中国教育

　　各位奔波在CFA考试冲刺第一线的筒子们，你们最近过得还好吗？在放暑假的同时，可不能分心刷剧哟。如果想成为投行精英安迪那样的金融佼佼者，可要抓紧最后的时刻，磨刀奋战即将到来的2016年CFA特许金融分析师考试！

　　CFA协会明确表示，每一位CFA考生都需要至少300个小时准备考试。如果你已经对CFA考试有了完全的准备，如何检验自己的考试成果呢？根据高顿财经研究院CFA考试研究发现，以下八道题目就可检测考生的CFA掌握水平。许多投行精英们都认为这八道题目非常棘手，堪称CFA一二三级中，遇到的"最难"题，快来看看你是否会解！

　　CFA一级试题：

　　1. 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

　　卡普兰教授:Tim Smaby 解析:

　　The correct answer is A.

　　You can select the correct answer without calculating the share values. 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.

　　Screen Shot 2015-05-22 at 11.36.52

　　Royal's valuation is $5.10 less that Knight's valuation."

　　2. 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%

　　知名投行培训主管Nicholas Blain 解析:

　　"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 = 0.30

　　The 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 = 0.57

　　Therefore, 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. 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 fall

　　C: Share increases in volatility; the firm cancels the next dividend

　　知名投行培训主管Nicholas Blain 解析:

　　"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 underlying

　　Interest Rates Fall = Option Price Down as this reduces the cost of carry of holding the underlying

　　Share increases in volatility = Option Price Up

　　Cancels next dividend = Option Price Up, as these dividends are not received by the option holder anyway

　　A 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."

　　CFA二级试题：

　　4.  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

　　卡普兰教授:Tim Smaby 解析:

　　"The correct answer is 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 million

　　Since 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

　　5. 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

　　高顿财经研究院主任 Feng 解析:

　　"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]."

　　CFA三级试题：

　　6.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.

　　卡普兰教授:Tim Smaby 解析:

　　"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. Within the 'Option Strategies' section

　　Option       Strike                    Premium

　　Call            1X1 = 20              c1 = 6

　　Call             2X2 = 30             c2 = 4

　　Put             1X1 = 20               p1 = 0.604

　　Put             2X2 = 30               p2 = 8.001

　　Risk-free rate continuously compounded: 4% annual

　　Option expiry: 6 months

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

　　高顿财经研究院主任 Feng 解析:

　　"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 = $9.397

　　The 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. 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.

　　知名投行培训主管Nicholas Blain 解析:

　　"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)."

　　看到这里，你是否都会做呢？如果还没有掌握好，可要在最后的一个月时间里抓紧时间查漏补缺了！高顿财经小编预祝各位CFA考生都能顺利通过此次考试！