FIN521 Chap.5 Margin, Short Selling and Leverage
Margin, Short Selling and Leverage
One identity, and only one thing in it moves
Buying on margin means borrowing part of the purchase price from a broker, who in turn borrows at the call money rate and charges the client that rate plus a service charge. The margin in the account is equity divided by the market value of the securities.
Written out, that is the number of shares times the price, less the loan, all over the number of shares times the price. The share count and the loan are both fixed by the transaction and do not change when the market moves, so the price is the only live variable in the whole chapter.
Every question here is that identity rearranged: set the price and read the margin, or set the margin and solve for the price.
Two requirements, set by different parties for different reasons
The initial margin requirement is the minimum proportion the investor must contribute at purchase, and it has been fifty per cent in the United States.
The maintenance margin is the minimum proportion the account must keep afterwards, and it is lower. The first is a regulatory limit on how much the market as a whole may borrow; the second is a commercial limit set by the lender to protect its own loan.
They answer different questions and they turn up in the same examination sentence, so read carefully which one the problem has supplied.
What a call actually does
Allow the ratio to fall past the maintenance threshold and a call arrives, demanding fresh cash or additional securities; ignore it and the broker may liquidate holdings from the account itself.
The call does not by itself crystallise a loss: an investor who can meet it keeps the position and keeps the chance of a recovery. The damage falls on investors who cannot, because the broker then liquidates at a price that is low by construction.
Leverage therefore changes not only the size of the outcome but who decides when the position closes, which is the part of the risk the arithmetic does not show.
Both tails, and the row in the middle
Borrowing magnifies a rise and magnifies a fall, which most students can recite.
Fewer notice the middle row of the standard table, where the share price does not move at all and the levered investor still loses the cost of the loan over the year. Interest accrues whether or not the thesis works, so a levered position is a bet on timing as well as direction.
Selling short is the mirror image and adds one asymmetry of its own: a long position can lose everything committed, while a short position can lose more, because the price at which the borrowed share must be repurchased has no ceiling.
What this chapter covers
- 01
The margin identity and the two quantities that do not move
- 02
Initial requirement against maintenance requirement
- 03
Deriving the call price from the maintenance margin
- 04
Reading a margin account as a balance sheet
- 05
Why the whole price fall lands on the equity line
- 06
Leverage as a rotation of the payoff line, not a shift
- 07
The cost of the loan when the share price does not move
- 08
Short sale mechanics, covering, and the dividend obligation
- 09
Margin on a short position and why the call price falls as the requirement rises
Solve for a call price on both sides of the market
- 3State the loan on the long position and the account balance on the short.
- 3Solve the long call price from the maintenance ratio.
- 4Solve the short call price and explain the direction.
Key terms
- Buying On Margin
- Funding part of a purchase with money advanced by the broker, so that a given amount of the investor's own capital supports a bigger holding.
- Initial Margin
- The minimum proportion of a position the investor must contribute at the time of purchase, set as a regulatory limit on market-wide borrowing.
- Maintenance Margin
- The minimum proportion of equity the account must retain after purchase, set commercially by the broker to protect its loan.
- Margin Call
- A broker's demand for further cash or securities once the ratio has dropped through the maintenance threshold.
- Call Money Rate
- The rate at which a broker borrows from banks to fund client margin loans, and the base on which the client is charged.
- Short Sale
- Borrowing a security, selling it, and buying it back later to return it, which profits from a fall and carries an unbounded loss.
- Covering
- Repurchasing the security sold short in order to return it to the lender and close the position.
- Leverage
- The use of borrowed money to increase exposure, which rotates the relationship between the asset's return and the investor's return rather than shifting it.
Margin, Short Selling and Leverage FAQ
Does a margin call mean I have lost money?
Not by itself. A call is a demand for more collateral, and an investor who meets it keeps the position and keeps whatever recovery follows. The loss becomes real for investors who cannot meet it, because the broker then sells from the account at whatever price prevails, and by construction that price is a low one.
The important consequence for an answer is that leverage transfers the decision about when to close a position from the investor to the lender.
Why can a short sale lose more than the amount deposited?
Because the obligation is to return a share, and the price of buying one back has no upper limit. A long position is bounded below by a price of zero, so the most that can be lost is what was committed. A short position has no such bound above, which is why brokers impose margin requirements on shorts and why the maintenance rule triggers as the price rises rather than as it falls.
Should the dividend be counted in a short position's return?
Yes, and against you. The short seller must pay the lender of the security any dividend paid while the position is open, so the cash outflow offsets the price fall that normally accompanies the ex-dividend date. The two move together by construction, which means an answer that counts the price drop as profit without the matching payment has counted one side of a matched pair and will be marked down for it.
Exam move
Work the call price for a long and a short position from the same starting numbers, then change only the maintenance requirement and check that the two answers move in opposite directions. That single pairing is the fastest way to stop the sign error that costs most of the marks here.
Then rebuild the three-row leverage table with your own borrowing rate and notice what the middle row costs, because a question that supplies both a rate and a holding period is usually testing exactly that.
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