Margin Call Question

John has 50,000 in cash in his margin account. The broker charges 6% on borrowed funds and commision of 3% on both buy and sell trades. Initial margin reqirement = 50% and maintenance margin = 30%. He uses maximum margin to SELL SHORT XYZ stock, currently trading at $34.9. XYZ pays no divdend. If he wants to maximize his margin, what is the max # of shares he could sell short, and what is the trigger margin price. A) # of shares = 2703 margin trigger = 58.17 B) # of shares = 2703 margin trigger = 40.27 C) # of shares = 2865 margin trigger = 58.17 D) # of shares = 2865 margin trigger = 40.27 I would love the explanation for this problem. Im having problems with these calcluations b/c of SELLING SHORT and not buying long, in which the calculations seem to be str8 forward.

is it D? Trigger Price = 34.9 * 1.5/1.3 = 40.27 Margin balance = 50,000. Intial margin is 0.5. So he can trade for 50000/0.5 = 100,000. 100,000/34.9 = 2865.

the answer is B

Whats the source of question?

Stalla. i have the explanation, its just long, ill post it later

Establishing a short position means borrowing shares from the broker and selling those shares in the market. The entire proceeds from the sale remain into an account with the broker, you get nothing until the closing of the position. Additionally, you have to deposit an amount equivalent to a % of the position; in this case 50%. You have in your account $50,000, and you need to cover with this position: - 50%, the margin requirement - 3%, the commission =53% To maximize your funds, 50,000 = 53%, that means the amount that would result from the position is =50,000/0.53 = 94,339.62 This amount would cover a number of 94,339.62/34.9 = 2,703.15 shares, that is rounded 2,703 At this time, you can strike C and D as wrong answers. For the second part of the question: The margin account erodes at security price increase (for a short position). The question is, how much should the stock price increase, to erode the margin account you deposited, so that you will receive a margin call? The current price of the underlying is X (that we will determine soon). At the time the stock was shorted, you had to deposit a margin of 50% of the assets, and the proceeds from the short sale were deposited in this account, so you will actually have: (1+50%)*2703*34.9 = 141,502.05 in your margin account Daily, the account is marked to market to account for gains or loses. At all times, your margin account has to have at least 30% of the current market value of your portfolio, or you will receive a margin call. Margin = (Initial margin account– Current value of your position)/ (Current value of your position) 0.3=(141,502.05 -2703*X)/(2703*X), solve for X, X=34.9*1.5/1.3=40.269~40.27

Back to review Equity for me!!! Totally missed the commission…

Hey man. Thanks for the answer. Im still not sure I understand the very last portion: I get the 141,502 = Initial Cash + Cash from Short Sale - Commission … thats fine I also get the P(2703) in the denominator as the “MV of the Marginzed Assets” Its just the amount owed in the numerator of - 2703*X that i dont understand. I know that this 2703*X is going to be paid to the owner of the shares at close. But what about the 50% margin that had to be put up with the broker? Should this be included in the calcualtion somewhere?

To establish a short position, you borrow the shares from the broker, and sell the shares in the market. You BORROW the shares, those shares are not yours. When you close the position, you’ll have to BUY the shares from the market, and return these shares to the broker you borrowed from. When the shares are sold, the amount received is deposited in the margin account (not at your disposal). You also have to deposit the initial margin, the 50%. So actually, you’ll have 1.5 times the value of the shares in the margin account (these is where you get the (1+50%)*2703*34.9 = 141,502.05, the 50% is the margin). As time go by, the position is marked to market each day, so each day, gains or losses are posted to the margin account. For the short position, if the price of the stock goes up, the increase in price would be deducted from the margin account. When all deductions get your margin to less than the 30% (maintenance margin) of the THEN current value of the position, you will receive a call and be required to deposit an amount that would bring the margin back to the maintenance margin (not the initial margin). The 2703*X is the THEN Current value of the position, this is deducted as if you would, have to buy the shares from the market and return those shares to the broker: Margin = (Initial margin account– Current value of your position)/ (Current value of your position) Is this helpful?

50000/.53 = 94339.62 1.5/1.3*34.9 = 40.27

the weird part is that stalla has a different formula. ive never seen this Margin call/Maintenance call X Price formula anywhere?