Consider two 1-year loans with a principal of $1 million and a default probability of 2% each. Assume that if one loan defaults, the other does not. Assume that in the event of default, the loan leads to a loss that can take any value between $0 and $1 million with equal probability, i.e., the probability that the loss is higher than $ x million is 1- x. If a loan does not default, it yields a profit equal to $0.02 million. a) Compute the 1-year 99% Value at Risk (VaR) and Expected Shortfall (ES) of a single loan. b) Compute the 1-year 99% VaR and ES for the portfolio of both loans. c) Does the VaR and the ES satisfy the subadditivity property in this case?

Consider two 1-year loans with a principal of $1 million and a default probability of 2% each. Assume that if one loan defaults, the other does not. Assume that in the event of default, the loan leads to a loss that can take any value between $0 and $1 million with equal probability, i.e., the probability that the loss is higher than $ x million is 1- x. If a loan does not default, it yields a profit equal to $0.02 million. a) Compute the 1-year 99% Value at Risk (VaR) and Expected Shortfall (ES) of a single loan. b) Compute the 1-year 99% VaR and ES for the portfolio of both loans. c) Does the VaR and the ES satisfy the subadditivity property in this case?

Essentials Of Investments

11th Edition

ISBN:9781260013924

Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Chapter1: Investments: Background And Issues

Section: Chapter Questions

Problem 1PS

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Consider two 1-year loans with a principal of $1 million and a default probability of 2% each. Assume that if one loan defaults, the other does not. Assume that in the event of default, the loan leads to a loss that can take any value between $0 and $1 million with equal probability, i.e., the probability that the loss is higher than $ ? million is 1 − ?. If a loan does not default, it yields a profit equal to $0.02 million. a) Compute the 1-year 99% Value at Risk (VaR) and Expected Shortfall (ES) of a single loan.
Assume you have the following asset and liability in your Balance Sheet: Asset - Bond A Modified Duration = 2.6 years Value = RM1.5 million Liability - Bond B Modified Duration = 3.1 years Value = RM1.0 million a. Calculate the duration gap. b. What is the expected change in Net Worth if interest increases by 1%? c. What should or could you to achieve immunised balance sheet? Note: Please show all workings.
Which of the following statements is CORRECT? Question 2 options: a) The proportion of the payment that goes toward interest on a fully amortized loan increases over time. b) An investment that has a nomiral rate of 6% with semiannual payments will have an effective rate that is smaller than 6%. c) If a loan or investment has annual payments, then the effective, periodic, and nominal rates of interest will all be different. d) The present value of a 3-year, $150 ordinary annuity will exceed the present value of a 3-year, $150 annuity due. e) if a loan has a nominal annual rate of 7%, then the effective rate will never be less than 7%.
Assess the following statements: Simple interest calculations assume the interest earned is never reinvested. The real interest rate is the increment to purchasing power that the lender earns in order to induce him or her to forego current consumption. Earning a 5% interest rate with annual compounding is better than earning a 4.95% interest rate with semiannual compounding. For any positive interest rate the present value of a given annuity will be less than the sum of the cash flows and the future value of the same annuity will be greater than the sum of the cash flows. a. Three statements are incorrect. b. Two statements are incorrect. c. Only one statement is incorrect. d. All statements are correct.
Assess the following statements: 1. Simple interest calculations assume the interest earned is never reinvested. II. The real interest rate is the increment to purchasing power that the lender earns in order to induce him or her to forego current consumption. II. Earning a 5% interest rate with annual compounding is better than earning a 4.95% interest rate with semiannual compounding. IV. For any positive interest rate the present value of a given annuity will be less than the sum of the cash flows and the future value of the same annuity will be greater than the sum of the cash flows. All statements are correct. Two statements are incorrect. O Three statements are incorrect. Only one statement is incorrect.
Assume you have the following asset and liability in your Balance Sheet: Asset - Bond A Modified Duration = 2.6 years Value = RM1.5 million Liability - Bond B Modified Duration = 3.1 years Value = RM1.0 million a. Calculate the duration gap. b. What is the expected change in Net Worth if interest increases by 1%? Assume previous interest is 10% c. What should or could you to achieve immunised balance sheet? Note: Please show all workings.
which of the following conditions indicates that a loan assumption is least advisable? An existing loan with a high loan-to-value ratio An existing loan with a due on sale clause A buyer who can make a 10% down payment Is scarcity of mortgage money
Assume you have the following asset and liability in your balance sheet Asset - Bond AModified Duration = 1.5 yearsValue = RM1 million Liability - Bond BModified Duration 2.6 yearsValue = RM2 million a. Calculate the duration gaps?b. What is the expected change in Net worth if interest increases by 1%?c. What should or could you to achieve immunised balance sheet?
D3) The value of a derivative that pays off $100 after one year if a company has defaulted during the year is $5. The value of a derivative that pays off $100 after one year if a company has not defaulted is $97. (a) What is the risk-free rate? (b) What is the risk-neutral probability of default?
which of the following statements are true? 1. there is an inverse relationship between interest rates and future vales 2. the effective annual interest rate (EAR) will be higher than the annual percentage rate (APR) for a loan that compounds interest annually 3. there is an inverse relationship between present value and interest rates 4. all else equal, the more frequent interest in compounded on a loan, the more interest you will have to pay.
Indicate whether the statement is true or false. 1. Given 10 and 30 year loans with the same interest rate, the 30 year loan results in a lower periodic payment. a. True b. False
Consider a loan repayment plan described by the following initial value problem, where the amount borrowed is B(0) = $40,000, the monthly payments are $600, and B(t) is the unpaid balance of the loan. Use the initial value problem to answer parts a through c. B' (+) =0.03B - 600, B(0) = 40,000 a) Find the solution of the initial value problem and explain why B is an increasing solution. B(t) = Why is B an increasing function? O A. The function is increasing because it is an exponential function with a positive coefficient and a negative exponent. O B. The function is increasing because it is an exponential function with a positive coefficient and a positive exponent. O C. The function is increasing because it is an exponential function with a positive exponent. O D. The function is increasing because it is an exponential function with a positive coefficient. b) What is the most that you can borrow under the terms of this loan without going further into debt each month? The…

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