8002 Questions and Answers

Let E(X ) = 1, E(Y ) = 3, Corr(X, Y ) = -0.2, E(X2 ) = 10 and E(Y2 ) = 13. Find the covariance between X and Y

The Newton-Raphson method

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

Identify the type and common element (that is, common ratio or common difference) of the following sequence: 6, 12, 24

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

The quarterly compounded rate of return is 6% per annum. What is the corresponding effective annual return?

What is the sum of the first 20 terms of this sequence: 3, 5, 9, 17, 33, 65,…?

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?

Variance reduction is:

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%?

The first derivative of a function f(x) is zero at some point, the second derivative is also zero at this point. This means that:

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?

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

Concerning a standard normal distribution and a Student's t distribution (with more than four degrees of freedom), which of the following is true?