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Augee · 2022年11月01日

这道题有疑问

  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

老师这道题初始保证金是50%，即自有资金10000元为保证金；题目中降到30%时即到维持保证金，即自有金额降到6000元，那么自有资金减少了4000元时候，需要受到margincall。那为什么思路不能是4000除以（20000/25）=5元时，即每股亏损5块钱时受到margin call这个思路来算呢？

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王园圆_品职助教 · 2022年11月01日

嗨，爱思考的PZer你好：


同学你好，如果按照你的思路，那股票亏损5元时，股价是20元/股。

此时实际的自有资金=6000，而整个持仓资产价值 = 20*（20000/25) = 16000

maintenance margin = 6000/16000 = 37.5%而不是30%，所以你的方法下计算的5元亏损金额是不对的

原理上，由于股票出现亏损的时候，不仅分子（自有资金）会下降，其实分母（整个持仓资产）也会下降。而你的方法用的分母其实是原来的股票初始价值*初始股份数（即初始持仓资产价值），所以计算出来的maintenance margin price就会偏高

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