Question

A mortgage company manages 1, 000 mortgages. Mortgages default at a rate of 10 per year (you can assume this rate remains constant and that defaults can be described as a Poisson process). Every defaulted mortgage gives a loss of $100, 000. Every mortgage that doesn’t default gives a yearly profit of $1, 000. Let X be the number of mortgages that default in a year and let F be the total earnings in a year.

1) Find the yearly earnings F as a function of X.

2) Find the expected yearly earnings, E[F].

3) Find the probability that earnings are negative, P(F < 0).

4) Find the probability that there are exactly five defaults in a given year, given that there have been no defaults in the first half of the year.

Answer #1

T/F
a. The one-year default rate on junk bonds reached double-digits
in 1991 and has never since exceeded even 4%. ____
b. The one-year default rate on investment-grade debt averages
about 2%. _____
c. Most defaults occur in recessions when investment-grade firms
experience a large drop in revenue._____
d. A bank that buys the CDX North America contract can reduce
its transactions costs relative to buying protection on all 125
single reference names.___
e. The typical spread on a junk...

Every week, 20,000 students flip a 10,000-sided fair dice,
numbered 1 to 10,000, to see if they can get their GPA changed to a
4.0. If they roll a 1, they win (they get their GPA changed). You
may assume each student’s roll is independent. Let X be the number
of students who win.
(a) For any given week, give the appropriate probability
distribution (including parameter(s)), and find the expected number
of students who win.
(b) For any given week,...

Juliet has a 10-year mortgage of $500,000 with an interest rate
of 3.5% APR, compounded quarterly. Mortgage payments are made at
the beginning of each month. What is the balance remaining on this
mortgage after the 60th payment? PLEASE DO NOT GIVE THE INCORRECT
ANSWER of
Find first month rate as given rate is compounded quarterly (1 +
r)^12 = (1 + 0.035/4)^4 r = (1 + 0.035/4)^(1/3) – 1 = 0.002908 =
0.2908% Set up the TVM parameters PV...

1. One advantage of Adjustable Rate Mortgages (ARM) is that
a. lenders face lower levels of interest rate risk than a fixed
rate mortgage.
b. the outstanding loan balance can be adjusted regularly.
c. the default risk of borrowers is lower than under a fixed
rate mortgage.
d. All of the above.
2. Gilbert takes out a 23-year adjustable rate mortgage loan for
$6,000,000 with monthly payments. The first two years of the loan
have a “teaser” rate of 2%,...

1. An investment is projected to generate income at the rate of
R(t)=20,000 dollars per year for the next 4 years. If the income
stream is invested in a bank that pays interest at the rate of 5%
per year compounded continuously, find the total accumulated value
of this income stream at the end of 4 years.
2. Find the average value of the function f(x)=∜(5x+1) over the
interval [0,3].

You have a 10-year- old, 1-acre, even-aged forest. You
estimate that if you spend $35 per acre fertilizing this f rest
every 5 years, you can receive $1,000/acre net stumpage returns 20
years from now. In 20 years, you predict a potential land sale
price f $300/acre. Four fertilizer applications will be made, the
first one now. Based only on the above value and cost projections,
what is your net present value per acre now for this forest, if
your...

Solutions for this exercise will not be posted. However, it is
possible that questions from this
exercise could appear on Midterm II. DEFINE ALL NOTATION!!!!!
1. Here is a pdf:
.
a) How do you know it is a continuous distribution?
b) The constant a is positive. What is a?
c) What is probability that the random variable X is equal to
1?
d) What is F(-0.5)?
e) What is the cdf of the random variable X?
f) What is...

Multiple Choice
11. Prepayment risk is:
A. the risk you will not receive the cash flows on a
mortgage-backed security
B. the risk that you will receive the cash flows sooner than
expected and be forced to invest at a lower rate.
C. the risk that you will receive the cash flows later than
expected and not be able to invest at current, higher rates.
12. Based on the video Inside the Meltdown, it appeared
that the main reason Lehman...

Problem 1: Relations among Useful Discrete Probability
Distributions. A Bernoulli experiment consists of
only one trial with two outcomes (success/failure) with probability
of success p. The Bernoulli distribution
is
P (X = k) =
pkq1-k,
k=0,1
The sum of n independent Bernoulli trials forms a binomial
experiment with parameters n and p. The binomial probability
distribution provides a simple, easy-to-compute approximation with
reasonable accuracy to hypergeometric distribution with parameters
N, M and n when n/N is less than or equal...

1.)
Sam Strother and Shawna Tibbs are vice presidents of
Mutual of Seattle Insurance Company and co-directors of the
company’s pension fund management division. An
important new client, the North-Western Municipal Alliance, has
requested that Mutual of Seattle present an investment seminar to
the mayors of the represented cities, and
Strother and Tibbs, who will make the actual presentation, have
asked you to help them by answering the following
questions.
a. What are the key features of a bond?
b....

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