Suppose we are in.
The Land of All Assets
The end result of our time spent in the Land of All Assets was that an investor in the
Mean-Variance World would complete the following process to construct her or his
optimal portfolio:
1) The investor would firs
Stochastic Risk Management Models
MRM 8320, Fall 2015
Solution of Assignment 3
1. Let X2013 be the loss distribution for 2013. Then, we get that X Pareto( = 3, = 2000).
Moreover, the loss for 2014 is X = 1.05 X2013 which is Pareto(3, 1.05 2000 = 2100). Th
The LEAST likely consequence of privatizing Social Security as proposed by President Bush
would be: (a) relative gains for astute and lucky investors who converted their Social
Security accounts into private accounts. (b) relatively increased disparities
1. Core concepts question
(a) Write down the general equation for the security market line, and briey define each of the symbols.
E(r,)=rf +,6,[E(rm)rf]
3(ri) is the expected return on the stock, rf is the riskfree rate of return, is the beta of stock i,
Position
Action /Right
/Obligation
Long Spot
Will be selling the
asset in the future
Short Spot
Will be buying the
asset in the future
Long Call
Right to buy the asset
Short Call
Obligation to sell the
asset
Long Put
Right to sell the asset
Short Put
Obli
Risk and Return
Craig Ruff, Ph.D.,
CFA
Part 1:
Expected Return, Variance
and Standard Deviation of a
Single Asset
Usually, when we discuss Risk and
Return, we hit on three main ideas
1) Quantify and Summarize Risk and
Return
2) Construct Efficient
Portfol
Put-Call Parity
SEEING THE RELATIONSHIP GRAPHICALLY
As a starting point, imagine you enter the following strategy at t=0:
STRATEGY A
Long one share of GE stock: Price = $50/share.
Long one Put on the GE stock: Price = $1
(Exercise price = $50 and the time
At the start of the period you have the following prices:
—the underlying stock is priced at $100. '
-the put option (EXERCISE = $105) on the underlying stock is priced at $6.
-the call option (EXERCISE = $95) on the underlying stock is priced at $7.
(Bot
Options
Craig Ruff, Ph.D., CFA
Georgia State University
1
Call option the basic description
The call owner has the right to buy the
underlying asset from the option writer at a
set price for a specified period of time.
The call writer has the obligation
Futures and Forward
Craig Ruff, Ph.D., CFA
Georgia State University
1
Futures and Forward (F/F) the basic description
A F/F is an agreement made today in terms of price, quality,
quantity, and location for an exchange that will occur in the
future.
The l
TERM STRUCTURE THEORIES
A
Introduction Informally, term structure is a broad term that deals with the relationships between yields on
bonds and the maturities of those bonds.
In essence, we are looking at one point in time and at one type of bond (for ins
Time Value of Money
Craig Ruff, Ph.D., CFA
Department of Finance
Georgia State University
1
(1) Future Value of a Single Sum: Annual Compounding
2
(1) Future Value of a Single Sum: Annual Compounding
Lets start with a very simple question.
Suppose you dep
Bond Yields
Craig Ruff, Ph.D., CFA
Department of Finance
Georgia State University
1
Bond Yields
Source: http:/reports.finance.yahoo.com/z1?b=6&cpl=4.000000&cpu=-1.000000&mtl=-1&mtu=1&pr=1&rl=-1&ru=-1&sf=m&so=d&stt=-&tc=1&yl=-1.000000&ytl=-1.000000&ytu=-1.
Stochastic Risk Management Models
MRM 8320, Fall 2015
Solution of Assignment 1
1. See the practice problem solutions.
2. [From the solution of the SOA Exam C May 2007] Shifting adds to the mean and median. The
median of the unshifted exponential distribut
Stochastic Risk Management Models
MRM 8320, Spring 2016
Assignment 3 - due on March 9th, 4:30pm.
1. Fire losses in 2013 follow a Pareto distribution with mean 1,000 and variance 3,000,000. An
insurance policy pays the losses considering a limit of 1,500.
Introduction to
Valuation
Craig Ruff, Ph.D., CFA
Department of Finance, J. Mack Robinson College of Business
Georgia State University
1
http:/www.merriam-webster.com/dictionary/intuition
2
Present Value and Valuation
3
Present Value and Valuation
Value is
Time Value of Money
Craig Ruff, Ph.D., CFA
Department of Finance
Georgia State University
1
(1) Future Value of a Single Sum: Annual Compounding
2
(1) Future Value of a Single Sum: Annual Compounding
Lets start with a very simple question.
Suppose you dep
Chapter Readings:
The Investment Environment
Please read this chapter. I will not directly cover
this material; however, it is good background
material. It will not be directly tested.
Chapter
2
Asset Classes and Financial Instruments
Please read this cha
Yates Spring 2016
FI 8000
Homework 3 Page 1 of 1
Homework 3
Assignment
As part of a legal settlement related to a concussion lawsuit, the NFL has agreed to pay
$900 million in damages to former players. The NFL will pay the total of $900 million in 65
equ
Yates Spring 2016
FI 8000
Homework 2 Page 1 of 2
Homework 2
Assignment
A spreadsheet named Assignment 2 Inputs is posted on D2L. This spreadsheet contains
weekly adjusted closing prices for four stocks and the market portfolio. Using this data, you
are to
Professor Yates
FI 8000 Quiz 2
April 11, 2016
Name (as it would appear on the roll): _
1. The prices of risk-free zero-coupon bonds with varying times to maturity are given in the
table below. All of the bonds have a face value of $1,000.
Maturity (years)
Professor Yates
FI 8000 Quiz 1
March 21, 2016
Name (as it would appear on the roll): _
1. Consider the following limit order book:
Bid
Ask
Price
Size
Price
Size
42.00
50
42.10
80
41.95
41.85
41.80
350
2000
500
42.20
42.25
42.35
200
200
1000
a. Suppose you
Yates Spring 2016
FI 8000
Homework 4 Page 1 of 1
Homework 4
Assignment
You will use Monte Carlo techniques to answer questions about an exotic option known as
a lookback option. In this assignment, we will consider a lookback call option whose payoff
in o
Stochastic Risk Management Models
MRM 8320, Spring 2016
Solution of Assignment 5
1. We normalize the time. Let T1 to be time of the first loss. Then:
Z
ST1 (x)dx,
E[T1 ] =
0
ST1 (x) = P r(T1 > x) = P r(Nx = 0) = em(x)
(R x
= 10x,
if x 1
0 10dt
Rx
m(x) =
Stochastic Risk Management Models
MRM 8320, Fall 2015
Assignment 4 - due on November 17th, 4:30pm.
Late submissions will not be accepted!
1. [10pt] The frequency distribution for the number of losses for a policy with no deductible is
Negative Binomial wi
Stochastic Risk Management Models
MRM 8320, Spring 2016
Solution of Assignment 4
1.
(a) Note that if Y p = X 100|X > 100, then the expected payment in case of a loss is equal
to Y p 10000. Also, we know that Y p is distributed Pareto with parameters = 3 a
Stochastic Risk Management Models
MRM 8320, Fall 2015
Solutions of Assignment 2
1. Let T be the future life of a randomly chosen individual. Note that T | is distributed EXP ( 1 ).
Therefore,
ST (x) = E [SX| (x)] = E E[ex ] =
Z 150 x
e
e50x e150x
d =
100