ECON 1095 - Quantitative Method In Finance - Economics Assignment Help

Assignment Task:

Task:

QUESTION 1

Calculate the average continuous monthly returns for the following dividend adjusted share price and market index.

Date Share Price (Ri) Market Index (Rm)
August-20 $2.75 1,285.00
September-20 $2.90 1,290.00
October-20 $2.95 1,340.00
November-20 $3.25 1,360.00
(a) Has this share under or over performed relative to the market?
(b) Suppose the share’s beta is 1.5 (? = 1.5) and the annual risk-free rate is 0.03. If you accept that past performance gives you the best guide to future returns, would you invest in this share? Briefly explain your decision.

QUESTION 2
Find the derivative of y with respect to x for these functions:
(a) x y x x e 3 )2ln(30 32 −= − +
(b)(1 2 ))2.5(3 x xx xy−−+=
(c)1)3+1)(22(4 +−y = x x
(d) 37.5(50 10)−y = x +
(e) Find the indefinite integral of the following function

6f(x) = 2x + 7x

(f) For the equation y = 2 - 2x - 2x2 + 3x3
i) Find the equation for the linear approximation when x = 2.
ii) Find the equation for the quadratic approximation, also when x = 2.

QUESTION 3
Using the following function: z = 20 + 100x - 3x2- 2y2 + x.y

Find the value(s) of x and y that maximise z, making sure that you check if your solution is a point of inflection or a saddle point.

(5 marks)

QUESTION 4
(a) A pension fund must pay $1,000 at the end of each of the next five years. Find the Present Value and Duration for this set of payments when the interest rate used to find the discounted value is 0.05 or 5 %.
(b) Suppose the pension fund invests in a portfolio of two- and five-year zero-coupon bondsand needs to satisfy the conditions to immunize its bond portfolio. It uses this portfolio to make these five payments of $1,000. Find the proportion of the fund allocated to two-year bonds.

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