Short Selling

1
Short Selling

• Objective Youre bearish on a stock --- you
  think its price will be lower in the future. You
  want to Sell high now, and in the future Buy at a
  lower price. (The opposite of buy now and sell
  later.)
• Short selling is set up to let people do this.
• How it works
• You borrow shares from another investor (i.e.,
  someone who owns the shares) through broker, and
  your broker sells them for you.
• Later you have your broker buy shares and these
  shares are used to repay the investor who lent
  you shares (i.e., your stock loan is repaid).
• If price drops, profit if price increases, loss.
• Short sellers have to reimburse the lender for
  any dividends.
• Short seller has to deposit margin / collateral.

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Short selling Problem 1

1. If the price keeps going up your losses
   areunlimited.

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Types of Orders

• Market orders
• Immediate execution of the order.
• Filled at best available price.
• Limit orders
• Only filled if marketable. i.e., if limit
  price (or better) can be achieved.
• Order may not get filled.
• To buy Buy only at that price or lower.
• To sell Sell only at that price or higher.

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Types of Orders

• Special orders
• Stop loss (sell if drops to specific price
  youre long and wrong)
• E.G. You own stock trading at 40. You could
  place a stop loss at 38. The stop loss would
  become a market order to sell if the price of the
  stock hits 38.
• Stop buy (buy if price increases to specific
  price youre short and wrong)
• E.G. You shorted stock trading at 40. You
  could place a stop buy at 42. The stop buy
  would become a market order to buy if the price
  of the stock hits 42.

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Short selling Problem 1

1. The stop-buy order at 128 limits your max loss
   to about 8 per share.

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Short selling Problem 2
(Round Trip)
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Buying on Margin

• Margin transactions Borrow part of the money to
  pay for the stock.
• Brokers lend the money and hold the stock as
  collateral. They charge an interest rate called
  the call money rate (about 1 less than prime).
• Equity is the stock value less the money borrowed
  from the broker.
• Margin (initial) requirement is the minimum
  equity percentage required and determines how
  much can be borrowed from the broker. Set by the
  Federal Reserve Broker. Current margin
  requirement is 50.
• Maintenance Margin is a required which is less
  than the initial margin. If the equity falls
  below the maintenance margin, a margin call is
  made and additional funds must be deposited to
  meet the Maintenance Margin. If not, broker can
  close the position/sell stock.
• Trading on margin increases risk. (see our
  example problems)

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Margin Trade Example

• You buy 200 shares _at_ 50/share 10,000.
• Interest on loan 6
• Commission 50 on the buy and 50 on the sell.
• Initial margin 50. So you have to come up
  with 50 of the 10,000 purchase (50)(10,000)
  5,000.
• You borrow the rest of the purchase price from
  the broker
• Loan 10,000 - 5,000 5,000.
• Initial Investment 5,000 50 5,050 (dont
  forget commission).
• Assume 1 year later
• Stock price increases 20 to 60/share (so youll
  sell for 12,000).
• Interest 6 5,000 300
• Profit 12,000 10,000 300 (250)
  1,600
• Profit 1,600 / 5,050 31.7

interest
commissions
sale
purchase
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Suppose we had been asked to ignore commissions
or interest?
9

• You buy 200 shares _at_ 50/share 10,000.
• Initial margin 50. So you have to come up
  with 50 of the 10,000 purchase (50)(10,000)
  5,000.
• You borrow the rest of the purchase price from
  the broker
• Loan 10,000 - 5,000 5,000.
• Initial Investment 5,000 (we are ignoring the
  commission here).
• Assume 1 year later
• Stock price increases 20 to 60/share (so youll
  sell for 12,000).
• Profit 12,000 10,000 2,000
• Profit 2,000 / 5,000 40
• Trading on margin increases risk. Borrowing 50
  of the stocks purchase amount means your
  leverage is 2. Trading on margin doubled your
  investment risk versus the change in stock price.

sale
purchase
10
What if the stock price had fallen 20?
10

• You buy 200 shares _at_ 50/share 10,000.
• Interest on loan 6
• Commission 50 on the buy and 50 on the sell.
• Initial margin 50. So you have to come up
  with 50 of the 10,000 purchase (50)(10,000)
  5,000.
• You borrow the rest of the purchase price from
  the broker
• Loan 10,000 - 5,000 5,000.
• Initial Investment 5,000 50 5,050 (dont
  forget commission).
• Assume 1 year later
• Stock price decreases 20 to 40/share (so youll
  sell for 8,000).
• Interest 6 5,000 300
• Profit 8,000 10,000 300 (250) -
  2,400 (i.e., a loss)
• Profit - 2,400 / 5,050 ? 47.5 (i.e., a
  loss)

interest
commissions
sale
purchase
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Margin Trade Example (continued)
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• Here is a shortcut you can use is you are asked
  to ignore commissions and interest on the loan
• Calculate stock prices change as a increase or
  decrease of initial price. Equals (Sales
  Price/Purchase Price) 1. Convert to .
• Calculate leverage, which equals (100) /
  (Initial Margin ).
• Multiply stock prices change by leverage.
  Thats your profit or loss.
• For gain example
• Stock prices change (60/50)-1 20.
• Leverage (100) / (Initial Margin )
  (100)/(50) 2.
• Profit (20)( 2 ) 40. (Compare why
  40 vs. 31.7?)
• For loss example (40/50)-1 - 20. Leverage
  2. Profit - 40.
• Trading on margin increases risk. Here your
  leverage was 2. Trading on margin doubled your
  investment risk versus the change in stock price.

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Margin Call Example
12
An investor buys 500 shares of ABC stock at the
market price of 70 on full margin. The initial
margin requirement is 45 and the maintenance
margin is 25. The commission is 10 each on the
purchase and sale. Interest is 5 per year. At
what stock price would the investor receive a
margin call?

• You will receive a margin call when your equity
  position is worth less than 25 (i.e., the
  maintenance margin) of the stocks value.
• Calculate stock price (P) when your equity
  exactly equals 25 of stock value.
• Your equity is worth the value of the stock less
  the amount of your loan.
• The amount of your loan (1 - .45) ( 500 )
  (70) 19,250.
• If the stocks price is P, then your stocks
  value (500)(P).
• Your equitys value (500)(P) - 19,250.
• We need to know the value of P that solves the
  equation
• Equitys value (500)(P) - 19,250 0.25
• Stocks value (500)(P)

Initial margin
shares
purchase price
Maintenance margin
CFALA/USC CFA Review Level 1, SS-13
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Margin Call Example (continued)
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An investor buys 500 shares of ABC stock at the
market price of 70 on full margin. The initial
margin requirement is 45 and the maintenance
margin is 25. The commission is 10 each on the
purchase and sale. Interest is 5 per year. At
what stock price would the investor receive a
margin call?

• Solve for P
• (500)(P) - 19,250 0.25
• (500)(P)
• Multiply both sides of the equation by (500)(P)
  gives us
• (500)(P) - 19,250 (0.25) (500)(P)
• (500)(P) - 19,250 (125) (P)
• (500 125) (P)
  19,250
• P
  19,250 / (500 125) 51.33/share
• If your stocks price falls below 51.33/shares,
  you will receive a margin call. Youll have to
  deposit enough to bring your equity back up to
  25.

Maintenance margin
CFALA/USC CFA Review Level 1, SS-13
14
Margin Call Example (continued)
14
An investor buys 500 shares of ABC stock at the
market price of 70 on full margin. The initial
margin requirement is 45 and the maintenance
margin is 25. The commission is 10 each on the
purchase and sale. Interest is 5 per year. At
what stock price would the investor receive a
margin call?

• Here is a shortcut formula if you can remember
  it
• Margin call price Loan amount per share divided
  by one minus margin maintenance requirement
  (MMR). So if Loan is in and N is the number of
  shares
• P (Loan / N) / (1-MMR)
• (19,250/500) / (1 - .25)
• (38.50) / (.75)
• 51.33.
• The solutions in the book write (Loan/N) as
  (original price) x (1 initial margin). Your
  initial margin was 45, so you borrowed the rest
  (55) of each shares purchase. So for each
  share you bought, you borrowed (70)(.55)
  38.50. You receive a margin call if your equity
  is less than 25 of the stocks value. So the
  loan cant be more than 75 of the stocks value.
  In other words, (75)(P) cant be more than
  38.50.

CFALA/USC CFA Review Level 1, SS-13
15
Short selling Problem 3

• You sell short 100 shares of stock priced at 60
  per share.
• The proceeds of 6000 must be pledged to broker.
• You must also pledge 50 margin.
• You put up 3000. Now you have 9000 invested in
  margin account.
• Short Sale Equity Total Margin Account - Market
  Value

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Short selling Problem 3

• Suppose the maintenance margin for short sale of
  a stock with price gt 16.75 is 30 of market
  value or
• So you have 1200 in excess margin. (This may be
  withdrawn at your pleasure but assume that it is
  not.)
• At what stock price do you get a margin call?

30 x 6,000 1,800
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Short selling Problem 3
When Equity ? (0.30 Market Value) Equity
Market Value 9,000 / (1 0.30)
6,923 Price at which get a margin call6,923
/ 100 shares 69.23
Total Margin Account Market Value
When Market Value Total Margin Account / (1
MMR)
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Short selling Problem 3

If this occurs Equity Equity as
market value You get a margin call and you
may have to restore the 50 initial margin. If
so you must deposit an additional (6,923 / 2) -
2,077 1,384.5
9,000 - 6,923 2,077
2,077 / 6,923 30
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Short selling Problem 4

• You are bearish on Telecom and decide to sell
  short 100 shares at the current market price of
  50 per share.
• How much in cash or securities must you put into
  your brokerage account if the brokers initial
  margin requirement is 50 of the value of the
  short position?
• How high can the price of a stock go before you
  get a margin call if the maintenance margin is
  30 of the value of the short position?

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Short selling Problem 5

• Suppose that you short sell 500 shares of Intel,
  currently selling for 40 per share, and give
  your broker 15,000 to establish your margin
  account.
• If you earn no interest in the funds in your
  margin account, what will be your rate of return
  after 1 year if Intel stock is selling at (i) 44
  (ii) 40 (iii) 36? Assume that Intel pays no
  dividends.
• If the maintenance margin is 25, how high can
  Intels price rise before you get a margin call?
• Redo parts (a) and (b), but now assume that Intel
  has paid a year-end dividend of 1 per share.
  Assume that the prices in part (a) are
  ex-dividend, that is, prices after dividends have
  been paid.

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Short selling Problem 5

• Suppose that you short sell 500 shares of Intel,
  currently selling for 40 per share, and give
  your broker 15,000 to establish your margin
  account.
• If you earn no interest in the funds in your
  margin account, what will be your rate of return
  after 1 year if Intel stock is selling at (i) 44
  (ii) 40 (iii) 36? Assume that Intel pays no
  dividends.
• The gain or loss on the short position is (500
  X change in price)
• Invested funds 15,000
• Therefore rate of return (500 x change in
  price)/15,000
• The rate of return in each of the three scenarios
  is
• rate of return (500 x 4)/15,000 0.1333
  13.33
• rate of return (500 x 0)/15,000 0
• rate of return 500 x (4)/15,000 0.1333
  13.33

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Short selling Problem 5

• Suppose that you short sell 500 shares of Intel,
  currently selling for 40 per share, and give
  your broker 15,000 to establish your margin
  account.
• If the maintenance margin is 25, how high can
  Intels price rise before you get a margin call?
• Total assets in the margin account are 20,000
  (from the sale of the stock) 15,000 (the
  initial margin) 35,000. Liabilities are 500P.
  A margin call will be issued when
• when P 56 or higher 

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Short selling Problem 5

• Suppose that you short sell 500 shares of Intel,
  currently selling for 40 per share, and give
  your broker 15,000 to establish your margin
  account.
• Redo parts (a) and (b), but now assume that Intel
  has paid a year-end dividend of 1 per share.
  Assume that the prices in part (a) are
  ex-dividend, that is, prices after dividends have
  been paid.
• With a 1 dividend, the short position must now
  pay on the borrowed shares (1/share x 500
  shares) 500. Rate of return is now (500 x
  change in price) 500/15,000
• rate of return (500 ? 4) 500/15,000
  0.1667 16.67
• rate of return (500 ? 0) 500/15,000
  0.0333 3.33
• rate of return (500) ? (4) 500/15,000
  0.1000 10.00
•  
• Total assets are 35,000, and liabilities are
  (500P 500). A margin call will be issued when
• when P 55.20 or higher