Short Selling

1. 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.

2. Short selling: Problem 1 • If the price keeps going up your losses areunlimited. 3-2

3. Types of Orders • Marketorders: • Immediate execution of the order. • Filled at best available price. • Limitorders: • 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.

4. Types of Orders • Special orders: • Stoploss (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. • Stopbuy (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

5. Short selling: Problem 1 • The stop-buy order at $128 limits your max loss to about $8 per share. 3-5

6. Short selling: Problem 2 (Round Trip) 3-6

7. 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)

8. 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% interest commissions sale purchase

9. Suppose 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. 9 sale purchase

10. 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) 10 interest commissions sale purchase

11. 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. Margin Trade Example (continued) 11

12. Margin 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) 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? Initial margin shares purchase price Maintenance margin CFALA/USC CFA Review Level 1, SS-13

13. Margin 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%. 13 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 CFALA/USC CFA Review Level 1, SS-13

14. Margin 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. 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? 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 3-15

16. Short selling: Problem 3 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 3-16

17. 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 call:$6,923 / 100 shares = $69.23 Total Margin Account – Market Value When: Market Value = Total Margin Account / (1 + MMR) 3-17

18. 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% 3-18

19. 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 broker’s 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?

20. 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 Intel’s 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.

21. 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%

22. 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 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 

23. 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