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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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.
Assume a borrower is purchasing a property for USD 100,000and faces two possible loan alternatives. A lender is willingto make an 80% first mortgage loan, or USD 80,000, for 25years at 12% interest. The same lender is willing to lend 90%, or USD 90,000, for 25 years at 13%. Both loans will have afixed interest rates and CPM. How should the borrowercompare these two alternatives?.
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%.
2) Solve the following NPV problems: Problem 1 . Suppose that a borrower receives a 1,000 euro loan from Bank A, with a 10-year maturity at an annual interest rate of 5% with the obligation to pay the interest at the end of each year for the next 10 years. However, at the end of the 6th year, due to financial difficulties, he borrows from the same bank an additional 1,000 euros at an annual interest rate of 5% making the following agreement: a. not to pay any installment at the end of the next two years, i.e. the 7th and 8th year, and b. then pay an equal amount of interest for the next 8 years (i.e. from the end of the 9th year until the end of the 16th year) in order to fully repay the first as well as the second loan. It is requested to calculate the interest-rate installment of the loan that occurred after the restructuring. Problem 2. Suppose that parents make family planning to finance their child's studies and buy a car. The expected costs for studies are EUR 10 000 per year…
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.
2
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?
FINCORP has two debtors who each make a $10, 000 purchase. Debtor 1 pays their account in 10 days, while debtor 2 pays in 30 days. a) In simple terms, what nominal annual interest rate is debtor 2 incurring for the benefit of delaying payment? Note: base your answer on the following logic. If a borrower pays 3% for a 30-day loan, we could express the nominal annual rate as roughly 36.5% i.e 3% x 365/30 = 36.5% that payment is due within 30 days but debtors will receive a 5 percent discount if they pay within 14 days. I'm quite unsure if that 5% as it is a discount, is handy or the steps to calculate the nominal interest rate

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