Risk Management s2

Risk Management

Module 4, April 2007

Final Exam

Part 1

One-point questions

1. Suppose that the market has been very volatile recently. Which of the main methods of measuring variance for the delta-normal method is the least suitable in this case?

Historical volatility (with equal weights)

2. Consider a coupon bond that matures in several years. How will the sensitivity to the interest rate risk change right after the coupon payment (compared to the moment just before the coupon payment): (i) increase, (ii) remain the same, (iii) decrease, (iv) none of above.

3. How will VaR computed using delta-normal approach change if we move from 99% to 95% confidence interval?

Decrease by the factor 1.65/2.33

4. Which measure is defined as (approximate) change in VaR due to a given change in the position computed on the basis of VaR delta?

Marginal VaR

5. Which type of systematic risk and the corresponding greek letter can only be hedged by options (and not by futures or swaps)?

Volatility, vega

6. Which of the four benchmark models of computing credit VaR (considered during the course) use the top down approach?

CreditRisk+, CreditPortfolioView

7. What are the minimum and maximum values of the (market risk) VaR multiplier (relative to capital/provisions) according to the Basel agreement?

3 and 4

8. VaR of a (long) American option is higher than VaR of a European option with the same characteristics. Evaluate the statement: (i) true, (ii) false, (iii) none of above.

9. Describe the two means by which the futures exchange solves the credit risk problem.

Margin requirements and marking-to-market

10. Which method allows risk managers assess the magnitude of the worst losses?

Stress testing, Monte Carlo analysis

Two-point questions

1. List three main applications of VaR.

· Asset allocation

· Position limits

· Economic capital

· Performance assessment

2. List main factors that influence the credit spread of a given instrument besides its credit rating.

· Liquidity

· Maturity

· Macroeconomic factors

· Market volatility

3. Describe three main differences between market and credit risk.

· P&L distribution: asymmetric for CR

· Occurrence: rare for CR

· Horizon: longer for CR

· Tradability: instruments exposed to CR are often non-tradable (e.g., credits)

· CR is more sensitive to the company-specific (rather than to market-wide) factors

· Hedging is typically more difficult for CR

4. Describe three different situations when VaR measured using delta-normal approach recommended by RiskMetrics may largely underestimate market risk of an actively trading financial company.

· The company has decided to rebalance its portfolio

· The market environment has changed (and so did risk factor distributions)

· Intraday trading

· Missing risk factors

· Wrong model

· Bad quality of data

5. Describe three different situations when the EDF (estimated according to the KMV Credit Monitor) cannot be used as a (precise) measure of the company’s probability of default.

· The company’s stock is illiquid or not traded.

· The company has a complicated or non-transparent capital structure.

· The stock volatility is largely driven by factors unrelated to the company.

· The distributional assumptions (e.g., about the log-normal distribution of the value of the company) are not correct.

Part 2

Four-point questions

1. What are the advantages of VaR as a risk measure compared to standard deviation? Under which conditions are they proportional to each other? What are the main drawbacks of VaR? Which risk measure(s) can effectively complement VaR?

STD works perfectly for the family elliptic distributions (such as normal) fully described by the first two moments. For them, VaR is proportional to STD. In the general case, VaR is better since it concentrates on the downside risk. The main VaR drawbacks are as follows (ranked in the decreasing order):

· The actual extreme losses are unknown

· Not subadditive

· Model risk and measurement error (esp. for a high confidence level)

· May be manipulated

The expected shortfall can complement VaR.

2. Describe how to hedge a 5-year short forward on oil with the settlement price $60 per barrel and nominal position of 1 mln barrels with 6-month oil futures. What are the main risks of this hedging strategy? Which company suffered great losses because of neglecting these risks? Which risk-factors should be present in a proper VaR model?

Follow the case of Metallgezellschaft

3. Which of the three main methods to measure (market risk) VaR uses a local estimation approach? What is the main distinguishing feature of such an approach (in comparison with the full estimation approach)? How can one compute VaR for the portfolio including options using such an approach? Will it give a precise result, good approximation or bad approximation? Explain why.

This is delta-normal approach, which relies on the first-order (i.e., linear) approximation. Delta-gamma(-vega) approximation can be used to account for nonlinear instruments like options. However, this provides a poor approximation.

4. What is the primary disadvantage of the (basic) historical simulation approach to measuring market risk? How can the inclusion of more observations remedy this problem and what is the general trade-off when choosing the length of the sample? What are the other problems and how can we modify the historical simulation approach to remedy them?

Few observations at the left tail, which is esp severe for the high confidence level. The general trade-off is that longer sample reduces the estimation error, but shorter sample reduces the risk of the structural break. The other problems are that all historical observations are treated as equally important. One can assume that they are assigned weights decreasing with time or reversely related to daily volatility.

5. What are the main objectives of stress testing? Explain why leading financial institutions pay so much attention to stress tests. What is the main advantage of the scenario approach relative to the factor push approach? What are the strong sides and weak sides of the historical and hypothetical scenarios? Describe how to compute stress VaR.

Stress tests show how much a financial institution can lose in an extreme case (beyond VaR). This is important if one wants to minimize the risk of company’s failure, even though it may happen with a very small probability. The company may choose to reject this risk or accept it and be ready to the possible crisis. The main advantage of the scenario approach is that accounts for the correlations between different factors, whereas the factor push approach assumes a change in only one of them. The strong side of the historical scenarios is that they truly reflect the interaction between different key factors. The hypothetical scenarios are constructed to better reflect the current situation. The stress VaR is computed as a regular VaR, but under a different set of parameters, which are likely to occur under the crisis.

Describe briefly the capital adequacy requirements set by the Basel Committee for market and credit risks (Basel II). Discuss the choice by Basel of the particular values of VaR parameters (time interval and confidence level) vs. other possible values (e.g. by RiskMetrics). Why did Basel introduce a multiplicative factor larger than 1 to compute economic capital based on VaR? How can you explain the difference between multiplicative factor for market and credit risk?

See ch. 7 in Hull.

7. Give a definition of the credit exposure. Why is the credit exposure for derivatives computed in a different way from that for loans? Explain why the credit exposure of an interest-rate swap changes non-monotonically with time.

Credit exposure (CE) is the amount we would lose in case of default with zero recovery. Usually, it is estimated as a current market value if it is positive and 0 otherwise. For loans it is close to the face value. For derivatives, the current market value is close to 0, but may quickly change. Therefore, CE of derivatives is usually computed as a quantile of the distribution of the future market value. For an interest-rate swap, CE changes non-monotonically with time due to 2 oppsite effects: diffusion (increasing risk over time) and amortization (decreasing duration)

Discuss whether and how it is possible to adjust the four benchmark models of computing credit VaR (considered during the course) to account for the interest rate risk.

In CreditMetrics, one can use simulated forward rates to compute the future price of the bond. The Monte Carlo analysis will produce the distribution accounting for the interest rate risk. In KMV Portfolio Manager, the default point may be made stochastic depending on the current term structure of the interest rates. CreditRisk+ focuses on modeling of the default and cannot be modified to account for the interest rate risk. In Credit Portfolio View, the model for PD may include interest rates among other macrofactors. At the final stage, the distribution of the future bond price may be found similarly to the adjusted Monte Carlo procedure for CreditMetrics.

Compute one-year 95% VaR of a three-year senior unsecured bond with BB credit rating and 8% coupon rate using Credit Metrics approach and data below.

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