Dear Sir

I would like the answers of the attached exams. only calculations

Student id. .................................. School of Business and Economics EXAMINATION Course : Risk Management Coordinator(s): Date Location Code:ECB4056 D. Bams : : Version: 7 / 8 / 9 / 10 July 2015 MECC Communications devices and watches are not allowed - put them in your bag (under your table) or on the floor, not within arm's reach! Otherwise this will be reported as possible fraud to the Board of Examiners. Any changes to the examination after the official end of the examination will be reported as possible fraud to the Board of Examiners. Sanctions by the Board of Examiners on fraud or irregularities include such measures as: - complete or partial voidance or annulment of the relevant examination; - exclusion from participation or further participation of one or more examinations or exams at the SBE for a period of time to be determined by the Board of Examiners, with a maximum period of one year; - termination of the student's registration for the concerning study programme. This examination consists of: start answering) 18 Pages (Front page included) 6 Questions (please check if you received all pages, before you You are allowed to make use of: 1. A non-programmable calculator 2. A two-sided signed-off formula sheet Norm: A total of 20 points can be received. The maximum points per question are provided within parentheses at the header of the question. Publication of the results: within 15 workdays A total of 20 points can be received. The maximum points per question are provided within parentheses at the header of the question. Procedure for objections: The inspection and complain procedure has been outlined in the block book on pages 6 and 7. Exam Inspection has been scheduled for Friday 17 July, 2015 after registration only. See ELEUM for details on registration. Particulars: You have to hand in the entire examination set. It is not allowed to take home, copy or photograph the examination or parts of it! (You can write your answers of MC questions on a piece of scrap paper and take it home). Student id. .................................. QUESTION 1 (4 points) Consider a 5-year, 5% coupon bond with a face value of 100. The yield on the bond is 8% per annum, compounded annually. Coupon payments are made every 12 months. (a) Calculate the price of the bond. (b)Calculate Macaulay's duration for the bond. (c) Calculate Modified Duration for the bond. (d)What does duration measure? Provide your interpretation. ANSWERS Student id. .................................. Student id. .................................. QUESTION 2 (3 points) The return distribution of a portfolio is normally distributed with a mean of 3 million and standard deviation of 8 million. (a) Calculate the 99% one-day VaR for the portfolio. Provide an interpretation of VaR. (b)Calculate the 10-day, 99% VaR for the portfolio. (c) Discuss the shortcomings of VaR, and how Expected Shortfall measure can be used to avoid them. ANSWERS Student id. .................................. Student id. .................................. QUESTION 3 (3 points) The current price of a stock is S t =$ 50 and the strike price is K=$ 50 . Assume the risk free rate is 2% and the asset pays 5% dividend per year. After fitting a GARCH (1, 1) model to the daily returns of a stock, we find =0.04 , =0.95 and =0.000001 . (a) What is the long-run volatility. (b) If today's volatility of return is estimated to be 2% per day, what is the expectation of the volatility value in 25 days. (c) What should be the price of a call option written on this stock with maturity of 25 days. ANSWERS Student id. .................................. Student id. .................................. QUESTION 4 (4 points) The price of derivative A at time t , indicated with A t , is calculated as: 2 A t =S t K St Where is the time-to-maturity of the derivative (measured in number of years), K is the strike price and S t shows the price of the underlying asset at time t . Today, the time-to-maturity of the derivative is =2 years , the underlying asset price is S t =$ 20 and the strike price of this derivative is K=$ 10. There is also a derivative B on the same underlying asset, with a delta of 4, and a gamma of 4. Derivati ve A B Delta ? 4 Gamm a ? 4 Vega Theta ? 0 ? 2 (a) Calculate the delta, the gamma, the vega and the theta of derivative (A). (b)) If you already have 1 unit of derivative A, what positions in derivative B and the underlying asset, would make the portfolio both delta neutral and gamma neutral? ANSWERS Student id. .................................. Student id. .................................. QUESTION 5 (2 points) You want to back-test the VaR (99%) of a portfolio consisting of two investments. You have 1200 days of data and observe 5 exceptions. You assume losses are iid. The significance level for your test is 2%. Should you reject the VaR? Why or why not? ANSWERS Student id. .................................. Student id. .................................. QUESTION 6 (4 points) You are reporting to the Chief Operational Officer (COO) at Maastricht Investments, LLC. You are responsible for estimating potential operational risk losses for your business line. The first step in achieving this is by estimating a loss frequency. You are given the following data: Student id. .................................. Figure 1: Distribution of the number of losses presented in Table 1 (a) Which distributional assumptions would you have to make in order to evaluate this data further? (b) According to your distributional assumption, what is the average number of yearly losses? (c) According to your distributional assumption, what is the variance of the frequency of losses? (d) What is the probability of having more than 5 losses in the next year? ANSWERS Student id. .................................. Student id. .................................. Student id. .................................. Appendix 1 Table for N(x) when x= 0 This table shows values for N(x) for x>= 0. The table should be used with interpolation. For example, N(0.6278) = N(0.62) + 0.78[N(0.63) - N(0.62)] = 0.7324+0.78 x (0.7357 - 0.7324) = 0.7350. Student id. .................................. In case you finished the exam before 16.00 hrs: please leave the examination hall as quiet as possible, so you will not disturb the students who still are trying to concentrate on their work! Student id. .................................. School of Business and Economics EXAMINATION Course : Risk Management Coordinator(s): Date Location Code: EBC4056 D. Bams : : Version: Monday, 1 June 2015 Time: 13.00 - 16.00 MECC Westhal Communications devices and watches are not allowed - put them in your bag (under your table) or on the floor, not within arm's reach! Otherwise this will be reported as possible fraud to the Board of Examiners. Any changes to the examination after the official end of the examination will be reported as possible fraud to the Board of Examiners. Sanctions by the Board of Examiners on fraud or irregularities include such measures as: - complete or partial voidance or annulment of the relevant examination; - exclusion from participation or further participation of one or more examinations or exams at the SBE for a period of time to be determined by the Board of Examiners, with a maximum period of one year; - termination of the student's registration for the concerning study programme. This examination consists of: start answering) 19 Pages (Front page included) 6 Questions (please check if you received all pages, before you You are allowed to make use of: 1. A non-programmable calculator 2. A two-sided signed-off formula sheet Norm: A total of 20 points can be received. The maximum points per question are provided within parentheses at the header of the question. Publication of the results: within 15 workdays Procedure for objections: The inspection and complain procedure has been outlined in the block book on pages 6 and 7. Exam Inspection has been scheduled for Friday 12 June, 2015 after registration only. See ELEUM for details on registration. Particulars: You have to hand in the entire examination set. It is not allowed to take home, copy or photograph the examination or parts of it! (You can write your answers of MC questions on a piece of scrap paper and take it home). 1 Student id. .................................. QUESTION 1 (3 points) The 1-day value-at-risk of a portfolio at 95% confidence level is found to be -5%. What is the 1-day value-at-risk of the same portfolio at 99% confidence level, under the three following scenarios: (A) The returns are independent and identically normally distributed, and =1 . (B) The tail of the distribution follows the power law such that and Prob ( v > x )=K x =1 . (C) The tail of the distribution follows the generalized Pareto distribution, such that =1 and =0.01. This generalized Pareto distribution is fitted to the loss values beyond 4%. ANSWERS 2 Student id. .................................. 3 Student id. .................................. QUESTION 2 (3 points) The price of derivative (A) at time t , shown with A t , is calculated as: 2 A t =S t K St Where is the time-to-maturity of the derivative (measured in number of years), K is the strike price and at date shows the price of the underlying asset t . Today, the time-to-maturity of the derivative is S t =$ 20 underlying asset price is K=$ 10. St =2 years , the and the strike price of this derivative is Assume derivative (B) with a delta of 4, and a gamma of 4. Derivat Delta Gamm a Vega Theta ive A B ? 4 ? 4 ? 0 ? 2 (A) Calculate the Delta, the Gamma, the Vega and the Theta of derivative A. (B) If you already have 1 unit of derivative A, what positions in derivative B and the underlying asset would make the portfolio both Delta neutral and Gamma neutral? (C) Using your results from question (A) and Taylor series expansion, write the changes in the price of derivative A (i.e. A ), in terms of S and S2 . ANSWERS 4 Student id. .................................. 5 Student id. .................................. QUESTION 3 (3 points) Assume that volatility is following a GARCH(1,1) process. After fitting a GARCH (1, 1) model to the daily returns of a stock, we find =0.000001 . The current price of the stock is particular call option is K=$ 50 S t =$ 50 =0.4 , =0.95 and and the strike price of a with maturity of 25 days.. Assume the risk free rate is 2% and the asset pays 5% dividend per year. (A) What is the long-run volatility? (B) If today's volatility of return is estimated to be 2% per day, what is the expectation of the volatility value in 25 days? (C) What should be the price of the call option written on this stock? ANSWERS 6 Student id. .................................. 7 Student id. .................................. QUESTION 4 (3 points) (A) What are Contingent Convertible Bonds? Why are they attractive for banks? (B) Name the seven categories of Operational Risk. (C) Explain moral hazard and adverse selection risks. ANSWERS 8 Student id. .................................. 9 Student id. .................................. QUESTION 5 (3 points) You are working as an adviser to a Portfolio Manager at Maastricht Investments, LLC where a group of Quants have provided you with some results obtained from a set of two models they have developed and executed. Table 2 provides some descriptive statistics of the data used to fit the model. The two models that the Quants fit are a (1) GARCH(1,1) model with a t conditional probability distribution and (2) a GARCH(1,1) with a Gaussian conditional probability distribution. Table 3 shows the model outputs including parameter estimates, standard errors, t-statistics, number of parameters, and the Akaike Information Criterion (AIC). During your Risk Management course, you learned about the dangers in model fitting. Based on the criteria addressed by Hull, you are requested to provide an advice to the Chief Risk Officer regarding the preference between the two models presented in Table 3. 10 Student id. .................................. In particular, answer the following questions: (A) List three dangers in model building. (B) Which one of the two models do you recommend to use? (C) Which information in Table 3 is useful in justifying your question above? ANSWERS 11 Student id. .................................. 12 Student id. .................................. QUESTION 6 (5 points) You are reporting to the Chief Operational Officer (COO) at Maastricht Investments, LLC. You are responsible for estimating potential operational risk losses for your business line. The first step in achieving this is by estimating a loss frequency. You are given the following data: 13 Student id. .................................. Figure 1: Distribution of the number of losses presented in Table 1 (A) Which distributional assumptions would you have to make in order to evaluate this data further? (B) According to your distributional assumption, what is the average number of yearly losses? (C) According to your distributional assumption, what is the variance of the frequency of losses? (D) What is the probability of having more than 5 losses in the next year? (E) What is the probability of having less than 2 losses in the next year? ANSWERS 14 Student id. .................................. 15 Student id. .................................. 16 Student id. .................................. Appendix 1 Table for N(x) when x= 0 This table shows values for N(x) for x>= 0. The table should be used with interpolation. For example, N(0.6278) = N(0.62) + 0.78[N(0.63) - N(0.62)] = 0.7324+0.78 x (0.7357 - 0.7324) = 0.7350. 18 Student id. .................................. In case you finished the exam before 16.00 hrs: please leave the examination hall as quiet as possible, so you will not disturb the students who still are trying to concentrate on their work! 19