Question

A portfolio has a value P(E, S), so that the value P is a function of E, the price of a Euro in Canadian dollars, and S, the level of the TSX stock index. Presently the portfolio is worth $207,000, while a Euro is $1.50 Canadian, and the index is S = 18,000. If the partial derivatives of P have values ∂P ∂E = 80,000, and ∂P ∂S = −20, what approximately will the portfolio value be if the price of a Euro goes down by 0.07 and the stock index goes down by 629?

Answer 1

The new value of the portfolio would be $207,000 - $18,180 = $188,820

Explanation:

Using the first-order partial derivatives, we can calculate the approximate change in the portfolio value due to changes in E and S using the formula:

ΔP ≈ ∂P/∂E * ΔE + ∂P/∂S * ΔS

where ΔE is the change in the price of a Euro and ΔS is the change in the TSX stock index.

Given that ∂P/∂E = 80,000 and ∂P/∂S = -20, and the changes ΔE = -0.07 and ΔS = -629, we can plug in the values and get:

ΔP ≈ 80,000 * (-0.07) + (-20) * (-629)

≈ -5,600 - 12,580

≈ -18,180

Therefore, the portfolio value is expected to decrease by approximately $18,180 if the price of a Euro goes down by $0.07 and the TSX stock index goes down by 629 points. The new value of the portfolio would be $207,000 - $18,180 = $188,820.