# What is a short position Margin Purchase?

For Margin purchase, there are 2 formulas: 1. Asset = Liability + Equity. 2. Maintenance Margin Call formulas 2a) Long position: P1 = P0*(1-IM)/(1-MM); 2b) Short position: P1 = P0*(1+IM)/(1+MM); where IM is initial margin and MM is maintenance margin. But somehow I couldn’t understand what is “Margin Purchase in short position”. for Long position, it is like this: Beginning, at Price P0, bought (long) N shares of stock using Initial Margin IM: A0 = L0 + E0 where A0 = P0*N, E0 = IM * A0, so the money borrowed from broker is: L0 = P0*N*(1-IM) Then price change to P1: A1 = L1 + E1 where A1 = P1*N, L1 = L0 (same money borrowed from broker), E1 = MM * P1, so, L0 = P0*N*(1-IM) = L1 = P1*N * (1-MM) hence we have: P1 = P0 * (1-IM) / (1-MM). The key concept of margin purchase in long position is, Investor has the whole asset (N shares of stock), just he borrowed some money (L0) from broker; If the stock price drops too much, then the portion of borrowed money is too big, or his own part is too small, smaller than the maintenance margin; At this time the broker will call the investor to pump in money buy more stock to balance the asset. But how is this going in short position? I just could not figure it out! Thanks in advance!

You borrow the stock from someone and sell it with the obligation to buy it back later on. Hopefully the price will fall and you can buy it back at the lower price, tyhen you give the stock back (as you borrowed it) and pay a small fee. Obviously if the price starts to rise you’ll have to buy it back at a higher price, in which case the balance in your margin account will start to drop. Does that clear it up?

so, at time 0, i borrowed 1 stock, priced \$100, sold it, gain \$100 cash; at time 1, price raised to \$260 per share, how to calculate the position to compare with the maintenance margin? shall it be \$100/\$260? if so, the formula is (Stock Price - Borrowed Money) / Stock Price, right? then, at time 0, the result is always 1, as Borrowed Money is 0, can I say that Initial Margin requirement is meaningless to short position?

I don’t tend to try and remember formulae for all of this, I would do it like this: \$100 in margin account (initial margin) If you’re maint margin worked out to \$50 Then if the price jumps up by \$55, you’ve lost \$55 You’re account now has \$45 So you receive a margin call and deposit \$55 Account balance is now \$100 Price now goes down \$20 Account balance is now \$120

I am not sure what is in the book, but you forget that you cannot borrow stock just like that. You would have to provide cash collateral which goes away (your money = initial margin + borrowed money). You sell the stock, repay the loan and the rest sits in the margin account. In reality it may work differently. But the logic is, that the one who lends you the stock wants to be protected…

Margin=Equity/Current Market value of shorted security IM=50% MM=30% 1. Suppose I wan to short sell a stock worth \$100. Before doing this I need to deposit %50 in the account to meet my Initial Margin. 2. Now price of stock goes up to \$200. My margin become (50/200)=25%. I cannot match the maintenance margin. I have to deposit cash (200*.30-50)=10 again to meet the maintenance margin of 30%. Now margin become (60/200)=30% 3. Later the stock price falls drastically to \$80. My margin now is (60/80)=75%. Now I have the freedom to bring cash out if I want or close the position by buying the stock at \$80 it giving it to the original owner with a gain of \$20. Remember, that the original owner of the stock does not know that his stock has been sold of. Also, any dividend is given during this period, the short seller must give the dividends to the original stock owner.

Thanks everyone! Let me do a short summary: 1. the mistake i made is, when investor shorts a future contract, he doesn’t get any cash, instead, he’s borrowing the contract from the broker, and short it to the market. 2. kurupt1’s post at May 29, 2009 08:46AM is correct, just the formula in CFA exam talks about margin in percentage, not in dollar per contract. 3. kh.asif’s post at May 29, 2009 10:19AM is correct on the definition: Margin=Equity/Current Market value of shorted security however, kh, u r wrong at the topping up process, pls refer to kurupt1’s post, also, when it’s below MM, investor need to top up to IM, not MM. User ur example, i guess what happened is (to make it clearer i replaced ur \$200 to \$190): a) stock goes up from \$100 to \$190, investor lost \$90 (\$190-\$100=\$90), b) so all \$50 in margin account is in, and he need to top up another \$40, (\$40=\$90-\$50), c) now Margin account has \$0, so need to top up to Initial Margin (50%) d) Current Market value of shorted security is \$190, according to Margin=Equity/Current Market value of shorted security , we have Equity = Margin * Current Market Value of Shorted security so investor need to top up 50% * \$190 = \$95 e) later price drops to \$80, then investor gains \$190-\$80=\$110, so the Margin Account has \$110 + \$95 = \$205 Please correct me if I’m wrong. thanks again!

Hmmmm, I’m convinced that you only need to bring the margin back to \$50, not \$95… Can someone clarify while I look through questions to find out the answer!

I think you are correct now take your fomula for short: P1 = P0*(1+IM)/(1+MM); example: IM = 50 % = 50 USD MM = 25 % P0 = 100 USD P1 = 100 x 1,50 / 1,25 = 120 USD, lost 20 USD -> Margin = 30 USD = 25 % of 120 USD -> margin call 30 USD

So is the initial margin on a position moving with price, rather than a fixed dollar amount?

I was fairly convinced that only in Futures we need to bring up to IM and in stocks to MM is okay.

yes, you are right, my mistake. no margin call there.