A bank’s estimate of next year profit (as a percentage of assets) is a normal distribution with mean and standard deviation of 1% and 2%, respectively. How much equity (as a percentage of assets) does the company need to be
September 29, 2020
Essayheroes
-
A bank’s estimate of next year profit (as a percentage of assets) is a normal distribution with mean and standard deviation of 1% and 2%, respectively. How much equity (as a percentage of assets) does the company need to be
(a) 95% sure that it will have a positive equity at the end of the year
(b) 99% sure that it will have a positive equity at the end of the year
(b) 99.9% sure that it will have a positive equity at the end of the year
(d) Assume the bank’s capital is 4% of assets. How much equity capital in addition to that should regulators require for there to be a 99.95% chance of the capital not being wiped out by losses?
-
In a defined benefit pension plan for public employees of Illinois:
(a) Employees work for 30 years earning wages that increase at a real rate of 1.5% per year.
(b) They retire with a pension equal to 70% of their final salary. This pension decreases at the real of rate of 1% per year.
(c) The pension is received for 20 years.
(d) The pension fund assets earn a real rate of 3%.
Find the percentage of an employee’s salary that must be contributed to the pension plan if it is to remain solvent.
-
A financial institution has the following portfolio of options a stock:
Type
|
Position
|
Delta of Option
|
Gamma of Option
|
Vega of Option
|
Call
|
−2,000
|
0.60
|
2.5
|
0.8
|
Call
|
−200
|
0.80
|
0.6
|
0.2
|
Put
|
−2,000
|
−0.70
|
1.1
|
0.9
|
Call
|
−500
|
0.70
|
1.8
|
1.4
|
An option is available with a delta of 0.5, a gamma of 2, and a vega of 1.5.
(a) What position in the traded option and in the stock would make the portfolio both gamma neutral and delta neutral?
(b) What position in the traded option and in the stock would make the portfolio both vega neutral and delta neutral?
(c) Another option with a delta of 0.2, a gamma of 0.5, and a vega of 1 is available. How could the portfolio become delta, gamma, and vega neutral?
-
The bidders in a Dutch auction are as follows:
Bidder
|
Number of Shares
|
Price
|
A
|
40,000
|
80
|
B
|
70,000
|
140
|
C
|
50,000
|
90
|
D
|
60,000
|
56
|
E
|
20,000
|
64
|
F
|
60,000
|
54
|
G
|
40,000
|
50
|
H
|
80,000
|
100
|
The number of shares being auctioned is 250,000. What is the price paid by investors? How many shares does each investor receive?
-
A fund of funds invests across many hedge funds with an expected return of 7% before fees in a particular year. Hedge funds charge 2% 20% for management and incentives fee, respectively. Fund of fund investors require an expected return of 3%. What type of fee structure (incentive fees and management fees) for the fund of fund delivers an expected return of 3%? Plot a graph (incentive fees as a function of management fees) that displays the plausible combinations.
-
An oil-linked bond issue works as follows. The holder receives no interest. At maturity, the company pays $1,000 plus a premium based on the price of oil at that time. The premium is the product of 100 and the lack (if any) of the price of a barrel of oil at maturity under $60. The premium is capped at $2,000. Plot the bond’s payoff as a function of price of oil. Decompose the payoff of this bond using a combination of long and short positions in a simple bond and options.
-
A company’s investments earn LIBOR minus 0.5%. Show how it can use the quotes in the following Table to convert the investments into 1 through 10-year fixed-rate investments.
Maturity
|
Swap Rates (%)
|
1
|
2.60
|
2
|
2.90
|
3
|
3.15
|
4
|
3.35
|
5
|
3.50
|
6
|
3.60
|
7
|
3.65
|
8
|
3.69
|
9
|
3.68
|
10
|
3.70
|
SAMPLE ASSIGNMENT
Sample-2
