Margin Calls
In our previous example (Example 2.6), at what price per share would you be subject to a margin call?
To answer this one, let P * be the critical price. The short liability then is 5,000 shares at a price of P *, or 5,000 X P *. The total account value is $225,000, so the account equity is $225,000 5,000 X P *. We can summarize this information as follows:
Short position = 5,000 X P *
Account equity = $225,000 5,000 X P *
Notice that the total account value, $225,000, is the sum of your initial margin deposit plus the proceeds from the sale, and this amount does not change. Your margin is the account equity relative to the short liability:
Margin = Account equity / Value of stock
=Initial margin deposit + Short proceeds Number of shares X P * / Number of shares X P *
=$150,000+75,000 5,00 0 X P* / 5,000 X P *
To find the critical price, we will set this margin equal to the maintenance margin and solve for P *:
Maintenance margin = Initial margin deposit + Short proceeds Number of shares X P * / Number of shares X P *
Solving for P * yields:
P * = (Initial margin deposit + Short proceeds)/Number of shares
/
1 + Maintenance margin
Finally, setting the maintenance margin equal to 40 percent, we obtain this critical price, P *:
P * = $225,000/5,000 /1.40= $32.14
At any price above $32.14, your margin will be less than 40 percent, so you will be subject to a margin call. So $32.14 is the highest possible price that could be reached before you are subject to a margin call.