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Augee · 2022年11月01日

这道题有疑问

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+P25P=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?

1 个答案
已采纳答案

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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