据说这是CFA考试史上难的八道题目，你要不要试试？

报考资讯  |  2017-03-01

　　听说想要通过CFA I，II 和 III 每个级别至少要进行300个小时的学习。否则，你将要参加各种培训班。即使如此，你可能会被非常棘手的问题击倒。金程CFA小编找来CFA考试的八道题目，据说这八个问题是CFA考试难的八道题目，现在跟随金程CFA小编来看看是哪八道题目，以及正确答案和解析吧！ 》》点我了解更多CFA考点

　　1

　　Level I: Beth Knight, CFA, and David Royal, CFA, are independently analyzing the value of Bishop, Inc. stock. Bishop paid a dividend of $1 last year. Knight expects the dividend to grow by 10% in each of the next three years, after which it will grow at a constant rate of 4% per year. Royal also expects a temporary growth rate of 10% followed by a constant growth rate of 4%, but he expects the supernormal growth to last for only two years. Knight estimates that the required return on Bishop stock is 9%, but Royal believes the required return is 10%. Royal’s valuation of Bishop stock is approximately:

　　A. $5 less than Knight’s valuation

　　B. Equal to Knights valuation

　　C. $5 greater than Knights valuation

　　答案解析

　　Tim Smaby, VP, Advance Designations, Kaplan Professional:

　　正确答案：A.

　　其实在计算 share values 之前你就可以选出正确答案啦。Royal is using a shorter period of supernormal growth and a higher required rate of return on the stock. Both of these factors will contribute to a lower value using the multistage DDM.

　　Royal’s valuation is $5.10 less that Knight’s valuation.

　　2

　　Level I: John Gray, CFA and Sally Miller are discussing what they think their year-end bonus will be and how they might spend them. Miller is new to working in finance and asks Gray what people usually get and what he has got in the past. Gray explains that the firm prohibits employees from discussing their exact bonus number but also says that 30% of people get ‘good’ bonus’, 50% ‘average’ and 20% ‘low’. Gray says that he really wants a new smart watch recently released by a large tech company and says that he will definitely buy it if he gets a ‘good’ bonus, while there is only a 50% and 10% probability he will get it with an ‘average’ or ‘low’ bonus respectively.

　　Two weeks later, Miller sees Gray in the office and asks him if he got a good bonus. Gray reminds Miller that the firm’s policy means he cannot say, but Miller notices that he is wearing the new smart watch they were talking about. Miller goes back to her desk and calculates the probability that Gray got a ‘good’ bonus is closest to:

　　A: 30%

　　B: 53%

　　C: 57%

　　答案解析

　　Nicholas Blain, chief executive, Quartic Training:

　　正确答案：B.

　　“Using Bayes’ Formula : P(Event|Information) = P(Event) * P(Information |Event) / P(Information)In this case, the event is getting a good bonus, and the information is that Gray has bought the new watch.

　　The probability that he got a good bonus and then bought the watch is given by:

　　P(Event)*P(Information |Event) = 0.3*1.00 = 0.30The total probability that he would buy the watch is given by:

　　P(Information) = 0.3*1.00 + 0.5*0.50 + 0.2*0.10 = 0.57Therefore, the probability that he got a good bonus is the proportion of probability that he got a good bonus and got the watch, to the total probability he got the watch:

　　P(Event|Information) = 0.30 / 0.57 = 0.53.”

　　3

　　Level I: For a European Call option on a stock, which of the following changes, (looking at each change individually and keeping all other factors constant) would an analyst be least likely confident about an up or down movement in the price of the option?

　　A: Share price goes up; dividend goes up

　　B: The demand for share increases / supply decreases; interest rates fallC: Share increases in volatility; the firm cancels the next dividend答案解析

　　Nicholas Blain, chief executive, Quartic Training:

　　正确答案：A.

　　“Share price up = Option Price Up

　　Dividend up = Option Price Down (dividends are benefits of holding the underlying share, when holding the option, you do not receive dividend)Share in High Demand = Option Price down as this is a benefit in holding the underlyingInterest Rates Fall = Option Price Down as this reduces the cost of carry of holding the underlyingShare increases in volatility = Option Price UpCancels next dividend = Option Price Up, as these dividends are not received by the option holder anywayA is the correct answer; as the increase in the option price due to the share going up could be offset by the decrease in the price due to the dividend going up.

　　B results in the option price falling for both scenarios and C results in the option price rising in both scenarios.”

　　4

　　Level II: Sudbury Industries expects FCFF in the coming year of 400 million Canadian dollars ($), and expects FCFF to grow forever at a rate of 3 percent. The company maintains an all-equity capital structure, and Sudbury’s required rate of return on equity is 8 percent.

　　Sudbury Industries has 100 million outstanding common shares. Sudbury’s common shares are currently trading in the market for $80 per share.

　　Using the Constant-Growth FCFF Valuation Model, Sudbury’s stock is:

　　A. Fairly-valued.

　　B. Over-valued

　　C. Under-Valued

　　答案解析

　　Tim Smaby, VP, Advance Designations, Kaplan Professional:

　　正确答案 A.

　　Based on a free cash flow valuation model, Sudbury Industries shares appear to be fairly valued.

　　Since Sudbury is an all-equity firm, WACC is the same as the required return on equity of 8%.

　　The firm value of Sudbury Industries is the present value of FCFF discounted by using WACC. Since FCFF should grow at a constant 3 percent rate, the result is:

　　Firm value = FCFF1 / WACC?g = 400 million / 0.08?0.03 = 400 million / 0.05 = $8,000 millionSince the firm has no debt, equity value is equal to the value of the firm. Dividing the $8,000 million equity value by the number of outstanding shares gives the estimated value per share:

　　V0 = $8,000 million / 100 million shares = $80.00 per share

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　　5

　　Level II: (Excerpt from item set)

　　Financial information on a company has just been published including the following:　　

　　Dividends and free cash flows will increase a growth rate that steadily drops from 14% to 5% over the next four years, then will increase at 5% thereafter.

　　The intrinsic value per share using dividend-based valuation techniques is closest to:

　　A. $121

　　B. $127

　　C. $145

　　答案解析

　　Nicholas Blain, chief executive, Quartic Training:

　　正确答案：B.

　　“The H-model is frequently required in Level II item sets on dividend or free cash flow valuation.

　　The model itself can be written as V0 = D0 ÷ (r - gL) x [(1 + gL) + (H x (gS - gL))] where gS and gL are the short-term and long-term growth rates respectively, and H is the “half life” of the drop in growth.

　　For this question, the calculation is: dividend D0 = $240m x 0.6 ÷ 20m = $7.20 per share.

　　V0 = $7.20 ÷ (0.12 - 0.05) x [1.05 + 2 x (0.14 - 0.05)] = $126.51, answer B.

　　However, there is a neat shortcut for remembering the formula. Sketch a graph of the growth rate against time: a line decreasing from short-term gS down to long-term gL over 2H years, then horizontal at level gL. Consider the area under the graph in two parts: the ‘constant growth’ part, and the triangle.

　　If you look at the formula, the ‘constant growth’ component uses the first part of the square bracket, i.e. D0 ÷ (r - gL) x [(1 + gL) …], which is your familiar D1 ÷ (r - gL). For the triangle, what is its area? Half base x height = 0.5 x 2H x (gS - gL) = H x (gS - gL). This is the second part of the square bracket.

　　Hence the H-model can be rewritten as V0 = D0 ÷ (r - gL) x [(1 + gL) + triangle].”

　　6

　　Level III: A German portfolio manager entered a 3-month forward contract with a U.S. bank to deliver $10,000,000 for euros at a forward rate of €0.8135/$. One month into the contract, the spot rate is €0.8170/$, the euro rate is 3.5%, and the U.S. rate is 4.0%. Determine the value and direction of any credit risk.

　　答案解析

　　Tim Smaby, VP, Advance Designations, Kaplan Professional:

　　“The German manager (short position) has contracted with a U.S. bank to sell dollars at €0.8135, and the dollar has strengthened to €0.8170. The manager would be better off in the spot market than under the contract, so the bank faces the credit risk (the manager could default).

　　From the perspective of the U.S. bank (the long position), the amount of the credit risk is:

　　Vbank (long) = €8,170,000 / (1.04)2/12 ? €8,135,000 / (1.035)2/12 = €28,278(The positive sign indicates the bank faces the credit risk that the German manager might default.)”

　　7

　　Level III: Within the ‘Option Strategies’ sectionOptionStrikePremium　　

　　Risk-free rate continuously compounded: 4% annualOption expiry: 6 months

　　Using the above data for a box spread, calculate what arbitrage profit can be achieved at the end of 6 months.

　　答案解析

　　Nicholas Blain, chief executive, Quartic Training:

　　“First, work out the cost of the box spread. Combine the two call options into a bull spread (buy the low strike call and sell the high strike call), and the two put options into a bear spread (buy the high strike put and sell the low strike put). Combining those two gives a box spread. To calculate the initial cost, work out the net premia:

　　Cost = c1 - c2 + p2 - p1 = 6 - 4 + 8.001 - 0.604 = $9.397The payoff from the box spread will be the difference between the strike levels, ie 30 - 20 = $10.

　　If you borrowed $9.397 at the beginning in order to enter the box spread, how much would you have to pay back after 6 months? You need to compound the cost at the risk-free rate:

　　$9.397 x e0.04 x 0.5 = $9.58683

　　So the arbitrage profit would be the difference between the payoff and what you have to pay back on the loan, ie $10 - $9.58683 = $0.41317”

　　8

　　Level III: Assume Felix Burrow is a US investor, holding some euro-denominated assets. Given the information below, calculate the domestic return for Burrow over the year.　　

　　答案解析

　　Nicholas Blain, chief executive, Quartic Training“The domestic return (return in USD terms) depends on the EUR-return of the asset, as well as on the change in exchange rates:

　　RDC = (1+RFC) (1+RFX) -1

　　where RFX is the change in spot rates, using the domestic currency as the price currency (ie we require a USD/EUR quote). In this example, the exchange rate is quoted as such, so we can use the quote provided (otherwise, if the domestic currency was the base currency, we would need to invert the quote first).

　　RFC = -1 = 0.0078 = 0.78%

　　RFX = -1 = 0.0261 = 2.61%

　　RDC = (1 + 0.78%)(1 + 2.61%) - 1 = 3.41%

　　Burrow’s domestic currency return was higher than the underlying asset return, because he further benefits from the appreciation of the Euro (depreciation of the USD).”　　

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