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1 QUANTITATIVE ANALYSIS 1. Assume you have a portfolio of 10 obligors that are not correlated. Given that each obligor's probability of default is 5%, what is the probability that no defaults will occur over the next year? A. 5.0% B. 50.0% C. 60.0% D. 95.0% 2. The annual marginal probability of default of a bond is 15% in year 1 and 20% in year 2. What is the probability of the bond surviving (i.e. no default) to the end of two years? A. 68% B. 65% C. 80% D. 85% 3. A portfolio of bonds consists of five bonds whose default correlation is zero. The one-year probabilities of default of the bonds are: 1%, 2%, 5%, 10% and 15%. What is the one-year probability of no default within the portfolio? A. 71% B. 67% C. 85% D. 99% 4. The characteristic function of the product of independent random variables is equal to the: A. square root of the product of the individual characteristic functions B. product of the individual characteristic functions C. exponential root of the product of the individual characteristic functions D. sum of the individual characteristic functions 5. An investor is choosing one of twenty securities. Ten of the securities are stocks and ten are bonds. Four of the ten stocks were issued by utilities; the other six were issued by industrial firms. Two of the ten bonds were issued by utilities; the other eight were issued by industrial firms. If the investor chooses a security at random, the probability that it is a bond or a security issued by an industrial firm is: A. 0.80 B. 0.70

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2 C. 0.60 D. 0.50 6. Dependent random variables are defined as variables where their joint probability is: A. equal to zero B. not equal to the product of their individual probabilities C. greater than the product of their individual probabilities D. equal to the product of their individual probabilities 7. Given the following data for a market variable, what is the best estimate of its variance? Probability Value 24% -12 40% 4 36% 14 A. 6 B. 10 C. 32 D. 97 8. An analyst is studying a stock that is currently trading at \$35. The analyst estimates that there is 33% probability that the stock will trade at \$50 after one year, a 20% probability that the stock will trade at \$42, and a 47% probability that the stock will trade at \$20. What is the volatility of this stock price? A. 13% B. 24% C. 31% D. 39% 9. Using the following joint probability distribution to answer the questions below. Y=1 Y=2 Y=3 X=1 0.05 0.05 0.10 X=2 0.05 0.10 0.15 X=3 0.15 0.15 0.20 The expected value of Y is closest to: A. 0.2 B. 2.2 C. 1.0 D. 2.3 ________________________________________
3 If you know that Y is equal to 2, the probability that X is equal to 1 is closest to: A. 0.05 B. 0.25 C. 0.20 D. 0.17 ________________________________________ The variance of X is closest to: A. 0.54 B. 0.67 C. 0.74 D. 0.61 10. Given two random variables X and Y, what is the Variance of X given Variance[Y] = 100, Variance [4X - 3Y] = 2,700 and the correlation between X and Y is 0.5? A. 56.3 B. 113.3 C. 159.9 D. 225.0 11. You are given that X and Y are random variables, and each of which follows a standard normal distribution with Covariance (X, Y) = 0.4. What is the variance of (5X + 2Y)?

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## This note was uploaded on 11/02/2011 for the course FINANCE 611 taught by Professor Liyang during the Spring '11 term at Covenant School of Nursing.

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V1_FRMä¸€çº§ä¹ é¢˜ï¼ˆæ•°

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