Q. An investor opens a margin account with an initial deposit of $5,000. He then purchases 300 shares of a stock at $30 each on margin, and his account requires a maintenance margin of 30%. Ignoring commissions and interest, the price at which the investor will receive a margin call is closest to:
Sure thing,
Margin call price: S0 + [ 1 - initial margin / 1- maintenance margin)
So first thing, what is our initial margin? Well the full position is 300*30= 9000 and we put only 5000 so our initial maintenance is 5/9= .555
Then apply the formula: 30 * ( .455 / .7 ) = 19.05
Another approach doesn’t require memorizing the formula: check the middle price.
You borrowed $4,000 to purchase the stock. If the price falls to $23.08/share, then the total stock value is $6,924 (= $23.08 × 300) and the equity is $2,924 (= $6,924 − $4,000). The percent equity is 42.23% (= $2,924 ÷ $6,924). This is higher than the maintenance margin requirement, so the margin call price has to be lower than $23.08: it’s $19.05.
I tell my candidates not to memorize that formula: you don’t need it. Memorize the things you need to memorize, and work out the ones you don’t.
5000 his money, 9000 total money
his money is 0,556 of the total
0,556*30 = 16,80
16,80+(P-30)/P = 30%
P = 19,05
I believe that you meant:
[16,80 + (P − 30)] / P = 30%
Exactly, I don`t have this parenthesis on my keyboard through