[soa真题怎么拿]SOA真题May2003Course6

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course 6
morning session
section a-written answer
course 6: spring 2003 - 1 - go on to next page
**beginning of examination**
1. (6 points) you are given the following with respect to corporate bonds:
rating spread over treasuries (basis points)
aaa 20
aa 30
a 40
the one-year rating transition matrix is as follows:
rating at end of year
rating at beginning of year aaa aa a
aaa 0.8 0.1 0.1
aa 0.1 0.7 0.2
a 0.0 0.1 0.9
(a) describe the top down value-added strategies for active bond management.
(b) describe the corporate bond sector selection strategies.
(c) calculate the expected two-year horizon spread over treasuries for a aaa-rated
bond.
show all work.
course 6: spring 2003 - 2 - go on to next page
2. (5 points) you are given the following:
probability one year return
stock x
0.60
0.20
0.20
10%
5%
-10%
stock y
0.75
0.25
20%
-20%
•risk-free rate is 4%
•the investor has a one-year horizon
•the investor is indifferent between investing in stock y and earning the risk-free rate
determine whether or not the investor would purchase stock x.
show all work.
course 6: spring 2003 - 3 - go on to next page
3. (5 points) you are given the following:
•margin requirement on short sales: 50%
•maintenance margin: 30%
•an investor’s account with a broker currently holds:
•value of t-bills: 10,000
•number of shares of xyz stock: 500
•stock prices:
date abc stock price xyz stock price
june 2, 2003 103 75
june 3, 2003 102 76
june 4, 2003 99 77
june 5, 2003 100 75
june 6, 2003 101 80
june 9, 2003 105 72
june 10, 2003 115 65
the investor tells the broker to short 1,000 shares of the abc stock on june 3, 2003. the
broker executes the order on the first day allowed. shares are traded once per day.
(a) calculate the additional cash (if any) necessary to satisfy the margin requirement.
(b) calculate the amount of the margin calls (if any) between june 3, 2003 and june 10,
2003.
show all work.
course 6: spring 2003 - 4 - go on to next page
4. (9 points) you are given the following with respect to an extended vasicek trinomial lattice
model:
•s 0.02
•t 1 year
•rb1g0.08
•rb2g 0.09
•rb3g 0.10
•a 0.4
(a) describe the key characteristics of this model.
(b) calculate the value of qb0g using the hull and white approximation.
(c) calculate the value of p2 a0,0f.
(d) calculate the value of a one-year cap with a notional amount of 100 and a strike interest
rate of 9.5%.
show all work.
course 6: spring 2003 - 5 - go on to next page

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