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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.
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.
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