NO.PZ2015122802000023
问题如下：
The current price of a stock is $25 per share. You have $10,000 to invest. You borrow an additional $10,000 from your broker and invest $20,000 in the stock. If the maintenance margin is 30 percent, at what price will a margin call first occur?
选项：
A.
$9.62.
B.
$17.86.
C.
$19.71.
解释：
B is correct.
A margin call will first occur at a price of $17.86. Because you have contributed half and borrowed the remaining half, your initial equity is 50 percent of the initial stock price, or $12.50 = 0.50 × $25. If P is the subsequent price, your equity would change by an amount equal to the change in price. So, your equity at price P would be 12.50 + (P – 25). A margin call will occur when the percentage margin drops to 30 percent. So, the price at which a margin call will occur is the solution to the following equation.
The solution is P = $17.86.
考点：Leveraged Position
这道题目，解题方法有两种：
方法一：期初股价25元，我们借钱买股票，所以自有资金是12.5，自有资金占股价比例12.5/25=50%。当股价从25元跌到P,那么自有资金就跟着减少，当自有资金比例减少到30%时：[12.5-（25-P）]/P=30%,低于这个P我们就要接到电话了。计算得到P=17.86
方法二：直接根据公式，PL=P0*（1-IM）/(1-MM)=25*(1-50%)/(1-30%)=17.86
分母没有争议，就是现在股价。 分子的话，之前一直没想通的一点是，既然自有资金和借的钱都投进去了，干嘛只减自有资金。 其实你借的钱赚了亏了都不变，你还是要还1w。变得只有你自有资金一万。 所以自有资金比例，即分子就是：初始自有资金 - 亏损的钱（也就是股价下跌）。所以分子就是12.5-（25-现在股价）。 我觉得我悟了。
