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Biubiubird · 2024年05月11日

老师可否给一个不剔除股票数量的计算过程？

  1. CFA I
  2. Equity

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.

Equity/SharePrice/Share=12.50+P−25P=30%\frac{Equity/Share}{Price/Share}=\frac{12.50+P-25}P=30\%

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

我自己想不出来，怎么算都有问题

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1 个答案

王园圆_品职助教 · 2024年05月11日

同学你好，可是margin call price的这个公式自己就没有带上股票数量啊？

本题你直接套公式就可以计算了（也就是解析的第二种方法），请看以下讲义截图

本题在这里给的“You have $10,000 to invest. You borrow an additional $10,000 from your broker and invest $20,000 in the stock”这些信息只是为了给考生信息计算期初的保证金比例，也就是IM = 自有资金/总投资比例 = 1000/2000 = 50%

然后这里只需要把P0（25）和MM（30%）带入公式就可以得到答案了哦


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