HEDGING WITH INTEREST RATE SWAPS PROBLEM
1. (a) You observe the following anticipated floating rate swap payments, each
based on a notional $ 100 M. Assume semi-annual compounding.
Floating Payments
t
MEASUREMENT OF INTEREST RATE RISK: PROBLEMS & ANSWERS
I. PROBLEMS
11. Assuming all four bonds are selling to yield 5%, compute the following for each bond:
a. duration based on a 25 basis point rate s
HOMEWORK SET for EQUITY PORTFOLIOS
1. Assume an investor may invest his wealth in a single, risky asset A and the risk-free
asset F in any desired proportion.
The return on F is rF = 10, the expected
IMMUNIZATION WITH DURATION
FIN 653
N. GERSHUN
1. From Bloomberg, download data on prices, coupon rates and YTM for 4
government bonds.
2. Using this information, calculate duration of these bonds taki
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HOMEWORK SET FOR MODULE 8
HEDGING WITH OPTIONS
Problem 1
What does it mean to assert that the delta of a call option is 0.7? How can a short
position in 1,000 options be made delta neutral when the de
PROJECT 4
OPTION PRICING
PART 1: THEORETICAL PROBLEMS
Please solve problems #13 and 17 from the problem set on Derivatives
PART 2: MONTE CARLO SIMULATION OF OPTIONS PRICE
A. Introduction
This part of
TUTORIAL FOR SOLVER
To define a problem in Solver, you need to follow these essential steps:
1. Choose a spreadsheet cell to hold the value of each decision variable in your model.
2. Create a spreads
OPTIONS THEORY
Basic Concepts
A. Objectives: our principal objectives are as follows:
i.
to understand how basic put and call options are priced in a
competitive market
ii.
to understand how the use o
PORTFOLIO ANALYSIS AND MANAGEMENT
BOND PROBLEM SET
1.
The term structure of interest rates is currently flat r = 10%. You own a portfolio
of bonds as follows:
500 bonds, each with a 9.5% coupon maturi
American Put with Binomial
S
E
T
rf
Sigma
n
50
52
1
0.05
0.1
3
European put with Black Sch
u
d
1.059434
0.9439
d1
d2
Prn
1-Prn
0.631037
0.368963
Exercise at expiraton
t
t+delta t t+2delta t t+3delta t
S
E
T
rf
Sigma
50
52
1
0.05
0.1
European put
n
delta t
3 number of periods in the model
0.333333 years
Step 1
u
d
Rf
prn
1-prn
Find inputs into the binomial model with three periods
1.059434
0.9439
1.
Data
S
Sigma
rf
T
N
delta t
45
0.35
0.0585
1
2
0.5
Parameters of the two-period binomial model
u
1.280803
d
0.78076
Rf
1.029682
prn
0.497801
1-prn
0.502199
Evolution of the stock price
Payoffs at expi
Asian Option
S
E
T
rf
Sigma
n
50
u
d
average of the stock prices over the life of the option
1.059434
0.9439
1
0.05
0.1
3
t
t+delta t
Prn
1-Prn
t+2delta t t+3delta t PT
59.4555
0
56.12005
0.016022
52.
THE CAPITAL ASSET PRICING MODEL
A.
Introduction: We have hypothesized that the relevant risk of an asset is that
portion of its total risk that cannot be diversified away when the asset is included
in
THE BLACK-SCHOLES FORMULA
A. In this set of notes we will review the Black-Scholes formula, its origins and its
use. There are, in particular, two perspectives, which we will consider. Recall also
tha
THREE PERSPECTIVES ON THE VALUATION OF DERIVATIVE INSTRUMENTS
N. Gershun
A. Introduction: We have introduced two models for the price process on the underlying asset.
They are:
1. Geometric Brownian m
FACTOR AND INDEX MODELS
A. Introduction
1. Previously, we observed that the greatest problem with the CAPM may be the
impossibility of finding an adequate real world counterpart to the market portfoli
HEDGING WITH OPTIONS
Our goals for this segment of material are (i) to understand how options are used
to manage portfolio risk and (ii) to understand how to profit from what we believe are
mispriced
RISK REDUCTION AND THE PRINCIPLE OF DIVERSIFICATION
A. Introduction. In this note set well answer the questions: How do we measure the
benefits to diversification and when can such benefits be achieve
PORTFOLIO ANALYSIS AND MANAGEMENT
BOND PROBLEM SET
1.
The term structure of interest rates is currently flat r = 10%. You own a
portfolio of bonds as follows:
500 bonds, each with a 9.5% coupon
maturi
Pace University
Fin 653
Professor
1. and 2. I used the information given in class material to calculate durations of these bonds taking into
account semiannual coupon payments.
2 year Bond
t
0.5
1
1.5
HOMEWORK SET 4
Derivatives
13. You are the senior assistant to the Chairman of the Board of Hi-Teck Inc. In order to
attract the chief operating officer of his choice from another firm, the Chairman o
HOMEWORK SET for EQUITY PORTFOLIOS
2.
(a)
(a)
The risk-free rate of return is 8 percent, the required rate of return on the market, rm
is 12 percent, and Stock X has a beta coefficient of 1.4. If the
PACE UNIVERSITY
PROJECT 2
CAPM AND FACTOR MODELS
Professor Name:
FIN 653
Part I CAPM
We decided to look for the data from IBM and BKS years 2010-2015, Below please se the
Market and book Value of the
HOMEWORK SET for EQUITY PORTFOLIOS
36.
Consider two assets A and B for which return distributions can be summarized as follows
E[ R A ] 3%
E[ R B ] 7%
A2 1 %
A 1%
B2 4 %
B 2%
2
2
AB = 0
What is
Portf
Name
Bond 1
Bond 2
Bond 3
Bond 4
Time
1
2
3
4
Amount
3994.3449
4106.6520
-3095.5280
-8.1859
4997
Face Value
$ 100.00
$ 100.00
$ 100.00
$ 100.00
Face Value
$
$
$
$
$
$
$
$
100.00
100.00
100.00
10
Return on F
expected return on A
sd(a)
10
0.2
0.2
(a).
CML
the CML of this risk-free asset F and risky asset A is not efficient.
(b).
Security A
Return
-10
50
Prob
0.5
0.5
Security B
Return
-20
60
(a)