5. (7 points) You are given the following with respect to non-callable default-free zero-coupon
bonds:
Time to Maturity atf Current Price
1 year 980.392
2 years 942.596
3 years 888.996
4 years 838.561
5 years 765.134
You are given the following with respect to a five-year option-free bond:
•annual coupons of b2 tg% are paid at the end of each year
•par value of 1,000
•yield-to-maturity byg of 5.50%
For the five-year annual coupon bond:
(a) Calculate the Macaulay duration.
(b) Calculate the Macaulay convexity.
(c) Calculate the Fisher-Weil duration.
(d) Calculate the Fisher-Weil convexity.
(e) Calculate the elasticity of the price using a discount factor of 1 / a1yf.
(f) Calculate the value of M-squared.
Show all work.
Course 6: Spring 2003 - 6 - GO ON TO NEXT PAGE
6. (8 points) You are given the following with respect to a defined benefit pension plan:
•final pension is based on career average salaries without an explicit provision for
post-retirement indexation
•assets of the pension plan are actively managed by two external managers
•no contributions were made to the fund in 2002
The plan balance sheet for the previous two years is as follows:
December 31, 2001 December 31, 2002
Assets
Fixed Income
Equities
100
100
104
80
Liabilities
Accumulated Benefit Obligation
Projected Benefit Obligation
180
195
198
213
The plan sponsor is concerned with the volatility of the pension plan surplus and is reviewing the
investment portfolio structure and asset allocation.
(a) Describe the fundamental decisions involved in the construction of a pension plan
investment portfolio.
(b) Compare active to passive investment management strategies.
(c) Recommend a strategy for the pension plan.
(d) Calculate the surplus rate of investment return for 2002.
(e) Formulate the surplus optimization analysis for the plan and recommend an asset
allocation.
(f) Propose stress tests to assess the sensitivity of the surplus to sharp changes in asset
prices.
Show all work.
Course 6: Spring 2003 - 7 - GO ON TO NEXT PAGE
7. (5 points) With respect to auto loan asset-backed securities (ABS) and auto lease ABS,
describe the risks associated with each of these securities and explain how these risks can be
mitigated.
Course 6: Spring 2003 - 8 - GO ON TO NEXT PAGE
COURSE 6
MORNING SESSION
SECTION B-MULTIPLE CHOICE
Course 6: Spring 2003 - 9 - GO ON TO NEXT PAGE
1. You are given the following with respect to an optimal risky portfolio:
•expected return: 7%
•risk premium: 3%
•variance: 100
Calculate the slope of the capital allocation line (CAL) for this portfolio.
(A) 0.03
(B) 0.04
(C) 0.30
(D) 0.40
(E) 3.00
Course 6: Spring 2003 - 10 - GO ON TO NEXT PAGE
USE THIS PAGE FOR YOUR SCRATCH WORK
Course 6: Spring 2003 - 11 - GO ON TO NEXT PAGE
2. You are given the following with respect to a portfolio consisting of two mutual funds:
Mutual Fund Weight Variance
Stock 25% 100
Bond 75% 36
The correlation coefficient between the fund returns is 0 5 . .
Calculate the variance of the portfolio.
(A) 3.91
(B) 15.25
(C) 26.50
(D) 37.25
(E) 40.75
Course 6: Spring 2003 - 12 - GO ON TO NEXT PAGE
USE THIS PAGE FOR YOUR SCRATCH WORK
Course 6: Spring 2003 - 13 - GO ON TO NEXT PAGE
3-8. Each of questions 3 through 8 consists of two lists. In the list at the left are two items, lettered
X and Y. In the list at the right are three items, numbered I, II, and III. ONE of the lettered
items is related in some way to EXACTLY TWO of the numbered items. Indicate the related
items using the following answer code:
Lettered Item
Is Related to Numbered Items
(A)
X
I and II only
(B)
X
II and III only
(C)
Y
I and II only
(D)
Y
I and III only
(E)
The correct answer is not given by (A), (B), (C) or (D).

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