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为了求职冲呀 · 2019年11月15日

问一道题: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%

在Tim‘s initial investment是4505,是因为需要加上五元钱的手续费,但是五元钱的手续费不是在倒数第三部算net gain的时候减去了吗?


老师这道题目题库里类似的一道题目:

Daisy shorts 1800 shares of KIY company's stock on a 30% initial margin and the broker's lending rate is 2.5%. The current price is $65 per share. The broker charges a commission of $0.02 per share on sales but purchases for free. KIY stock pays an annual dividend of $1 per share. One year later, Daisy buys the 1800 shares at a price of $58 per share and close the position. calculating the rate of return.


答案:1800x65=11700. 11700x0.3=35100. lending interest:2047.5,dividend:1800,commission:36.

return on investment: 1800x65 - 1800x58-2047.5 -1800=8716.5

Yield: 8716.5/(35100+36)=24.81%


想麻烦老师解释一下为什么Daisy题库里面这道题和本题的Net gain有什么不同的地方?为什么本题的最后Net gain 有加又有减,但是Daisy题的哪一步就是只有减,最后的commission36和35100加在一起?辛苦老师啦

1 个答案

maggie_品职助教 · 2019年11月15日

当然不同了,一个是卖空股票一个是买股票,获得的收益和需要支付的成本是不一样的,请不要靠背答案来解题。

1、本题是借钱买股票,日后再卖出。那么收益等于买卖股票获得的价差收益(先买入说明现金流出所以是-9000,之后再卖出所以是现金流入7500)加上持有股票期间的股利,但是需要减掉借钱产生的利息以及手续费。

2、DAISY那道题是举杠杆卖空,你不仅要借钱还要借股票,你借来股票就卖掉了,等日后下跌再买回来。如果你卖股票qi期间发了红利你要支付给你借股票的一方。因此收益等于买卖股票的价差(先卖出说明现金流入所以是1800*65,之后再买入所以是现金流出-1800*58)-36手续费-1800股利-2047.5利息。

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NO.PZ2018062002000021问题如下When the stopriof PZ company w$30, Tim purchase300 shares. He bought the stocks on 50 percent margin. One month later, Tim receivea vinof $1 per share anhto pinterest on the amount borrowea rate of 4% per month. After receivevin, Tim solthe shares $25 per share immeately. The commissions for both the purchase anthe sale of the stocks are $5. Whiof the following statements is correct?A.The rate of return on this investment for the one-month periois -30.71%.B.The rate of return on this investment for the one-month periois –30.85%.C.The rate of return on this investment for the one-month periois –30.60%. B is correct.The totcosts for the purchase is 300 × $30=$9000Equity investeTim equals 0.5 × $9000=$4500Tim borroweamount is $9000-$4500=$4500Interests are neeto paiTim month enis $4500×0.04=$180vin are receivemonth enis $1×300=$300Procee on stosale=$25×300=$7500Totcommissions paiTim is $5+$5=$10Net gain/loss=-$9000-$180+$300+$7500-$10=$-1390The initiinvestment of Tim is $4505The rate of return on this investment for the one-month periois −$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。 为什么最终不是-1385/4505. 初始增加5,末尾为什么是减少10不是减少5呢

2024-01-08 17:06 1 · 回答

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2023-09-09 16:01 2 · 回答

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2023-03-03 01:52 1 · 回答

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2023-02-08 22:23 2 · 回答

NO.PZ2018062002000021 初始投资Tim确实花了9000呀?这个地方没太搞懂,希望老师解答一下

2021-09-07 11:31 2 · 回答