Online Access Free 8002 Exam Questions

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.None of the above
• D.x = 5, y = 0

You intend to invest $100 000 for five years. Four different interest payment options are available. Choose the interest option that yields the highest return over the five year period.

• A.an annually compounded rate of 4.15%
• B.a lump-sum payment of $22 500 on maturity (in five years)
• C.a continuously-compounded rate of 4%
• D.a quarterly-compounded rate of 4.1%

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

• A.4%
• B.20%
• C.14.4%
• D.24%

Which of the following is not a sequence?

• A., , , , , , ...
• B., , , , ...
• C.30
• D., , , ... , , ...

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

• A.0.49%
• B.0.488%
• C.0.25%
• D.0.495%