Financial institutions need to take volatility clustering into account:
1. To avoid taking on an undesirable level of risk
2. To know the right level of capital they need to hold
3. To meet regulatory requirements
4. To account for mean reversion in returns
Answer : B
Volatility clustering leads to levels of current volatility that can be significantly different from long run averages. When volatility is running high, institutions need to shed risk, and when it is running low, they can afford to increase returns by taking on more risk for a given amount of capital. An institution's response to changes in volatility can be either to adjust risk, or capital, or both. Accounting for volatility clustering helps institutions manage their risk and capital and therefore statements I and II are correct.
Regulatory requirements do not require volatility clustering to be taken into account (at least not yet). Therefore statement III is not correct, and neither is IV which is completely unrelated to volatility clustering.
Which of the following statements are true in relation to Historical Simulation VaR?
1. Historical Simulation VaR assumes returns are normally distributed but have fat tails
2. It uses full revaluation, as opposed to delta or delta-gamma approximations
3. A correlation matrix is constructed using historical scenarios
4. It particularly suits new products that may not have a long time series of historical data available
Answer : A
Historical Simulation VaR is conceptually very straightforward: actual prices as seen during the observation period (1 year, 2 years, or other) become the 'scenarios' forming the basis of the valuation of the portfolio. For each scenario, full revaluation is performed, and a P&L data set becomes available from which the desired loss quantile can be extracted.
Historical simulation is based upon actually seen prices over a selected historical period, therefore no distributional assumptions are required. The data is what the data is, and is the distribution. Statement I is therefore not correct.
It uses full revaluation for each historical scenario, therefore statement II is correct.
Since the prices are taken from actual historical observations, a correlation matrix is not required at all. Statement III is therefore incorrect (it would be true for Monte Carlo and parametric Var).
Historical simulation VaR suffers from the limitation that if enough representative data points are no available during the historical observation period from which the scenarios are drawn, the results would be inaccurate. This is likely to be the case for new products. Therefore Statement IV is incorrect.
Which of the following statements are true in relation to Monte Carlo based VaR calculations:
1. Monte Carlo VaR relies upon a full revalution of the portfolio for each simulation
2. Monte Carlo VaR relies upon the delta or delta-gamma approximation for valuation
3. Monte Carlo VaR can capture a wide range of distributional assumptions for asset returns
4. Monte Carlo VaR is less compute intensive than Historical VaR
Answer : A
Monte Carlo VaR computations generally include the following steps:
1. Generate multivariate normal random numbers, based upon the correlation matrix of the risk factors
2. Based upon these correlated random numbers, calculate the new level of the risk factor (eg, an index value, or interest rate)
3. Use the new level of the risk factor to revalue each of the underlying assets, and calculate the difference from the initial valuation of the portfolio. This is the portfolio P&L.
4. Use the portfolio P&L to estimate the desired percentile (eg, 99th percentile) to get and estimate of the VaR.
Monte Carlo based VaR calculations rely upon full portfolio revaluations, as opposed to delta/delta-gamma approximations. As a result, they are also computationally more intensive. Because they are not limited by the range of instruments and the properties they can cover, they can capture a wide range of distributional assumptions for asset returns. They also tend to provide more robust estimates for the tail, including portions of the tail that lie beyond the VaR cutoff.
Therefore I and III are true, and the other two are not.
Which of the following decisions need to be made as part of laying down a system for calculating VaR:
1. The confidence level and horizon
2. Whether portfolio valuation is based upon a delta-gamma approximation or a full revaluation
3. Whether the VaR is to be disclosed in the quarterly financial statements
4. Whether a 10 day VaR will be calculated based on 10-day return periods, or for 1-day and scaled to 10 days
Answer : C
While conceptually VaR is a fairly straightforward concept, a number of decisions need to be made to select between the different choices available for the exact mechanism to be used for the calculations.
The Basel framework requires banks to estimate VaR at the 99% confidence level over a 10 day horizon. Yet this is a decision that needs to be explicitly made and documented. Therefore 'I' is a correct choice.
At various stages of the calculations, portfolio values need to be determined. The valuation can be done using a 'full valuation', where each position is explicitly valued; or the portfolio(s) can be reduced to a handful of risk factors, and risk sensitivities such as delta, gamma, convexity etc be used to value the portfolio. The decision between the two approaches is generally based on computational efficiency, complexity of the portfolio, and the degree of exactness desired. 'II' therefore is one of the decisions that needs to be made.
The decision as to disclosing the VaR in financial filings comes after the VaR has been calculated, and is unrelated to the VaR calculation system a bank needs to set up. 'III' is therefore not a correct answer.
Though the Basel framework requires a 10-day VaR to be calculated, it also allows the calculation of the 1-day VaR and and scaling it to 10 days using the square root of time rule. The bank needs to decide whether it wishes to scale the VaR based on a 1-day VaR number, or compute VaR for a 10 day period to begin with. 'IV' therefore is a decision to be made for setting up the VaR system.
A risk management function is best organized as:
Answer : B
The point that this question is trying to emphasize is the independence of the risk management function. The risk function should be segregated from the risk taking functions as to maintain independence and objectivity.
Choice 'd', Choice 'c' and Choice 'a' run contrary to this requirement of independence, and are therefore not correct. The risk function should report directly to senior levels, for example directly to the audit committee, and not be a part of the risk taking functions.
An investor enters into a 5-year total return swap with Bank A, with the investor paying a fixed rate of 6% annually on a notional value of $100m to the bank and receiving the returns of the S&P500 index with an identical notional value. The swap is reset monthly, ie the payments are exchanged monthly. On Jan 1 of the fourth year, after settling the last month's payments, the bank enters bankruptcy. What is the legal claim that the hedge fund has against the bank in the bankruptcy court?
Answer : C
According to ISDA standard definitions, the legal claim for OTC derivatives is the current replacement value of the contract. Therefore Choice 'c' is the correct answer. None of the other choices are correct.
Concentration risk in a credit portfolio arises due to:
Answer : C
Concentration risk in a credit portfolio arises due to a high degree of correlation between the default probabilities of the issuers of securities in the portfolio. For example, the fortunes of the issuers in the same industry may be highly correlated, and an investor exposed to multiple such borrowers may face 'concentration risk'.
A low degree of correlation, or independence of individual defaults in the portfolio actually reduces or even eliminates concentration risk.
The fact that issuers are from the same country may not necessarily give rise to concentration risk - for example, a bank with all US based borrowers in different industries or with different retail exposure types may not face practically any concentration risk. What really matters is the default correlations between the borrowers, for example a lender exposed to cement producers across the globe may face a high degree of concentration risk.