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Complications of the mixed processes of short sale, aggregate short sale and buying on Margin

See the attached file.

In order to understand clearly the complications of the mixed processes of Short Sale, Aggregate Short Sale and Buying on Margin and the Aggregate of both Short Sale and Buying on Margin I need an elaborate solution to the questions in the two problems as per attached file showing the formulas, writing the formula manually in front of each showing the steps of calculations in order to know and understand clearly the components of the formulas relating to each question so that the solution gives me an elaborate understanding of the concepts of this hybrid stock trading concepts..

Short sale
PROBLEM (1)
First:

Assume that the investor give an order to his broker to sell (short sale) 300 shares from stock (A) which has a price $ 100 per share

1) Prepare a balance sheet for this investor if the initial margin is 60%.
2) Assume that the price of stock (A) declined to $ 60 per share, prepare a balance sheet for this investor.
3) If the Market Price increased to $130 per share, show the investor Balance Sheet and what is the type of his account considering the following cases?

SEE ATTACHED

Do you think that the investor will receive a margin call if the maintenance margin is 30%? Prepare a balance sheet for this investor.

4) How far can the price increase before the investor receives a margin call?
5) Calculate the rate of return if the stock price increased to $120 and the

Aggregate Short Sale:

Assume that the investor gave an order to his broker to sell (short sale) 100 shares from stock (A) that has a price $ 150 per share and another order to sell (short sale) 250 shares from stock (B) with the market price $ 50 per share.

1) Prepare a balance sheet for this investor if the initial margin is 60%.
2) Assume that the price of stock (A) goes up to be $170 per share, and the price of stock (B) increase also to be $60, what is the position of this investor if the maintenance margin is 30%?

Buying on margin and Short Sale:

Assume that another investor asked his broker to sell (short sale) 500 shares from stock (A) that has a price of $ 300 per share and another order to buy on margin 400 shares from stock (B) with the market price of $ 250 per share.

1) Prepare a balance sheet for this investor if the initial margin is 60%.
2) Assume that the price of stock (A) declined to $ 250, and the price of stock (B) increased to $270, do you think that the investor will receive a margin call if the maintenance marging is 30%?

Short sale
PROBLEM (2)
First:

Assume that the investor give an order to his broker to sell (short sale) 500 shares from stock (A) which has a price $ 80 per share
1) Prepare a balance sheet for this investor if the initial margin is 60%.
2) Assume that the price of stock (A) declined to $ 50 per share; prepare a balance sheet for this investor.
3) If the Market Price increased to $110 per share show the investor Balance Sheet and what is the type of his account considering the following cases?

SEE ATTACHED

Do you think that the investor will receive a margin call if the maintenance margin is 30%? Prepare a balance sheet for this investor.
4) How far can the price increase before the investor receives a margin call?
5) Calculate the rate of return if the stock price increased to $90 and the interest

Aggregate Short Sale:

Assume that the investor gave an order to his broker to sell (short sale) 400 shares from stock (A) that has a price $ 150 per share and another order to sell (short sale) 500 shares from stock (B) with the market price $ 70.
1) Prepare a balance sheet for this investor if the initial margin is 60%.
2) Assume that the price of stock (A) goes up to be $170 per share, and the price of stock (B) declined to be $40, what is the position of this investor if the maintenance margin is 30%?

Buying on margin and Short Sale:

Assume that another investor asked his broker to sell (short sale) 300 shares from stock (A) that has a price of $ 120 per share and another order to buy on margin 600 shares from stock (B) with the market price of $ 350 per share.
1) Prepare a balance sheet for this investor if the initial margin is 60%.
Assume that the price of stock (A) goes up to $ 150 and the price of stock (B) also increased to $370, do you think.

Attachments

Solution Preview

Answer:
Given that,
Number of shares short sale=100
Stock price=$100 per share
We have,
Initial margin=60%
Value of stock borrowed=100*$100-$10,000
Initial Margin=$10,000*60%=$6,000

Assets Liabilities and Equity
Sale Proceeds $10,000 Short Position $10,000
Initial Margin Deposit $6,000 Account Equity $6,000
Total $16,000 Total $16,000

Price of stock declined to $60 per share:
Investor is ahead by an amount= ($100-$60)*100=$4,000
Hence,
Assets Liabilities and Equity
Sale Proceeds $10,000 Short Position $6,000
Initial Margin Deposit $6,000 Account Equity $10,000
Total $16,000 Total $16,000

New Margin=$10,000/$6,000=166.67%
Price of stock increased to $130:
Investor is behind by an amount= ($130-$100)*100=$3,000
Hence,
Assets Liabilities and Equity
Sale Proceeds $10,000 Short Position $13,000
Initial Margin Deposit $6,000 Account Equity $3,000
Total $16,000 Total $16,000
New Margin=$3,000/$13,000=23.08%

If maintenance Margin=30% then yes the investor would receive a margin call.

To receive a margin call the share price has to increase at a level the margin of the investor reaches the maintenance margin of 30%
(100*P-$100*(1-60%)*100)/(100*P)=30%
Or,
100P-30P=$4,000
Or,
P=$4,000/70=$57.14
We have,

Rate of return=(($120-$100)*100+$4*100-$1*100-$2*100)/$16,000=13.125%

We have,
Number of stock A shares for short sell=100 shares
Number of stock B shares for short sell=250 shares
Price of stock A=$150 per share
Price of stock B=$50 per share
Initial Margin=60%
We have,
Value of stocks borrowed=100*$150+250*$50=$27,500
Now,
Initial Margin=$27,500*60%=$16,500
Assets Liabilities and Equity
Sale Proceeds from Stock ...

Solution Summary

The complications of the mixed processes of short sales. The concepts of the hybrid stock trading concepts.

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