Short Sale. Dr. Patrick Toche

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1 Short Sale Dr. Patrick Toche References : Zvi Bodie, Alex Kane, Alan J. Marcus. Essentials of Investment. McGraw- Hill Irwin. Chapter 3 of the Bodie-Kane-Marcus textbook will be followed closely. Other references may be given from time to time. In this chapter you will learn... going long and going short initiating and covering a short position margin calls on short sales

Chapter 3 of the Bodie-Kane-Marcus textbook will be followed closely.

2 Long and Short Positions The most common investment strategy is to buy shares and hold them for some time before selling them. This is referred to as holding a long position or going long in the stock. A short sale is the reverse strategy: borrow shares from a broker, sell them right away without holding them, and buy them back later to return them to the broker. In both long and short trades, you start and end with no shares. Investors take a long position if they expect the price to rise they take a short position if they expect the price to fall. Short Sales In a short sale, an investor borrows a share from a broker and sells it. This is referred to as initiating the short position. At a later stage, the investor buys a share of the same stock from the market and returns it to the broker in replacement for the borrowed share. This is referred to as covering the short position. In a short sale, investors must return the borrowed shares but also pay any cash dividends paid during the short position. Neither the broker nor the short-seller have received the dividends payments since neither was the legal owner of the stock. However, the broker would have been entitled to the dividends if they had not lent the shares to the investor. When shares are shorted over brief horizons, such as a few hours or a few days, dividends are not typically due.

A short sale is the reverse strategy: borrow shares from a broker, sell them right away without holding them, and buy them back later to return them to the broker.

3 Short Sales When investors initiate a short position, the broker borrows the shares on their behalf. To satisfy its settlement obligation with the clearinghouse, the broker provides the lender with a cash deposit in an amount equal to or greater than the value of the loaned securities. The lender charges a fee for providing this service. The fee may be quoted as a short rebate. The lender earns all of the interest which accrues on the cash collateral, but may rebate an agreed rate of interest to the borrower. Most brokers do not rebate interest on the cash proceeds of small short trades, but do so on large trades, and may also agree to increase the rebate when the availability of a stock is relatively high. Most brokers will only lend shares for a short if they have other clients who hold the shares long. Short Sales Because short sales are risky, short-sellers are required to post margin with the broker to cover potential losses. The margin could be cash or other securities held as collateral. For instance, you may hold a long position in Microsoft shares as collateral for a short position in Apple shares. In a long position, the most you can lose is about 150% if you borrowed on margin to leverage your investment (initial margin cannot exceed 50% in the U.S. and rarely does in other countries). With a short position, your potential loss is theoretically unlimited since the security s price could go on rising forever. If you short a stock trading at $10 and the price rises to $100, then your loss is $90 per share 9 times your original investment!

The lender charges a fee for providing this service. The fee may be quoted as a short rebate.

4 Regulation T Under Regulation T, it is mandatory for short sales that 150% of the value of the position at the time the short is created be held in a margin account. This 150% is comprised of 100% of the value of the short plus an additional margin requirement of 50%. A short sale must be conducted in a margin account. A margin account entitles the broker to liquidate your position if your account fails to satisfy margin requirements. This is part of the agreement that is signed when the margin account is created. If your broker has a 30% margin requirement on short sales, the equity in your account must be at least 30% of the value of your short position at all times. Short Sales: Margin Suppose you instruct your broker to sell short 1,000 shares at the market price of $100 per share. The broker borrows 1,000 shares and credits your account with $100, 000. Suppose the broker has a 50% initial margin requirement on short sales. Thus, you must have other cash or securities in your account worth at least $50, 000. Suppose you transfer $50,000 of equity in your account. Your initial percentage margin is: margin = value of equity = 50, ,000 = 50% If the stock price falls to $70 per share, you can now close out your position at a profit. To cover the short sale, you buy 1,000 shares to replace the ones you borrowed. The purchase costs only $70,000 and since your account was credited for $100,000 when the short sale was initiated, your profit is $30,000.

A margin account entitles the broker to liquidate your position if your account fails to satisfy margin requirements. This is part of the agreement that is signed when the margin account is created.

5 Short Sales: Margin Calls Suppose the broker has a maintenance margin of 30%. How much can the price rise before you get a margin call? Let P be the price of the stock. The value of the shares you must pay back is 1,000P and the equity in your account is $150,000 1,000P. The margin for any price P is: margin = value of equity = 150,000 1,000P 1, 000P The price at which the percentage margin equals the maintenance margin of 30% is the solution of: 150,000 1,000P 1, 000P = 0.3 Solving the equation yields P = $ The investor gets a margin call if the price of the stock rises above $ Margin Percentage on Short and Long Positions The general principle is: margin = value of equity I: total value of Investment in margin account (including cash, collateral and borrowed securities) S: number of Securities P: Price of the securities L: value of the Loan The margin M L of a long position is: M L = L The margin M S of a short position is: M S = I minus loan = = value of investment minus securities

The margin for any price P is: margin = value of equity = 150,000 1,000P 1, 000P The price at which the percentage margin equals the maintenance margin of 30% is the solution of: 150,000 1,000P 1,

6 Margin Calls on Short and Long Positions A margin call on a long position occurs when: L P = = M L S(1 M) = 4, (1 0.3) $57 A margin call on a short position occurs when: I P = = M I S(1 + M) = 150,000 1,000( ) $115 where the numbers come from our previous examples. Summary 1. Short-selling is the practice of selling borrowed securities. 2. The short-seller borrows the securities through a broker. 3. The broker requires that the short-seller deposit cash or securities to serve as collateral for the short sale. 4. The short-seller may be required to cover the short position at any time on demand. 5. A short sale must be conducted in a margin account. A margin account entitles the broker to liquidate your position if your account fails to satisfy margin requirements.

Short-selling is the practice of selling borrowed securities. 2. The short-seller borrows the securities through a broker. 3.

7 Problems and Applications 1. Suppose that you sell short 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 on 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? Problems and Applications 2. You are bearish on Telecom stock 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 the stock go before you get a margin call if the maintenance margin is 30% of the value of the short position?

You are bearish on Telecom stock 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?

Margin Requirements & Margin Calls

Margin Requirements & Margin Calls Dr. Patrick Toche References : Zvi Bodie, Alex Kane, Alan J. Marcus. Essentials of Investment. McGraw- Hill Irwin. Chapter 3 of the Bodie-Kane-Marcus textbook will be