Buying on Margin and Short Selling

Balance Sheet

Assets (100 shares): $4,500 (value of collateral is variable) Liabilities (dollar loan): $2,250 (value of the loan is fixed) Equity: $2,250 The value of the collateral may not fully sustain the value of the loan!!! Next, we describe the procedure that brokers follow to protect themselves against credit risk.

Short Sell Balance Sheet

Assets (IM): $2,200 Assets (SSP): $4,400 (value of collateral is fixed) Liabilities (loan = 100 shares): $4,400 (value of the loan is variable) Equity: $2,200 The value of the collateral may not fully sustain the value of the loan!!! Next, we describe the procedure that brokers follow to protect themselves against credit risk.

Short Selling

Borrow one share at time 0; Sell the share at time 0 for $500; Buy back the share at time 1 for $400 and payback the loan of one share; The profit is $100 [= $500 - $400 = P0 - P1]; In sum, short selling allows investors to profit when the stock price declines.

Example 2

Find the stock price at which you would receive a margin call. Recall that Q = 100, Loan = $2,250, and MM (%) = 40%. You receive a margin call when AM = MM. Intuitively, we have: Stock Price Actual Margin $45.00 50.00% $42.82 47.47% ? 40.00% Hence, the price at which you would receive a margin call is less than $42.83. Formally, the stock price at which you receive a margin call, P, solves: (100 x P - 2,250)/(100 x P) = 0.4. Therefore:1 P = $37.50.

Example 4

Find the stock price at which you would receive a margin call. Recall that Q = 100, SSP = $4,400, IM = $2,200, and MM (%) = 40%. Note that you receive a margin call when AM = MM. Hence, the price at which you would receive a margin call is strictly between $44 and $47.56. Find the stock price at which you would receive a margin call. Recall that Q = 100, SSP = $4,400, IM = $2,200, and MM (%) = 40%. Note that you receive a margin call when AM = MM. Formally, the stock price at which you receive a margin call, P, solves: (4,400 + 2,200 - 100 P)/(100 P) = 0.4. Therefore:2 P = $47.14.

Initial Margin Requirement

If you buy Q shares at price P (per share), then the initial margin requirement (IM) is given by: IM = P x Q x IM (%). Example You bought 100 shares of Microsoft on margin at the price of $45 per share. Assuming that IM (%) = 50%, find the initial margin requirement. The initial margin requirement is $2,250 [= $45 x 100 x 0.5]. Since IM (%) = 50%, the value of the loan is also $2,250 [= $45 x 100 x (1 - 0.5)]. However, if IM differs from 50%, then the value of the loan will differ from the initial margin requirement.

Short Sell Initial Margin Requirement

If you short sell Q shares at price P (per share), then the initial margin requirement (IM) is given by: IM = P x Q x IM (%) = SSP x IM (%), where SSP denotes the short sale proceeds. Example You short sold 100 shares of Coke at the price of $44 per share. Assuming that IM (%) = 50%, find the initial margin requirement. The initial margin requirement is $2,200 [= $44 x 100 x 0.5]. (the short sale proceeds are $4,400 [= $44 x 100]).

Example 3

Suppose that the maintenance margin for Coke is 40%. On the next day, Coke closed at $47.56. Did you receive a margin call? Recall that the value of the short sale proceeds is $4,400, whereas the value of the initial margin requirement is $2,200. The value of the loan is $4,756 [= $47.56 100 ]. Hence, the actual margin is: AM = ( SSP + IM - Loan) / Loan = ($4,400 + $2,200 - $4,756)/$4,756 = 38.77%. Since AM = 38.77% < 40% = MM, you received a margin call.

Example

Suppose that the maintenance margin for Microsoft is 40%. On the next day, Microsoft closed at $42.83. Did you receive a margin call? Recall that the value of the loan is $2,250. The market value of assets (MVA) is $4,283 [= $42.83 100]. Hence, the actual margin is: AM = (MVA - Loan)/MVA = (4,283 - 2,250)/4,283 = 47.47%. Since AM = 47.47% > 40% = MM, you did not receive a margin call.

Buying on Margin

Suppose that you: -have $50; -borrow $50; and -buy one share that is priced at $100. If the share price goes up 10% (i.e., to $110), then you have: -a profit of $10; and -a return of 20% [= $10/$50], ignoring the interest on the loan. If the share price goes down 10% (i.e., to $90), then you have: -a loss of $10; and -a return of -20% [= -$10/$50], ignoring the interest on the loan. In sum, buying on margin: -increases buying power (you have $50, but you buy shares worth $100); and -leverages returns (e.g., if the share price increases 10%, the return is 20%).

Actual Margin and Maintenance Margin

The daily procedure to protect the broker consists of: Computing the actual margin (AM): AM = (MVA - Loan)/MVA, where MVA denotes the market value of assets; and Comparing it with the maintenance margin (MM). If AM < MM, then the investor receives a margin call. He or she must take corrective action (e.g., deposit more collateral). If the investor fails to respond, then the broker will close the investor's position.

Short Sell - Actual Margin and Maintenance Margin

The daily procedure to protect the broker consists of: Computing the actual margin (AM): AM = (SSP + IM - Loan)/Loan. Comparing it with the maintenance margin (MM); If AM < MM, then the investor receives a margin call and must take corrective action (e.g., deposit more collateral). If the investor fails to respond, then the broker will close the investor's position.

More on Margin Accounts (Vangaurd)

When an investor opens a margin account at Vanguard, he or she agrees that securities purchased on margin can be loaned by Vanguard (so that other investors can short sell such securities). This practice does not prevent the investor from buying and selling the securities or from continuing to receive income on the loaned shares. Importantly, an investor can lose more than his or her initial investment (margin): Consider an investor who buys on margin a given stock (with positive price); Suppose that overnight (there are very 'bad' news and) the stock price goes to zero; Then, the investor loses the initial investment along with the funds that he or she borrowed (i.e., loses more than his or her initial investment). A short position can result in an unlimited liability: Suppose that overnight (there are very 'good' news and) the stock price goes up 500%; Then, the borrowed shares will be bought back (so that they are returned) at a huge loss. Vanguard can increase the initial and maintenance margin requirements at any time without advance written notice. Vanguard can sell the securities in a margin account without contacting the holder of the account.

Financial Leverage

You purchased one share of IBM on margin at the price of $100. The initial margin requirement is 50% and the annual cost of the margin loan is 6%. For simplicity, ignore dividends. Returns for various IBM stock prices one year from now appear below. The initial investment is $50 [= $100 x 1 x 0.5]. If IBM's stock price one year from is $100, then the capital gain is zero [= ($100 - $100) x 1]; Since loan = $50 [= $100 x 1 x (1 - 0.5)], the interest on the loan is $3 [= $50 x 6%]; Hence, the loss is $3; The return is -6% [= -$3/$50]. 2:1 leverage: the return on the margin purchase changes twice as fast [20% = 14% - (- 6%)] as the return when buying with cash [10% = 10% - 0%].