SOA真题May20XXCourse6第3页-精算师考试.doc

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北美精算师真题course1

北美精算师真题course1

Calculate the percentage of the group that watched none of the three sports during the last year.
(A) (B) (C) (D) (E)
24 36 41 52 60
Course 1
6
Form 03A
2.
c f ( x ) − dg ( x ) . x →0 f ( x ) − g ( x )
(A) (B) (C) (D) (E)
0 cf ′ ( 0 ) − dg ′ ( 0 ) f ′ ( 0) − g′ ( 0)
f ′ ( 0) − g′ ( 0) c−d c+d
Course 1
8
Form 03A
(A) (B) (C) (D) (E)
0.07 0.29 0.38 0.42 0.57
May 2003
9
Course 1
5.
An insurance company examines its pool of auto insurance customers and gathers the following information:
Each of the graphs below contains two curves.
Identify the graph containing a curve representing a function y = f ( x ) and a curve representing its second derivative y = f ′′ ( x ) .
Calculate the rate at which the value of the investment is changing after 8 years.

09年SOA北美精算师考试第二门FM官方样题第一部分(主要是金融数学)答案

09年SOA北美精算师考试第二门FM官方样题第一部分(主要是金融数学)答案

09年SOA北美精算师考试第二门FM官方样题第一部分(主要是金融数学)答案SAMPLE SOLUTIONS FOR DERIVATIVES MARKETSQuestion #1Answer is DIf the call is at-the-money, the put option with the same cost will have a higher strike price.A purchased collar requires that the put have a lower strike price. (Page 76)Question #2Answer is C66.59 – 18.64 = 500 – K exp(–0.06) for K = 480 (Page 69)Question #3Answer is DThe accumulated cost of the hedge is (84.30-74.80)exp(.06) = 10.09.Let x be the market price.If x < 0.12 the put is in the money and the payoff is 10,000(0.12 – x) = 1,200 – 10,000x. The sale of the jalapenos has a payoff of 10,000x –1,000 for a profit of 1,200 –10,000x + 10,000x – 1,000 – 10.09 = 190.From 0.12 to 0.14 neither option has a payoff and the profit is 10,000x – 1,000 – 10.09 = 10,000x – 1,010.If x >0.14 the call is in the money and the payoff is –10,000(x – 0.14) = 1,400 – 10,000x. The profit is 1,400 – 10,000x + 10,000x – 1,000 – 10.09 = 390.The range is 190 to 390. (Pages 33-41)Question #4Answer is BThe present value of the forward prices is 10,000(3.89)/1.06 + 15,000(4.11)/1.0652 +20,000(4.16)/1.073 = 158,968. Any sequence of payments with that present value is acceptable. All but B have that value. (Page 248)Question #5Answer is EIf the index exceeds 1,025, you will receive x – 1,025. After buying the index for x you will have spent 1,025. If the index is below 1,025, you will pay 1,025 – x and after buying the index for x you will have spent 1,025. One way to get the cost is to note that the forward price is 1,000(1.05) = 1,050. You want to pay 25 less and so must spend 25/1.05 = 23.81 today. (Page 112) Question #6Answer is EIn general, an investor should be compensated for time and risk. A forward contract has no investment, so the extra 5 represents the risk premium. Those who buy the stock expect to earn both the risk premium and the time value of their purchase and thus the expected stock value is greater than 100 + 5 = 105. (Page 140)Question #7Answer is CAll four of answers A-D are methods of acquiring the stock. The prepaid forward has the payment at time 0 and the delivery at time T. (Pages 128-129)Question #8Answer is BOnly straddles use at-the-money options and buying is correct for this speculation. (Page 78)Question #9Answer is DThis is based on Exercise 3.18 on Page 89. To see that D does not produce the desired outcome, begin with the case where the stock price is S and is below 90. The payoff is S + 0 + (110 – S) –2(100 – S) = 2S – 90 which is not constant and so cannot produce the given diagram. On the other hand, for example, answer E hasa payoff of S + (90 – S) + 0 – 2(0) = 90. The cost is 100 + 0.24 +2.17 – 2(6.80) = 88.81. With interest it is 93.36. The profit is 90 –93.36 = –3.36 which matches the diagram.Question #10Answer is D[rationale-a] True, since forward contracts have no initial premium[rationale-b] True, both payoffs and profits of long forwards are opposite to short forwards.[rationale-c] True, to invest in the stock, one must borrow 100 at t=0, and then pay back 110 = 100*(1+.1) at t=1, which is like buying a forward at t=1 for 110. [rationale-d] False, repeating the calculation shown above in part c), but with 10% as a continuously compounded rate, the stock investor must now pay back100*e.1 = 110.52 at t=1; this is more expensive than buying a forward at t=1for 110.00.[rationale-e] True, the calculation would be the same as shown above in part c), but now the stock investor gets an additional dividend of 3.00 at t=.5, which theforward investor does not receive (due to not owning the stock until t=1). [This is based on Exercise 2-7 on p.54-55 ofMcDonald][McDonald, Chapter 2, p.21-28]Question #11Answer is CSolution: The 35-strike call has future cost (at t=1) of 9.12*(1+.08) = 9.85The 40-strike call has future cost (at t=1) of 6.22*(1+.08) = 6.72The 45-strike call has future cost (at t=1) of 4.08*(1+.08) = 4.41If S1<35, the profits of the 3 calls, respectively, are -9.85, -6.72, and -4.41.If 35<s1<="" -6.72,="" 3="" and="" are="" bdsfid="114" calls,="" of="" p="" profits="" respectively,="" s1-44.85,="" the=""></s1If 40<s1<="" 3="" and="" are="" bdsfid="116" calls,="" of="" p="" profits="" respectively,="" s1-44.85,="" s1-46.72,="" the=""></s1If S1>45, the profits of the 3 calls, respectively, are S1-44.85, S1-46.72, and S1-49.41.The cutoff points for when the relative profit ranking of the 3 calls change are:S1-44.85=-6.72, S1-44.85=-4.41, and S1-46.72=-4.41, yielding cutoffs of 38.13, 40.44, and 42.31.If S1<38.13, the 45-strike call has the highest profit, and the 35-strike call the lowest.If 38.13<s1<="" p="" profit,="" the=""></s1If 40.44<s1<="" p="" profit,="" the=""></s1If S1<42.31, the 35-strike call has the highest profit, and the 45-strike call the lowest.We are looking for the case where the 35-strike call has the highest profit, and the 40-strike call has the lowest profit, which occurs when S1 is between 40.44 and 42.31.[This is based on Exercise 2-13 on p.55-56 of McDonald][McDonald, Chapter 2, p.33-37]Question #12Answer is BSolution: The put premium has future value (at t=.5) of 74.20 * (1+(.04/2)) = 75.68 Then, the 6-month profit on a long put position is: max(1,000-S.5,0)-75.68. Correspondingly, the 6-month profit on a short put position is 75.68-max(1,000-S.5,0). These two profits are opposites (naturally, since long and short positions have opposite payoff and profit). Thus, they can only be equal if producing 0 profit. 0 profit is only obtained if 75.68 = max(1,000-S.5,0), or 1,000-S.5 = 75.68, or S.5 = 924.32. [McDonald, Chapter 2, p.39-42]Question #13Answer is DSolution: Buying a call, in conjunction with a short position in a stock index, is a form of insurance called a cap. Answers (A) and (B) are incorrect because they relate to a floor, which is the purchase of a put to insure against a long position in a stock index. Answer (E) is incorrect because it relates to writing a covered call, which is the sale of a call along with a long position in the stock index, so that the investor is selling rather than buying insurance. Note that a cap can also be thought of as ‘buying’ a covered call. Now, let’s calculate the profit: 2-year profit = payoff at time 2 – the future value of the initial cost to establish the position = (-75 + max(75-60,0)) –(-50 + 10)*(1+.03)2 = -75+15+40*(1.03)2 = 42.44-60 = -17.56. Thus,we’ve lost more from holding the short position in the index (since the index went up) than we’ve gained from owning the long call option.[McDonald, Chapter 3, p.59-65]Question #14Answer is ASolution: This consists of standard applications of the put-call parity equation on p.69. Let C be the price for the 40-strike call option. Then, C + 3.35 is the price for the 35-strike call option. Similarly, let P be the price for the 40-strike put option. Then, P –x is the price for the 35-strike put option, where x is what we’re trying to find. Using put-call parity, we have:(C + 3.35) + 35*e-.02 - 40 = P – x (this is for the 35-strike options)C + 40*e-.02 – 40 = P (this is for the 40-strike options)Subtracting the first equation from the second, 5*e-.02 – 3.35 = x = 1.55.[McDonald, Chapter 3, p.68-69]Answer is CSolution: The initial cost to establish this position is 5*2.78 –3*6.13 = -4.49. Thus, you are receiving 4.49 up front. This grows to 4.49*e .08*.25 = 4.58 after 3 months. Then, the following payoff/profit table can be constructed at T=.25 years: S T : 5*max(S T – 40, 0) – 3*max(S T – 35, 0) + 4.58 = Profit S T <35 0 - 0 + 4.58 = 4.58 35 <= S T <= 40 0 - 3*(S T – 35) + 4.58 = 109.58-3S T S T > 40 5*(S T -40) - 3*(S T – 35) + 4.58 = 2S T -90.42Thus, the maximum profit is unlimited (as S T increases beyond 40, so does the profit) Also, the maximum loss is 10.42(occurs at S T = 40, where profit = 109.58-120 = -10.42) [Notes] The above problem is an example of a ratio spread.[McDonald, Chapter 3, p.73]Question #16Answer is DSolution: The ‘straddle’ consists of buying a 40-strike call and buying a 40-strike put. This costs 2.78 + 1.99 = 4.77 at t=0, and grows to 4.77*e .02 = 4.87 at t=.25. The ‘strangle’ consists of buying a 35-strike put and a 45-strike call. This costs 0.44 + 0.97 = 1.41 at t=0, and grows to 1.41*e .02 = 1.44 at t=.25. For S T <40, the ‘straddle’ has a profit of 40-S T -4.87 = 35.13, and for S T >=40, the ‘straddle’ has a profit of S T -40-4.87 = 44.87. For S T <35, the ‘strangle’ has a profit of 35-S T -1.44 = 33.56, and for S T >45, the ‘strangle’ has a profit of S T -45-1.44 = 46.44. However, for 35<=S T <=45, the ‘strangle’ has a profit of -1.44 (since both options would not be exercised). Comparing the payoff structures between the ‘straddle’ and ‘strangle,’ we see that if S T <35 or if S T >45, the ‘straddle’ would outperform the ‘strangle’ (since 35.13 > 33.56,and since -44.87 > -46.44). However, if 35<=S T <=45, we can solve for the two cutoff points for S T , where the ‘strangle’ would outperform the ‘straddle’ as follows:-1.44 > 35.13 – S T, and -1.44 > S T - 44.87. The first inequality gives S T > 36.57, and the second inequality gives S T < 43.43. Thus, 36.57 < S T < 43.43.[McDonald, Chapter 3, p.78-80]Answer is B[rationale I] Yes, since Strategy I is a bear spread using calls, and bear spreads perform better when the prices of the underlying asset goes down.[rationale II] Yes, since Strategy II is also a bear spread – it just uses puts instead! [rationale III] No, since Strategy III is a box spread, which has no price risk; thus, the payoff is the same (1,000-950 = 50), no matter what the price of theunderlying asset.[Note]: An alternative, but much longer, solution is to develop payoff tables for all 3 strategies.[McDonald, Chapter 3, p.70-73]Question #18Answer is BSolution: First, let’s calculate the expected one-year profit without using the forward. This would be .2*(700+150-750) + .5(700+170-850) + .3*(700+190-950) = 20 + 10 - 18 = 12. Next, let’s calculate the expected one-year profit when buying the 1-year forward for 850. This would be 1*(700+170-850) = 20. Thus, the expected profit increases by 20 - 12 = 8 as a result of using the forward.[This is based on Exercise 4-7 on p.122 of McDonald][McDonald, Chapter 4, p.98-100]Question #19Answer is DSolution: There are 3 cases, one for each row in the above probability table.For all 3 cases, the future value of the put premium (at t=1) = 100*e.06 = 106.18.In Case 1, the 1-year profit would be: 750 - 800 - 106.18 + max(900-750,0) = -6.18In Case 2, the 1-year profit would be: 850 - 800 - 106.18 + max(900-850,0) = -6.18In Case 3, the 1-year profit would be: 950 - 800 - 106.18 +max(900-950,0) = 43.82 Thus, the expected 1-year profit = .7 * -6.18 + .3 * 43.82 = -4.326 + 13.146 = 8.82.[This is based on Exercise 4-3 on p.121 of McDonald][McDonald, Chapter 4, p.92-96]Answer is BSolution: This is an example of pricing a forward contract using discrete dividends. Thus, we need the future value of the current stock price minus the future value of each of the 12 dividends, where the valuation date is T=3. Thus, the valuation equation is: Forward price = 200*e.04(3) –[1.50*e.04(2.75) + 1.50*1.01*e.04(2.5) + 1.50*(1.01)2*e.04(2.25) + …1.50*(1.01)12] = 200*e.12 - 1.50*e.11{[1-(1.01*e-.01)12]/[1-(1.01*e.01)]}, using the geometric series formula from interest theory. This simplifies numerically to 225.50 -1.67442*11.99666 = 205.41.[This problem combines the material from interest theory and derivatives, although one could also simplify the above expression by brute force (instead of geometric series), since there are only 12 dividends to accumulate forward to T=3.] [McDonald, Chapter 5, p.133-134]Question #21Answer is ESolution: Here, the fair value of the forward contract is given by S0 * e(r-d)T =110 * e(.05-.02).5 = 110 * e.015 = 111.66. This is 0.34 less than the observed price. Thus, one could exploit this arbitrage opportunity by selling the observed forward at 112 and buying a synthetic forward at 111.66, making 112-111.66 = 0.34 profit.[This is based on Exercise 5-8 on p.163-164 of McDonald][McDonald, Chapter 5, p.135-138]Answer is BSolution: First, we must determine the present value of the forward contracts. On a per ton basis, this is: 1,600/1.05 + 1,700/(1.055)2 + 1,800/(1.06)3 = 4,562.49.Then, we must solve for the level swap price, which is labeled x below, as follows:4,562.49 = x/1.05 + x/(1.055)2 + x/(1.06)3 = x*[1/1.05 + 1/(1.055)2 + 1/(1.06)3] =2.69045*x.Thus, x = 4,562.49 / 2.69045 = 1,695.81.Thus, the amount he would receive each year is 50*1,695.81 = 84,790.38. [McDonald, Chapter 8, p.247-248]Question #23Answer is ESolution: First, note that the notional amount and the future 1-year LIBOR rates (not given) do not factor into the calculation of the swap’s fixed rate. All we need at the various zero-coupon bond prices P(0, t) for t=1,2,3,4,5, along with the 1-year implied forward rates, which are given by r0(t-1,t), for t=1,2,3,4,5. These calculations are shown in the following table:t 1 2 3 4 5P(0,t) (1.04)-1(1.045)-2 (1.0525)-3 (1.0625)-4 (1.075)-5=.96154 =.91573 =.85770 =.78466 =.69656 r0(t-1,t) s1[1.0452/1.04]-1 [1.05253/1.0452]-1 [1.06254/1.05253]-1 [1.0755/1.06254]-1 =.04000 =.05002 =.06766 =.09307 =.12649 Thus, the fixed swap rate = R = [(.96154)*(.04)+…+(.69656)*(.12649)] / [.96154 +…+.69656]= [.03846 + .04580 + .05803 + .07303 + .08811]/[.96154 + .91573 + .85770 + .78466 +.69656]= .30344 / 4.21619 = .07197 = 7.20% (approximately).[Note: This is much less calculation-intensive if you realize that the numerator (.30344) for R can also be obtained by taking 1- P(0,n) = 1 – P(0,5) = 1 - .69656 = .30344. Then, you would not need to calculate any of the implied forward rates!][McDonald, Chapter 8, p.255-258]Answer is D[rationale-a] True, hedging reduces the risk of loss, which is a primary function of derivatives.[rationale-b] True, derivatives can be used the hedge some risks that could result in bankruptcy.[rationale-c] True, derivatives can provide a lower-cost way to effect a financialtransaction.[rationale-d] False, derivatives are often used to avoid these types of restrictions. [rationale-e] True, an insurance contract can be thought of as a hedge against the risk of loss.[McDonald, Chapter 1, p.2-3]Question #25Answer is C[rationale-a] True, both types of individuals are involved in the risk-sharing process. [rationale-b] True, this is the primary reason reinsurance companies exist.[rationale-c] False, reinsurance companies share risk by issuing rather than investing in catastrophic bonds. In effect, they are ceding this excess risk to thebondholder.[rationale-d] True, it is diversifiable risk which is reduced or eliminated when risks are shared.[rationale-e] True, this is a fundamental idea underlying risk management andderivatives.[McDonald, Chapter 1, p.5-6]Question #26Answer is B[rationale-I] True, the forward seller has unlimited exposure if the underlying asset’s price increases.[rationale-II] True, the call issuer has unlimited exposure if the underlying asset’s price rises.[rationale-III] False, the maximum loss on selling a put is FV(put premium) – strike price. [McDonald, Chapter 2, p.43 (Table 2.4)]Answer is A[rationale-I] True, as prices go down, the value of holding a put option increases.canbe thought of as a put option.insuranceHomeowner’s[rationale-II] False, returns from equity-linked CDs are zero if prices decline, but positive if prices rise. Thus, owners of these CDs benefit from rising prices. [rationale-III] False, a synthetic forward consists of a long call and a short put, both of which benefit from rising prices (so the net position also benefits as such). [McDonald, Chapter 2, p.44-48]Question #28Answer is E[rationale-a] True, derivatives are used to shift income, thereby potentially lowering taxes.[rationale-b] True, as with taxes, the transfer of income lowers the probability ofbankruptcy.[rationale-c] True, hedging can safeguard reserves, and reduce the need for external financing, which has both explicit (e.g. – fees) and implicit (e.g. –reputational) costs.[rationale-d] True, when operating internationally, hedging can reduce exchange rate risk. [rationale-e] False, a firm that credibly hedges will reduce the riskiness of its cash flows, and will be able to increase debt capacity, which will lead to tax savings, since interest is deductible.[McDonald, Chapter 4, p.103-106]Question #29Answer is ASolution: If S0 is the price of the stock at time-0, then the following payments are required: Outright purchase – payment at time 0 – amount of payment = S0.Fully leveraged purchase – payment at time T – amount of payment = S0*e rT.Prepaid forward contract – payment at time 0 – amount of payment = S0*e-dT.Forward contract – payment at time T – amount of payment = S0*e(r-d)T.Since r>d>0, it must be true that S0*e-dT < S0 < S0*e(r-d)T < S0*e rT.Thus, the correct ranking is given by choice (A).[McDonald, Chapter 5, p.127-134]Answer is C[rationale-a] True, marking to market is done for futures, andcan lead to pricedifferences relative to forward contracts.[rationale-b] True, futures are more liquid; in fact, if you use the same broker to buy and sell, your position is effectively cancelled.[rationale-c] False, forwards are more customized, and futures are more standardized. [rationale-d] True, because of the daily settlement, credit risk is less with futures (v.forwards).[rationale-e] True, futures markets, like stock exchanges, do have daily price limits. [McDonald, Chapter 5, p.142]。

【SOA】关于北美精算师,你必须知道的入门级知识——Exam P

【SOA】关于北美精算师,你必须知道的入门级知识——Exam P

关于北美精算师,你必须知道的入门级知识——Exam P成为一名北美准精算师(ASA)必须要经历五门SOA的准精算师考试,而其中最简单也是大部分人最先开始学习准备的就是Exam P,即probability。

顾名思义,Exam P考察的就是最基本的数理统计与概率问题。

下面我们就来了解一下Exam P的考试形式与内容。

考试目的考生可以掌握用于定量评估风险的基本的概率方法,并着重于用这些方法应用解决精算学中遇到的问题。

参加这门考试的考生应具有一定的微积分基础,并了解基本的概率、保险和风险管理的概念。

考试形式Exam P采用机考的形式,总共30道单项选择题,考试时间为3个小时。

每道选择题共有5个选项,其中只有一个正确选项。

与SAT考试不同的是,Exam P考试答错并不会额外扣分,也就是说考生一定不要空任何一道题。

Exam P中会随机分布几道“pilot question”,这些题目是主办方用来分析从而改进将来的考试而出现的,它们的正确与否并不会影响到考生的实际分数。

但是由于考生并无法分辨出这些题目,所以对每一道题目,考生都要同样认真地对待。

考试内容概率(占总分10%-20%)最基本的事件概率计算问题。

包括集合方程与表示(sat functions)、互斥事件(mutually exclusive events)、事件独立性(independence of events)、组合概率(Combinatorial probability)、条件概率(Conditional probability)以及贝叶斯定理(Bayes theorem)等。

拥有单因素概率分布的随机变量(占总分35%-45%)连续分布或离散分布的单因素随机变量的研究。

包括PDF&CDF(Probability density functions and Cumulative distribution functions)、独立随机事件的和的分布、众数(Mode)、中位数(Median)、百分位数(Percentile)、动差(Moment)、方差(Variance)以及变形等问题。

北美精算师(SOA)考试 FM 2001 November 年真题和注解

北美精算师(SOA)考试 FM 2001 November 年真题和注解

22.
D requity = 0.035 + 1.2(0.144 – 0.035) = 0.1658 rdebt = 0.035 + 0.2(0.144 – 0.035) = 0.0568 rassets = (0.0568)(200/500) + (0.1658)(300/500) = 0.1222
20.
C Dollar weighted return K: I = 125 – 100 – 2x + x = 25 – x 25 − x = (25 – x)/100; (1 + i) = (125 – x)/100 i= 1 1 100 − x + 2 x 2 4 Time weighted return L: (1 + i) = 125/100 ◊ 105.8/(125 – x) = 132.25/(125 – x) = (125 – x)/100 (125 – x)2 = 13,225 \ x = 10 i = (25 – x)/100 = 15%
21.
B The equilibrium market price and quantity are 80 and 20, respectively. The marginal cost function is the derivative of the TVC function: MC = 76 + 2q . For the competitive firm, P = MC, 80 = 76 + 2q , q = 2 .
Course 2 Solutions
1
November 2001
5.
A ¬9.2 + 10 ⋅V Present value = 10 ⋅ a5

北美精算学会-SOA-考试制度第2页-精算师考试.doc

北美精算学会-SOA-考试制度第2页-精算师考试.doc

财务课程编号名称学分p385财务管理20f580公司财务15f585应用公司财务20f590公司战略和偿付能力管理10团体和健康保险课程编号名称学分g320团体和个人健康保险30的设计和销售g421团体和个人健康保险25的财务管理和法规g422团体和个人健康保险25的定价g522高级品种10g523非养老年金的退休后10和就业前的福利g525灵活的福利计划10g528健康保险专题15个人人寿和年金保险课程编号名称学分l340个人人寿和年金保险30的精算实务调查l343 人寿保险法和税收15n41高级设计和定价25n43估价和财务报告专题25l540个人人寿和年金保险10的营销l545丧失工作能力收入15l550再保险专题15养老金课程编号名称学分p360养老金估价原理15p362退休计划设计15p363养老金筹资工具15p365养老金计划的法律规定25p461养老金估价原理ii和20养老金计划会计标准p560 国际养老金问题20p564作为专家证人的10p567退休收入保障25投资课程编号名称学分v480衍生证券:理论和应用20v485高级资产组合管理15v595资产和负伤管理应用20要取得fsa资格必须通过以上一个方向的所有课程考试,以及再选择以上方向的其他课程,使学分达到150分,即学分总计要达到450分。

此外,当fsa要素的课程考试全部通过后,考生还要参加最后一门课程一一正认可课程(fac),其内容主要是职业道德和案例,时间为二天半,一般只要自始自终参加,在结束后的晚宴上会获得fsa证书。

到1996年,北美精算学会共有会员16,558名,其中美国11,961名,加拿大3,161名,其他国家1,436名,(除了fsa、asa外,还包括少量的财产和意外险和美国养老金)20,592人,其中美国15,695人,加拿大3,355人,其他国家1,542人。

北美精算学会的考点分布在全世界28个国家和地区,考试每年在春季(五月)和秋季(十一月)举行两次,全世界每年有数干人参加asa一万多门次课程的考试,其中asa的平均通过率为40%。

北美精算师(SOA)考试P 2001 November年真题

北美精算师(SOA)考试P 2001 November年真题
3 . The number of accidents that occur in any given month 5
is independent of the number of accidents that occur in all other months.
Calculate the probability that there will be at least four months in which no accidents occur before the fourth month in which at least one accident occurs.
(A) (B) (C) (D) (E)
0.0000 0.0004 0.0027 0.0064 0.3679
Course 1, November 2001
9
9.
Among a large group of patients recovering from shoulder injuries, it is found that 22% visit both a physical therapist and a chiropractor, whereas 12% visit neither of these. The probability that a patient visits a chiropractor exceeds by 0.14 the probability that a patient visits a physical therapist.
(–1)n n
− an = 1 2n n
Course 1, November 2001
11
11.
A company takes out an insurance policy to cover accidents that occur at its manufacturing plant. The probability that one or more accidents will occur during any given month is

精算师综合辅导-SOA网站考试服务常见问题二

1 精算师综合辅导:SOA网站考试服务常见问题二

精算师综合辅导:SOA网站考试服务常见问题二精算师综合辅导:SOA网站考试服务常见问题二refunds:

how do i obtain an examination refund? if you have registered for but did not sit for an exam, you may request a refund by contacting the exam department at refund@soa.org. you may also mail in the bottom portion of your ticket of admission (indicating which exams need to be refunded). faxed requests may be sent to (847) 706-3599. a $50 administrative fee is assessed on all refunds. the exam department must receive requests no later than june 30 for the spring session and december 31 for the fall session. refunds will be processed approximately 6 weeks after all examinations have been administered for that particular session. refunds will be returned in the payment form that accompanied the original exam application. if your employer paid your exam fee, the employer will receive the refund on your behalf. 2

CFA特许金融分析师考试真题.doc

CFA特许金融分析师考试真题1. A portfolio of no-dividend-paying common stocks earned a geometric mean return of 5 percent between 1 January 1996 and 31 December 2002. The arithmetic mean return for the same period was 6 percent. If the market value of the portfolio at the beginning of 1996 was $100,000, the market value of the portfolio at the end of 2002 was closest toA . 135,000B. 140,710C. 142,000D. 150,363Answer: BThere are seven annual periods between I January 1996 and 31 December 2002, the market value of the portfolio2. Which of the following statements about standard deviation is most accurate? Standard deviation:A. is the square of the variance.B. can be a positive number or a negative number.C. is denominated in the same units as the original data.D. is the arithmetic mean of the squared deviations from the mean.Answer: CThe arithmetic average of the squared deviations around mean is the variance. The standard deviation is the positive square root of the variance and is denominated in the same units as the original data3. An analyst developed the following probability distribution of the rate of return for a common stock Scenario Probability Rate of Return1 0.25 0.082 0.50 0.123 0.25 0.16The standard deviation of the rate of return is closest toA. 0.0200B. 0.0267C. 0.0283D. 0.0400Answer:CExpected value=0.12Variance=0.0008Standard deviation=0.0284. A common stock with a coefficient of variation of 0.50 hasa (n):A. Variance equal to half the stock’s expected returnB. Expected return equal to half the stock’s varianceC. Expected return equal to half the stock’s standard deviationD. Standard deviation equal to half the stock’s expected returnAnswer: DThe coefficient of variation is a measure of relative dispersion that indicates how much dispersion exists relative to the mean of the distribution the coefficient of variation is the standard deviation divided by the mean5. If no other estimator of a given parameter has a sampling distribution with a smaller variance, the estimator used is best characterized asA. accurateB. efficientC. unbiasedD. consistentAnewser B. An unbiased estimator is efficient if no other unbiased estimator of the same parameter has a sampling distribution with smaller variance1. A portfolio of no-dividend-paying common stocks earned a geometric mean return of 5 percent between 1 January 1996 and 31 December 2002. The arithmetic mean return for the same period was 6 percent. If the market value of the portfolio at the beginning of 1996 was $100,000, the market value of the portfolio at the end of 2002 was closest toA . 135,000B. 140,710C. 142,000D. 150,363Answer: BThere are seven annual periods between I January 1996 and 31 December 2002, the market value of the portfolio2. Which of the following statements about standard deviation is most accurate? Standard deviation:A. is the square of the variance.B. can be a positive number or a negative number.C. is denominated in the same units as the original data.D. is the arithmetic mean of the squared deviations from the mean.Answer: CThe arithmetic average of the squared deviations around mean is the variance. The standard deviation is the positive square root of the variance and is denominated in the same units as the original data3. An analyst developed the following probability distribution of the rate of return for a common stockScenario Probability Rate of Return1 0.25 0.082 0.50 0.123 0.25 0.16The standard deviation of the rate of return is closest toA. 0.0200B. 0.0267C. 0.0283D. 0.0400Answer:CExpected value=0.12Variance=0.0008Standard deviation=0.0284. A common stock with a coefficient of variation of 0.50 hasa (n):A. Variance equal to half the stock’s expected returnB. Expected return equal to half the stock’s varianceC. Expected return equal to half the stock’s standard deviationD. Standard deviation equal to half the stock’s expected returnAnswer: DThe coefficient of variation is a measure of relative dispersion that indicates how much dispersion exists relative to the mean of the distribution the coefficient of variation is the standard deviation divided by the mean5. If no other estimator of a given parameter has a sampling distribution with a smaller variance, the estimator used is bestcharacterized asA. accurateB. efficientC. unbiasedD. consistentAnewser B. An unbiased estimator is efficient if no other unbiased estimator of the same parameter has a sampling distribution with smaller variance1. What are the mean and standard deviation of a standard normal distribution?Mean Standard deviationA 0 0B 0 1C 1 0D 1 1Answer: B. The standard normal distribution (unit normal distribution) has a mean of zero and a standard deviation deviation of one2. The population mean and standard deviation of monthly netsales for a company are $100 million and $30 million, respectively. if monthly net sales are normally distributed, which of the following best describes the interval that would be expected to contain approximately 95 percent of the monthly net sales?A. $10 million to $190 million.B. $30 million to $170 million.C. $40 million to $160 million.D. $70 million to $130 million.Answer: C. In normal distribution, about 95 percent of the observations will fall within standard deviations of the mean $100-2*(30)=$40and $100+2*(30)= $1603. A mutual fund manager wants to create a fund based on a high-grade corporate bond index. She first distinguishes between utility bonds and industrial bonds; she then for each segment defines maturity intervals of less than 5 years, 5 to 10 years, and greater than 10 years. For each segment and maturity level, she classifies the bonds as callable or non-callable. For the manager’s sample, which of the following best describes theSampling approach Number of sampling cells?A Simple random sample 3B Simple random sample 12C Stratified random sample 3D Stratified random sample 12Answer: D.The mutual fund manager is using a stratified random sampling approach with 12 cells: 2*3*2=12 sampling cells4. A utility analyst performed a regression analysis relating monthly energy consumption to average monthly temperature over the last four years. Total variation of the dependent variable was 58.6 and the unexplained variation was 31.3. The coefficient of determination and standard error of the estimate, respectively, for the regression model are closest toCoefficient of determination Standard error of the estimateA 0.4659 0.8075B 0.4659 0.8249C 0.5341 0.8075D 0.5341 0.8249Answer: B. The coefficient of determination is explained variation divided by total variation (58.6-31.3)/58.6=0.4659. There are a total of 48 observations in the sample the standard error of the estimate is(31.3/(48-2))1/2=0.82495. A lognormal distribution differs from a normal distribution in that a lognormal distribution:A. is skewed to the leftB. cannot contain negative valuesC. has less complicated confidence intervalsD. is completely described by two parametersAnswer: B. The lognormal distribution is bounded on the left by zero, but a normal distribution contains negative values.技术性分析的两个基本假定是,证券价格能够:a.逐步地根据新的信息作出调整,研究经济环境能够预测未来市场的走向。

北美精算师(SOA)考试P 2001 November年真题

K , for N = 1, . . . , 5 and K a constant. These N
are the only possible loss amounts and no more than one loss can occur.
Determine the net premium for this policy.
(–1)n n
− an = 1 2n n
Course 1, November 2001
11
11.
A company takes out an insurance policy to cover accidents that occur at its manufacturing plant. The probability that one or more accidents will occur during any given month is
7
7.
Let X denote the size of a surgical claim and let Y denote the size of the associated hospital claim. An actuary is using a model in which E(X) = 5, E(X 2) = 27.4, E(Y) = 7, E(Y 2) = 51.4, and Var(X+Y) = 8 .
Given that a patient survived, what is the probability that the patient was categorized as serious upon arrival?
(A) (B) (C) (D) (E)

精算师综合辅导-SOA网站考试服务常见问题一

精算师综合辅导:SOA网站考试服务常见问题一精算师综合辅导:SOA网站考试服务常见问题一精算师综合辅导:SOA网站考试服务常见问题一for questions on exam registrations, schedules, and centers, contactfor all other questions, including grading concerns, defective questions, syllabus information, general course studies, contact education & exams ombudsperson.examination services frequently asked questionsaddress changes:how do i change my address for receipt of admission ticket or grade slip?to change your address on our database, e-mail the correct information to please put “address change”in the subject line of your e-mail. include your date of birth and/or your previous address for positive identification. you may notify the exam department directly at (847) 706-3583.applications:when is the registration deadline?your application(s) must be received on or before april 1 for the spring session, and september 24 for the fall session. applications received after the deadline will not be accepted. please be aware that it takes approximately 10 days for your application to arrive by regular mail. we encourage you to use an overnight delivery service to ensure delivery by the deadline date. please retain your tracking number in the event that you would need to trace your package for proof of delivery. your original signature is required for your application to be valid. a photocopy or facsimile of your signature is not acceptable. applications are processed in the order they are received. it may take a few weeks for your application to be processed due to the volume of applications received. when your registration is entered into our computer you will receive an e-mail confirmation.download fall 2004 exam applicationscalculators:what are the approved calculators and how can i obtain one?you may use the battery –or solar powered texas instruments ba-35 model calculator, ba ii plus, ba ii plus professional edition, ti-30x, ti-30xa, or ti-30x ii (iis solar or 11b battery). you may use more than one of the approved models during the examination. upon entrance to the examination room, candidates must show the supervisor that the memory has been cleared for all of the calculators brought in. calculator instructions are not allowed in the exam room. for the ba ii plus, clearing will reset the calculator to the factory default settings. you can purchase calculators at any office supply store or directly from: texas instruments, attention: order entry, po box 650311, mail station 3962, dallas, tx 75265. for phone orders please call 1-800-842-2737. the texas instruments web site iscandidate numbers:i’ve misplaced my candidate number and want to check if i passed, what can i do?if you have lost or misplaced your ticket of admissionindicating your candidate number, this information cannot be given over the phone, faxed or e-mailed. you may request your candidate number by e-mail to please put “candidate number”in the subject line of your e-mail. you may also contact the exam department at (847) 706-3583. please confirm your mailing address and date of birth. candidate numbers are sent by mail only.change of center:how do i request a change of center?you may request a change of center by contacting the exam department at (847) 706-3583. there is a non-refundable fee of $50 which will be assessed at the time of the request. candidates are not allowed to walk-in to take an exam at a center where they have not registered. supervisors must confirm registration with the soa prior to being allowed to write.精算师综合辅导:SOA网站考试服务常见问题一相关内容:。

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SOA真题May2002Course6第3页-精算师
考试
5.
You
are
given
the
following
information
for
a
15-year
callable
bond:
annual
coupon
rate:
9%
payable semi-annually price:
95.32 effective duration:
3.17 convexity measure
(C):
(67.31)CV
V
VV
y
22002
b
gCalculate the
price
of
the
bond after
a
50
basis point increase in interest rates.(A) 93.65(B) 93.97(C)
95.32(D)
96.67(E)
96.99COURSE 6:
MAY
2002
GO
ON
TO
NEXT PAGEMORNING SESSION6.
You
are
given
the
following
information with respect
to
a
single-period securities model:S
PS0
10
10111
33
011
011
22b
g LNMMMOQPPPDetermine the
value
of
P
which
makes
the
model
arbitrage-free.(A)
14(B)
15(C)
16(D)
17(E)
18COURSE
MAY
2002
GO
ON
TO
NEXT PAGEMORNING SESSION7-16. Each
of
questions
7
through
16
consists
of
lists.
In
the
list
at
the
left
are
two items,lettered X
and
Y.
In
the
list
the
right
are three items, numbered I,
II,
and
III.
ONE ofthe lettered items
is related
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)
I
and
II
only(D) Y
I
and
III only(E) The correct answer is
not given by
(B),
(C)
or (D).7. X. Asian call options I. Payoffs depend on
the average priceof the
underlying asset during thelife
of
the option.Y. Lookback call options II. Guarantees the purchase of
the assetat
lowest
price
during
the
life
ofthe option.III. Can
use averages
for
the exerciseprice.8. X.
Cliquet option
Guaranteed exchange-rate contracts.Y. Quanto option
II.
A
series
of
standard
call
options thatpays
the
annual increase
theunderlying assets.III. The
strike
resets
at
the beginning ofeach year.COURSE 6:
MAY
2002
GO
ON
TO
NEXT PAGEMORNING SESSION9.
X.
Interest
rate
corridor
I.
The
purchase
of
a
cap
at
one
strikerate
and
sale
of
a
floor
at
a lowerstrike rate.Y. Interest rate
collar
II.
The purchase of
a
at
one strikerate and
the
sale
of another cap
at ahigher strike rate.III. Sometimes described as
swappinginto a
bond.10. X.
Zero-coupon convertible bond
I.
Sacrifice yieldY. Putable convertible bond
II.
Greater credit riskIII.
premium11. X. Modified duration I.
Allows
for changing cash
flows asinterest rates change.Y. Effective duration II.
not
allow
for
changing cashflows
as
interest
rates change.III.
Not
an appropriate measure forcallable bonds.COURSE 6:
2002
GO
ON
TO
NEXT PAGEMORNING SESSION7-16. Each
of
questions
7
through
16
consists
of
two
In
the
list
at
the
left
are
two items,lettered X
and
Y.
In
the
list
at
right
are three items, numbered I,
II,
and
III.
ONE ofthe lettered items
is related
in
way
to EXACTLY TWO
of
the numbered items.Indicate the
related items
using
the following answer code:Lettered
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。

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