Buying stocks through margin lending

Margin transactions involve buying securities with borrowed money.

Brokerage firms can lend their customers money to purchase securities and keep the securities as collateral, allowing the customer ride the inherent risk of the stock without the requirement of purchasing 100% of the stock.

The example below taken from a study guide to corporate finance that I am reading outlines how margin lending operates in U.S and defines some of the key concepts in margin lending.

The required equity position and the initial margin requirement

The margin lending rate is usually 1.5 percentage points above the bank call money rate (which is about 1 percentage point below the prime rate). In the U.S., margin lending limits are set by the Federal Reserve Board under Regulations T and U. The required equity position is called the margin requirement. The initial margin requirement is currently 50 percent. This means the borrower must provide 50 percent of the funds in the trade. An initial margin requirement of 40 percent would mean that the investor must put up 40 percent of the funds and the brokerage firm may lend the 60 percent balance.

After the trade, the price of the stock will change, causing the balance of the margin account to fluctuate. Should the stock price go up, the customer’s profits accumulate at a faster pace than a 100 percent equity position. This is the benefit of margin trading–leverage as it allows investors to gain more from the stock they choose to invest in than they would be able to with their capital alone.

The margin lending leverage ratio

The leverage ratiocan be calculated as [1/ margin %]. For example, at a 40 percent initial margin requirement, profits will accrue at a [1/.4] 2.5 leverage rate or 150 percent faster rate than a 100 percent equity position. The customer can remove any funds in the account in excess of the original margin requirement.

The rate of return on margin transactions

Assume that an investor purchases 100 shares of a stock for $75 per share (total cost = $7,500). If the stock is then sold for $150 per share (total value of $15,000), the investor would have had a 100 percent return on her initial investment [(15,000/7,500)-1*100].

Now, assume she purchased the same 100 shares with an initial margin of 50 percent. The cost of her investment would be only $3,750. The other $3,750 of the purchase will be borrowed from the brokerage firm. If the shares were then sold at $150 per share, her position would be worth $11,250 (i.e., 15,000-3,750). In this situation, the investor would have had a 200% return on her investment [(11,250/3,750)-1*100]. This calculated return is before commission costs and interest paid on the loan to the brokerage firm.

Determining the stock price at which an investor would receive a margin call.

A maintenance margin is the required fraction of an investor’s equity compared to the total value of the stock. The Federal Reserve has currently set the maintenance margin (the minimum equity portion of the account) at 25 percent on a stock purchase. If the customer’s balance falls below the maintenance margin, the customer will receive a margin call. The following formulas indicate the stock price that will trigger a margin call:

Long = [(original price)(1 - initial margin %)]/[1 - maintenance margin %]

Short= [(original price)(1+ initial margin %)]/[1 + maintenance margin %]

Question:

You buy a stock for $40. If the initial margin requirement is 50 percent and the maintenance margin requirement is 25 percent at what price will you get a margin call?

Answer: [($40)(1 - .5)]/[1 - .25] = $26.67.

Question:

You short a $40 stock. If the initial margin requirement is 50 percent and the maintenance margin requirement is 30 percent, at what price will you get a margin call?

Answer: [($40)(1 + .5)]/[1 + .30] = $46.15.