Question

After inheriting $50,000 you open up two separate brokerage accounts and divide your

inheritance equally in both accounts ($25,000 in each). You use only these funds to

trade in two stocks for two months at the end of which you clear both your positions and

evaluate your performance. Assume the following:

- You pay $50 per transaction (use only your inheritance as source of funds)

- Call money rate is 3.5% (APR compounded daily – 365 days a year)

- Initial margin is 50% and maintenance margin is 30%. The maximum amount in

‘borrowed’ funds is based on the number of ‘whole’ shares.

- Only your equity funds in the short arrangement earn interest.

- Treat each account separately for purposes of this assignment.

On 7/1 you did the following:

1. Buy stock SOFT for $40 (account 1) and short stock XESLA for $250 (account 2)

using initial margin is 50% in each of the two accounts. Provide the following

information (it is advisable to answer 1 and 2 one account at a time):

a. For each account, describe the price change (increase or decrease) that would

be desirable.

b. Number of shares bought/sold of each stock.

c. Amount of money borrowed for the margin trade in each account.

d. The price will you receive a margin call for each account.

2. Suppose you close out of each position at the end of the two months at the following

prices:

a. Suppose SOFT price has increased to $50.

b. Suppose SOFT price has decreased to $30.

c. Suppose XESLA price has increased to $275.

d. Suppose XESLA price has decreased to $225.

For each ending price, evaluate your performance by computing the following:

• The holding period return of each account2

• The annualized holding period return of each account.

3. Assume that you did not pay brokerage fees what would be the difference in

performance in each account in #2 above?

4. Compute the holding period return of the combined accounts (portfolio) when the

prices of the stocks increase (ignore # 3 above).

Answer 1

1.

a.

for each account stock total value decrease up to maintenance margin in both account and total value must increase up to two moths call money rate = 0.035* 2/12 = 0.00583 in account 2 only because of shot position have

b.

Total fund available under margin account 1 = $25000/initial margin = $25000/0.5 =$50000

  account 2 = $25000/initial margin = $25000/0.5 =$50000

no of stock bought in account 1 = fund / stock price = $50000/ $40 = 1250 soft stock bought in account 1

no of stock sold in account 2 = fund / stock price= $50000/ $250 =200 stock of XELSA sold in account 2

C.

amount of money borrowed = total fund under margin - available cash fund

Account 1 = $50000-$25000 = $25000

Account 2 = $50000-$25000 = $25000

D.

Account 1

lets assume price of stock SOFT at which margin call receive = PS

maintenance margin =[ (No of stock * PS) -  amount broker owe ] / (No of stock * PS)

0.3 = [ (1250*PS) - $25000] / 1250*PS

1250*0.3*PS = 1250*PS - $25000

$25000 = 1250 PS -  375 PS

PS = $25000 / 875

PS = $28.75

where broker owe = total value - initial margin = $50000 - $25000 = $25000

for long position in account 1 margin call receive at SOFT stock price $28.75

account 2

here we have short position

lets assume price of stock XELSA  at which margin call receive = PS

maintenance margin ={[ (No of stock * current price) + initial margin ] - (No of stock * PS) } / (No of stock * PS)

0.3 = {[( 200*$250) + $25000] - 200* PS} / 200*PS

0.3 = ($75000 - 200 PS) / 200PS

60 PS + 200 PS = $ 75000

PS = $75000/260

PS = $ 288.46

for short position in account 2 margin call receive at XELSA stock price $288.46