FRM一级模拟题(1)

FRM一级模拟题（1）

1、The price of INDO stock on any trading day can either increase or decrease. A risk analyst estimates that there is a 20% probability that the price of INDO stock will increase on any trading day. This probability is assumed to be the same for all trading days and the price changes on any given trading day are independent of changes on other days. Based on this information, what is the expected number of days the share price will decrease in the coming five days?

A. 3

B. 5

C. 4

D. 1

2. Which one of the foll owing four statements about hypothesis testing holds true if the level of significance decreases from 5% to 1%?

A.It becomes more difficult to reject a null hypothesis when it is actually true.

B.The probability of making a type I error increases.

C.The probability of making a type II error decreases.

D.The failure to reject the null hypothesis when it is actually false decreases to 1%.

3. Assume that a rand om variable foll ows a normal distribution with a mean of 100 and a standard d eviation of

17.5. What is the probability that this rand om variable value is between 82.5 and 135?

A.68%

B.81.9%

C.82.8%

D.95%

4. In country X, the probability that a letter sent through the postal system reaches its destination is 2/3. Assume that each postal delivery is independent of every other postal delivery, and assume that if a wife receives a letter from her husband, she will certainly mail a response to her husband. Suppose a man in country X mails a letter to his wife (also in country X) through the postal system. If the man d oes not receive a response letter from his wife, what is the probability that his wife received his letter?

A.1/3

B.3/5

C.2/3

D.2/5

5. Let X and Y are two rand om variables representing the annual returns of two different portfolios. If E[X ] = 3, E[Y ] = 4, and E[XY ] = 11, then what is Cov[X, Y ]?

A.-1

B.0

C.11

D.12

6. Kelly Lewis is analyzing daily return data for a stock market ind ex. From the available data, she calculates that the average daily return is 0.0% and the standard deviation is 1.5%. Concerned that a normal distribution likely underestimates tail risk, she recalls from extreme value theory that a generalized Pareto distribution (GPD) can be used to approximate the probability that the daily return is greater than a loss level y, given the daily return is a loss. That is, if X represents the daily return, then:

Using maximum likelihood estimation with the available historical data, she finds that parameter values of? = 0.005 and? = 0.015 provid e the best fit. Given the daily return is a loss, what is the probability that the daily return exceeds –4.5% using a normal distribution and a generalized Pareto distribution?

ing a normal distribution: 99.74%; using a generalized Pareto distribution: 94.91%

ing a normal distribution: 99.87%; using a generalized Pareto distribution: 94.91%

ing a normal distribution: 99.74%; using a generalized Pareto distribution: 97.45%

ing a normal distribution: 99.87%; using a generalized Pareto distribution: 94.45%

7. Rational Investment Inc. is estimating a daily VaR for its fixed-income portfolio currently valued at $800 million. Using returns for the past 400 days (ord ered in decreasing order, from highest daily return to lowest daily return), the daily returns are the foll owing: 1.99%, 1.89%, 1.88%, 1.87%, . . . , –1.76%, –1.82%, –1.84%, –1.87%, –1.91%.

At the 99% confidence l evel, estimate the daily d ollar VaR using the historical simulation method.

A.$14.08mm

B.$14.56mm

C.$14.72mm

D.$15.04mm

8. Assume that the P/L distribution of a liquid asset is i.i.d. normally distributed. The position has a one-day VaR