1 short selling objective: you’re bearish on a stock --- you think its price will be lower in the...
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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.
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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.
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• 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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Short selling: Problem 1
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b. The stop-buy order at $128 limits your max loss to about $8 per share.
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Short selling: Problem 2
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
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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
$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 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
$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 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
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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 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)
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CFALA/USC CFA Review Level 1, SS-13
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
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CFALA/USC CFA Review Level 1, SS-13
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%.
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?
Maintenance margin
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CFALA/USC CFA Review Level 1, SS-13
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.
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?
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• 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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Short selling: Problem 3
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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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Short selling: Problem 3
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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)
Short selling: Problem 3
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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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Short selling: Problem 3
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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.
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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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.
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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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.
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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