Risk Management
Chapter 2
Objective of Risk Management
I. Multiple Choice
1. The fundamental objective of risk management is:
a. diversification
b. minimize the cost of risk
c. hedging
d. loss control
Answer: b
Type: K
2. If unexpected increases in losses
Rank of a matrix
If the maximum number of linearly independent rows (columns) that can be found in such a
matrix is r , the matrix is said to be of rank r .
Example 1
3 0 4 1 R1
1 1 2 2 R2
1 2 2 1 R3
1 1
2
2
1 1 2 2 R1
1 1
1
3 0 4 1 R 2 R1 3 + R 2 0
Selected properties of eigenvalues and eigenvectors:
If a n n matrix has eigenvalues 1 , 2 , n and corresponding eigenvectors
x1 , x 2 , , x n , then
11
1
a. The eigenvalues of A 1 are , , , , with eigenvectors x1 , x 2 , , x n
1 2
n
b. The eigenvalues of
Diagonalization of Symmetric Matrices
Every symmetric matrix can be diagonalized. If A is a symmetric n n matrix, then there exists
an orthogonal matrix P such that P 1 AP = P T AP = D, a diagonal matrix. The eigenvalues of A
lie on the main diagonal of D
Lecture 3 - 4
Elementary Linear Algebra (II)
Eigenvectors and Eigenvalues
Definition
Given a square matrix A , if there exist a vector x and scalar , such that
Ax = x, then x is said to be an eigenvector of A and is the corresponding
eigenvalue of A.
Exam
Example: (Two-variable case)
Optimize the utility function u = f ( x, y ) = xy + 2 x subject to the budget constraint
4 x + 2 y = 60 .
Step (1): rewrite the objective function as the Lagrangian function, which is a modified
version of the objective functi
Lecture 18-19
Difference Equations
Finding the solution to the difference equations
The general solution consists of the sum of two components:
y t = complementary function + particular solution
yt = yc + y p
Complementary function yc : the general solut
Solutions: Chapter 3:
13.
Homework Set 2
(16 Oct 28 Oct)
Modeling & Solving LP Problems In A Spreadsheet
B = Amount invested in Bonds M = Amount invested in Mortgages C = Amount invested in Car loans P = Amount invested in Personal Loans MAX ST .10 B + .0
Chapter 3 - Modeling & Solving LP Problems In A Spreadsheet : S- 1
Chapter 3
Modeling & Solving LP Problems In A Spreadsheet
1.
In general, it does not matter what is placed in a variable (changing) cell. Ultimately, Solver will
determine the optimal valu
Chapter 2 - Introduction to Optimization & Linear Programming : S- 1
Chapter 2
Introduction to Optimization & Linear Programming
1.
If an LP model has more than one optimal solution it has an infinite number of alternate optimal
solutions. In Figure 2.8,
Chapter 2 - Introduction to Optimization & Linear Programming : S- 1
Chapter 2
Introduction to Optimization & Linear Programming
1.
If an LP model has more than one optimal solution it has an infinite number of alternate optimal solutions. In Figure 2.8,
Chapter 2
Objective of Risk Management
I.
Multiple Choice
1.
The fundamental objective of risk management is:
a.
b.
c.
d.
diversification
minimize the cost of risk
hedging
loss control
Answer: b
Type: K
2.
If unexpected increases in losses from price risk
Chapter 1
Risk and Its Management
Multiple Choice
1.
The major types of business risk include all of the following except:
a.
b.
c.
d.
price risk
diversification risk
pure risk
credit risk
Answer: b
Type: K
2.
a.
b.
c.
d.
Credit risk is:
the risk that a f
Chapter 3
Risk Identification and Measurement
I.
Multiple Choice
1.
A listing of a random variables possible outcomes and the respective probabilities of
those outcomes is called the:
a.
b.
c.
d.
expected value
standard deviation
probability distribution
Chapter 4
Pooling Arrangements and the Diversification of Risk
I.
Multiple Choice
1.
Which of the following is not a type of contracting cost associated with the creation
and operation of pooling arrangements:
a.
b.
c.
d.
distribution costs
underwriting e
Chapter 20
Risk Management and Shareholder Wealth
I.
Multiple Choice
1.
The value of a firm is:
a.
b.
c.
d.
the present value of the firms expected future cash flows.
impossible to estimate.
dependent on its capital structure.
all of the above.
Answer: a
Chapter 22
Risk Retention/Reduction Decisions
I.
Multiple Choice
1.
Which of the following is not a potential benefit to a firm from increasing retention?
a.
b.
c.
d.
savings on premium loadings
increased moral hazard
avoiding implicit taxes that arise fr
Chapter 25
Alternative Risk Transfer
I.
Multiple Choice
1.
All of the following are examples of loss sensitive policies except:
a.
b.
c.
d.
retrospectively rated policies
experience rated policies
investment credit program
excess policies
Answer: d
Type:
Solutions to Chapter 12
Risk, Return, and Capital Budgeting
6.
a.
The expected cash flows from the firm are in the form of a perpetuity. The
discount rate is:
rf + (rm rf ) = 4% + 0.4 (11% 4%) = 6.8%
Therefore, the value of the firm would be:
Cash flow $1
Solutions to Chapter 13
The Weighted Average Cost of Capital and Company Valuation
8.
The rate on Buildwells debt is 5 percent. The cost of equity capital is the required
rate of return on equity, which can be calculated from the CAPM as follows:
4% + (0.