short selling

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Short Selling

• Objective: You’re 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.

Short selling: Problem 1

a. 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.

• Special orders: Stop loss (sell if drops to specific price; you’re 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; you’re 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.

CFALA/USC CFA Review Level 1, SS-13

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Types of Orders


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

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Note that your profit ($200) equals (100 shares profit per share of $2). Your net proceeds per share was:

$14 selling price of stock –$ 9 repurchase price of stock –$ 2 dividend per share –$ 1 2 trades $0.50 commission per share $ 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 @ $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 (don’t forget commission).

• Assume 1 year later: Stock price increases 20% to $60/share (so you’ll sell for $12,000). Interest: 6% × 5,000 = $300

Profit = $12,000 – $10,000 – $300 – (2×$50) = $1,600

Profit % = $1,600 / $ 5,050 = 31.7%

sale purchase interest commissions

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

• You buy 200 shares @ $50/share = $10,000. Initial margin = 50%. So you have to come up with 50% of the


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 you’ll 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 stock’s purchase amount means your “leverage” is 2. Trading on margin doubled your investment risk versus the change in stock price.

sale purchase

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What if the stock price had fallen 20%?

• You buy 200 shares @ $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


Loan = $10,000 - $5,000 = $5,000. Initial Investment: $5,000 + $50 = $5,050 (don’t forget commission).

• Assume 1 year later: Stock price decreases 20% to $40/share (so you’ll sell for $8,000). Interest: 6% × 5,000 = $300

Profit = $ 8,000 – $10,000 – $300 – (2×$50) = - $ 2,400 (i.e., a loss)

Profit % = - $ 2,400 / $ 5,050 = 47.5% (i.e., a loss)

sale purchase interest commissions

Here is a shortcut you can use is you are asked to ignore commissions and interest on the loan:

• Calculate stock price’s 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 price’s change by leverage. That’s your profit or loss.

For gain example: • Stock price’s 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 Trade Example (continued)


12Margin Call Example:

• You will receive a margin call when your equity position is worth less than 25% (i.e., the maintenance margin) of the stock’s 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 stock’s price is “P”, then your stock’s value = (500)(P). Your equity’s value = (500)(P) - $19,250. We need to know the value of “P” that solves the equation:

Equity’s value = (500)(P) - $19,250 = 0.25 Stock’s value (500)(P)

Initial margin

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?

shares purchase price

Maintenance margin


13Margin Call Example: (continued)

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 stock’s price falls below $51.33/shares, you will receive a margin

call. You’ll have to deposit enough to bring your equity back up to 25%.


Maintenance margin


14Margin Call Example: (continued)

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 share’s 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 stock’s value. So the loan can’t be more than 75% of the stock’s value. In other words, (75%)(P) can’t be more than $38.50.


• You sell short 100 shares of stock priced at $60 per share.

o The proceeds of $6000 must be pledged to broker.

o 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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•Suppose the maintenance margin for short sale of a stock with price > $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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When: Equity (0.30 * Market Value)

Equity =

Market Value = $9,000 / (1 + 0.30) = $6,923

Price at which get a margin call:$6,923 / 100 shares = $69.23

Total Margin Account – Market Value

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When: Market Value = Total Margin Account / (1 + MMR)


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•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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You are bearish on Telecom and decide to sell short 100 shares at the current market price of $50 per share.

a.How much in cash or securities must you put into your brokerage account if the broker’s initial margin requirement is 50% of the value of the short position?b.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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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.

a.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.b.If the maintenance margin is 25%, how high can Intel’s price rise before you get a margin call?c.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 5Suppose 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.

a.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 = $15,000Therefore: rate of return = (–500 x change in price)/15,000The 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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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.

b.If the maintenance margin is 25%, how high can Intel’s 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

25.0500

500000,35$

P

P

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Short selling: Problem 5Suppose 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.

c.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

(i)rate of return =[(–500 $4) – $500]/$15,000 = –0.1667 = –16.67%

(ii)rate of return = [(–500 $0) – $500]/$15,000 = –0.0333 = –3.33%(iii)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

25.0500

500500000,35$

P

P

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short selling

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