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

1. You are to perform a simple linear regression using the dependent variable Y and the independent variable X (Y = a + bX). Suppose that cov(X,Y)=10, var(X)= 5, and that the mean of X is 1 and the mean of Y is 2. What are the values for the regression parameters a and b?

A) b=0.5, a=2.5
B) b=0.5, a=1.5
C) b=2, a=4
D) b=2, a=0

2. The natural logarithm of x is:

A) the inverse function of exp(x)
B) 46
C) log(e)
D) always greater than x, for x>0

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

4. Suppose 60% of capital is invested in asset 1, with volatility 40% and the rest is invested in asset 2, with volatility 30%. If the two asset returns have a correlation of -0.5, what is the volatility of the portfolio?

A) 36.33%
B) 36%
C) 20.78%
D) 26.33%

5. Consider an investment fund with the following annual return rates over 8 years: +6%, -6%, +12%, -12%,
+3%, -3%, +9%, -9% .
What can you say about the annual geometric and arithmetic mean returns of this investment fund?

A) The arithmetic mean return is zero and the geometric mean return is negative
B) The arithmetic mean return is negative and the geometric mean return is zero
C) None of the above
D) The arithmetic mean return is equal to the geometric mean return

Solutions: