Title Reading 4 Common Probability Distributions - Answers.pdf ✅

Which of the following portfolios provides the optimal "safety first" return if the minimum acceptable return is 9%? Portfolio Expected Return (%) Standard Deviation (%) 1 13 5 2 11 3 3 9 2 A) 2. B) 3. C) 1. Explanation Roy's safety-first criterion requires the maximization of the SF Ratio: SF Ratio = (expected return – threshold return) / standard deviation Portfolio Expected Return (%) Standard Deviation (%) SF Ratio 1 13 5 0.80 2 11 3 0.67 3 9 2 0.00 Portfolio #1 has the highest safety-first ratio at 0.80. (Module 4.2, LOS 4.k) Question #4 of 96 Question ID: 1456515 A random variable with which of the following probability distributions will have the greatest probability of an outcome more than two standard deviations from the mean? A) Student’s t-distribution with 18 degrees of freedom. B) Student’s t-distribution with 15 degrees of freedom. C) Standard normal distribution. Explanation
For degrees of freedom less than about 120, Student's t-distribution has fatter tails and larger probabilities of extreme outcomes compared to the standard normal distribution. For Student's t-distribution, the lower the degrees of freedom, the fatter the tails and the greater the probability of extreme outcomes. (Module 4.3, LOS 4.n) Question #5 of 96 Question ID: 1456453 A casual laborer has a 70% probability of finding work on each day that she reports to the day labor marketplace. What is the probability that she will work three days out of five? A) 0.3087. B) 0.3192. C) 0.6045. Explanation P(3) = 5! / [(5 – 3)! × 3!] × (0.7 3 ) × (0.3 2 ) = 0.3087 = 5 →2nd→ nCr → 3 × 0.343 × 0.09 (Module 4.1, LOS 4.e) Question #6 of 96 Question ID: 1456465 Multivariate distributions can describe: A) discrete random variables only. B) continuous random variables only. C) either discrete or continuous random variables. Explanation Multivariate distributions can describe discrete or continuous random variables. (Module 4.2, LOS 4.g) Question #7 of 96 Question ID: 1456520
Which of the following statements describes a limitation of Monte Carlo simulation? A) Outcomes of a simulation can only be as accurate as the inputs to the model. B) Simulations do not consider possible input values that lie outside historical experience. C) Variables are assumed to be normally distributed but may actually have non- normal distributions. Explanation Monte Carlo simulations can be set up with inputs that have any distribution and any desired range of possible values. However, a limitation of the technique is that its output can only be as accurate as the assumptions an analyst makes about the range and distribution of the inputs. (Module 4.3, LOS 4.p) Question #8 of 96 Question ID: 1456477 A stock portfolio has had a historical average annual return of 12% and a standard deviation of 20%. The returns are normally distributed. The range –27.2 to 51.2% describes a: A) 68% confidence interval. B) 99% confidence interval. C) 95% confidence interval. Explanation The upper limit of the range, 51.2%, is (51.2 – 12) = 39.2 / 20 = 1.96 standard deviations above the mean of 12. The lower limit of the range is (12 – (-27.2)) = 39.2 / 20 = 1.96 standard deviations below the mean of 12. A 95% confidence level is defined by a range 1.96 standard deviations above and below the mean. (Module 4.2, LOS 4.h) Question #9 of 96 Question ID: 1456510 With 60 observations, what is the appropriate number of degrees of freedom to use when carrying out a statistical test on the mean of a population?