Consider two local banks. Bank A has 100 loans outstanding, each for $0.9 million, that it expects will be repaid today. Each loan has a 7% probability of default, in which case the bank is not repaid anything. The chance of default is independent across all the loans. Bank B has only one loan of $90 million outstanding, which it also expects will be repaid today. It also has a 7% probability of not being repaid. Calculate the following: a. The expected overall payoff of each bank. b. The standard deviation of the overall payoff of each bank.
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- Problem 3 There are two types of banks, A and B. Each bank has 20 loans. Each loan of type A bank generates $500 with probability 0.9 and $200 with probability 0.1, and these cash flows are independently distributed. Each loan of the type B bank generates $600 with probability 0.4 and $200 with probability 0.6, and these cash flows are independently distributed, too. Suppose that the bank XYZ is type A. However, the investors believe that XYZ is type A with probability 0.3 and type B with probability 0.7. Ignore investors’ opportunity cost of investment (or assume that that the risk-free interest rate is 0%.) The investors are risk neutral. Consider the following securitization options for the bank XYZ. 1. Suppose XYZ wants to securitize the portfolio of loans as a two-class bond. • If the class 1 bondholders would be promised certain payoff for sure, what is the amount the bank should promise? What is the market price of the class 1 bond? • If the class 2 bondholders are…15. A city mayor decides to construct a new bridge over the major river in the town. The estimated life of such a structure will be 20 years. There is a 70% probability that the total initial costs (consulting fees and construction) will be $800,000 and a 30% probability that such costs would be $1 million. There is 100% probability that the maintenance costs would be $30,000 every 5 years. How much money should the city borrow now in order to carry out the entire project including maintenance? The interest rate is 5%.4) You are a financial professional working in a corporate loan department. A company named Mitch Hedberg Inc. (MH) comes to you for a loan. MH has debt from a previous loan (given by a different firm than yours) of 200. Your company analysts say that MH is likely to earn either 180, 240, or 300 this year - each with a probability of 1/3. MH wants you to lend them 100. MH could use this borrowed 100 to do either project X or project Y. Project X has a guaranteed return of 125 if the 100 is put there. Project Y may return either 0 or 210; each has probability of 1/2 and also costs 100 to do. a) Which project, X or Y, has the larger expected value? b) If you lend MH the 100, what will they do with the money? Why? Show your math. c) Should you lend MH the money or not? Show your math. d) Why did I choose the letters "MH" for this problem? What financial economic concept with initials "MH" is important in this problem?
- You have $1,000 that you can invest. If you buy Ford stock, you face the following returns and probabilities from holding the stock for one year: with a probability of 0.2 you will get $1,500; with a probability of 0.4 you will get $1,100; and with a probability of 0.4 you will get $900. If you put the money into the bank, in one year’s time you will get $1,100 for certain. a) What is the expected value of your earnings from investing in Ford stock? b) Suppose you are risk-averse. Can we say for sure whether you will invest in Ford stock or put your money into the bank?A small bakery serves very popular fresh meat pies every day. The cost of making each pie is $2, and they are sold for $5 each. Unsold pies at the end of the day will be put for a quick sale for $1.00 each, and they are always sold out. The record of the past daily sales of the pies is presented below. Demand 100 150 200 250 300 350 Probability 10% 20% 25% 25% 15% 5% Answer the following question by showing the calculations: a. Construct a table of profits or losses for each possible quantity of the pies based on the demands as recorded above. How many pies should the bakery make every day to maximize the profit? b. Confirm your answer in sub-question a) using a full marginal analysis based on the costs of overestimating and underestimating demands.BN10.2 Case: Jennifer is willing to Pay $300 to Insure against the Theft of a $8,000 Necklace. The Probability of Theft is 4%. Question: What is Jennifer's Risk Tolerance?
- In a final round of a MegaMillion TV show a contestant has a won $1 million and has a chance of doubling the reward. If he loses his winnings drop to $500,000. The contestant thinks his chances of winning is 50%. Should he play? What is the lowest probability of a correct guess that will make his betprofitable? Please show your work.Question 5 You negotiate with a retailer over a contract according to which the retailer would buy a large fraction of your current production for next year. The retailer is perfectly informed about consumer demand, but you do not know whether demand is high or low. You only know that the probability for high demand is 80%. If demand is high, the retailer's profit is £5 million minus what he pays to you according to your contract. If demand is low, the retailer's profit is £3 million minus what he pays to you. Your costs of producing the output specified in the contract are £1 million. You can make sequential offers for the retailer's total payment for you to deliver a fixed quantity of your production. As you know that your competitor is also seeking a similar contract with this retailer, and the retailer can only supply one firm due to limited shelf space, you know that you can only make at most two offers. If your first offer is rejected, the retailer will strike the deal with your…A wheel of fortune in a gambling casino has 54 different slots in which the wheel pointer can stop. Four of the 54 slots contain the number 9. For a 1 dollar bet on hitting a 9, if he or she succeeds, the gambler wins 10 dollars plus the return of the 1 dollar bet. What is the expected value of this gambling game? What is the meaning of the expected value result?
- Yuri owns just one ship, he calls it Previt. The ship is worth $25 million dollars. If the ship sinks, Yuri loses $25 million. The probability that it will sink is .02. Yuri's total wealth, including the value of the ship is $50 million. He is an expected utility maximizer with utility U(W) equal to W?. What is the maximum amount that Yuri would be willing to pay in order to be fully insured against the risk of losing his ship? a. $4 million b. $ 1.96 million c. $ 0.39 million d. $ 3.9 million e. $ 5.96 million f. None of the above, the right answer is:Gavin Jones’s friend is planning to invest $1 million in a rockconcert to be held 1 year from now. The friend figures that he will obtain $2.8 million revenue from his $1 million investment—unless it rains. If it rains, he will lose his entire investment. There is a 50% chance that it will rain the day of the concert. Gavin suggests that he buy rain insurance. He can buy one unit of insurance for $0.50, and this unit pays $1 if it rains and nothing if it does not. He may purchase as many units as he wishes, up to $2.8 million.(a) What is the expected rate of return on his investment if he buys u units of insurance? (The cost of insurance is in addition to his $1 million investment.)(b) What number of units will minimize the variance of his return? What is this minimum value? And what is the corresponding expected rate of them? [Hint: Before calculating a general expression for variance, think about a simple answer.]A wheel of fortune in a gambling casino has 54 different slots in which the wheel pointer can stop. Four of the 54 slots contain the number 9. For $3 bet on hitting a 9, if he or she succeeds, the gambler wins $16 plus return of the $3 bet. What is the expected value of this gambling game? (Present your answer in dollars with 2 decimal places but without $ sign)