NO.PZ2015122802000021
问题如下：
Jason Williams purchased 500 shares of a company at $32 per share. The stock was bought on 75 percent margin. One month later, Williams had to pay interest on the amount borrowed at a rate of 2 percent per month. At that time, Williams received a dividend of $0.50 per share. Immediately after that he sold the shares at $28 per share. He paid commissions of $10 on the purchase and $10 on the sale of the stock. What was the rate of return on this investment for the one-month period?
选项：
A.−12.5 percent.
B.–15.4 percent.
C.–50.1 percent.
解释：
B is correct.
The return is –15.4 percent.
Total cost of the purchase = $16,000 = 500 × $32
Equity invested = $12,000 = 0.75 × $16,000
Amount borrowed = $4,000 = 16,000 – 12,000
Interest paid at month end = $80 = 0.02 × $4,000
Dividend received at month end = $250 = 500 × $0.50
Proceeds on stock sale = $14,000 = 500 × $28
Total commissions paid = $20 = $10 + $10
Net gain/loss = −$1,850 = −16,000 − 80 + 250 + 14,000 − 20
Initial investment including commission on purchase = $12,010
Return = −15.4% = −$1,850/$12,010
考点：杠杆投资
J同学借钱买股票，其中75%是自有资金（bought on 75 percent margin你就把它想象成首付比例75%），而剩余的25%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32跌倒28，再乘股票数量500）-买卖股票的手续费-一个月借款的利息费用+股息=−1,850
其中：
自有资金出资=0.75*(500*32)=12000，借款额=0.25*（500*32）=4000
一个月的借款利息=0.02*4000=80
一个月的红利所得=500*0.5=250
初始投资=自有资金出资的部分+买股票的手续费=12,010
因此投资收益计算可得−1,850/12,010= −15.4%
这道题的问题主要集中在分母为什么要加上commission10？
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12000的自有资金以外，还支付了10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10元。
根据课上讲的，return= profit / 初始投资 ，然后profit包含了投资收益（28-32）500，分红，两次佣金，及借款利息，然后初始投资就是自己投的75%的本金和买入佣金。那么25%*500*32的这笔借款本金不需要在计算中考虑吗？（我知道利息是在借款数额的基础上再乘的2%）
