Financial Risk Management Final

Losses to underlying subprime portfolios 5% < loss < 25% of principal

Losses to equity tranche: -Yes, absorb first 5% of losses Losses to mezanine tranche: -Yes, absorb next 20% of losses Losses to senior tranche: -No

Losses to underlying subprime portfolios loss > 25% of principal

Losses to equity tranche: -Yes, absorb first 5% of losses Losses to mezanine tranche: -Yes, absorb next 20% of losses Losses to senior tranche: -Yes, absorb losses in excess of 25%

Losses to underlying subprime portfolios loss < 5% of principal

Losses to equity tranche: -Yes, absorbs first 5% of losses Losses to mezanine tranche: -No Losses to senior tranche: -No

The two distributions are assumed

independent of each other

Estimating μ and σ

1) select the risk factors. 2) assume that the distribution of the changes in the portfolio values is normal and can be completely characterized by mean and variance. 3) derive the mean and variance of the portfolio under the normality assumption 4) using the mean and variance, calculate the VaR

In a normal distribution if c = 99% then α =

-2.33

Things that cause an increase in liquidity risk

-Credit rating falls -Sudden unexpected cash outflows, or some other event -counterparties avoid trading with or lending to the institution -Markets on which the firm depends are subject to loss of liquidity

• Consumer Financial Protection Bureau

-Oversees credit reporting agencies, credit and debit cards, consumer loans -Regulates credit, mortgage underwriting and bank fees -Requires homeowners to understand mortgage loans -Requires banks to verify borrower's income, credit history and job status Some have criticized it for being politicized

Scenario

-a combination of several stress shocks -Scenarios can be replications of real historical events, or they may be hypothetical. •The combination is arbitrary but should make economic sense. Each scenario is evaluated to determine the loss of market value of the portfolio if the scenario occurs. example: -Shock 1: 25% fall in the North American equity indices -Shock 2: 25% fall in European equity indices -Shock 3: 200 basis point fall in the North American short-term interest rates •This scenario is internally consistent as it assumes the "flight to quality": as equity prices drop, investors flock to the safe short-term North American government obligations such as T-bills, causing short-term yields to drop.

Loss severity

-distribution is assumed lognormal -with parameters estimated from historical data.

Liquidity risk is

-financial risk due to uncertain liquidity -tends to compound other risks -Limited ability to liquidate an illiquid position compounds market risk -inability to raise cash to make payments required by contract => default => compounds credit risk -Even if hedged, liquidity risk is usually present Example two offsetting positions with different counterparties. Since the two payments are offsetting, there is no market risk. However, there is liquidity risk and credit risk

•Market risk for commodities can be further stratified into

-price risk -basic risk -cost of carry risk -time spread (forward gap) risk

In a Student-T distribution if c = 99% then α =

3.365

Advanced measurement approach

Capital is calculated internally by the bank, similar to market VAR. Capital = Expected operational loss - (99.9% Worst-case loss.)

Standardized approach.

Income by business line, multiplied by betas. Specified by Basel II (See next slide).

Basel I

Key Innovation •A key innovation was the inclusion of off-balance-sheet exposures in the risk weighting framework, by converting these exposures into credit equivalents.

Basic indicator approach

Operational risk capital = 15% of annual gross income over the previous three years.

Minimum capital requirements

Pillar I of Basel II -rules and methodologies that are available for calculating the minimum capital -raises the capital required to support securitization of high-risk assets. •The capital requirements include credit risk, market risk, and operational risk (new)

supervisory review process

Pillar II of Basel II -role and responsibilities of banks, their boards, and their supervisors •Supervisors have ability to require banks to hold capital in excess of minimum required regulatory ratios depending on a variety of factors: -existence and quality of management and control processes -track record in managing risk -nature of the market in which the bank operates -volatility of earnings •Danger: determination of capital adequacy on a bank-by-bank basis will be arbitrary and inconsistent.

Market Discipline

Pillar III of Basel II -disclose sufficient information on Pillar 1 risks •Pillar III introduces a radical new requirement for banks to disclose risk information to the equity and credit markets. •Regulatory disclosures are different from accounting disclosures and need not be made in accounting reports.

Delta-VaR measures

The change in VaR if you had one more unit of asset A

Beta serves as

a proxy for the industry-wide relationship between the operational risk loss experience for a given business line and the aggregate level of gross income for that business line.

Basic risk

movement in the price differential between related commodities (esp. important in energy)

Cost of carry risk

risk that cost of financing an investment in the commodity will change

waterfall principal

senior first, then mezzanine, then equity.

This worst possible loss determines

the minimum capital requirement for financial institutions, scaled by an (arbitrary) multiplier to compensate for model errors and imperfect risk assessment. The multiplier can be increased by regulators.

time spread (forward gap) risk

the risk of forward price movements for reasons of change in supply and demand and fundamental factors other than interest rates

Price risk

the risk of price movements in spot prices

Increases in regulations

•1927 McFadden Act: prohibited banks from interstate branching •1929 stock market crash led to increased focus on systemic risk •1933 Glass-Steagall established FDIC. Initial insurance limit $2500 •1933 Glass - Steagall Act separated commercial and investment banks •1933 Regulation Q: a ceiling on interest rates on saving accounts •1956 Bank Holding Company Act limited nonbanking activities of commercial banks •1966 Congress set limits on savings rates for Savings and Loans (S&Ls) and commercial banks

Cash flows are allocated to the tranches according to the

waterfall principal

Leveraging and Deleveraging

• High liquidity - > easy credit - > more borrowing -> asset prices increase -> collateral values increase -> more borrowing -> etc. •Less liquidity -> less lending -> less borrowing -> asset prices decrease -> collateral value decreases -> less lending -> etc.

Approaches to Measurement

•"top-down" -Estimate the volatility of bank's assets -Calculate the probability that the value of assets will fall below liabilities •"bottom-up" -Estimate loss distribution for different risks -Aggregate •By risk type •By business unit •Total

Decreases in regulations

•1980 Depository Institutions Deregulation and Monetary Control Act (DIDMCA): phase-out for Regulation Q •1982 Garn - St. Germain Depository Institution Act (DIA): allowed banks to offer interest paying money market deposit accounts with withdrawal rights •1999 Financial Services Modernization Act: Glass-Steagall Act of 1933 repealed concerning separation of financial industry

Basel I, II, III

•1980s Bank of England and the Federal Reserve Bank require that banks set aside more capital than before (8%) against risky assets; charge BIS (Bank for International Settlements) with development of common capital standards and procedures for quantifying, evaluating, pricing and monitoring risks for international banks •1988 BIS Accord (Basel I) •1990s The role of regulators shifts from that of setting up to that of monitoring sophisticated banks' internal risk management systems. Large sophisticated banks have a growing role in setting up their own risk management •1996 Market Risk Amendment to Basel I (implemented in 1998) •1999 Basel II proposed (agreed upon 2004, updated in 2005, implementation began 2007) •December 2011: Basel 2.5. Substantiated by the need to modify Basel II amid the onset of financial crisis. Deals mostly with the risks of credit sensitive products in the trading book. •2013-2019: Gradual implementation scheduled of Basel III: capital requirement for liquidity risk. •The 1988 Basel Accord (now known as Basel I) introduced international standards for risk-based capital requirements. •Under Basel I, banks have to hold capital equivalent to 8% of their risk-weighted assets. •This number is commonly referred to as the capital adequacy ratio, or Cooke ratio. In many countries, this ratio is higher than 8 percent to reflect national circumstances. •Each type of asset has a risk weight that reflects its riskiness.

Regulatory Principles: Banks Should

•A bank must take responsibility for liquidity management •A bank should clearly articulate a liquidity risk tolerance •Senior management should monitor liquidity •Liquidity costs and benefits of new positions must be considered Procedures must be in place for projecting cash flows from positions •A bank should manage liquidity both within subsidiaries and on a consolidated basis •Banks should regularly gauge its ability to raise funds and develop a funding strategy •A bank should manage intraday liquidity positions and risks •A bank should actively manage its collateral •A bank should conduct stress tests and scenario analysis •A bank should have a contingency plan to address liquidity shortfalls in emergency •A bank should maintain a cushion of high-liquid assets •A bank should disclose information about liquidity of positions

Securitization

•A securitization is a financial transaction in which assets are pooled and securities representing interests in the pool are issued. •If a securitization is correctly implemented, investors face no credit risk from the originator because the assets are transferred to SPV in a legal sale and the originator retains to claim to the assets.

AIG (2008)

•A series of insurance contracts AIG entered intofrom 1998 through 2005 •AIG insured CDOs for Merrill Lynch, UBS, Citigroup, etc. •AIG wrote credit default swaps (CDS) on about 420 CDO deals: if CDO rating deteriorated, the owner (buyer) of the CDS would get AIG to pay the face value of the CDO no matter what the market value. By 2005, AIG had committed to backing about $63 billion in increasingly illiquid CDOs. •September 2008, the government acquired 80% stake in AIG and extended a $85 billion loan to be repaid within two years by quickly selling-off assets

Trader's Problem

•A trader wishing to unwind a large position has to decide on the best trading strategy •If the position is liquidated quickly the trader faces large spreads but the potential loss from price moving is small •If the trader chooses to trade over several days to liquidate the position, there will be lower bid-ask spread losses but a larger potential loss from price moves

Basel III

•Added a capital conservation buffer 2.5% •Total capital 10.5% of risk-weighted assets •Minimum "leverage ratio" in excess of 3% •LR = Tier 1 capital / Average total assets •LR = 6% for SIFI banks (Systemically Important Financial Institutions)

Crisis of 2007 - 2008

•Basel committee proposed the following revisions : -Revised guidance for bank supervisors on the assessment of adequacy of banks' liquidity risk management -Issued guidance on scenario analysis and stress testing -Proposed capital requirements for resecuritizations(CDOs and CDOs of CDOs) -Introduced Incremental Risk Charge (IRC) for instruments in the trading book that are subject to credit risks such as default, credit migration, widening of credit spreads, as well as to loss of liquidity -Stressed VaR using data from bad time periods (like during the financial meltdown)

Major Trends in Financial Institutions

•Consolidation •Increased competition •Lower credit quality customers •Risk sharing activities for customers •Expansion of bank activities •Explosion of derivative trading •Off-balance sheet accounting •Exotic derivatives, CDO, ABS, CDS, etc. •Securitization

The Dodd-Frank Act of 2010

•Consumer financial protection •Addressing systemic risks •Too big to fail •Transparency and accountability for derivatives •Mortgage reform •Credit rating agencies •Executive compensation and corporate governance •Securitization Other

Operational Risk: Definition

•Definition (Basel): "Operational risk is the risk of loss resulting from inadequate or failed internal processes, people, and systems or from external events." •Much more difficult to quantify and manage Operational Risk than Credit or Market risk

Operating Risk Regulatory Capital - How Much Do Regulators Require?

•Determination of regulatory capital: Types of approaches: -Standard -Advanced Measurement -Basic indicator •Large internationally active banks are encouraged to move toward accepting the internal (advanced measurement) approach. Some banks still use the basic indicator approach. To use standardized approach, need to qualify with regulators.

VaR: Disadvantages

•Does not tell which components contribute most to total risk •Based on distributions derived under normal market conditions and does not incorporate crises characterized by large price changes, high volatility and a breakdown in correlations among the risk factors •Does not account for liquidity risk: the risk that trading will be too costly •Some methodologies provide no or poor statistical estimation of error term (VaR is not exact due to measurement error in estimating means and variances) •VaR may take too much computational resources

Managing Operational Risk

•Establish causal relationships between decisions and operational risk losses •Install self-assessment techniques (such as questionnaires) •Develop key risk indicators (staff turnover, number of failed transactions, etc.) •Allocating operational risk capital -Better units are required to hold less capital, which means they can do more business. How are better units identified? Scorecard approach •Operational risk insurance - this can reduce the required capital Possibility of moral hazard Possibility of adverse selection

Misleading Readings

•Even though senior tranches are rated AAA, and mezzanine tranches BBB, the risk of those is actually higher than that of correspondingly-rated bonds. •In stressed market conditions, very high default rates are possible even for AAA-rated tranches. •Also, CDOs are complex instruments and many investors did not carefully analyze them to evaluate risks properly. Sometimes, they did not use risk management models but relied on the ratings instead.

Oversee Insurance Companies

•Federal Insurance Office under the Treasury Department •Identifies insurance companies like AIG that create systemic risk and limits their activities •Assists in making insurance available to underserved communities

Oversee Hedge Funds

•Hedge funds must register with the SEC •Must provide data about their trades and portfolios to the SEC •Banks to limit their hedge fund activity and register derivative transactions with CFTC

Sources of Liquidity

•Holdings of cash and securities convertible into cash -Disadvantage: low interest income •Ability to liquidate trading book positions -Disadvantage: liquidity trading risk •Ability to borrow wholesale •In stressed market conditions, financial institutions are reluctant to lend to each other. Collateral and lines of credit help with wholesale borrowing. •Ability to attract depositors •Ability to securitize assets -Securitization was in part responsible for the financial crisis, but not as it related to liquidity. •Borrowings from central bank -May adversely affect bank's reputation (Northern Rock). •Hedging liabilities -Problems may arise if bank hedges illiquid assets with contracts that are subject to margin requirements -Metallgesellschaft •Reserve requirements - bank regulators enforce a minimum level of liquidity

How the 2008 financial crisis started

•House prices went up since about 2000 faster than normally. •Higher prices meant better collateral, which made lending more attractive. •At the same time, higher prices meant fewer families could afford housing, which led to a relaxation of lending standards as originators tried to increase profits. •At the same time, the US government did not regulate lending standards because it tried to expand home ownership. -teaser rates -liar loans - borrower asked to state his income. Not confirmed. -NINJA loans - No Income No Job No Assets. Still gets loan. Subprime loan: credit score between 450 and 680 •In 2007, many families struggled with their mortgages as teaser rates ended. •A large number of foreclosures led to a decline in housing prices. •At this point, many speculators who had bought homes to rent, and who borrowed close to 100% of the home price, experienced negative equity and decided to exercise a put option and sell the houses to originators for the amount of the outstanding principal (many mortgages are nonrecourse).

Monte Carlo Approach

•Identify the risk factors (as with the previous approaches) •Specify the stochastic processes that describe their dynamics (have to assume). Could be an AR(1) process or some other type. •Using historical data, estimate the parameters of the specified stochastic processes •Using these stochastic processes and the parameter estimates, simulate about 10,000 possible price paths for your portfolio value •From the simulated distribution, derive VaR as the difference between expected change and the 1st percentile change in the value of your portfolio.

Securitization typical process

•In a typical arrangement, the owner—or "originator"—of assets sells those assets to a special purpose vehicle (SPV). •The SPV sells bonds to investors. It uses the proceeds from those bond sales to pay the originator for the assets. •If a securitization is correctly implemented, investors face no credit risk from the originator because the assets are transferred to SPV in a legal sale and the originator retains to claim to the assets.

Long-Term Capital Management (LTCM)

•LTCM was a U.S. hedge fund that used various arbitrage trading strategies. •LTCM was founded in 1994 by John Meriwether, the former vice-chairman at Salomon Brothers. Board of directorsmembers included 1997 Nobel Prize in Economics winners Myron Scholes and Robert Merton. •As a hedge fund LTCM avoided the financial regulation imposed on mutual funds. •To establish and maintain its arbitrage positions, LTCM had very high leverage. At the beginning of 1998, the firm had equity of $4.72 billion and debt over $124.5 billion for a debt-to-equity ratio of 25 to 1. •LTCM had off-balance-sheet derivative positions with a notional value of approximately $1.25 trillion, most of which were in interest rate derivatives. •Early returns were good. 21% in first year. 43% in second year. 41% in third year. •One of the main positions of the hedge fund was to short the benchmark or 'on the run' Treasury bond and go long on the old benchmark bond (off the run).

Types of liquidity risks

•Liquidity funding risk •Liquidity trading risk

Barings (1995) and Societe Generale(2008)

•Major losses on derivative positions as a result of one trader's actions and failure of the management •Failure to account for operational risk •Failure to monitor risk during period of success

Components of Economic Capital

•Market risk -Estimate the one-year worst-case loss similar toVaR •Credit risk -Estimate one-year loss from downgrading and default using CreditMetrics (recall our exercise with transition probability matrix) •Operational risk •Business risk -Strategic risk -Reputational risk

•Standard categories of securitizations are

•Mortgage-backed securities (MBS), which are backed by mortgages •Asset-backed securities (ABS), which are mostly backed by consumer debt •Collateralized debt obligations (CDO), which are mostly backed by commercial loans or other debt and divided into tranches.

Liquidity Trading Risk

•The price at which an asset can be sold depends on -Bid -ask spread and MidMarket price -trade size -expected time to execution -economic environment

Stress Testing; Scenario Analysis

•The purpose of stress testing and scenario analysis is to determine the size of potential losses related to specific scenarios. •A scenario is usually modeled after extreme historical events, such as - October 1987 stock market crash - Asian flu 1997 -Russian default 1998

VAR with the confidence level of 1% means

•the worst possible loss such that there is less than 1% chance of losing more than that in a single trading day.

LTCM: Problems in 1998

•Negative returns in May and June (-6.42% and -10.14% respectively) reduced LTCM's capital by $461 million. • Salomon Brothers (partner) quit arbitrage business in July. Liquidation of their portfolio depressed value of LTCM's positions. •Russian Government defaulted on their government bonds in August and September. LTCM's arbitrage positions in U.S. Treasury bonds and interest rate derivatives incurred major losses. Flight to quality bid up prices of on-the-run Treasuries •LTCM's losses occurred just as market liquidity dried up, causing losses from liquidating positions (example: Royal Dutch Shell arbitrage position was liquidated when the arbitrage window widened from 8-10% to 22%) •In the first three weeks of September, LTCM's losses caused its equity to fall from $2.3 billion to $600 million. •The Federal Reserve Bank of New York organized a bailout of $3.625 billion by the major banks in return for a 90% share in the fund. •Merrill Lynch observed that mathematical risk models "may provide a greater sense of security than warranted; therefore, reliance on these models should be limited." •LTCM's strategies were compared to "picking up nickels in front of a bulldozer"

Historical Simulation

•No assumptions are made regarding any distributions. Instead: •For each combination of changes, calculate the corresponding change in the value of your portfolio •This way, you have the empirical distribution of your portfolio value •Find the expected value and the 1st percentile of this distribution and the difference is your VaR.

Data issues

•Not enough data! Traditionally, banks have done better documenting their credit and market losses than their operational losses. •Loss frequency distribution: From own data. •Loss severity distribution: Own + external data from other banks or from data vendors, scale adjusted and inflation adjusted. •Caution: Public data is biased toward larger losses and toward institutions with weaker controls.

Oversee Credit Rating Agencies

•Office of Credit Ratings at the SEC •Regulates credit ratings agencies like Moody's and Standard & Poor's •Can require agencies to submit methodologies for review •Can deregister an agency for misleading ratings

Basel II

•Pillar I (minimum capital requirements) •Pillar II (supervisory review process) •Pillar III (market discipline)

Dynamic VaR

•Portfolio positions are allowed to evolve, such as unwinding of positions •Liquidity is allowed to change •Stochastic processes for the risk factors are not stationary: they are allowed to jump or to change regime •Trading rules are pre-specified (for example, hedge if a certain scenario occurs) •Run a large number of simulations •For each simulation, record profits and losses •From the distribution of profits and losses, calculate percentiles and expected values

RAROC

•RAROC = (Revenues - Costs - Expected Losses)/Economic Capital

Savings &Loan Crisis (1980s)

•S&Ls engaged in imprudent real estate lending (too much into too risky ventures): outstanding US mortgage loans in 1976 were $700 billion, in 1980 $1.5 trillion. •Tax Reform Act of 1986 and high interest rates of the 1980s (an attempt to end inflation) significantly reduced the value of mortgages. • Long-term mortgages were financed by short-term liabilities (asset-liability mismatch). When interest rates rose the value of the mortgages dropped and income decreased, while the cost of capital increased. •Pre-1980, limit on savings rates pushed away depositors that withdrew their funds and placed them in accounts that earned market rates. The Deregulation Act (DIDMCA of 1980) was an attempt to help S&Ls grow out of their problems but in effect reduced oversight over their activities - allowed thrifts to offer a wider array of savings products - expanded their lending authority - authorized the use of more lenient accounting rules to report their financial condition - phased out ceilings on interest rates on deposits •The result was the failure of 745 S&Ls. The crisis cost around $160.1 billion, about $124.6 billion of which was directly paid for by the U.S. government, feeding the budget deficit of the early 1990s.

Disadvantages of stress testing/scenario analysis

•Scenarios are based on arbitrary combinations of stress shocks •Economic sense is not always present •Correlations are handled poorly (Variance - Covariance matrix may not be internally consistent, or positive definite) •Only a relatively small number of scenarios are realistically analyzed in practice •Scenarios are static and one-period only. They do not allow for trading and unwinding of positions. Hence, liquidity is not handled.

Rogue Trader Insurance

•Some insurance companies offer policies on this •Insurance company may require that the purchase of the policy not be revealed to traders or their co-workers

Supervisors (Regulators) Should

•Supervisors should regularly assess a bank's liquidity management procedures •Supervisors should monitor internal reports and market information •Supervisors should intervene in an efficient and timely manner to address liquidity issues •Supervisors should share information with other supervisors to facilitate cooperation

Example of securitization

•Suppose a financing company has issued a large number of auto loans and wants to raise cash so it can issue more loans. But the market for individual loans is not liquid. The firm pools a large number of its loans and sells interests in the pool to investors. •For the financing company, this raises capital and gets the loans off its balance sheet, so it can issue new loans. •For investors, it creates a liquid investment in a diversified pool of auto loans

Liquidity: Scenario Analysis

•The Simple Liquidity Measurement cannottake into account cash flows from derivatives •In this case, use scenario analysis. -Construct multiple scenarios for market movements and defaults over a given period of time. -Assess day-to-day cash flows under each scenario. •Balance sheets differ from one organization to another => little standardization in how such analyses are implemented.

Economic capital

•The amount of capital a bank needs to make sure that the probability of running out of capital within one year is no more than (100-c)% •Where c% is confidence level •C=99.97% to maintain a AA rating, since probability of default is about 0.03%.

Advantages and Disadvantages of historical simulation

•The biggest advantage is no need to assume any distribution. •The biggest disadvantage is that the method relies heavily on the sample period.

Basel I: Disadvantages

•The risk-weighted ratios don't differentiate adequately between the riskiness of bank's assets •Rules assume that all corporate borrowers pose an equal credit risk •Maturity is not taken into effect (the 364-day facility) •No incentives are provided for the use of credit derivatives to mitigate credit risk •Portfolio effects (default correlation) are not considered •Operational risk was not considered (the risk of loss resulting from inadequate internal processes, people, systems, or external events)

Liquidity Black Holes

•These arise when everybody is on one side of the market. Positive feedback trading contributes to liquidity black holes. Why would there be positive feedback trading? -Stop-loss orders -Margins -Irrational exuberance

Liquidity Funding Risk

•This is the risk that the financial institution will not meet cash needs. Financial institution may be solvent (assets > liabilities), yet may have cash problems. •Example: Northern Rock Bank (UK) -Relied heavily on debt instruments for funding -Amidst the subprime crisis in August 2007 the bank could not replace maturing instruments -Although the bank was not insolvent it did not have sufficient funding to do business -On September 13, 2007, BBC broke news that the bank had requested emergency funding from the Bank of England -Run on the bank [UK's first in 150 years} -Had to sell assets -In February 2008 the bank was nationalized and the management changed

Types of Capital

•Tier 1 Capital consists of items such as common equity and some preferred stock •Tier 2 Capital (supplementary capital) includes loan loss reserves, some preferred stock, certain debenture issues, and subordinated debt. •Total Capital is the sum of the two.

Requirements to VAR models

•To calculate market risk, banks are allowed to take into accountcorrelations between risk categories. Volatilities and correlations should be estimated based on historical data. •Model parameters should be updated regularly. •To calculate market risk related to derivative positions, linear risks are not enough. (delta) = sensitivity of the position to the price change of the underlying factor. Convexity (gamma) and volatility (vega) risks are also important. •In developing VAR models, most parameters are set during "normal" market conditions. Therefore, VAR models are complemented by stress-testing (more later). •Models should be back-tested. •Back testing compares the bank's internally generated VAR figures with the actual performance of the bank's portfolio over an extended period of time. •Back tests must compare daily VAR to the actual net trading profit (loss) for the next trading day and to the theoretical profit (loss) that would have occurred if the position at the close of the previous trading day had been carried forward to the next day. •Back testing should be performed daily. •The bank must count the number of days in which loss for that day exceeded the corresponding daily VAR. If, over a period of 250 days, the number of such days exceeds 5 (5/250 = 2%), then the model has error and multiplier for minimum capital requirement will increase.

VaR equation variables

•V Current marked-to-market value of the position •E(V) Expected value of the position at the end of the holding horizon •H Holding horizon (1 day, 1 week, 1 month, etc) •R Return over the holding horizon (this is a random variable) •μ Expected return •c Confidence level, say 99% •R* Return corresponding to the worst-case loss at c •V* "Worst-case-loss-at-c" value of the position after 1 day

VaR: Benefits

•VaR provides a common, consistent, and integrated measure of risk across risk factors, instruments, and asset classes •VaR provides a single number that can be easily translated into a capital requirement •VaR allows for risk monitoring across businesses in a consistent way •VaR is easy to communicate and understand •VaR allows the firm to assess the benefits of diversification VaRhas become an internal and external reporting tool

Value at Risk DOES ATTEMPT to answer the question

•What is the maximum loss over a given time period such that there is only a 1 percent probability that the actual loss over the given period will be larger? •In other words, what is the loss such that there is only a 1% chance of losing more than that over a given period of time?

In all but the most simple of circumstances,

•comprehensive measures of liquidity risk don't exist.

Financial Stability Oversight Council

•concerned with systemic risks (risk that affect the entire financial industry) •If a bank "poses a grave threat to the financial stability of the United States," the board can vote -to ban it from merging with or acquiring other business; -to restrict its business; and / or -to sell its assets

Loss frequency

•distribution is assumed Poisson -with parameters estimated from historical data. -Poisson is a discrete distribution useful for modelling the number of times an event occurs.

Total loss

•distribution is determined using Monte-Carlo simulations -combining the loss frequency with the loss severity.

A simplistic liquidity measurement system

•for a bank or other financial institution -Credit a liability-gathering unit for supplying liquidity -Debit an asset-generating unit for using liquidity •"Stable funds" are assigned a higher rank than "hot funds"

Examples of Operational Risk

•internal fraud •external fraud •employment practice •safety violations •business practices •damage to physical assets •business disruptions and system failures •execution, delivery, and process management

Because of its tendency to compound other risks,

•it is difficult or impossible to isolate liquidity risk.

Credit default swaps must be regulated by

•the Securities Exchange Commission (SEC) or the Commodity Futures Trading Commission (CFTC).

Credit risk

•the risk that a change in the credit quality (default, downgrading) of a counterparty - a "credit event" - will affect the value of a bank's position

Market risk

•the risk that changes in financial market prices and rates will reduce the value of the bank's positions •interest rates (bonds and derivatives) •equities (stocks and derivatives) •foreign exchange (currencies and derivatives) •commodities (commodities and derivatives) •Specific <Idiosyncratic> risk •Systematic risk, or general market risk