8007 Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition Question and Answers

You want to test the hypothesis that a population parameter β of a regression model is zero. Your alternative hypothesis is that β≠0. Denote by SD(β) the estimated standard deviation of β, and by MEAN(β) the estimated mean of β. Which test statistic is appropriate, and what is its distribution?

For a quadratic equation, which of the following is FALSE?

What is the maximum value for f(x)= 8-(x+3)(x-3)?

A 95% confidence interval for a parameter estimate can be interpreted as follows:

I have a portfolio of two stocks. The weights are 60% and 40% respectively, the volatilities are both 20%, while the correlation of returns is 100%. The volatility of my portfolio is

For each of the following functions, indicate whether its graph is concave or convex:

Y = 7x2 + 3x + 9

Y = 6 ln(3x)

Y = exp(-4x)

Which of the following statements is true for symmetric positive definite matrices?

A biased coin has a probability of getting heads equal to 0.3. If the coin is tossed 4 times, what is the probability of getting heads at least two times?

Which of the following can be used to evaluate a regression model?

(i) Magnitude of R2

(ii) Magnitude of TSS (total sum of squares)

(iii) Tests for statistical significance

(iv) Sign and magnitude of each regression parameter

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

If A and B are two events with P(A) = 1/4, P(B) = 1/3 and P(A intersection B) =1/5, what is P(Bc | Ac) i.e. the probability of the complement of B when the complement of A is given?

In a 2-step binomial tree, at each step the underlying price can move up by a factor of u = 1.1 or down by a factor of d = 1/u. The continuously compounded risk free interest rate over each time step is 1% and there are no dividends paid on the underlying. Use the Cox, Ross, Rubinstein parameterization to find the risk neutral probability and hence find the value of a European put option with strike 102, given that the underlying price is currently 100.

An indefinite integral of a polynomial function is

Bond convexity is closely related to …

A 2-year bond has a yield of 5% and an annual coupon of 5%. What is the Macaulay Duration of the bond?

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