Final answer:
Amber needs $34,682.16 in cash to open a short position on 244 shares of the 3x Leveraged ETF on Gold (UGLD) by applying the initial margin requirement of 69% to the total value of the shares.
Step-by-step explanation:
The student's question concerns the calculation of the initial cash required to open a short position on an exchanged-traded fund (ETF) with leverage. Since the price of one share of the 3x Leveraged ETF on Gold (UGLD) is $206 and Amber wants to short 244 shares, she will have to come up with the initial margin to open the position. The initial margin requirement is 69%.
To calculate the amount of cash Amber needs, we multiply the total value of the shares she wants to short by the initial margin percentage:
Total value of shares = Price per share × Number of shares
Total value = $206 × 244 shares = $50,264.
Initial margin required = Initial margin percentage × Total value
Initial margin required = 0.69 × $50,264 = $34,682.16.
Therefore, Amber needs to have $34,682.16 in cash to open the short position on the 3x Leveraged ETF on Gold.