonds
-red: below par (c = 1%)
-green: at par (c=10%)
-blue: above par (c=20%)
- Duration is a good measure of the sensitivity of a bond's price to changes in interest rates. Therefore
duration measures the interest rate elasticity of the security's price to small interest rate changes.
- Modi ed Duration (MD) - a local measure of bond price risk:
- Bond’s percentage price change:
- Dollar duration:
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Lecture 14: Interest rate risk (2/2)
Duration of a portfolio of assets
- This is an approximation to ptf duration. In order to hold true exactly, one needs all securities' cash ows
(coupons/installments) to be synchronized, eg. semi-annual payments with rst payment, say, in six
months.
- Change in the asset value (the same for liabilities, but note that DA ≠ DL):
- Change in the market value of equity for a change in interest rates is:
-k is the bank leverage (i.e. the amount of borrowed funds (rather than
the owners' equity) used to fund its asset portfolio)
-[DA DLk] is the Duration Gap (note that DA = DLk)
-Duration Gap can be reduced to zero (perfect immunization):
Implications
- The larger the duration gap [ DA DLk ] (in absolute terms) the more exposed is the bank to interest rate risk.
- Positive equity holders loose when interest rates increase.
- The larger the interest rate shock [ ∆R / (1 + R ) ], the larger the bank’s exposure.
- A bank’s manager can insulate the balance sheet against interest rate risk by reducing the (abs. value of
the) duration gap.
Convexity adjustment
- Error in the duration model gets larger with larger interest rate shocks. The duration model under-predicts
the bond price increase (when rates decrease) and over-predicts the bond price decrease (when rates
increase).
- A better approximation can be obtained correcting the duration model with the convexity adjustment:
Lecture 15: Futures
Derivatives
- A derivative security is a security with payo s explicitly linked to the payo s of some other asset
(underlying security).
- A forward contract is an agreement between a buyer (long position) and a seller (short position) at the
present time (settlement date, date 0) to exchange the underlying asset at a speci c future time (maturity or
delivery date, date T) for cash (forward price, PF).
- Notation:
- Maturity of the derivative: T.
- If the underlying is a bond, then it has maturity: N>T
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Forwards
- Notation:
- PF: Forward price.
- PT: Price at maturity.
- At maturity, the buyer of a forward makes a pro t of: PT - PF .
- At maturity, the seller of a forward makes a pro t of: PF - PT .
Futures
- A futures contract is an agreement between two parties to buy or sell an asset (commodity, currency, stock
index, etc.) at a predetermined price and date in the future.
- The contract is arranged through a centralized exchange, such as CBOE, CME, or Borsa Italiana.
- Futures contracts are similar to forward contracts, with some key di erences.
- Standardization: The terms of a futures contract, including the underlying asset, maturity date, contract
size, trading hours, and delivery arrangements, are determined by the exchange.
- Marked-to-Market: Futures contracts are marked-to-market on a daily basis, meaning that the changes
in the value of the contract are re ected and settled between the buyer and seller each day.
- Exchange as Counter-party: The exchange acts as the counter-party for both parties involved in the
futures contract, reducing counter-party risk.
Hedging
- There are two types of hedging:
- Microhedging: Banks can use futures contracts to hedge the interest rate risk of individual bonds they
hold in their portfolio. This allows them to mitigate potential losses due to changes in interest rates.
Equation: ∆B + ∆F = 0 .
- Macrohedging: Banks can also use futures contracts to hedge the duration gap of their entire balance
sheet. The duration gap measures the sensitivity of a bank's assets and liabilities to changes in interest
rates. By taking o setting positions in futures contracts, banks can manage their overall interest rate risk.
Equation: ∆E + ∆F = 0 .
- Forward hedging (short hedge): selling the bond forward (maturity T) for a price PF . Change in the value of
the hedged position is:
- In case of forwards, the value of the hedged position is not a ected by interest rates movements, in
futures, it is. Hence, in case of futures, it is crucial to hedge against interest rate risk.
-∆B: Change in the bond price (change in spot position).
-D: Duration.
-B: Bond price (old).
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- Price quote: USD per $100 of face value Notional amount: Size (units) * Bond price
Macrohedging
- Fully hedging prescribes that gains/losses in equity value are o set by losses/gains in futures position
according to: ∆E + ∆F = 0 .
- What futures position shall the manager take? If the equity value is decreasing (∆F < 0), the manager should
go short. If the duration gap is positive, then changes in interest rates are hedged by a short futures hedge.
- How many futures contracts should he short?
Complication: basis risk
- Interest rates on spot and futures position may not be perfectly correlated (br - basis risk).
- Immunization, as before, is achieved setting NF such that ∆B + ∆F = 0 (microhedging) or ∆E + ∆F = 0
(macrohedging).
Lecture 16: Options and swaps
De nitions
- Call option: A call option contract, speci cally a European call option, grants the holder the right (but not
the obligation) to purchase the underlying asset at a predetermined price (known as the exercise price or
strike price, X) on a future date (referred to as the maturity date or expiration date, T). The exercise price is
xed at the present time (date 0), and the holder pays a premium (C) upfront for acquiring this right.
- Put option: A put option contract, also a European put option, provides the holder with the right (but not the
obligation) to sell the underlying asset at a speci ed price (exercise price or strike price, X) on a future date
(maturity date or expiration date, T). Similar to a call option, the exercise price is determined at date 0, and
the holder pays a premium (P) upfront to obtain this right.
- Distinctions between Options and Forwards/Futures:
- Premium and Cash Payment: Options require the buyer to pay a premium upfront, whereas for futures,
cash settlement occurs at maturity.
- Right vs. Obligation: Options provide the holder with the right (but not the obligation) to buy or sell the
underlying asset, while futures involve an obligation to buy or sell.
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Interest rates futures - US treasuries
- Underlying asset: 2YR, 5YR, 10YR T-note, T-bond
- Size/minimum lot: $200,000 (2YR), $100,000 (others) of face value (equivalently, 2,000 and 1,000
units)
- Delivery date: March, June, September, December (3 quarters); last business day of contract
month
- Delivery method: physical (maturity range, e.g. maturity 15-25 years for T-bond futures)
- Non-linearity of Pro ts: The pro ts of options are non-linear, whereas futures o er linear pro t potential.
- Exchange-Traded Options:
- Similar Features to Futures: Exchange-traded options share features like standardization and daily
marking-to-market.
- Absence of Margin System: Unlike futures, options do not require a margin system since the premium is
paid at settlement.
- Collateral Requirements for Naked Options: Naked option positions (selling options without owning the
underlying asset) usually have collateral requirements, which are more speculative in nature.
Notation
- X: Exercise Price or Strike Price
- T: Maturity Date or Expiration Date
- C / P: Call / Put option premium
Proft / loss
- Buyer of a call option
- If bond value at T ≥ X: Pro
- If bond value at T < X: Pro
- Seller of a call option
- If bond value at T ≥ X: Pro
- If bond value at T < X: Pro
- Buyer of a put option
- If bond value at T ≤ X: Pro
- If bond value at T > X: Pro
- Seller of a put option
- If bond value at T ≤ X: Pro
- If bond value at T > X: Pro
t = (bond value at T - X) - C
t=-C
t=-C
t = (bond value at T - X) - C
t = (X - bond value at T) - P
t=-P
t=-P
t = (X - bond value at T) - P
Options hedging
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Plain vanilla IRS
- A plain vanilla interest rate swap (IRS) is a nancial agreement between a buyer and a seller. It involves the
exchange of cash ows at predetermined future dates until the maturity of the swap. The cash ows are
based on interest payments calculated on a notional value.
- Components of a Plain Vanilla IRS:
- Swap Buyer (Fixed Leg): The swap buyer makes periodic xed-rate payments.These payments are
based on a predetermined xed rate known as the swap rate.
- Fixed-Rate Payments = Fixed rate * (Notional Value / m)
- Swap Seller (Floating Leg): The swap seller makes periodic oating-rate payments. The oating rate is
usually based on a reference rate (e.g., LIBOR) plus a xed rate.
- Floating-Rate Payments = (Reference Rate + Fixed Rate) * (Notional Value / m)
- IRS contracts are traded OTC.
- The notional value is the predetermined value used to calculate the interest payments. It does not actually
change hands between the buyer and the seller.
- Interest rates in IRS contracts are expressed on an annual basis. If there are m payments per year, each
periodic cash ow is calculated as (rate/m), where rate is the annual interest rate.
- The oating rate payment at each future date (t+1) is determined by the reference rate observed at the
previous date (t).
- IRS contracts also specify a day count convention, which determines how interest calculations are
performed.
Floating Rate Note (FRN)
- A Floating Rate Note (FRN) is a type of xed-income instrument where the interest rate is linked to a
reference rate, such as LIBOR.
- For FRNs, the rst cash ow (CF1) is xed, similar to other xed-income instruments.
- FRNs are known for their annual repricing feature, where the interest rate adjusts annually based on the
prevailing reference rate. Due to the nature of FRNs repricing annually, their duration is relatively low.
- The interest rate risk associated with FRNs is primarily related to the xed cash ow (CF1), and the
Macaulay duration is equal to the time until the next payment.
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Hedging with IRS
- Hedging with IRS means nding a swap position so that its change in value, ∆S, when rates change
satis es: ∆E + ∆S = 0
- Duration of a swap buyer (negative): D oat - D xed
- D oat is duration of a ( oating rate) bond with: same duration of swap-payment interval (in the example, 6
months). Maturity and oating rate are irrelevant (for duration determination).
- D xed is the duration of a ( xed rate) bond with: same maturity of IRS, coupon rate equal to swap rate,
and coupon payment frequency identical to IRS payment frequency.
- Duration of a swap seller (positive): - ( D oat - D xed )
- As long as ed D oat - D xed < 0 (the typical case), then as rates rise, the present value of xed payment falls
more than the present value of oating payments. Thus, the swap buyer gains (and swap seller loses) in
present value terms.
Lecture 17: Market risk (1/2)
Introduction
- The banking book refers to instruments held by banks that are expected to be held until maturity, such as
real estate holdings, commercial and industrial credits, and derivatives used for risk hedging purposes.
- On the other hand, the trading book consists of instruments held by banks for short-term resale, pro ting
from short-term price movements, arbitrage opportunities, and hedging risks associated with these
activities.
- The Basel Committee on Banking Supervision provides guidelines for distinguishing between the banking
book and the trading book.
Motivating Example: LTCM and On-The-Run Bonds
- Long-Term Capital Management (LTCM) was a hedge fund management company that focused on
convergence trading and xed income arbitrage.
- They utilized a strategy involving the purchase of o -the-run (OTR) bonds and the sale of on-the-run (OTR)
bonds with similar maturities.
- OTR bonds have a higher price and lower yield compared to similar old (o -the-run) bonds due to liquidity
preferences.
- The strategy aimed to pro t from the convergence of valuations between the two bonds over time.
- However, in August 1998, Russia defaulted on its local currency bonds, causing a ight to quality in the
market.
- As a result, there was an increase in prices for the most liquid treasuries (including on-the-run bonds) and a
decrease in prices for less liquid treasuries (including o -the-run bonds).
Market Risk
- Market risk refers to the risk associated with changes, particularly extreme changes, in market conditions
that can impact the value of a portfolio or trading book.
- Measuring market risk requires a speci c focus on downside (or tail) risk, which answers the question,
"How bad can things get?"
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- Classical risk measures like standard deviation from portfolio theory do not fully capture downside risk.
- Two common approaches to measuring market risk are Value at Risk (VaR) and Expected Shortfall (ES).
- Value at Risk (VaR):
- VaR is a widely used measure for quantifying the maximum potential loss of a portfolio or trading book
over a speci ed time horizon, with a given con dence level.
- Parametric approach (JP Morgan/Reuters Riskmetrics): This approach uses statistical methods to
estimate VaR based on the mean and standard deviation of portfolio returns.
- Historical approach: This approach uses historical data to estimate VaR by analyzing the distribution of
past portfolio returns.
- Monte Carlo simulation approach: This approach involves generating random scenarios and simulating
portfolio returns to estimate VaR.
- Expected Shortfall (ES):
- Expected Shortfall is another risk measure that provides an estimate of the average loss in the tail of the
distribution, beyond the VaR.
- ES calculates the average value of losses that exceed the VaR, considering the tail of the distribution.
- ES provides a more comprehensive assessment of the potential losses compared to VaR alone.
VaR
- VaR depends on α (con dence level) and N (holding period): VaR(α,N)
- We will use: VaR(0.95,1)
- VaR is identi ed as a positive number although it corresponds to a loss. Higher con dence level α (keeping
N xed) corresponds to larger VaR values, i.e. more adverse conditions.
- Uses of VaR:
- Micro/internal: Bank wants to limit the risks taken by its traders, e.g. a VaR(0.99,1) less than $10 mln.
- Macro/external: Regulator wants to limit the risk taken by the banking system.
- Parametric (or model-building) approach assumes that:
- Asset/portfolio returns are normally distributed with mean μ and standard deviation σ
- Asset/portfolio returns are independent and identically distributed (i.i.d.) across time
Lecture 18: Market risk (2/2)
Portfolio VaR
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- Portfolio volatility:
- Unless the assets are perfectly positively correlated, then VaR of a portfolio is less than the sum of
individual VaRs. This is due to diversi cation.
- Adding more and more assets requires knowledge (estimation) of individual volatilities as well as
correlations. This increases the complexity of the problem as the portfolio grows larger and larger.
- For FX there is not much one can do each currency is a source of risk. For other asset classes, thinking in
terms of risk factors helps in simplifying the variance-covariance matrix structure (delta-normal method).
Delta-normal method
- For equities we use:
-W0: value of trading position in stocks
-βp: portfolio beta
-σm: standard deviation of the market
-α-th centileSN = 2.33
- For the xed income portfolio (bonds) we use:
- When aggregating across asset classes, one has to estimate correlations among risk factors (on top of their
volatilities) as well to compute portfolio VaR.
- A further re nement is the delta-gamma method, which corrects for non-linear e ects (think of convexity for
bonds). This is particularly relevant for portfolios that include (non-linear) derivatives such as options.
Expected shortfall
- VaR is a single number which, under the parametric approach, hinges upon normally distributed asset
returns.
- Expected shortfall (also called expected tail loss) is a measure of market risk that estimates the expected
value of losses beyond a given con dence level. For given α it is the area to the left of Π.
- Formally, after xing con dence level α and holding period N, it is given by:
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PART IV
Lecture 19: Risk and insurance
Risk De nition
- Risk is the possibility of a future uncertain event or the possibility of an unfavorable uncertain event
occurring, which may result in unexpected economic outcomes.
- Risk can be broken down into di erent concepts:
- Risk unit: The person, object, activity, or situation in relation to which exposure to risk exists.
- Peril: The aleatory event that could impact the risk unit and create some form of e ect.
- Risk exposure: The circumstances that connect the risk unit to the peril and determine the exposure to
the risk.
- Damage: The type of e ect that the combination of peril and exposure could generate for the risk unit.
- Insurance primarily deals with "pure risks," which are uncertain events that only involve the possibility of
loss, without potential for gain.
- Pure risks can be divided into: Property risk, Liability risk, and Personal risk.
- Depending on the category, we have di erent types of insurance coverages and di erent management
methodologies. In the context of insurance business these types of insurance coverages are usually
called lines of business.
- Speculative risks, on the other hand, involve events that can generate either a loss or a pro t.
The Insurance Process
- The insurance process involves the collection of advance contributions (premiums) from a group of
individuals exposed to the same risk in order to compensate those who experience losses from the
unfortunate event.
- There are various ways individuals can handle pure risks:
- Retaining the risk: Choosing to do nothing and accepting the potential consequences.
- Avoiding the risk: Taking actions to eliminate exposure to the risk.
- Reducing the risk: Taking measures to lower the probability or intensity of the risk.
- Saving: Accumulating resources to cover or partially cover any potential loss resulting from the risky
situation.
- Transferring the risk: Shifting the risk to another party through the insurance process.
- Key features of the insurance process:
- Transferring risk from an individual to a group of individuals.
- Sharing losses equitably among all members of the group.
- The insurance process relies on determining the probability of uncertain future events.
- Important concepts in the insurance process:
- A posteriori probability: Probability calculated after studying past empirical data.
- Law of large numbers: The observed frequency of an event approaches the a priori probability as the
number of trials increases.
- A priori probability: Probability based on the underlying conditions that cause the event.
- The a priori probability can be approximated using the a posteriori probability thanks to the law of large
numbers.
- Challenges in the insurance process:
- Limited sample size and statistical observations can a ect the reliability of estimates.
- Smaller risk units, greater dispersion of individual values, and less stable risk conditions can also impact
the accuracy of estimates.
- Insurers rely on statistical estimation to predict the probability of certain events occurring based on past
observations.
- Calculations:
M
- Expected losses (weighted average): x1 p1 + x2 p 2 + ... + x M p M = xi pi
å
M
i =1
- Standard deviation: å pi (xi - µ )
2
i =1
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-The pooling arrangement of similar and uncorrelated
rms does not change rms’ expected cost, but it
reduces the standard deviation of costs from €
1,000,000 to € 707,000
-This means that possible accident costs become more
predictable.
- As the number of participants in the pooling arrangement increases:
- the probability of the extreme outcomes decreases;
- the probability that average losses (the amount paid by each
participant) will be close to € 500,000 increases;
the probability distribution of each rm’s cost becomes more bell
shaped.
- Pooling arrangements in insurance have two important e ects when
losses are independent and equally distributed among risk units:
- The standard deviation of each participant's cost decreases,
reducing the risk of gaps between expected and actual losses. This is known as the law of large
numbers.
- The probability distribution of losses becomes more bell-shaped and approaches a normal distribution
as the number of participants increases.
- While identical distribution and independence of risk units are not essential, they still contribute to risk
reduction:
- Adding participants with di erent loss distributions still leads to a decline in the standard deviation of
average loss.
- Pooling arrangements can reduce risk for each participant even if losses are not fully independent, as
long as they are not perfectly positively correlated.
-
- However, the presence of perfect positive correlation (where
losses move in perfect sync) does not reduce risk, while less
than perfect positive correlation reduces risk but not to the
same extent as independent losses.
Mutual insurance plans
- Unfunded” mutual insurance plan: a possible solution is that all of you agree to share (ex post) total losses
incurred by the “pool” of rms on some equitable basis.
- Funded mutual insurance plan: all of you agree to make an advance payment for predicted future losses on
some equitable basis.
- As each participant’s risk provision (advance payment) becomes larger than the expected loss, the
probability that the overall provision is able to fund the pool’s actual total losses increases.
Insurance features
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Individual vs pooling risk management solutions
- Example:
application of the law of large numbers and reduces individual risk.
- Homogeneity: The exposed units should have similar probability distributions of risk. This enables the
calculation of aggregate risk and facilitates risk pooling.
- Independence: As much as possible, the exposed units should be independent of each other, meaning
the occurrence of a loss for one unit does not a ect the occurrence of losses for others. Independence
reduces the potential for correlated losses.
- Conditions for insurability:
- De nite or Measurable Loss: The loss resulting from the risk must be clearly de ned and quanti able.
This allows for the determination of appropriate insurance coverage and indemni cation.
- Fortuitous or Accidental: The loss must be caused by an unforeseen or accidental event, rather than a
deliberate or intentional act. Insurance is designed to cover unexpected losses and not intentional acts.
- Limitations of the insurance process:
- Catastrophic Events: The insurance process may not work well when losses are caused by catastrophic
events that a ect a large percentage of exposure units simultaneously. In such cases, the dependence
among exposure units increases, making it challenging to accurately assess and manage risk.
The Insurance Firm
- The Insurance Firm as a Pooling Risk Management Solution:
- The insurance rm acts as an arranger of a pooling arrangement to manage risks.
- The pooling solution can be implemented by the participants themselves or by a third party, which is the
insurer.
- The insurer performs various tasks related to managing the pooling arrangement.
- Role of the Insurer:
- Collection of Exposure Units: The insurer collects information about the units exposed to risks and brings
them together in a portfolio.
- Computation of Insurance Premium: The insurer calculates the advance payment required from the
participants, known as the insurance premium.
- Management of Monetary Resources: The insurer handles the collected premiums and manages the
nancial resources.
- Claims and Bene ts Payments: The insurer pays out claims and bene ts to policyholders as they
become due.
- Key Tasks of the Insurer:
- Pooling of Risk Units: The insurer brings together numerous, equally distributed, and independent risk
units in a portfolio through underwriting activities.
- Calculation of Premium: The insurer determines the premium to be collected from participants to cover
potential losses from the risk units in the portfolio.
- Investment Management: The insurer invests the collected resources considering future expected
payments, including their amount, timing, and uncertainty.
- Conditions for E ective Insurance Process:
- High Number of Risk Units: A large number of units exposed to the same risk within the group is
essential.
- Qualitative Homogeneity: Risk units in the portfolio should have similar characteristics.
- Quantitative Homogeneity: Risk units should have similar quantitative measures of risk.
- Independence of Risk Units: Risk units should be independent of each other.
- Stability of Statistical Estimation: The conditions used to estimate the premium should remain stable
compared to the actual risk conditions of the portfolio.
- Investment Return Expectations: The insurer should be able to meet their expected return on
investments.
- Challenges and Trade-o s:
- Balancing Portfolio Size, Homogeneity, and Independence: The objective of having a large portfolio size
may con ict with the need for homogeneity and independence of risks.
- Competition Pressure: Competition can hinder accurate risk selection and pricing, potentially leading to
underwriting of non-insurable risks.
- Cross Subsidization: Insurers may implement cross-subsidization strategies between di erent lines of
business based on market conditions.
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- Features of insurable risks:
- Su cient Large Number: There must be a large number of exposed units, which allows for the
- Insurance and Investment Risks: The key risks for the insurance rm include the possibility of inadequate
premiums to cover losses (insurance risk) and negative investment returns (investment risk).
Lecture 20: The insurance business model
The underwriting activity
- Inverted Production Cycle: Insurance operates on an inverted production cycle. Insurers receive premiums
upfront from policyholders but are only obligated to pay out claims if the insured risk materializes in the
future.
- Consequences of Inverted Production Cycle:
- Correct Pricing: Pricing insurance policies accurately is essential to ensure that premiums collected
are su cient to cover potential losses.
- Temporary Investment of Premiums: Insurers invest the premiums collected for a temporary period to
generate returns and support their nancial operations.
- Regulatory Control: Insurance activities need to be regulated and supervised by public authorities to
protect policyholders and maintain stability in the insurance market.
- Underwriting Risk: The primary risk for insurers is not whether the insured event occurs or not but rather
the potential di erences (gaps) between the estimated damage used for premium calculation and the
actual damage experience in the portfolio of risk units. This is known as underwriting risk.
- Types of Gaps:
- Normal Gaps: These are the expected variations between estimated and actual damage experience.
Insurers account for normal gaps by applying a "risk loading" factor to the premiums.
- Systematic Gaps: These gaps arise due to consistent patterns or trends in the actual damage
experience. Re-pricing is necessary to address systematic gaps.
- Exceptional Gaps (not included in the exam): These gaps occur due to unforeseen and extraordinary
events that lead to higher-than-expected losses. Insurers may set aside additional reserves, known as
equalization reserves, to cover exceptional gaps.
- Factors A ecting Gap Frequency and Intensity:
- Homogeneity: The similarity of risk units in the portfolio in uences the predictability of damage
experience.
- Number: The larger the number of risk units in the portfolio, the more reliable the estimates and the
lower the impact of individual variations.
- Independency: Independent risks reduce the likelihood of correlations and systemic losses.
- Stability of Conditions: Consistency in risk conditions over time helps in accurate estimation and
reduces the occurrence of gaps.
- Managing Underwriting Risk:
- Portfolio Selection: Insurers face di culties and constraints in selecting ideal risk units for their
portfolios.
- Risk Reduction Measures: Once risk units are selected, insurers can implement actions to reduce
underwriting risk, such as:
- Contractual Conditions and Limitations: Imposing terms, like excess clauses, to shift some risk to
policyholders.
- Speci c Pricing Methods: Using experience rating or other techniques to adjust premiums based on
policyholders' historical loss experience.
- Reinsurance: Transferring a portion of the risks to other insurance companies through reinsurance
agreements.
The Insurance Contract
- Overview:
- The insurance contract regulates the relationship between insurers and policyholders (risk units).
- It is a contract in which one party pays a xed price (premium) to an insurer in exchange for the right to
receive a bene t (compensation) following the occurrence of a speci ed adverse event.
- Insurance contracts are distinct from other risk transfer arrangements due to their legal aspects, the
creation of aleatory obligations, and the mitigation of pure risk.
- Insurable Interest:
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- Insurable interest is a key characteristic of insurance contracts.
- It requires the purchaser of insurance coverage to have a nancial stake or be exposed to economic
losses (pure risk) related to the insured event.
- Insurable interest distinguishes insurance from gambling and is essential for a contract to be considered
an insurance contract.
- Obligations in Insurance Contracts:
- Premium: The premium is the price paid by the policyholder to obtain insurance coverage.
- Bene t: The bene t refers to the compensation the insured receives in the event of a covered loss.
- Reimbursement of expenses, indemnity payments, and forfeiture amounts are common types of bene ts
in non-life insurance.
- Life insurance often provides bene ts such as payouts upon survival, death, or disability.
- Aleatory Nature of Insurance Contracts:
- Insurance contracts are considered "random" or "aleatory" contracts.
- The premium is a xed amount, but the payment received by the insured (bene t) depends on the
occurrence of an uncertain future event.
- The aleatory nature is characterized by the trigger (event determining payment) and the uncertain amount
of the bene t.
- For an insurance contract to be aleatory, the trigger and/or bene t amount must be based on an
uncertain event unresolved at the contract's inception.
- Principle of Indemnity:
- Many insurance contracts operate based on the principle of indemnity.
- The insurer agrees to pay no more than the actual amount of loss incurred by the insured.
- The principle of indemnity aims to prevent the insured from pro ting from a loss intentionally.
- Insurers are responsible for determining the appropriate indemnity amount, and fair treatment is
regulated and enforced by supervisory authorities.
- Indemnity vs Valued Contracts:
- Insurance contracts can be classi ed into two types based on the bene t provision:
- Indemnity Contract: The insurer pays an amount equal to or proportional to the actual value of the loss
after its occurrence.
- Valued Contract: The insurer pays a predetermined amount speci ed at the contract's inception,
irrespective of the actual loss.
- Terminology and Typical Sequence in Non-Life Insurance:
- Peril: The possible event or risk insured against.
- Event: An accident or incident, such as a re, car accident, or theft.
- Damage: Loss, liability, or expenses resulting from the event.
- Claim: A formal request made by the insured to the insurer for compensation.
- Assessment and Claim Settlement: The process of evaluating the claim and reaching a settlement.
- Payment: The amount paid by the insurer to the insured based on various parameters.
- Terminology and Typical Sequence in Life Insurance:
- Event: Refers to events like survival, death, or disability, which trigger the bene ts in life insurance
contracts.
- Payment: The xed amount paid by the insurer to the insured.
Asymmetric Information and Insurance Contract Design
- Issues with Unit Selection and Risk Mitigation:
- Adverse Selection:
- Arises from hidden information where insurers cannot distinguish between "good" and "bad" risk
units.
- Premiums are based on average estimations across both types of customers, leading to potential
underpricing for riskier units.
- Adverse selection can result in a disproportionate number of high-risk units in the portfolio.
- Moral Hazard:
- Arises from hidden actions where insurance coverage may reduce the insured's incentive to prevent or
mitigate risks.
- The insured may engage in riskier behavior or neglect risk prevention measures, knowing they are
protected by insurance.
- Mitigating Risks:
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- Appropriate Risk Rating Methodologies:
- Risk rating methodologies aim to price the risk associated with each unit accurately.
- The objective is to re ect the actual loss probability in the premium charged.
- Individual ratings would be the ideal approach, pricing each risk unit based on its speci c loss
experience.
- However, practical reasons often require faster methods.
- Class Ratings:
- Insurance companies de ne risk classes based on a proxy of risk intensity.
- Risk units (policyholders) are then classi ed into the most tting class rating.
- Class ratings provide a quicker way to assess risk, but they may introduce some inaccuracy.
- Experience Rating:
- Experience rating is a way to mitigate the inaccuracy of class ratings.
- Risks are initially priced based on the assigned class rating.
- However, in subsequent periods, the price is adjusted based on the actual loss experience of the
speci c risk unit.
- This allows for more accurate premium adjustments, taking into account individual risk characteristics.
- Risk Rating Methodologies:
- Risk rating methodologies aim to determine the appropriate premium for each risk unit.
- The objective is to price the risk associated with the unit in a way that re ects its actual loss probability.
Contractual Clauses and Coverage Limitations in Non-Life Insurance Contracts
- Contractual Clauses for Mitigating Moral Hazard:
- Appropriate contractual clauses can help mitigate moral hazard in non-life insurance contracts.
- Moral hazard refers to the potential reduction in risk prevention or mitigation by the insured due to the
presence of insurance coverage.
- Common Contractual Provisions that Limit Coverage in Non-Life Contracts:
- Deductibles: Fixed (Straight or Aggregate) or Percentage.
- Franchises.
- Policy Limits.
- Other-Insurance Provisions.
- Exclusions.
- Contractual Provisions that Limit Coverage in Non-Life Contracts:
- Deductibles:
- Deductibles can be quoted as a xed quantity (common in non-industrial risks) or a percentage
(common in industrial risks) of the loss.
- Deductibles can be straight (per-loss) (if applied to a single loss) or aggregate (if applies to the sum of
all losses occurring during a speci ed time period).
- A xed deductible subtracts a speci ed amount (d) from the total loss payment that would otherwise
be payable.
- Example: With a deductible of €10,000, a claim of €9,900 is borne entirely by the insured, while a claim
of €10,500 results in the insurer paying only €500. The insured is responsible for the deductible, and
the insurance company covers the remaining amount.
- A percentage deductible requires the insured to pay a speci ed proportion (α) of the loss.
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- Example: With a 10% deductible on a €25,000 claim, the deductible is €2,500 (10% of the loss), and
the insured receives an indemnity payment of €22,500 from the insurer.
- Franchises:
- A franchise is a threshold (f) that must be exceeded for the insurer to be liable for the entire claim.
- Example: With a franchise of €10,000, a claim of €9,900 is borne entirely by the insured, while a claim
of €10,500 results in the insurer being liable for the entire amount.
- Purposes of Deductibles and Franchises:
- Eliminating small claims that are expensive to handle and process.
- Reducing premiums paid by the insured.
- Reducing moral hazard by discouraging the insured from taking excessive risks.
- Policy Limits:
- Insurance policies often set an upper limit, known as a policy limit, on the amount the insurer will pay
for any loss.
- Policy limits are always used in liability insurance policies, due to the fact that indemnities are by
de nition uncapped.
- Example: With a policy limit of €100,000, a claim of €120,000 would result in the insurer being liable
only for €100,000.
- Exclusions:
- Insurance policies may contain exclusions that exclude coverage for speci c types of losses.
- Reasons for exclusions include high costs of insuring certain types of losses or eliminating coverage
not needed by typical buyers.
Life Insurance Contracts
- Peculiarities of Life Insurance Contracts:
- The adverse event in life insurance contracts is certain to occur (death), but the timing of the event is
uncertain.
- Life insurance contracts are valued contracts.
- These contracts typically have long durations.
- Surrendering the contract is possible before maturity, but usually after a speci ed minimum period (e.g.,
three years).
- Classi cations of Life Insurance Contracts:
- By type of underlying event/risk/need:
- (Early) Death:
- Term Insurance: The insurer pays a xed amount to the bene ciaries upon the death of the
policyholder within a speci ed timeframe.
- Whole Life Insurance: The insurer pays a xed amount to the bene ciaries upon the death of the
policyholder at any point in their life.
- Survival/Need for Resources at Retirement:
- Pure Endowment Insurance: The insured pays premiums, and if they are alive at the stated maturity,
they receive the agreed amount.
- Annuities: The insurer pays xed or with-pro t annuities to the insured from a certain date until the
insured is alive, typically starting around retirement age.
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- By type of premium:
- Single Premium: One-time payment at the beginning of the contract.
- Recurring Premium: Premium payments made at the policyholder's discretion.
- Annual or Regular Premiums: Premiums paid at regular intervals.
- By type of return (bene t):
- Traditional Contracts:
- Fixed: Premiums and bene ts are set at the beginning of the contract with a guaranteed total return.
No participation in excess pro ts.
- With-Pro t: Minimal return is guaranteed, and policyholders participate in excess pro ts through
bonuses distributed on a discretionary basis.
- "Linked" Contracts:
- Unit-Linked Products: Bene t value is linked to the value of an underlying mutual fund, with the
return denominated in units of the fund.
- Index-Linked Products: Bene t value is linked to an underlying nancial index.
- Investment Risks:
- With-Pro t: Insurer's risk is associated with the level of guaranteed interest rate for policyholders.
- Unit-Linked Products: No additional nancial guarantees, so no investment risks for the insurer.
- Surrender Option:
- Policyholders have the option to surrender the contract before its natural term and receive the
bene t as provided in the contract.
- Surrender may involve penalties, introducing additional uncertainty in the amount and timing of
payments.
- Factors in uencing policyholder surrender behavior include monetary penalties, tax considerations,
and loss of associated contract protection.
The insurance premium
- "Fair" Insurance Premium:
- The fair insurance premium is the amount that adequately covers the expected bene t costs, expenses
incurred by the insurer, and provides a fair return on invested capital.
- Major determinants of the fair premium include:
- Expected bene t cost;
- Investment income;
- Expense loading;
- Risk loading.
- Insurance prices are in uenced by market forces and competitive considerations.
- Expected Bene t Cost:
- Pricing is based on informed estimates of potential claims' (indemnity or bene t) cost in the future,
known as the "expected bene t cost."
- Insurers use historical loss information and statistics on the events/risks relevant to the group of
policyholders to estimate future losses.
- The expected bene t cost considers:
- Expected frequency of loss (including timing for life contracts)
- Expected intensity (amount) of the loss (for non-life indemnity contracts)
- The expected bene t cost is the product of the best estimates (means) of the probability distributions for
frequency and intensity: P(B) = E[B] = E(frequency) x E(intensity)
- For a group of n items exposed to the same risk, with r observed claims totaling D, the statistical
premium is: P = (r/n) x (D/r)
- Investment Income and Timing of Bene t Payment:
- Insurers may consider their ability to earn investment income between premium payment and bene t
payment when determining the premium.
- A premium that includes a "negative" component, accounting for investment income, is called a
"discounted expected bene t cost."
- The size of the discount in the expected bene t cost depends on:
- The advance interest rate used (guaranteed to policyholders)
- The length of the contract period to which the premium is related (pay-o tail)
- Example 1 - Non-life insurance (Claims paid at the end of one year):
- An insurer sells a policy that will result in €100 in claim payments at the end of one year.
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- The insurer needs to collect the premium amount, denoted as P, at the beginning of the year to cover
the claims.
- With an annual interest rate, denoted as r, the insurer will have P·(1+r) at the end of the year.
- The sum P·(1+r) must equal €100, the amount of claims to be paid.
- Solving the equation P·(1+r) = €100 for P gives P = €100/(1+r).
- If r = 10%, then P = €90.91.
- If r = 5%, then P = €95.24.
- Example 2 - Non-life insurance (Claims paid at the end of two years):
- An insurer sells a policy that will result in €100 in claim payments at the end of two years.
- The insurer needs to collect the premium amount, denoted as P, at the time the contract is sold to
cover the claims.
- With an annual interest rate, denoted as r, the insurer will have P·(1+r)² at the end of the second year.
- The sum P·(1+r)² must equal €100, the amount of claims to be paid.
- Solving the equation P·(1+r)² = €100 for P gives P = €100/(1+r)².
- If r = 10%, then P = €82.64.
- If r = 5%, then P = €90.71.
- Summary of the Examples:
- The discounted expected bene t cost (insurance premium) is negatively related to the interest rate and
the length of the payo tail.
- Consideration of the time value of money poses additional risk for insurers if the guaranteed interest
rate exceeds the actual return earned on investments.
- The time value of money is important in life insurance and certain non-life business lines.
- Investment risk becomes signi cant for insurers, particularly in life insurance.
- Pricing policies with consideration for the time value of money requires attention to the characteristics
of the payo tail when choosing investment assets.
- Investment income and “with pro t” contracts:
- "With pro t" contracts in life insurance involve the allocation of investment returns to policyholders
during the policy's duration.
- The interest rate transferred to policyholders is not xed at the beginning and is usually not guaranteed.
- Insurers have discretion in transferring investment income to policyholders based on contract conditions.
- "With pro t" contracts lower the investment risk for insurers compared to traditional contracts.
- Administrative costs:
- Insurers incur various expenses known as administrative costs.
- These costs include general expenses, distributing expenses, and loss adjustment expenses.
- Administrative costs must be covered by including an "expense loading" in the insurance premium.
- Risk loading:
- Bene t costs in insurance are uncertain, leading to the need for additional pro t to o set potential
losses.
- Charging a premium equal to the expected bene t costs, investment income, and administrative costs
would result in no expected pro t and a high probability of negative gaps between premiums and claims.
- To ensure expected pro t and cover potential losses, insurers charge premiums in excess of the
discounted expected bene t cost and administrative costs. This additional amount is called "pro t
loading" or "risk loading."
Factors in uencing the risk/pro t loading include:
- The size of the risk pool (-);
- Correlation in bene t payments (+);
- Lack of heterogeneity of riskiness (+);
- Pressure from competitors (-);
- Return required by capital providers (+).
The risk/pro t loading is proportionate to the portfolio's riskiness and inversely proportionate to the
insurer's risk appetite.
Its purpose is to cover gaps between actual claims and the claim "best estimate" while providing an
additional expected pro t for the insurer.
In statistical terms, the amount of risk/pro t loading is proportionate to the dispersion (e.g., standard
deviation) of the loss probability distribution around its best estimate.
-
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Summary - example
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- The loss distribution describes the potential losses associated with a group of non-life insurance policies.
- In this example, the loss distribution consists of two possible outcomes:
- A loss of €10,000 with a probability of 0.1 (10%)
- No loss (€0) with a probability of 0.9 (90%)
- Calculation Steps:
- Step 1: Calculate the expected claim payment:
- Expected Claim Payment = (Loss1 * Probability1) + (Loss2 * Probability2)
- Expected Claim Payment = (€10,000 * 0.1) + (€0 * 0.9) = €1,000
- Step 2: Discounted expected bene t (claim) cost:
- Discounted expected bene t payment = Expected Claim Payment / 1.1
- Discounted expected bene t payment = €1,000 / 1.1
- Step 3:Calculate administrative expenses (Expense loading):
- Administrative Expenses = Percentage * Expected Claim Payment
- Administrative Expenses = 0.2 * €1,000 = €200
- Step 4: Calculate the pro t loading:
- Pro t Loading = Percentage * Expected Claim Payment
- Pro t Loading = 0.05 * €1,000 = €50
- Step 5: Calculate the fair premium:
- Fair Premium = Expected Claim Payment + Administrative Expenses + Pro t Loading
- Fair Premium = €1,000 + €200 + €50 = €1,250
- The di erences between the estimated and actual cost experience are the main sources of pro t or losses
for the insurer. These sources can be classi ed into di erent components of the premium, which include:
- Expected Bene t (Claim) Cost: This component represents the di erence between the estimated and
actual claim experience. It is based on the expected probability and severity of losses.
- Discounting of Expected Bene t (Claim) Cost: This component accounts for the di erences between the
interest rate used in pricing the premium and the actual return earned from investing the premium. The
insurer may earn more or less than the anticipated investment income.
- Expense Loading: Expense loading refers to the di erences between the estimated and actual amount of
expenses incurred by the insurer. Administrative costs, distribution expenses, and loss adjustment
expenses contribute to this component.
- Pro t Loading: The pro t loading represents unexpected pro t that was not considered in determining
the initial premium. It covers the gaps between the best estimate and the actual experience, providing an
additional source of expected pro t for the insurer.
On going developments - Innovation technology and big data
- Impact of IT Innovation:
- Design of Contracts: IT innovation allows for the design of contracts that are more tailored to speci c
needs. Coverages and clauses can be customized to provide better coverage and meet individual
requirements.
- Pricing of Policies: The availability of increased data and advanced tools enables insurers to price
individual risk units more accurately. Techniques like black box models use data to assess risk and
determine appropriate premiums.
- Marketing and Consumer Identi cation: Apps and technology enable insurers to identify potential
consumers based on their speci c needs and current situations. Personalized policies can be o ered to
individuals, enhancing marketing e orts.
- Distribution of Policies: Technology facilitates the distribution of insurance policies through apps and
websites. Consumers can conveniently access and purchase policies online.
- Contract Execution Modalities: IT innovations streamline processes such as claims reporting and
payment. Prevention measures can be implemented using technology to reduce the occurrence of
claims.
- Bene ts and Risks:
- IT innovations and big data o er several bene ts to policyholders, such as personalized coverage and
convenient access to policies.
- However, these advancements also introduce new risks and challenges.
- Insurer’s Perspective:
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- Risk Selection: IT innovations and big data empower insurers to select risk units for their portfolios more
e ectively. Detailed data analysis allows insurers to identify low-risk individuals or groups to manage
their overall risk exposure.
- Risk Pricing: Insurers can leverage advanced tools and data to accurately price associated risks. This
helps ensure that premiums align with the level of risk, promoting fair pricing practices.
- Impact on Insurability: In extreme cases, the increased reliance on IT innovations and big data may a ect
the insurability of certain risk units. Insurers may decline coverage or charge higher premiums for risks
deemed unpro table or di cult to assess accurately.
Lecture 21: Mitigating risks and protecting policyholder
Mitigating Risks in Insurance
- Insurers face various risks, and it is important for them to manage and limit these risks in line with their risk
appetite.
- Insurance regulation and supervision play a role in limiting an insurer's risk exposure to protect
policyholders.
- Good practices in internal risk governance and management are increasingly relied upon by supervisors to
achieve their objectives.
- Underwriting Risks:
- Underwriting risks are a major concern in non-life insurance, while life insurance is comparatively less
exposed.
- Non-Life Insurance:
- Estimation of claim frequency and intensity: Adequacy of expected bene t cost.
- Uncertainty (dispersion) of claim probability distribution: Adequacy of risk loading.
- Estimation of expenses: Adequacy of expenses loading.
- Consideration of nancial aspects in the premium: Adequacy of implicit discount rate.
- Life Insurance:
- Estimation of life assumptions: Adequacy of expected bene t cost.
- Estimation of nancial assumptions ( nancial guarantee): Adequacy of discount rate or other
guaranteed interest.
- Estimation of expenses and adequacy of expenses loading.
- Simpli ed Model of Underwriting Risk Status:
- Insurers face a trade-o dilemma between applied risk loading, available own funds, and the riskiness
of their portfolio.
- The solvency index can be represented as: (Applied Risk loading + Available Own funds) / Riskiness of
portfolio = Solvency index
- Riskiness of the portfolio is measured by the standard deviation of claims probability distribution.
- Mitigating Underwriting Risks:
- Underwriting risk is the major source of risk in Non Life. The fact that in most cases the bene ts are
determined in advance (valued contract), make Life Insurance less exposed to underwriting gaps.
- Life Insurance contracts are exposed to “longevity risk” (because the contracts are long-term). The
insurer is exposed to decreasing mortality trends over the long term.
- Non-Life Insurance are exposed to:
- Legal limitations (e.g., randomness, indemnity principle).
- Portfolio selection for optimal insurability criteria (number, independence, homogeneity).
- Contractual limitations (e.g., deductibles, franchises, policy limits).
- Premium adjustment based on experience rating (actual claim experience).
Reinsurance:
- Reinsurance is an "insurance for insurers", it transfers or shares risk between insurers. By using
reinsurance, the insurer can decrease the riskiness of its portfolio and optimize its solvency index.
- Types of reinsurance: facultative and automatic treaty.
- Main purpose of reinsurance are:
- Increasing of insurance capacity: Companies can underwrite risks which could otherwise not be
underwritten based on their i) capital dimension, ii) ability to apply risk loading and iii) risk appetite.
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- Improving quantitative harmonization of portfolio: Excess of certain risks could be transferred, leaving
the retained portfolio more harmonized under a quantitative point of view.
- Improving segmentation and diversi cation of risks: Risks can be segmented and transferred, leading to
risk sharing between many companies, frequently at international level: risk diversi cation
- Main types of reinsurance:
- Proportional reinsurance (percentage of the insured amount/premium):
- Quota share: The insurer and reinsurer agree to share risks by a certain percentage, which increases
capacity and segments the portfolio. However, it doesn't a ect portfolio alignment.
- Surplus: The reinsurer accepts insurance beyond the direct insurer's retention, contributing to portfolio
alignment.
- Non-proportional reinsurance (percentage of the claim):
- Excess loss: The reinsurer pays only when a claim loss exceeds a speci c amount. It provides more
protection for the ceding company compared to proportional reinsurance, as it guards against
incorrect premium determination.
- Stop loss:Similar to excess loss, but it applies to the entire portfolio of speci c risks. It o ers even
greater protection by insuring against poor overall portfolio performance.
Market Risks:
- Interest rate risk: Losses due to changes in interest rates.
- Equity risk: Losses due to changes in equity market prices.
- Real estate risk: Losses due to changes in real estate market prices.
- Exchange risk: Losses due to currency exchange rate uctuations.
- Counterparty risk: Deterioration of credit standing of issuers or default of reinsurers.
- Liquidity risk: Inability to realize investments and assets to meet obligations when due.
Mitigating Asset Risks:
- Risk governance and techniques used in other nancial institutions are applied in insurance.
- Integrated consideration of assets and liabilities (ALM) is crucial, particularly for interest rate, exchange
rate, and liquidity risks.
- Diversi cation and credit assessment of counterparties help mitigate risks.
- Matching assets and liabilities is challenging due to the uncertainty of insurance liabilities in amount and
timing.
- Interest rate risk is critical in life insurance due to its impact on assets and liabilities.
- Persistent low interest rate scenario poses challenges to insurers, especially for long-term contracts with
minimum interest rate guarantees.
Protecting Policyholders
- Policyholders need con dence that insurers will ful ll their commitments.
- Factors that increase con dence:
- Proper computation of insurer's liabilities towards policyholders according to strict prudential rules.
- Backing of liabilities with properly managed assets according to strict prudential rules.
- Availability of adequate capital to face unfavorable circumstances.
Technical Reserves
- Insurers set aside a portion of premiums received to cover future obligations towards policyholders and
future expenses.
- These reserved amounts are called "technical reserves." They represent the expected value of the insurer's
obligations towards policyholders at a speci c point in time.
- Estimations used to calculate technical reserves are similar to those used in premium calculations (e.g.,
event intensity, frequency, nancial assumptions).
- The insurer's nancial statements may recognize pro t or loss based on the assumptions used.
- Adjustments may be made to the assumptions if circumstances change, resulting in positive or negative
adjustments to the insurer's pro t and loss account.
- Negative adjustments require the insurer to cover the loss with its own funds, while positive adjustments
contribute to pro ts.
- Correct and prudent assumptions and methodologies in calculating technical reserves are crucial to protect
policyholders' interests.
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- Authorities responsible for supervising insurance companies play a vital role in ensuring accurate and
prudent calculations of technical reserves.
- Under the Solvency II regime, insurers should recognize both positive and negative adjustments if justi ed
by the current scenario (market-based approach.
- A ow chart describing the destination of the premium in the insurance company:
- The simpli ed insurer balance sheet is the following:
Technical Reserves in Non-Life Insurance
- Loss (Claim) Reserve:
- Estimation of the cost of all known and unknown claims that have already occurred but are yet to be
paid.
- Three types of loss reserves:
- Claims reported and adjusted but still unpaid.
- Claims reported but not yet adjusted.
- Claims incurred but not yet reported (IBNR).
- Unearned Premium Reserve:
- Represents the expected cost for future claims that may occur during the policy period.
- It is the portion of the premium paid in advance for insurance coverage not yet provided.
- Set aside to cover potential future claim costs.
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Technical Reserves in Life Insurance
- Net Premium Reserves:
- When a life insurance policy is issued, premiums are determined to cover expected bene t payments.
- Initially, the present value of expected premiums equals the present value of future bene t payments
(expected loss = 0).
- Over time, this equivalence may change.
- Net premium reserve (Mathematical reserve) is the di erence between the present value of future bene t
payments and future premium payments at a speci c time.
- Mathematical Reserves:
- Calculated by considering the present value of the insurer's future obligations and the insured's future
obligations.
- Factors in demographic assumptions (e.g., death probability) and nancial assumptions (e.g., discount
interest rate).
- Net premium reserve serves as a reserve to cover the di erence between expected values.
- Similar to unearned premium reserve in non-life insurance.
- If expenses are included in the reserve calculation, they are called modi ed reserves.
Assets Backing Technical Reserves
- Prudential Investment Rules:
- Premiums collected by insurers are invested in assets for a certain period.
- The safety, pro tability, and liquidity of investments should be ensured.
- Prudential regulations in each country set asset allocation rules, including limitations and conditions.
- Asset allocation policy must be appropriate for the nancial characteristics of insurance liabilities
(technical provisions).
- Prudent-Man Rules vs Quantitative Requirements:
- Regulations have shifted from detailed quantitative restrictions to more general guidelines.
- The "prudent-man" approach allows managers, rather than national regulations, to determine investment
policies for assets backing technical reserves.
- The approach requires strict corporate governance and appropriate management quali cations.
- This approach is followed in the European "Solvency II" regime.
Capital Requirements
- Solvency Requirement:
- Insurers in the European Union (EU) must have su cient own capital as a prudential bu er to cover
unexpected losses and meet contractual obligations.
- Solvency requirement absorbs remaining risks even with prudent liabilities calculation and appropriate
asset allocation.
- Minimum capital requirements (solvency requirement) exist in jurisdictions globally, but there is no single
worldwide standard.
- The EU's Solvency II regime, implemented since 2016, introduced a harmonized, risk-sensitive
framework for solvency requirements.
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Lecture 22: The EU prudential regime: Solvency II
Solvency II: Reasons and Drivers of the Regime
- The EU Prudential Regime:
- Prudential Regime is a set of principles, rules, and guidelines applied to insurance companies to ensure
their ability to ful ll nancial obligations and reduce the risk of insolvency.
- Di erent from the conduct of business regulations that aim to protect policyholder interests.
- The existing EU prudential regime, the so called Solvency II regime, has been applied since 1 January
2016. It replaces the so called Solvency I regime, which had been in force in EU for more than 30 years.
- Why a New Solvency Regime in EU?
- Solvency I, the previous regime, had several disadvantages:
- Con icted with good risk management practices.
- Capital requirements were simplistic and not risk-speci c.
- Inconsistent levels of policyholder protection across the EU.
- Valuation of assets and liabilities was inconsistent with international standards.
- Driving Principles of Solvency II:
- Solvency II aims to overcome the limitations of Solvency I by:
- Adopting a market-consistent approach to valuing assets and liabilities.
- Implementing risk-sensitive capital requirements aligned with economic capital.
- Focusing on governance and enhancing Enterprise Risk Management (ERM).
- Introducing an enhanced supervisory approach and early interventions.
- Strengthening market discipline through increased transparency and disclosure.
- Establishing a harmonized EU regulatory regime for consistent supervision.
Outline of the Regime - Three Pillars
- Solvency II encompasses all aspects of the insurance business that in uence solvency. It consists of three
pillars:
- Pillar 1: Focuses on nancial requirements and available capital to meet those requirements.
- Pillar 2: Establishes requirements for governance, risk management, and the supervisory review process.
- Pillar 3: Focuses on supervisory reporting and public disclosure to enhance market discipline.
- Pillar I: Main Conceptual Framework
- Solvency II follows a risk-based, economic approach to nancial requirements.
- Capital available to cover requirements is determined based on market-consistent valuation of assets
and liabilities.
- There are two levels of capital requirements:
- Solvency Capital Requirement (SCR): Potential loss under an adverse scenario assumption.
- Minimum Capital Requirement (MCR): Triggers supervisory action if breached.
- The solvency ratio is a measure that compares the available capital of an insurer to its capital
requirements. It provides an indication of the nancial strength and level of solvency of the insurer.
Supervisors and other stakeholders use the solvency ratio to assess an insurer's ability to withstand
serious loss scenarios.
- The solvency ratio allows for a "ladder" of supervisory interventions, which increase in intensity as the
solvency ratio decreases and approaches critical levels.
- As the available capital gets closer to the Solvency Capital Requirement (SCR) and eventually
breaches it, supervisors take actions with increasing intensity. These actions may include requesting a
recovery plan from the insurer.
- If the solvency ratio further deteriorates and breaches the Minimum Capital Requirement (MCR),
supervisors are required to take ultimate actions.
- Pillar II: Central Role of Risk Governance
- In addition to nancial requirements, good governance practices and strong risk management are
crucial.
- Solvency II requirements on the quality of governance:
- Fit and proper requirements of the persons managing the company;
- Internal control systems should be proportionate to risks;
- Severe qualitative risk governance standards.
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- The ORSA is one of the main and most innovative tools in the Solvency II framework. It has a twofold
purpose:
- A process to support internal business decisions, which should be always based on their risks
implications.
- A report to supervisors which explain how the company measures and asses its risk pro le.
- Supervisors review compliance, can require additional capital (capital add-on), and address de ciencies.
- Pillar III: Broad and risk based disclosure
- Solvency II introduces public disclosure requirements to foster market discipline.
- Insurers must provide clear and accurate information on risk pro le and risk management.
- External stakeholders should understand insurers' risk appetite and strategy.
- Supervisory reporting ensures supervisors have su cient information on risk pro les.
Insights on nancial requirements (Pillar I)
- Market consistent valuation of assets and liabilities:
- Assess the solvency position of the company is the determination of the so called “Solvency II” balance
sheet, where all assets and liabilities of the company are recognized and valued according to the
Solvency II valuation criteria: the market consistent valuation. Its purpose is:
- To determine the “available capital” of the company, i.e. the own funds (di erence between assets and
liabilities) which are available to cover the capital requirements.
- To determine the value of assets and liabilities which should be used to calculate the capital
requirements (SCR and MCR) , according to prescribed methodologies and following a “total balance
sheet approach.
- Di erent valuation methods are used:
- If the cash ows of insurance liabilities can be replicated by instruments with market prices, the
transfer value is derived from those instruments.
- If no market prices are available, a mark-to-model approach is used, following the criteria provided by
Solvency II.
- Calculations of technical provision:
- Steps:
- Step 1: Determining the amount and timing of all cash out- ows stemming from the insurance contract
in force, including those which depends on insurer’s discretion or policyholder behavior;
- Step 2: Discounting these cash out- ows using a pre-determined “risk free” interest rate term
structure. This would lead to the determination of the best estimate of insurance liabilities;
- Step 3: Adding a risk margin to the value of the best estimate.
- Best estimate:
- The present value of probability-weighted average future cash ows related to existing contracts.
- All expected cash ows should be projected.
- No allowance for prudential bu er or surrender value oor (in life insurance).
- Separate projection of guaranteed bene ts from discretionary bene ts (with-pro t contracts).
- Discount rate:
- A pre-determined interest rate set by EIOPA (European Insurance and Occupational Pensions
Authority) for each currency.
- The rate represents the rate an insurer can reasonably earn in a risk-free manner.
- It should re ect the least risky nancial instrument available to the insurer at the valuation time.
- After determining the best estimate of their liabilities, insurers should add a “risk margin”.
- Risk margin is calculated based on the cost of providing eligible own funds (capital) equal to the
Solvency Capital Requirement (SCR) necessary to support the insurance obligations during their
lifetime.
- The cost of capital is the additional rate over the risk-free rate, currently set at 6%.
- Risk-based Solvency Capital Requirement (SCR)
- The market-consistent value of assets and liabilities forms the basis for calculating the SCR.
- Any change in market values of assets and liabilities a ects the solvency ratio by altering available
capital and the determination of SCR.
- The e ect on available capital is usually more signi cant.
- SCR standard calculation approach:
- Solvency II provides a formula for calculating the SCR.
- The formula considers each quanti able risk individually based on a modular approach.
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- Prescribed factor-based or scenario-based calculations are used for each risk, considering all assets
and liabilities sensitive to that risk.
- Risk mitigation mechanisms (e.g., derivatives, reinsurance) are accounted for.
- Factors or scenarios are calibrated statistically to cover
- Risk Charge Calculation in Solvency II: The Interest Rate Risk Module
- The module measures the impact on the balance sheet of potential changes in the term structure of riskfree interest rates.
- Companies simulate the impact of up and down stresses on the risk-free curve, varying by term to
maturity.
- All assets and liabilities sensitive to interest rates are stressed, and the change in value is recorded.
- Insurance liabilities are a ected through changes in discount rates, value of options and guarantees, and
management actions.
- The Solvency Capital Requirement (SCR) is the larger net result of the two stress scenarios.
- Consideration of Loss Absorption Capability in the Balance Sheet
- The capital requirement for each risk is reduced, where relevant, to account for the potential reduction in
value or elimination of certain liabilities in a stressed situation.
- Examples of liabilities with loss absorption capability include technical provisions for "with pro t" life
contracts and deferred tax liabilities.
- Aggregation of Risks in the Formula
- Capital charges for each risk are aggregated using prescribed correlation matrices to account for
diversi cation e ects between risks.
- Diversi cation e ects recognize the potential reduction in overall risk when risks are not fully correlated.
- The calculation of diversi cation e ects is subjective and debated due to changing correlations over
time, particularly during crises.
- Calculation of the Solvency Ratio
- The solvency ratio is calculated by dividing available own funds by the Solvency Capital Requirement
(SCR).
- The solvency ratio provides an indicator of an insurer's solvency position.
- Changes in the balance sheet and market values of assets and liabilities can a ect both available capital
and the SCR.
- Balancing Simplicity and Sensitivity in Calculating the SCR
- Solvency II allows for adjustments or replacements of the standard formula results with more companyspeci c calculations, subject to supervisory approval.
- Simpler calculations may be applied when risks are not signi cant, following the principle of
proportionality.
- Options are available to balance the need for simplicity and risk sensitivity across insurers and markets.
- Internal Model Authorization
- The SCR standard formula is an average calibration based on European-wide data and may not fully
re ect a company's speci c risk pro le.
- Insurers can use an internal model, subject to strict standards, to make the SCR calculation based on
their own risk pro le.
- Approval of internal models requires demonstration of e ective use and sound governance.
- Supervisors may require the use of internal models when a rm's risk pro le deviates signi cantly from
the assumptions in the standard formula.
- Entity-speci c parameters can be used as an intermediate option between the standard formula and
internal models.
- Minimum Capital Requirement (MCR)
- In addition to the SCR, Solvency II establishes a lower capital requirement called the Minimum Capital
Requirement (MCR).
- The MCR serves as a trigger for supervisory actions and acts as a safety net against model errors.
- It is based on an objective calculation approach that is easily auditable.
- The level of the MCR should be consistent with the SCR to allow for a reasonable "distance" and a
ladder of supervisory interventions.
- The MCR calculation is based on percentages applied to premiums, technical provisions, and insured
amounts at risk, with certain caps, oors, and minimum requirements.
- Eligibility Criteria for Own Funds
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- SCR and MCR should be covered by eligible elements of available capital (own funds) that can absorb
losses when needed.
- Eligible own funds include the di erence between assets and liabilities, subordinated debts, and ancillary
own funds.
- Own funds are allocated into three tiers based on their quality, measured by criteria such as
subordination, loss absorbency capability, duration, absence of mandatory servicing costs, and absence
of encum
Expected Main Challenges for Supervisors
- Increased complexity of supervisory tools and the need for improved technological and human resources.
- Ability to appropriately use increased discretion and stand against reactions of companies and
stakeholders.
- Establishing a new risk supervisory culture at all levels of the organization.
- Convergence of European Union supervisory practices in day-to-day operations.
- E ective cooperation at the international level, considering di erences in legal and cultural frameworks.
Major Challenge: Volatility and Pro-cyclicality
- The potential volatility of Solvency II solvency measurements and the risk of pro-cyclical interventions are
controversial aspects of the regime.
- The legislation includes "Long Term Guarantee" (LTG) measures to soften the e ects of short-term market
volatility.
- LTG measures include volatility adjustment, matching adjustment, and extrapolation to make the balance
sheet less volatile.
- Volatility Adjustment: Margin added to the risk-free rate curve to reduce technical provisions in case of
abnormal widening of credit spread.
- Matching Adjustment: Margin added to the risk-free rate curve to re ect the credit spread of speci c
assets.
- Extrapolation: Method to determine the curve for maturities with no reliable market data, reducing
dependence on market volatility.
Other Critical Aspects of the New Framework
- Complex quantitative and qualitative requirements may penalize small companies and drive market
consolidation.
- Use of internal models, if not well calibrated, understood, and managed, can be misleading.
- Risk diversi cation may force small companies to exit the market, and bene ts are challenging to measure
during crisis situations.
- Severity of capital requirements for certain businesses, such as long-term guarantees, can signi cantly
increase the capital absorbed.
- Ensuring a level playing eld in a principle-based regime requires convergent day-to-day supervisory
practices.
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