soa真题怎么拿|SOA真题May2002Course6

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course 6
morning session
section a – written answer
course 6: may 2002 go on to next page
morning session
**beginning of course 6**
morning session
1. (5 points) you are given the following information:
stock
price at beginning
of period
price at end of
period
number of shares
outstanding
i 10 15 100
ii 9 10 125
iii 15 15 200
(a) describe and compare:
(i) price-weighted index
(ii) market-value-weighted index
(iii) equally-weighted index
(b) calculate the percentage change over the period for:
(i) price-weighted index
(ii) market-value-weighted index
(iii) equally-weighted index
(c) calculate the end of period price for stock iii that results in an equivalent
percentage increase in the price-weighted index and the market-value-weighted
index.
show all work.
course 6: may 2002 go on to next page
morning session
2. (6 points) an investor has the following securities available for investment:
expected annual return standard deviation of annual return
stock i 9% 13%
stock ii 12% 20%
t-bills 5% 0%
the covariance between the two risky assets is 0.93%.
construct the optimal portfolio using the three available assets, assuming:
(i) an investor’s degree of risk aversion is 4
(ii) an investor’s degree of risk aversion is 2
show all work.
3. (10 points) you are given the following information:
•all options have nine months to expiry
•all options have a strike price of 49
•current stock price is 50
•volatility is 30%
•risk-free rate is 5% per annum
using the binomial option pricing model and a three-month step, calculate the cost of
(i) a european put;
(ii) an american put;
(iii) a european call.
show all work.
course 6: may 2002 go on to next page
morning session
4. (5 points)
(a) describe the obligations of the trustee of a pension fund.
(b) describe the key considerations in selecting an appropriate pension funding
method.
course 6: may 2002 go on to next page
morning session
5. (6 points) you are given the following financial data for company abc:
•capital and surplus: 800,000
•total company assets:
bond book value c1 factor
aaa 2,000,000 0.3%
bb 5,000,000 4%
b 3,000,000 12%
•other required capital components:
risk base required capital factor
c2 150,000,000 0.1%
c3 4,000,000 1%
c4 500,000 2%
•required capital components for whole life block:
risk base required capital factor
c1 8,000,000 6%
c2 100,000,000 0.1%
c3 3,000,000 1%
c4 400,000 2%
•ceding allowance for a reinsurance treaty is 3% of assets transferred
•c1 required capital factor for assets ceded to reinsurer is 0.5%
•required capital formula: c 4 c22 c1 c3 2 b g
•risk based capital ratio = available capital ¸required capital
(a) describe the weaknesses of using the required capital formula when comparing
two companies that have healthy risk based capital ratios.
(b) evaluate the impact on required capital if you entered into a 50% coinsurance
agreement for the whole life business.
(c) evaluate the impact on required capital of upgrading all assets to a minimum
rating of bb.
(d) recommend which capital management action the company should use.
show all work.
course 6: may 2002 go on to next page
morning session

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