8007 Sample Questions Answers

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

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

Which statement regarding the matrix below is true?

An underlying asset price is at 100, its annual volatility is 25% and the risk free interest rate is 5%. A European put option has a strike of 105 and a maturity of 90 days. Its Black-Scholes price is 7.11. The options sensitivities are: delta = -0.59; gamma = 0.03; vega = 19.29. Find the delta-gamma approximation to the new option price when the underlying asset price changes to 105

In a multiple linear regression, the significance of R2 can be tested using which distribution?

Stress testing portfolios requires changing the asset volatilities and correlations to extreme values. Which of the following would lead to a non positive definite covariance matrix?

The natural logarithm of x is:

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

The gradient of a function f(x, y, z) = x + y2 - x y z at the point x = y = z = 1 is

An indefinite integral of a polynomial function is

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?

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

Evaluate the derivative of exp(x2 + 2x + 1) at the point x = -1

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

The determinant of a matrix X is equal 2. Which of the following statements is true?

A simple linear regression is based on 100 data points. The total sum of squares is 1.5 and the correlation between the dependent and explanatory variables is 0.5. What is the explained sum of squares?

What is the maximum value of the function F(x, y)=x2+y2 in the domain defined by inequalities x ≤ 1, y ≥ -2, y-x ≤ 3 ?

Maximum likelihood estimation is a method for:

In a portfolio there are 7 bonds: 2 AAA Corporate bonds, 2 AAA Agency bonds, 1 AA Corporate and 2 AA Agency bonds. By an unexplained characteristic the probability of any specific AAA bond outperforming the others is twice the probability of any specific AA bond outperforming the others. What is the probability that an AA bond or a Corporate bond outperforms all of the others?

You are given the following values of a quadratic function f(x): f(0)=0, f(1)=-2, f(2)=-5. On the basis of these data, the derivative f'(0) 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)

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

Variance reduction is:

Which of the following can induce a 'multicollinearity' problem in a regression model?

For the function f(x) =3x-x3 which of the following is true?

Consider two securities X and Y with the following 5 annual returns:

X: +10%, +3%, -2%, +3%, +5%

Y: +7%, -2%, +3%, -5%, +10%

In this case the sample covariance between the two time series can be calculated as:

Which of the following statements are true about Maximum Likelihood Estimation?

(i) MLE can be applied even if the error terms are not i.i.d. normal.

(ii) MLE involves integrating a likelihood function or a log-likelihood function.

(iii) MLE yields parameter estimates that are consistent.

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?

In a binomial tree lattice, at each step the underlying price can move up by a factor of u = 1.1 or down by a factor of . The continuously compounded risk free interest rate over each time step is 1% and there are no dividends paid on the underlying. The risk neutral probability for an up move is:

Let A be a square matrix and denote its determinant by x. Then the determinant of A transposed is:

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

The fundamental theorem of analysis establishes a relation between

A bond has modified duration 6 and convexity 30. Find the duration-convexity approximation to the percentage change in bond price when its yield increases by 5 basis points

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?