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

1. I have $5m to invest in two stocks: 75% of my capital is invested in stock 1 which has price 100 and the rest is invested in stock 2, which has price 125. If the price of stock 1 falls to 90 and the price of stock 2 rises to 150, what is the return on my portfolio?

A) -2.50%
B) -5%
C) 5%
D) 2.50%

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

3. The Lagrangian of a constrained optimisation problem is given by L(x,y,) = 16x+8x2+4y-(4x+y-20), where is the Lagrange multiplier. What is the solution for x and y?

A) x = -1, y = 0
B) x = 0, y = 20
C) x = 5, y = 0
D) None of the above

4. When a number is written with a fraction as an exponent, such as , which of the following is the correct computation?

A) Square 75, then take the fifth root of it
B) Multiply 75 by 2.5
C) Take the square-root of 75 and raise it to the 5th power
D) Divide 75 by 2, then raise it to the 5th power

5. 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) 18.75
B) 20.54
C) 17.33
D) 19.23

Solutions: