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FRM考试一级模拟试题一

来源：高顿网校 2015-03-02

　　1. Consider a convertible bond that is trading at a conversion premium of 20 percent. If the value of the underlying stock rises by 25 percent, the value of the bond will:

　　A. Rise by less than 25%.

　　B. Rise by 25%.

　　C. Rise by more than 25%.

　　D. Remain unchanged.

　　2. If a cash flow of $10,000 in two years' time has a PV of $8,455, the annual percentage rate, assuming continuous compounding is CLOSEST to:

　　A. 8.13%.

　　B. 8.39%.

　　C. 8.75%.

　　D. 8.95%.

　　3. The current values of a firm's assets and liabilities are 200 million and 160 million respectively. If the asset values are expected to grow by 40 million and liability values by 30 million within a year and if the annual standard deviation of these values is 50 million, the distance from default in the KMV model would be closest to:

　　A. 0.8 standard deviations.

　　B. 1.0 standard deviations.

　　C. 1.2 standard deviations.

　　D. Cannot not be determined.

　　4. What is the semiannual-pay bond equivalent yield on an annual-pay bond with a yield to maturity of 12.51 percent?

　　A. 12.00%.

　　B. 11.49%.

　　C. 12.51%.

　　D. 12.14%.

　　5. You want to test at the 0.05 level of significance that the mean price of luxury cars is greater than $80,000. A random sample of 50 cars has a mean price of $88,000. The population standard deviation is $15,000. What is the alternative hypothesis?

　　A. The population mean is greater than or equal to $80,000.

　　B. The population mean is less than $80,000.

　　C. The population mean is not equal to $80,000.

　　D. The population mean is greater than is $80,000.

　　Answers:

　　1. Correct answer: A

　　The convertible bond implicitly gives bondholders a call option on the underlying stock. The delta of this option will vary between 0 (when the option is extremely out of the money) and 1 (when the option is extremely in the money). In this case, the bond is trading at a conversion premium of 20% so the delta must be somewhere between zero and one, and hence the price of the convertible bond will rise by less than the price of the underlying stock.高顿题库——全球财经*9题库（精题真题、全真模考系统、名师答疑）点击进入“每日一练——免费在线测试”

　　2. Correct answer: B

　　Continuously compounded rate = ln(FV/PV)/N = ln(10000 / 8455) / 2 = 8.39%.

　　3. Correct answer: B

　　Distance from default = (Expected value of assets - Expected value of liabilities) / Standard deviation = (240 - 190)/50 = 1.0.

　　4. Correct answer: D:

　　The semiannual-pay bond equivalent yield of an annual-pay bond = 2 * [(1 + yield to maturity on the annual-pay bond)*0.5 -1] = 12.14%.

　　5. Correct answer: D

　　The alternate hypothesis is the statement which will be accepted if the null hypothesis is proven wrong. Therefore, we make whatever we are trying to test as the alternate hypothesis - in this case that the mean price of luxury cars is greater than $80,000, and the null hypothesis as the opposite (the mean price of luxury cars is less than or equal to $80,000). This problem is a common example of how statisticians establish hypotheses by proving that the opposite (i.e. the null hypothesis) is false.　各位考生想顺利通过FRM考试，除了掌握专业知识和答题技巧之外，还可以关注高顿网校的精品网课，高顿网校专业讲师为考生们提供考试复习笔记汇总，帮助考生更好地理解FRM知识，高顿祝各位考生考试大捷！进入直播

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