Leveraged positions and margin call

CFA level I / Equity Investments: Market Organization, Market Indices, and Market Efficiency / Market Organization and Structure / Leveraged positions and margin call

45.f: Leveraged positions and margin call

Traders can buy securities by funding part of the purchase price through borrowings. The amount borrowed to fund such a purchase is called margin loan. Interest paid on margin loan is called call money rate. Buyers dealing with large volume of securities get lower call money rates.

The initial margin requirement is the minimum equity that the buyer must put in to fund the purchase of security. The requirement may be set by the exchange, the clearinghouse or the government.

Leveraged position increases the potential profit/loss of a position since the trader has bought more securities than she would have with could have otherwise. Financial leverage is the ratio of total position to equity invested. Higher the financial leverage, higher the profit/loss potential. The maximum possible financial leverage of a position is 1/minimum margin requirement.

For e.g. if margin requirement is 50 percent, the financial leverage would be 1/0.5 or 2.

Financial leverage can also be understood as the factor by which a levered position is riskier than an unleveraged position.

For a position with 50 percent margin requirement, the rise in the price of the security by 10 percent would imply 1/0.5 = 2 * 10 percent or 20 percent return. For an unleveraged position, the return would be only 10 percent.

Example 4

A trader buys 1,000 shares of a company priced at $100/share and holds it for a year. During the holding period, he receives $40 dividend. The position had 30% margin requirement and he sells the security at $110/share. The call money rate is 5 percent for the holding period of one year. Calculate the total return. The brokerage commission paid is $0.01/share. Solution: Total amount spent on the investment by the trader = Amount paid for shares + Brokerage commission = 0.3*1,000*100 + 0.01*1,000 = $30,010. Net profit in the investment = Profit due to increase in the share price + Dividends received - Total commission paid for brokerage - Interest paid on the margin loan = (110-100)*1,000 + 40 - 0.01*(1,000 + 1,000) - 0.7*1,000*100*0.05 = 10,000 + 40 - 20 - 3,500 = $6,520. Total return = 10,000/30,010 = 21.73 percent. Note: The calculation is pretty simple if you remember to add the brokerage commission for buying to the initial investment and reduce the profit by the brokerage commission for buying and selling and interest paid for the margin loan. If there are no brokerage commissions and no interest on the margin loan, then the return on the leveraged position would be simple the leverage ratio multiplied by the cash return. The leverage ratio is one divided by the margin percentage.

If the price of security in the above example falls by more than 50 percent (more than the initial margin requirement), his equity would be wiped off and broker (who has lent him the money) may lose his money as well. To offset this risk, brokers ask for maintenance margin requirement, which is the minimum equity the buyer has to maintain in the account. If the equity falls below this level, the buyer will receive a margin call from the broker to invest more equity, failing which the broker can close the position to recover his dues.

Example 5

A trader bought a security at $100/share with initial and maintenance margin requirement of 50 percent and 25 percent respectively. At what price will the buyer receive a margin call? Solution: Initial trade equity = 0.50*$100 = $50 Trader equity during the position = $50 + (P-$100), where P is the price of security at any time during the holding period For margin call to be issued, the trigger price is the price where the maintenance margin = $50 + (P-$100) Or, 0.25*P = 50 + (P-100) Solving for P, We get P=$66.7, if the price falls below this price then the margin call would be triggered.

Trigger price for the long position = P₀*(1 - Initial Margin)/(1-Maintenance Margin)

Trigger price for the short position = P₀*(1 + Initial Margin)/(1 + Maintenance Margin)

If the price falls below the trigger price for the long position or the price rises above the trigger price for the short position, a margin call would be issued.

Note: In a short position, the trader’s minimum equity must at all times be equal initial value of position times the margin requirement.

Check your concepts:

(45.18) Which of the following factors is most likely to lead to an increase in leveraged return for a profitable position?

(a) An increase in the call money rate
(b) An increase in the brokerage commission
(c) An increase in the leverage ratio

(45.19) For a leveraged long position in a stock, the leveraged return is 40 percent if the stock price rises by 10 percent. What will be the most likely value of the leveraged return if the stock falls by 10 percent?

(a) -45 percent
(b) -40 percent
(c) -35 percent

(45.20) A trader took a short position in a stock for a price of $120 per share. The initial margin requirement and the maintenance margin requirement are 30 percent and 20 percent respectively. What will the trigger price for the margin call for a short position?

(a) $130.00
(b) $132.00
(c) $135.00

Solutions:

(45.18) Correct Answer is C: An increase in the expenses i.e. call money rate and the brokerage commissions would lead to a decrease in the leveraged return. An increase in the leverage ratio will increase the return for the profitable position and decrease the return for the loss-making position.

(45.19) Correct Answer is A: For a leveraged position, the loss is always greater than the profit because of the expenses (brokerage commissions and interest on margin loan) involved. Therefore, the return has to be lower than -40 percent.

(45.20) Correct Answer is A: For the short position, the initial equity = Initial value + Margin requirement = 120 + 120*0.3 = 156. The trigger price will occur when the equity in the position becomes equal to 120 + P*0.2. Equity position for short position at a share price of P = 120 + 120*0.3 + (120 - P). Solving for P, we get P = 120*1.3/1.2 = $130. If the price rises above this price, then the margin call will be issued. It can be solved using the formula as well. Trigger price = P0*(1+Initial Margin)/(1+Maintenance Margin) = 120*1.3/1.2 = $130.

Exam Alert: Candidates should be comfortable in calculating the leveraged return and the trigger price for the margin call. You are likely to get one question from this in the examination.