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北美精算师资格考试2003年5月真题：Course6（一）

来源：高顿网校 2014-08-31

　　高顿网校北美精算师小编们友情提醒——高顿网校小编为您精心编制的北美精算师资格考试2003年5月真题：Course6（一），全英文模式，请认真阅读。
　　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

　　? Dt = 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
　　读书是学习，摘抄是整理，写作是创造。——高顿网校名人语录

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