NO.PZ2018062002000021
问题如下：
When the stock price of PZ company was $30, Tim purchased 300 shares. He bought the stocks on 50 percent margin. One month later, Tim received a dividend of $1 per share and had to pay interest on the amount borrowed at a rate of 4% per month. After received dividends, Tim sold the shares at $25 per share immediately. The commissions for both the purchase and the sale of the stocks are $5. Which of the following statements is correct?
选项：
A.The rate of return on this investment for the one-month period is -30.71%.
B.The rate of return on this investment for the one-month period is –30.85%.
C.The rate of return on this investment for the one-month period is –30.60%.
解释：
B is correct.
The total costs for the purchase is 300 × $30=$9000
Equity invested by Tim equals 0.5 × $9000=$4500
Tim borrowed amount is $9000-$4500=$4500
Interests are needed to paid by Tim at month end is $4500×0.04=$180
Dividends are received at month end is $1×300=$300
Proceeds on stock sale=$25×300=$7500
Total commissions paid by Tim is $5+$5=$10
Net gain/loss=-$9000-$180+$300+$7500-$10=$-1390
The initial investment of Tim is $4505
The rate of return on this investment for the one-month period is −$1390/$4505=-30.85%
考点：杠杆投资
T同学借钱买股票，其中50%是自有资金（bought on 50 percent margin你就把它想象成首付比例50%），而剩余的50%是从broker那里借来的，借来的资金就会产生利息费用。整个投资期是一个月，相当于投资者将在一个月后把股票卖出，一卖一买还需要支付手续费。此外，投资者在持有股票的期间还将获得红利收益，让我们计算一下这一个月投资者通过举杠杆来投资所能获得的收益率。收益率等于profit(净收益：资本利得扣减各项成本后的收益)除以初始总的投资资金。那我们就分子分母分别来计算一下。因为股票在一个月后是下跌了，所以这道题最后算得分子净收益为负相当于是净亏损。先计算分子净收益=资本利得（股价从30跌倒25，再乘股票数量300）-买卖股票的手续费-一个月借款的利息费用+股息=−1,390
其中：
自有资金出资=0.50*(300*30)=4500，借款额=0.50*（300*30）=4500
一个月的借款利息=0.04*4500=180
一个月的红利所得=300*1=300
初始投资=自有资金出资的部分+买股票的手续费=4505
因此投资收益计算可得−$1390/$4505=-30.85%
这道题的问题主要集中在分母为什么要加上commission5？
需要特别明确一下我们现在算的是投资收益率，收益率等于的是投资总的收益除以一开始的初始投入资金，我们初始投入的钱除了4500的自有资金以外，还支付了5的手续费，不交手续费就买不到股票。所以总的初始投入就要加上这5元。
这个题目不严谨吧，for both the purchase and the sale of the stocks are $5，就是总共是$5, 按照题目的解析，应改是respectively ,各自是$5.
