ActSc 445/845 Spring 2006
Assignment 2
Due Date: June 23, Friday (beginning of class)
1. (a) Let s(t) be the continuously compounded t-year spot rate (annualized) and f (t1 , t2 ) be
the continuously compounded annualized forward rate, between years t1 an
n = 10000
U = runif(n)
X = 5*abs(-100*sin(1/100*5*U*exp(5*U)+100*cos(1/100*5*U)
Y = 5*abs(-100*sin(1/100*5*U)+100*cos(1/100*5*U)
E_Y = 10000*(-1+sin(1/20)+cos(1/20)
Xbar = mean(X)
Ybar = mean(Y)
c = -cov(X,Y)/var(Y)
Z = X + c*(Y-E_Y)
mean(Z)
var(Z)
Stat 340 Spring 2010
Test 1 Stat 340
Last (Family) Name: First (Given) Name:
Note: The back is easier than this page.
1. In Wiarton (a small town north of here), there is a 2 taxi service (no kidding) to shuttle people from place to
place. The interarri
ActSc 445/845 Spring 2007
Assignment 1
Due Date: May 22 (5:00pm) Outside MC 6016
Please answer the following questions. Use matlab for the numerical work
and place all your programs in an appendix.
1. (40/100) Determination of the Yield Curve
In practice,
ActSc 445/845 Spring 2006
Assignment 1 Due Date: May 24, Wednesday (beginning of class)
traded: (For simplicity, assume all bonds are assumed to make annual coupon payments (for
simplicity and are redeemable at par.)
Bond # Price Maturity (years) Annua
ActSc 445/845 Spring 2005
Assignment 3
Due Date: July, 14 Thursday (beginning of class)
1. A xed-income portfolio manager is unwilling to realize a rate of return of less than 4 percent
annual eective over a ve-year investment period on a portfolio curren
ActSc 445/845 Spring 2005
Assignment 2
Due Date: June 14, Tuesday (beginning of class)
1. You are given a security that pays 1000, 2000 and 3000 at the end of years 1, 2 and 3, respectively. Given further the 1-year, 2-year and 3-year spot rates (continuo
Assignment #2: Solution
3. (Total: 10 Marks)
(a) (3 Marks) Note that I have used more decimal places in my calculation than they are
shown here.
Maturity
0.5
1.0
1.5
2.0
2.5
3.0
Spot Rates
5.00
5.00
5.50
6.00
6.50
7.00
(b) (2 Marks) Price of 6% 3-year bon
Rebalancing Immunized Portfolios
The portfolio must be rebalanced (i.e. buying or selling
assets) continuously so that the asset duration is aligned
with the liability duration. Reasons ?
due to a change in yield, and
shortening of maturity
Example: Assum
Society of Actuaries
Professional Actuarial Specialty Guide
Asset-Liability Management
BB - 1- 03
2002-2003 SOA Asset-Liability Management Specialty Guide Task Force Members:
Warren R. Luckner, FSA, Chairperson
Mark C. Abbott*
James E. Backus, FSA, MAAA
S
REPORT
RESULTS OF THE SURVEY ON
ASSET LIABILITY MANAGEMENT PRACTICES OF
CANADIAN LIFE INSURANCE COMPANIES
COMMITTEE ON INVESTMENT PRACTICE
WORKING GROUP ON ASSET LIABILITY MANAGEMENT
MAY 2002
2002 Canadian Institute of Actuaries
Document 202029
This doc
ActSc 445/845 Spring 2007
Assignment 4
Due Date: Aug 3 (5:00pm) Outside MC 6016
1. Consider a portfolio consisting of a $100,000 investment in asset A and a $100,000 investment
in asset B. Assume that the daily volatilities of both assets are 1% and that
ActSc 445/845 Spring 2007
Assignment 2
Due Date: June 22 (5:00pm) Outside MC 6016
Please answer the following questions. Use either excel or matlab for the
numerical work and place all your programs in an appendix.
1. Consider a two-year bond with 6% coup
Lecture
Feb. 8th 2010
Montreal Problem
James
Bay
Chenier
Duvernay
Boucher-
Montreal
ville
Chateauguay
Hertel
Montreal Problem
Problem:
Details
Electrical lines are denoted by:
James
Bay
Chenier
1
And each line has a time to failure denoted
by Ti where i i
Brief R Tutorial
The following are examples of R code for possible use in Assignment 3 (please ignore
any arrows at the end of the lines. At the end of this document is an example of R code
to simulate Brownian motion. The arrows notify you of the overow
ACTSC 445/845
Final EXAM
December 19, 2015
Answer the questions in the booklet provided. Show your work.
DO NOT WRITE BELOW THIS LINE.
number points score
1
9
2
12
3
8
4
13
5
4
6
6
7
10
8
8
Total
70
1. (a) (4 points) Define each of the following terms: i)
ACTSC 445/845
Final EXAM
December 19, 2015
Answer the questions in the booklet provided. Show your work.
DO NOT WRITE BELOW THIS LINE.
number points score
1
9
2
12
3
8
4
13
5
4
6
6
7
10
8
8
Total
70
1. (a) (4 points) Define each of the following terms: i)