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懒惰的土豆 · 2024年09月25日

关于佣金

NO.PZ2023040301000027

问题如下:

You decide to sell short 100 shares of Charlotte Horse Farms when it is selling at its yearly high of 56. Your broker tells you that your margin requirement is 45% and that the commission on the purchase is $155. While you are short the stock, Charlotte pays a $2.50 per share dividend. At the end of one year, you buy 100 shares of Charlotte at 45 to close out your position and are charged a commission of $145. What is your rate of return on the investment?

选项:

A.

20.56%

B.

22.65%

C.

18.56%

解释:

Profit on a short sale = Begin value — Ending value — Dividends( Interest)— Trans. costs

ü Beginning value of investment = $56.00 x 100 =$5,600 (Sold under a short sale arrangement)

ü Ending value of investment = $45.00 x 100=$4,500

ü Transaction costs= $155 + $145 =$300.00

ü Dividends = $2.50 x 100 shares =$250.00

ü Profit= $5,600 — $4,500 — $250 — $300= $550.00

Ø Initial investment = Margin requirement + Commission = (0.45 x $5,600) + $155= $2,520 + $155= $2,675

The rate of return on your investment is 20.56%=$550.00 / $2,675

请问老师我是否可以这样理解,在之前的一道问题中我们是拥有多头头寸,因此收益率的计算思路是用期末资产减去期初投入的自有资金然后再除以自由资金,这个过程中佣金已经被分别扣减了两次,但是是分散在两次计算过程中的,实际上利润也是扣减了两次的佣金;但在这道题中我们持有的是空头头寸,就是直接计算利润去除以期初的自有资金,不用再计算期末的资产,因此体现在计算过程中就是直接一次性扣减了两次的佣金,这样理解正确吗

1 个答案

王园圆_品职助教 · 2024年09月26日

同学你好,助教好像没有看懂你的思路呢

在助教看来,卖空和多头头寸本质是一样的计算思路

都是通过Profit/(期初自有资金+期初commission)来计算收益率的

主要不同点是,1. 由于卖空是股价下跌赚钱,所以期末股价低于期初股价其实是产生profit的,所以profit中的一大部分是(期初股价-期末股价)*总股数

2. 一个投资者卖空股票,那其实股票是属于lender的(也就是lender才享有股票的分红收益权),所以如果卖空期间股票有分红,而股票此时由于已经被投资者卖空(也就不在投资者手中,而在市场上别的买入该股票的投资者手里了),所以卖空的投资者拿不到分红但是又必须把分红支付给股票真正的拥有者(也就是lender),那投资者就必须自己掏腰包把分行的钱给到lender了——所以股票一旦有分红,对卖空者来说就会使profit进一步下降而不是上升

3.就是和普通的多头一样的,如果有借款卖空或借款买入的行为,还需要就借款支付相应的利息

所以最后空头的利润profit = (期初股价-期末股价)*总股数 - 分红 -借款利息 -2次commission

多头的利润 profit = (期末股价-期初股价)*总股数 +分红 -借款利息-2次commission

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NO.PZ2023040301000027 问题如下 You ci to sell short 100 shares of Charlotte Horse Farms when it is selling its yearly high of 56. Your broker tells you thyour margin requirement is 45% anththe commission on the purchase is $155. While you are short the stock, Charlotte pays a $2.50 per share vin the enof one year, you buy 100 shares of Charlotte 45 to close out your position anare chargea commission of $145. Whis your rate of return on the investment? 20.56% B.22.65% C.18.56% Profit on a short sale = Begin value — Enng value — vin( Interest)— Trans. costsü Beginning value of investment = $56.00 x 100 =$5,600 (Solunr a short sale arrangement)ü Enng value of investment = $45.00 x 100=$4,500ü Transaction costs= $155 + $145 =$300.00ü vin = $2.50 x 100 shares =$250.00ü Profit= $5,600 — $4,500 — $250 — $300= $550.00Ø Initiinvestment = Margin requirement + Commission = (0.45 x $5,600) + $155= $2,520 + $155= $2,675The rate of return on your investment is 20.56%=$550.00 / $2,675 如题

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