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

See similar textbooks

Similar questions

Suppose that you want to take out a loan and that your local bank wants to charge you an annual real interest rate equal to 3%. Assuming that the annualized expected rate of inflation over the life of the loan is 1%, determine the nominal interest rate that the bank will charge you. What was the actual real interest rate on the loan if, over the life of the loan, actual inflation is 0.5%?
Suppose the risk-free interest rate is 4.6%. Having $600 today is equivalent to having what amount in one year? (Round to the nearestcent.) Having $600 in one year is equivalent to having what amount today? (Round to the nearestcent.) Which would you prefer, $600 today or $600 in one year? Does your answer depend on when you need the money? Why or why not? (Round to the nearestcent.)
Suppose that as a loan officer for a bank you just completed a £1 million loan to a small business. This is a senior unsecured loan, with one-year maturity and carries a 10% p.a. interest rate. You rate the borrower internally as B-, which translates into a one-year probability of default (PD) estimate of 10%. Loss given default (LGD) for the loan is estimated as 30%. Determine the expected cash flow from the loan at maturity. O a. £1,034,000 O b. £1,067,000 O c. £1,123,000
You borrow $1,000 from a bank at 6% annual interest and promise to pay it back after a year. As you sign the loan documents, both you and the bank expect inflation to be 3% in the coming year. During the course of the year, however, the average price level rises by only 1%. What best describes this situation? Select one: a. Both you and the bank are better off because the inflation rate is less than the nominal interest rate but greater than zero. O b. The bank has gained at your expense because the real interest rate on the loan is higher than expected. c. Neither you nor the bank has gained anything extra because the inflation rate is less than the nominal interest rate. O d. You have gained at the bank's expense because you can pay the bank back in inflated dollars.
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%.
You borrow $2mn at an interest rate of 5% per year to purchase a real estate property for the cost of $2.5mn. The borrowing costs are due only at the end of the year. 1). At what property price is it optimal to default on the loan when the borrowing rate is 1%, 5% and 10%?2). Consider three different interest rates of 1%, 5% and 10% and different equity shares of 5%, 20% and 50%. Discuss how the different interest rates and leverage affect the return on equity.
Which of the following statements is most correct? The first payment under a 3-year, annual payment, amortized loan for $1,000 will include a smaller percentage (or fraction) of interest if the interest rate is 5 percent than if it is 10 percent. If you are lending money, then, based on effective interest rates, you should prefer to lend at a 10 percent nominal, or quoted, rate but with semiannual payments, rather than at a 10.1 percent nominal rate with annual payments. However, as a borrower you should prefer the annual payment loan. The value of a perpetuity (say for $100 per year) will approach infinity as the interest rate used to evaluate the perpetuity approaches zero. Statements a, b, and c are all true. Statements b and c are true.
A borrower can obtain an 80% loan with an 8% interest rate and monthly payments. The loan is to be fully amortized over 25 years. Alternatively, he could obtain a 90% loan at an 8.5% rate with the same loan term. The borrower plans to own the property for the entire loan term. solve with finanical calucltor What is the incremental cost of borrowing the additional funds? How would your answer change if 2 points were charged on the 90% loan? Would your answer to part (b) change if the borrower planned to own the property for only 5 years?
A firm has obtained a 3-year floating rate loan paying a premium of 2%. Given the prime rate is 5%. Immediately after the loan is taken, the prime rate increases to 6%. Which of the following is TRUE? Question 49 options: 1) The interest rate payable is 3%. 2) The interest rate payable is 5%. 3) The interest rate payable is 7%. 4) The interest rate payable is 8%.
D3) Finance ABC is currently paying 7.5% fixed rate on S$10m. ABC can borrow at LIBOR. XYZ is paying LIBOR + 0.8% on S$10m. XYZ can borrow fixed at 9.5%. ABC and XYZ agree to swap interest payments to take advantage of the arbitrage created by their respective interest rate differentials. Which of the following is correct? A. ABC ends up paying LIBOR - 0.6%, XYZ ends up paying 8.9% B. ABC ends up paying 7.5%, XYZ ends up paying LIBOR + 0.8% C. ABC ends up paying LIBOR, XYZ ends up paying 9.5% D. None of the above
A borrower can obtain an 80 percent loan with an 9 percent interest rate and monthly payments. The loan is to be fully amortized over 25 years. Alternatively, he could obtain a 95 percent loan at an 9.5 percent rate with the same loan term. The borrower plans to own the property for the entire loan term. Required: a. What is the incremental cost of borrowing the additional funds? (Hint: The dollar amount of the loan does not affect the answer.) b. What is the incremental cost of borrowing the additional funds if 2 points were charged on the 95 percent loan? c. What is the incremental cost of borrowing the additional funds if the borrower planned to own the property for only five years? Complete this question by entering your answers in the tabs below. Required A Required B Required C What is the incremental cost of borrowing the additional funds if the borrower planned to own the years? (Do not round intermediate calculations. Round your final answer to 2 decimal places.) Incremental…
Suppose that the current rates on 60 and 120 day GICs are 5.50% and 5.75%, respectively. An investor is weighing the alternatives of purchasing a 120 day GIC versus purchasing a 60 day GIC and then reinvesting its maturity value in a second 60 day GIC.What would the interest rate on 60 day GICs have to be 60 days from now for the investor to end up in the same financial position with either alternative?

SEE MORE QUESTIONS

Recommended textbooks for you

Essentials Of Investments

Finance

ISBN:

9781260013924

Author:

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

Publisher:

Mcgraw-hill Education,

FUNDAMENTALS OF CORPORATE FINANCE

Finance

ISBN:

9781260013962

Author:

BREALEY

Publisher:

RENT MCG

Financial Management: Theory & Practice

Finance

ISBN:

9781337909730

Author:

Brigham

Publisher:

Cengage

Foundations Of Finance

Finance

ISBN:

9780134897264

Author:

KEOWN, Arthur J., Martin, John D., PETTY, J. William

Publisher:

Pearson,

Fundamentals of Financial Management (MindTap Cou…

Finance

ISBN:

9781337395250

Author:

Eugene F. Brigham, Joel F. Houston

Publisher:

Cengage Learning

Corporate Finance (The Mcgraw-hill/Irwin Series i…

Finance

ISBN:

9780077861759

Author:

Stephen A. Ross Franco Modigliani Professor of Financial Economics Professor, Randolph W Westerfield Robert R. Dockson Deans Chair in Bus. Admin., Jeffrey Jaffe, Bradford D Jordan Professor

Publisher:

McGraw-Hill Education

Essentials Of Investments

Finance

ISBN:

9781260013924

Author:

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

Publisher:

Mcgraw-hill Education,

FUNDAMENTALS OF CORPORATE FINANCE

Finance

ISBN:

9781260013962

Author:

BREALEY

Publisher:

RENT MCG

Financial Management: Theory & Practice

Finance

ISBN:

9781337909730

Author:

Brigham

Publisher:

Cengage

Foundations Of Finance

Finance

ISBN:

9780134897264

Author:

KEOWN, Arthur J., Martin, John D., PETTY, J. William

Publisher:

Pearson,

Fundamentals of Financial Management (MindTap Cou…

Finance

ISBN:

9781337395250

Author:

Eugene F. Brigham, Joel F. Houston

Publisher:

Cengage Learning

Corporate Finance (The Mcgraw-hill/Irwin Series i…

Finance

ISBN:

9780077861759

Author:

Stephen A. Ross Franco Modigliani Professor of Financial Economics Professor, Randolph W Westerfield Robert R. Dockson Deans Chair in Bus. Admin., Jeffrey Jaffe, Bradford D Jordan Professor

Publisher:

McGraw-Hill Education

SEE MORE TEXTBOOKS