Rate of Return on the investment

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sukhbir_riar

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Could anyone please help me to understand the below problem
Problem
You decide to sell short 100 shares of Charlotte Horse Farms when it is selling at its high of 56. Your broker tells you that your margin requirement is 45 percent 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 requirement.
Thanks in advance
 
You are borrowing 100 shares of CHF from someone. Its value at borrowing is $5,600. You betting that it will go down at which point you can purchase the stock and “replace” the borrowed stock. So basically you sell something and get $5,600 later you buy it and return it for, in this case $4,500 and you profit $1,100 dollars.
Margin is required. So, in this case, you need to post 45% of the value of the trade so your initial investment is not $5,600, but $2,520.
From your profit you will need to subtract the total commissions and the dividend must be paid to the shareowner.
Your ending account value when you close the trade will be
2520+1100(profit)-155(purchase commission)-145(sale commission)-250=3070
I assume they want Holding Period Return
3070-2520/2520=21.8%
 
I think…
Initial Margin + Sell Commission = 100*56*.45+155
Ending Gain - Purchase Commission = 100*(56-45)-145
Dividends doesn’t go to you since it’s a short.
(Ending Gain+Initial Margin)/(Initial Margin+Sell Commission) - 1 = 29.9%
 
cfagoal2 Wrote:
——————————————————-
> I think…
>
> Initial Margin + Sell Commission = 100*56*.45+155
> Ending Gain - Purchase Commission =
> 100*(56-45)-145
> Dividends doesn’t go to you since it’s a short.
> (Ending Gain+Initial Margin)/(Initial Margin+Sell
> Commission) - 1 = 29.9%
True dividends don’t go to you, but you have to pay them to the owner of the stock. The stock price should fall by an amount about equal to the dividend anyway so it is almost an “artificial” short gain. In real life the dividend is taken out of the shorter’s cash holdings and paid to the owner of the stock which would ultimately reduce the gain
 
You don’t pay dividends, the company does. In real life the dividend is taken out because it is actually transferred over to you for a net of 0. In your calculation you are just subtracting out the the dividend payment even when it was never added in the first place.
 
devildog is right in the treatment of dividends for short sales.
excerpt from http://www.sec.gov/answers/shortsale.htm
Short Sales
A short sale is generally the sale of a stock you do not own. Investors who sell short believe the price of the stock will fall. If the price drops, you can buy the stock at the lower price and make a profit. If the price of the stock rises and you buy it back later at the higher price, you will incur a loss.
When you sell short, your brokerage firm loans you the stock. The stock you borrow comes from either the firm’s own inventory, the margin account of another of the firm’s clients, or another brokerage firm. As with buying stock on margin, you are subject to the margin rules. Other fees and charges may apply. If the stock you borrow pays a dividend, you must pay the dividend to the person or firm making the loan.
 
cfagoal2 Wrote:
——————————————————-
> You don’t pay dividends, the company does. In real
> life the dividend is taken out because it is
> actually transferred over to you for a net of 0.
> In your calculation you are just subtracting out
> the the dividend payment even when it was never
> added in the first place.
I know the COMPANY pays dividends, but they don’t pay them to you as the borrower of the stock because you borrowed it to sell, when they should be going to the owner. When a company pays dividends and you shorted the stock you need to pay that amount to the person you borrowed the stock from because they would have received it if you had not borrowed it.
I add it in because when a dividend is paid the stock price will move lower to reflect that dividend paid out. So, in effect, part of the move from 56-45 is reflected by the dividend which you did not keep.
Dividend declared $250
You then pay that $250
Now the price reflects the dividend and moves to 53.50
giving you a $250 gain.
You don’t get the 250 from the company because you sold the stock planning to buy it back later. The only reason you have to pay it is because the owner should have received that stock. Therefore the 250 needs to be subtracted from the 1100 total gain.
That is why I subtracted the dividend from the total gain. I wish I wasn’t at work because I would check the text and see if I am right or not LOL
 
thanks for replying….
But as we had borrowed the money from the broker ($3080), dont we need to pay him back, as well as the HPR should be based on the beginning value of investment
Should it not be:
Beginning value of investment = 100*56*.45+155
= 2675
Ending value of investment = 4500
So why the solution is not:
=2675 - (4500-3080) - 145 - 250 / 2675
Hope you understand my query ….
 
Looks like the problem is in ending investment.
Returns = Profit / Investment
Profit from shares = (56-45)*100 = $1100
Dividends and commission paid reduce your profit. i.e. $1100 - $500 - $145 = $455
Therefore, returns = 455/2675 = 17%
Correct me if I’m wrong.
 
Revenant:
1100(profit)-155(purchase commission)-145(sale commission)-250(dividend)=550
Why did you subtract 500?
And I believe the starting investments should be 2520 as I outline below.
Suk
I calculated the initial investment as your required margin deposit; 5600*.45=2520
You are adding the commissions to your total investment. The easier way is to subtract all your transaction costs from any gain/loss on the trade.
In the second part, you are confusing borrowing money from the broker with borrowing shares. You borrowed 100 shares at a value of 56/sh. Remember that this is a short sale so the borrowed shares are immediately sold. You don’t owe him 5600 you owe him 100 sh. If the price goes up dramatically and you have to replace the shares at a higher price which equates to a loss for you. If the shares drop, as in this case, you profit $100 for each dollar of share value lost. (In this case $11/ share drop from 56-45 times 100 Sh) Now you purchase 100 shares at 45/sh to close your position return the shares to the broker and pocket the difference between what you sold them for at (56) and what you were able to buy them back at (45).
Now for the gain
Forget the 5600, 4500, and everything else. Your gain is based on how much cash you invested to start. You are using leverage by selling 100 sh at 56 while only putting down 2520
So your initial investment, in cash, is 2520 add the 1100 (profit you made on the trade)
Your final cash balance was 3620 (Subtract transaction costs and dividends paid)-155 to purchase-145 to sell -250 dividend owed=3070 ending balance
OR
1100(profit)-155(purchase commission)-145(sale commission)-250(dividend)=550+2520(beginning value)=3070(ending value)
HPY=End value-initial value/initial value
=3070-2520/2520
=550/2520=0.218
21.8%
 
@ devildog
My mistake, should be $250 instead of $500 for the dividend.
The situation whether to include transaction cost/commission in the initial investment is up to individual. It make sense to include in the initial investment if we are doing Time Weighted Returns (which we really should, instead of using the biased Money Weighted aka IRR).
I have not come across any question that includes the commission, so I do not know the textbook style with regards to the way its being used. Please enlighten me.
@ sukhbir_riar
Is there a solution for this?
 
I say don’t complicate it. They didn’t ask for TW return. There is a formula and I will look it up later. I think it is EV-IV-Dividends-transaction costs
 
Now the things are pretty much clear…
Please find the solution below (CFAI textbook - practice prblme reading 52)
Profit on a short sale = Begin. value - Ending value - Dividends - Trans. cost - Interest
Beginning value of investment = 56 * 100 shares = $5600
Your investmet = Margin requirement + Commissions
= (.45 * $5600) + $155
= $2675
Ending value of investment = $45 * 100 = $4500
Dividends = $2.50 * 100 = $250
Transaction cost = $155 + $145 = $300
Therefore
Profit = 5600 - 4500 - 250 - 300
= 550
The rate of return on your investment of $2675 is
$550/2675 = 20.56%
 
OK so I was right to subtract it at the end and Ren was right to add it at the beginning. Maybe they will let us combine to pass this thing
 
sukhbir_riar Wrote:
——————————————————-
> Now the things are pretty much clear…
>
> Please find the solution below (CFAI textbook -
> practice prblme reading 52)
>
> Profit on a short sale = Begin. value - Ending
> value - Dividends - Trans. cost - Interest
>
> Beginning value of investment = 56 * 100 shares =
> $5600
>
> Your investmet = Margin requirement + Commissions
> = (.45 * $5600) + $155
> = $2675
>
> Ending value of investment = $45 * 100 = $4500
>
> Dividends = $2.50 * 100 = $250
>
> Transaction cost = $155 + $145 = $300
>
> Therefore
> Profit = 5600 - 4500 - 250 - 300
> = 550
>
> The rate of return on your investment of $2675 is
>
> $550/2675 = 20.56%
If this calculation method is correct, then wasn’t it in conflict with the December 2009 Exam Errata found from cfa website (http://www.cfainstitute.org/cfaprog/resources/cfa_program_errata.html) - page 3, for the example on pg 28 cfal1 textbook?
anyone?
 
Come on guys,
Shall the commission/transaction costs charged both on purchese and sale be deducted from the profit in the numerator? From the discussion above, seems like it has to be deducted as both are outflows…??
 
the commission for purchase and sale should both be deducted in the numerator but in the denominator/initial investment only the purchase(or initial) commission. I think sukhbir_riar has the correct answer.
 
They double counted the commission in the answers to the problems at the end of the chapter (of CFA text).
I’m with desmond~ they corrected themselves in the errata for the example problem in the book.
Unfortunately, they did not include a correction for the practice problem solution in the latest errata.
What makes it all the more confusing is that schweser’s interpretation of equity margin does not seem consistent [at all] with the CFAI text’s interpretation of investor’s equity.
 
I’m with Desmond too.
Initial investment = Margin Put in + Purchase Commission
Profit = (Difference between stock price X No. of Shares) - Dividends (If any) - Sell Commission
Doesn’t make sense to include purchase commission in denominator again.
 
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