PRMIA PRM Certification - Exam II: Mathematical Foundations of Risk Measurement - 8002 Exam Practice Test

I have a portfolio of two stocks. The weights are equal. The one volatility is 30% while the other is 40%. The minimum and maximum possible values of the volatility of my portfolio are:

You invest $100 000 for 3 years at a continuously compounded rate of 3%. At the end of 3 years, you redeem the investment. Taxes of 22% are applied at the time of redemption. What is your approximate after-tax profit from the investment, rounded to $10?

What is the probability of tossing a coin and getting exactly 2 heads out of 5 throws?

The correlation between two asset returns is 0.5. What is the largest eigenvalue of their correlation matrix?

Let N(.) denote the cumulative distribution function and suppose that X and Y are standard normally distributed and uncorrelated. Using the fact that N(1.96)=0.975, the probability that X
0 and Y 1.96 is approximately

Which of the following is not a direct cause of autocorrelation or heteroskedasticity in the residuals of a regression model?

On average, one trade fails every 10 days. What is the probability that no trade will fail tomorrow?

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%?

If a random variable X has a normal distribution with mean zero and variance 4, approximately what proportion of realizations of X should lie between -4 and +4?