Financial Risk Management Final

VAR with the confidence level of 1% means - answer-•the worst possible loss such that there is less than 1% chance of losing more than that in a single trading day. This worst possible loss determines - answer-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. Value at Risk DOES ATTEMPT to answer the question - answer-•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? VaR equation variables - answer-•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 In a normal distribution if c = 99% then α = - answer--2.33 In a Student-T distribution if c = 99% then α = - answer-3.365 VaR: Benefits - answer-•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 Estimating μ and σ - answer-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 Historical Simulation - answer-•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. Advantages and Disadvantages of historical simulation - answer-•The biggest advantage is no need to assume any distribution. •The biggest disadvantage is that the method relies heavily on the sample period. Monte Carlo Approach - answer-•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. VaR: Disadvantages - answer-•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 Delta-VaR measures - answer-The change in VaR if you had one more unit of asset A Stress Testing; Scenario Analysis - answer-•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 Scenario - answer--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. Disadvantages of stress testing/scenario analysis - answer-•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. Dynamic VaR - answer-•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 Requirements to VAR models - answer-•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. Liquidity risk is - answer--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 Things that cause an increase in liquidity risk - answer--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 Because of its tendency to compound other risks, - answer-•it is difficult or impossible to isolate liquidity risk. In all but the most simple of circumstances, - answer-•comprehensive measures of liquidity risk don't exist. A simplistic liquidity measurement system - answer-•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" Liquidity: Scenario Analysis - answer-•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. Types of liquidity risks - answer-•Liquidity funding risk •Liquidity trading risk Liquidity Trading Risk - answer-•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 Trader's Problem - answer-•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 Liquidity Funding Risk - answer-•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 Sources of Liquidity - answer-•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 Liquidity Black Holes - answer-•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 Leveraging and Deleveraging - answer-• 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. Regulatory Principles: Banks Should - answer-•A bank must take responsibility for liquidity management •A bank should clearly articulate a liquidity risk tolerance