[SOLVED] FBE 506 Quantitative Methods in Finance Assignment 6

FBE 506 Quantitative Methods in Finance

Assignment #6

1. The production technology of a manufacturer is estimated to be Q = 150N – .025N², where Q is output and N is labor input. The manufacturer has no constraint in hiring labor.

a.  What will be the optimum N and Q under the given assumption.

The tight job market and the skill requirement of the industry that the manufacturer is operating has limited the hiring of the labor to no more than 250.  

b.  Formulate the optimizing problem of the manufacturer under the new job market condition.

c.  Find the optimum N and Q under new condition.

d.  What does Lagrangian multiplier imply in this problem?

2. Find the critical points of Y = X³ -11X² + 14X + 80.  Test for the second-order condition to find which point is maximum, minimum, or inflection point.

3.  The variance/covariance matrix of two assets A and B are given as:

The average annual returns to two assets are A and B are .13 and .21, respectively. The return to risk-free asset is 0.03.

a. Construct the portfolio possibilities curve (efficient frontier) by assuming no short sales and by minimizing the risk of the portfolio (GMV). Graph the efficient frontier and find the risk and return of the portfolio.

b. Construct the portfolio possibilities curve assuming that short sale is allowed.

c. Graph the two curves together distinguishing them with different colors.

d. Construct a portfolio that the investor tries to minimize the risk of the portfolio subject to portfolio return of the be higher than return to risk-free asset.

e.  Graph the efficient frontier, CAL, and find the tangency point.

f. What will be the expected return to portfolio if the investor is willing to take 25% risk?