Download APS 502 Financial Engineering 1 Winter 2015

APS 502
Financial Engineering 1
Winter
2015, March 12
Instructions: Closed book and closed notes except for one side of a 3 by 5 inch
notecard. Only a simple scienti…c non-…nancial calculator with no programming
capability is allowed. Please write neatly as this will aid in providing maximum
partial credit. IMPORTANT: Interpretation of the exam questions is
part of the exam and so no questions will be taken that ask for clari…cation of the question. You must turn in this question sheet with
your answer booklet or else your exam will NOT be marked.
Problem 1 (18 points, 6 points each)
An internet company i-Money is o¤ering a savings account with a nominal
annual interest rate of 4.75%. What is the e¤ective annual interest rate o¤ered
by i-Money if the compounding is
(a) Annual
(b) Monthly
(c) Continuously
Problem 2 (15 points)
You are considering buying a car whose price is $30,000. The car salesman,
who is eager to sell the car, o¤ers you an attractive …nancing (loan) package:
you need to make a down payment of $3,500 and pay the rest over 5 years in
equal annual payments at an annual interest rate of 2%. The o¤ered interest
rate of 2% is not necessarily the market interest rate.
(a) (7 points) What is the annual payment to the care salesman?
(b) (8 points) The car salesman o¤ers you a second option: you pay cash
for the car, but get a $2,500 rebate. Which is better for you getting the loan or
paying cash? Assume the market annual interest rate is constant at 5%.
Problem 3 (18 points, 6 points each)
Suppose you are given the following information about three zero coupon
bonds:
Bond Maturity Price
A
1
95.92
B
2
92.01
C
3
87.00
(a) Compute the implied spot rates s1 ; s2 ; s3
(b) Compute the implied forward rate between years 2 and 3 i.e. f2;3 :
(c) Compute the yield of a 2 year bond with coupon rate of 4.25% and annual
coupon payments. The face value of the bond is $100.
Problem 4 (24 points, 8 points each)
You have an obligation (liability) of $1 million per year for the next 20 years
(a liability payment is due at the end of each year), and you wish to invest now
to meet that obligation. You can invest in the following two zero coupon bonds:
Bond A
Bond B
maturity
5 years
20 years
1
(a) What is the duration of your obligations(liabilities)?
(b) What dollar amount of bonds A and B should you invest in so that you
immunize against changes in interest rates while meeting the liabilities? Assume
the annual interest rate is constant at 4%. Show all work.
(c) What should be the face value of each bond?
Problem 5 (25 points)
Consider the following two risky assets:
asset expected return standard deviation
1
20%
20%
2
15%
25%
also the correlation between the returns of assets 1 and 2 is 0:04.
(a) (5 points) Suppose you invest 70% of your wealth in asset 1 and 30% in
asset 2. What is the expected return of this portfolio?
(b) (5 points) What is the standard deviation of portfolio returns for the
portfolio in part (a)?
(c) (5 points) Would anyone ever be interested in investing in asset 2? Why
or who not? Explain BRIEFLY.
(d) (10 points) Using the information of the 2 assets above …nd the portfolio
that minimizes variance. SHOW ALL WORK i.e. you must show all steps in
computing the portfolio and not just plug into some formula to get the weights
directly (any such formula must be derived). What is the expected return and
variance of the portfolio obtained in part (c).
2