6. Suppose you are a broker (of junk bonds) who buys only bonds that have a 55% chance of not defaulting. Youwant to put together a portfolio of bonds with at least three that will not default. You want to be 95% sure thatat least three will not default. How many bonds should you buy?Ans.

Answered: Image /qna-images/answer/0678e5d3-b717-4964-b80b-4b696e555a13.jpg

Answered: 6. Suppose you are a broker (of junk…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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14. Please answer the following question.
Suppose you are a broker (of junk bonds) who buys only bonds that have a 55% chance of not defaulting. You want to put together a portfolio of bonds with at least four that will not default. You want to be 93.9% sure that at least four will not default. How many bonds should you buy?
1. Consider the gambler's ruin problem. Alice starts with £a; her opponent Bob starts with £(ma). In each round, Alice wins £1 from Bob with probability p, or loses £1 to Bob with probability q = 1 - p. Alice ruins if she is reduced to £0; Bob ruins if he is reduced to £0, which means Alice would have £m. Let X denote the amount of money in pounds that Alice has after n rounds. Consider the stochastic process (✗n). pri+1ri+gri-1 = 0 for i = 1, 2,..., m — 1, Assuming p, solve the linear difference equation in part (c), to show that the ruin probability is pm - pa ra pm 1 ' where you should identify p in terms of p and q.
MotoWin Auto Superstore is thinking about offering a two-year limited warranty for $915 on all new cars of a certain model. The terms of the warranty would be that MotoWin would replace the car free of charge under certain, specified conditions. Replacing the car in this way would cost MotoWin $15,700. Suppose that under the warranty, there is a 6% chance that MotoWin would have to replace the car one time and a 94% chance they wouldn't have to replace the car. (If necessary, consult a list of formulas.). If MotoWin knows that it will sell many of these warranties, should it expect to make or lose money from offering them? How much? To answer, take into account the price of the warranty and the expected value of the cost from replacing the car. MotoWin can expect to make money from offering these warranties. In the long run, they should expect to make dollars on each warranty sold. O MotoWin can expect to lose money from offering these warranties. In the long run, they should expect to…
A stock index consists of businesses in both Europe and the United States. Assume that each business comprising the stock index makes a profit or loss independently of the other businesses in the index. Suppose that an American business on the stock index makes a profit 60%60% of the time and a European business makes a profit 80%80% of the time. If there are 840 American businesses and 720 European businesses in the stock index, what is the expected number of businesses in the stock index to make a profit?
1. A certain stock price has been observed to follow a pattern. If the stock price goes up one day, there's a 20% chance of it rising tomorrow, a 30% chance of it falling, and a 50% chance of it remaining the same. If the stock price falls one day, there's a 35% chance of it rising tomorrow, a 50% chance of it falling, and a 15% chance of it remaining the same. Finally, if the price is stable on one day, then it has a 50-50 change of rising or falling the next day. Which matrix below is the transition matrix for this Markov chain, if we list states in the order: (rising, falling, constant). 20 30 50 35 50 15 50 50 0 ). 0.2 0.35 0.5 0.3 0.5 0.5 0.5 0.15 20 35 50 30 50 50 50 15 0 0.2 0.3 0.5 0.35 0.5 0.15 0.5 0.5 2. Choose the correct transition matrix representing the Markov chain with state diagram shown below. Assume the states are ordered with A before B. 0.13 0.87 0.09 В 0.91 0.13 0.87 0.91 0.09 0.13 0.91 0.87 0.09 0.13 0.87 0.09 0.91 0.87 0.09 0.13 0.91 3. Given the initial state…
Many investors and financial analysts believe the Dow Jones Industrial Average (DJIA) gives a good barometer of the overall stock market. On January 31, 2006, 9 of the 30 stocks making up the DJIA increased in price (The Wall Street Journal, February 1, 2006). On the basis of this fact, a financial analyst claims we can assume that 30% of the stocks traded on the New York Stock Exchange (NYSE) went up the same day.A sample of 80 stocks traded on the NYSE that day showed that 11 went up.You are conducting a study to see if the proportion of stocks that went up is is significantly less than 0.3. You use a significance level of α=0.02α=0.02.What is the test statistic for this sample? (Report answer accurate to three decimal places.)test statistic = What is the p-value for this sample? (Report answer accurate to four decimal places.)p-value = The p-value is... less than (or equal to) αα greater than αα This test statistic leads to a decision to... reject the null accept the null fail…
2. On Black Friday, you budget B for Christmas shopping. Here at the facts: 1. At the first site, you bought a gift for your mother and spent half of the budget. 2. At the second site, you bought a gift for you father and spent half of the remaining amount in the budget. 3. At the third site, you spend an additional half of the remaining budget for a third present. 4. You are now left with $10 remaining dollars from your original budget. How much did you budget for the purchase of Christmas presents?
A customer has approached a bank for a $100,000 one-year loan at an 8% interest rate. If the bank does not approve this loan application, the $100,000 will be invested in bonds that earn a 6% annual return. Withoutadditional information, the bank believes that there is a 4% chance that this customer will default on the loan, assuming that the loan is approved. If the customer defaults on the loan, the bank will lose $100,000. At a cost of $1000, the bank can thoroughly investigate the customer’s credit record and supply a favorable or unfavorable recommendation. Past experience indicates that the probability of a favorable recommendation for a customer who will eventually not default is 0.80, and the chance of a favorable recommendation for a customer who will eventually default is 0.15.a. Use a decision tree to find the strategy the bank should follow to maximize its expected profit.b. Calculate and interpret the expected value of information (EVI) for this decision problem.c.…
3) At time 0, Elon Musk (the cool guy these days) has $2. At times 1, 2,..., he independently plays a game in which he bets $1. With probability p = 0.49, he wins the game and with probability 1 - p = 0.51, he loses the game. His goal is to increase his capital to $3, and as soon as he does, the game is over. The game is also over if his capital is reduced to zero. Construct an absorbing Markov chain and answer the following questions. • What is the expected duration of the game? • What is the probability that he goes broke?

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6. Suppose you are a broker (of junk bonds) who buys only bonds that have a 55% chance of not defaulting. Yo want to put together a portfolio of bonds with at least three that will not default. You want to be 95% sure ti at least three will not default. How many bonds should you buy?