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PRMIA 8007 Exam Syllabus Topics:

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

1. What can be said about observations of random variables that are i.i.d. a normally distributed?

A) The estimated mean divided by the estimated standard deviation has a t-distribution
B) The estimated mean divided by the estimated variance has a t-distribution
C) The estimated mean divided by the estimated variance has a Chi2-distribution
D) The estimated mean divided by the estimated standard deviation has a Chi2-distribution

2. An underlying asset price is at 100, its annual volatility is 25% and the risk free interest rate is 5%. A European call option has a strike of 85 and a maturity of 40 days. Its Black-Scholes price is 15.52. The options sensitivities are: delta = 0.98; gamma = 0.006 and vega = 1.55. What is the delta-gamma-vega approximation to the new option price when the underlying asset price changes to 105 and the volatility changes to 28%?

A) 19.23
B) 17.33
C) 20.54
D) 18.75

3. The first derivative of a function f(x) is zero at some point, the second derivative is also zero at this point. This means that:

A) f has necessarily a minimum at this point
B) f has necessarily a maximum at this point
C) f has necessarily neither a minimum nor a maximum at this point
D) f might have either a minimum or a maximum or neither of them at this point

4. Consider the linear regression model for the returns of stock A and the returns of stock B. Stock A is 50% more volatile than stock B. Which of the following statements is TRUE?

A) The stocks must be positively correlated ( )
B) Beta must be positive ( )
C) Alpha must be positive ( )
D) Beta must be greater in absolute value than the correlation of the stocks ( )

5. A linear regression gives the following output:
Figures in square brackets are estimated standard errors of the coefficient estimates.
What is the value of the test statistic for the hypothesis that the coefficient of is less than 1?

A) 1.92
B) 0.32
C) 0.96
D) 0.64

Solutions: