Homework Help is Here – Start Your Trial Now!
Math
Probability
Standard and Poor's is a financial services company, that, among other things, gives credit ratings to corporate borrowers. The ratings are labeled with letters, and we consider four ratings: AAA, AA, A, B-D (AAA is the best). In reality, there are ratings BBB through D, but for our purposes we combine them all into group B-D. From historical data we can estimate the following rating transition matrix, which gives the probabilities of rating changes from one year to another, for example, an A-rated company will remain A-rated next year with probability 0.9176. P = 0.0011 0.9366 0.0583 0.004 0.0066 0.9172 0.0694 0.0068 0.0007 0.0225 0.9176 0.0592

Standard and Poor's is a financial services company, that, among other things, gives credit ratings to corporate borrowers. The ratings are labeled with letters, and we consider four ratings: AAA, AA, A, B-D (AAA is the best). In reality, there are ratings BBB through D, but for our purposes we combine them all into group B-D. From historical data we can estimate the following rating transition matrix, which gives the probabilities of rating changes from one year to another, for example, an A-rated company will remain A-rated next year with probability 0.9176. P = 0.0011 0.9366 0.0583 0.004 0.0066 0.9172 0.0694 0.0068 0.0007 0.0225 0.9176 0.0592

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
See similar textbooks
icon
Related questions
Question

Please provide steps for how you got the solution to the problem provided in the photos below.

Standard and Poor's is a financial services company, that, among other things, gives credit ratings to corporate borrowers. The ratings are labeled with letters, and we consider four ratings: AAA, AA, A, B-D (AAA is the best). In reality, there are ratings BBB through D, but for our purposes we combine them all into group B-D. From historical data we can estimate the following rating transition matrix, which gives the probabilities of rating changes from one year to another, for example, an A-rated company will remain A-rated next year with probability 0.9176. Note that P = p² = p3. p4= p5 || /0.9366 0.0583 0.004 0.0011 0.0066 0.9172 0.0694 0.0068 0.0007 0.0225 0.9176 0.0592 0.003 0.002 0.04 0.955 0.87761 0.10817 0.01151 0.00271 0.01230 0.84322 0.12763 0.01685 0.00162 0.04144 0.84592 0.11101 0.00572 0.00482 0.07505 0.91441, 0.82270 0.15064 0.02168 0.00497 0.01723 0.77702 0.17636 0.02939 0.00272 0.05736 0.78354 0.15638 0.00818 0.00827 0.10580 0.87774) /0.77157 0.18663 0.03384 0.00796) 0.02148 0.71771 0.21700 0.04381 0.00394 0.07071 0.72922 0.19612 0.01042 0.01220 0.13280 0.84457/ 0.72393 0.21694 0.04741 0.01173) 0.02514 0.66451 0.25076 0.05959 0.00526 0.08189 0.68190 0.23095 0.01247 0.01647 0.15653 0.81452/
Transcribed Image Text:Standard and Poor's is a financial services company, that, among other things, gives credit ratings to corporate borrowers. The ratings are labeled with letters, and we consider four ratings: AAA, AA, A, B-D (AAA is the best). In reality, there are ratings BBB through D, but for our purposes we combine them all into group B-D. From historical data we can estimate the following rating transition matrix, which gives the probabilities of rating changes from one year to another, for example, an A-rated company will remain A-rated next year with probability 0.9176. Note that P = p² = p3. p4= p5 || /0.9366 0.0583 0.004 0.0011 0.0066 0.9172 0.0694 0.0068 0.0007 0.0225 0.9176 0.0592 0.003 0.002 0.04 0.955 0.87761 0.10817 0.01151 0.00271 0.01230 0.84322 0.12763 0.01685 0.00162 0.04144 0.84592 0.11101 0.00572 0.00482 0.07505 0.91441, 0.82270 0.15064 0.02168 0.00497 0.01723 0.77702 0.17636 0.02939 0.00272 0.05736 0.78354 0.15638 0.00818 0.00827 0.10580 0.87774) /0.77157 0.18663 0.03384 0.00796) 0.02148 0.71771 0.21700 0.04381 0.00394 0.07071 0.72922 0.19612 0.01042 0.01220 0.13280 0.84457/ 0.72393 0.21694 0.04741 0.01173) 0.02514 0.66451 0.25076 0.05959 0.00526 0.08189 0.68190 0.23095 0.01247 0.01647 0.15653 0.81452/
i. What is the probability that in three years a B-D company can climb to AAA rating? ii. For an A-rated company which is more likely to happen in four years: that it improves or worsens its rating? iii. What is the probability that an AAA-rated company keeps its AAA rating for five years never dropping below AAA? iv. You own shares of three A-rated companies, two AA-rated companies and one AAA-rated company. What is the probability that any of these companies are downgraded to B-D after two years? v. Suppose that AAA companies give an expected return of 10%, AA give an average of 6%, A give 2% and B-D have an average loss of 5%. If you own stock in a AAA company now, what is your expected return for year 3?
Transcribed Image Text:i. What is the probability that in three years a B-D company can climb to AAA rating? ii. For an A-rated company which is more likely to happen in four years: that it improves or worsens its rating? iii. What is the probability that an AAA-rated company keeps its AAA rating for five years never dropping below AAA? iv. You own shares of three A-rated companies, two AA-rated companies and one AAA-rated company. What is the probability that any of these companies are downgraded to B-D after two years? v. Suppose that AAA companies give an expected return of 10%, AA give an average of 6%, A give 2% and B-D have an average loss of 5%. If you own stock in a AAA company now, what is your expected return for year 3?
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 6 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer