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PRMIA Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition Sample Questions:

1. Your stockbroker randomly recommends stocks to his clients from a tip sheet he is given each day. Today, his tip sheet has 3 common stocks and 5 preferred stocks from Asian companies and 3 common stocks and 5 preferred stocks from European companies. What is the probability that he will recommend a common stock AND/OR a European stock to you when you call and ask for one stock to buy today?

A) 9/16
B) 7/8
C) None of these
D) 11/16

2. You work for a brokerage firm that charges its client x per share. The volume of trade of a client of type A depends on the per share commission in the following manner. If the commission is x, the client of type A will trade e-ax shares on average each week. What is the optimal commission x that maximizes the income from client A, noting that a is greater than zero?

A) a2
B) 1
C) 42
D) a

3. Which of the following is consistent with the definition of a Type I error?

A) The probability of a Type I error is 100% minus the significance level
B) A Type I error would have occurred if the performance of a stock was positively correlated with the performance of a hedge fund, but in a linear regression, the hypothesis of positive correlation was rejected
C) A Type I occurs whenever data series are serially correlated
D) A Type I error would have occurred if the performance of a stock was positively correlated with the performance of a hedge fund, but in a linear regression, the hypothesis of no correlation was rejected

4. Which of the following can induce a 'multicollinearity' problem in a regression model?

A) The omission of a relevant explanatory variable
B) A high positive correlation between the dependent variable and one of the explanatory variables
C) A high positive correlation between two explanatory variables
D) A large negative correlation between the dependent variable and one of the explanatory variables

5. Maximum likelihood estimation is a method for:

A) Solving a portfolio optimization problem
B) Finding parameter estimates of a given density function
C) Estimating the implied volatility of a simple European option
D) Estimating the solution of a partial differential equation

Solutions: