FRM一级模考
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FRM一级模拟题
1 . Which of the following exhibit positively skewed distributions?
I Normal Distribution.
II LognormaIDistribution.
III The Returns of Being Short a Put Option.
IV The Returns of Being Long a Call Option.
A. Ilonly
B. Illonly
C. II and IV only
D. I, III, and IV only
Answer: C A lognormal distribution is positively skewed because it cannot contain negative values. The retums on a long call position cannot be more negative than the premium paid for the option but has unlimited potential positive value, so it will also be positively skewed.
2 .The distribution of one-year returns for a portfolio of securities is normally distributed with an expected vajue of 45 mⅢion, and a standard deviation of 16million. What is the probability that the value of the portfolio, one year hence,
will be between e39 million and ~43 million?
C. 10.6%
D. 1 1 .6%
Answer: B
We can compute how many standard deviations away from the mean each value would be and refer to the cumujative distribution tables to determine what portion of the probability distribution Jies under these points. With a standard deviation of 16 million, the value of 43 million woujd be: (43-45)/16 or -0.125 standard deviations from the mean 45. and the vajue 16 of 39 million would be: (39-45y16 or -0.375 standard deviations from the mean. By referring 16 to the distribution tables, we can ascertain how much of the distribution lies under these points. The area between the mean and 39 is 0.14615; and between the mean and 43 is 0.04975. The difference of 0.096 is the value ofthe distribution which lies between 39 and 43.
3 .If we say that commodity returns follow a lognormal distribution, we mean that over time:
A. The natural logarithm of the price is normally distributed
B. The change in the price is normally distributed.
C. The change in the natural logarithm of the price is normally distributed over time
D. The reciprocal of the price is normally distributed
Answer: C
A random variable has a lognormal distribution if its logarithm is itself normally distributed.
4 . Astock trading at a price of 90 has a (lognormal) price volatility of 40%. The range of prices covered by a l standard deviation move up and a l standard deviation move down over one year is about:
B. 72 points
C. 62 points
D. 74 points
Answer: B
One standard deviation up and one standard deviation down would constitute a range of two standard deviations. lf the standard deviation is 40% and the mean is 90, the range would be
[90-(0.4X90)] to [90+(0.4)(90)] or 54 t0 126, a range of 72 points.
5 . The return on a portfolio is normally distributed with an expected rate of return of 10%, and a standard deviation of 20%. What is the probability that the return will be between 0% and 5%?
A. 7%
B. 9%
C. 11 %
D. 13%
Answer: B
We can compute how many standard deviations away from the mean each value would be and refer to the cumulative distribution tables to determine what portion of the probability distribution lies under these points. With a mean 10% and standard deviation of 20%, the value of 0% would be (0%-10%)/20% or -0.5 standard deviation from the mean, and the value of 5% would be
(50/o-10%y20% or -0.25 standard deviations from the mean. By referring to the distribution tables,
we can ascertain how much of the distribution lies under these points. The area between the mean and 5% is 0.0987, and 0.1915 between the mean and 0%. the difference of 0.0928(approximately g%) is the value ofthe distribution which lies between 0% and 5%.。
