Securities Markets: Buying on Margin and Short Sales

Securities Markets: Chapter 3 Part 2

3.8 Buying on Margin

  • Margin: Refers to securities that have been purchased partly with money borrowed from a broker.

    • It represents the net worth of the investor's account relative to the market value of the securities.

  • Initial Margin Requirement (IMR):

    • This is the minimum percentage of the initial investment that an investor must contribute from their own funds, rather than borrowing.
    • Set by the Federal Reserve under Regulation T.
    • Currently, it is set at 50\% for stocks, a level maintained since 1974 . This means an investor must initially pay for at least 50\% of the stock purchase price with their own money.
    • The maximum percentage amount an investor can borrow is calculated as: (1 - IMR) .

  • Equity:

    • In a margin account, equity is the investor's actual ownership stake.
    • Calculated as: Position~Value - Borrowing + Additional~Cash

  • Maintenance Margin Requirement (MMR):

    • This is the minimum amount of equity that must be maintained in the account, expressed as a percentage of the current market value of the securities.
    • If the equity falls below this level, the investor will receive a margin call.

  • Margin Call:

    • A notification from the broker requiring the investor to deposit additional funds or securities into their account to bring the equity back up to the maintenance margin level.
    • Failure to meet a margin call will result in the broker liquidating (selling) the position to cover the borrowed funds.

  • Condition for a Margin Call (Long Position):

    • A margin call occurs when: Equity / Market~Value \leq MMR
    • This can also be expressed as: (Market~Value - Borrowed) / Market~Value \leq MMR
    • The specific market value at which a margin call will occur for a long position is: Market~Value = Borrowed / (1 - MMR)

Example 1: Buying on Margin Calculation

An investor buys 100 shares at \$100 per share, for a total value of 100 \times \$100 = \$10,000 . The investor pays \$6,000 and borrows the remaining amount from a broker. Therefore, the borrowed amount is \$10,000 - \$6,000 = \$4,000 .

a) What is the initial percentage margin?
* Percentage margin is the ratio of the net worth (equity value) of the account to the market value of the securities.
* Initial~Equity = \$6,000
* Market~Value = \$10,000
* Initial~Percentage~Margin = (\$6,000 / \$10,000) = 0.60 = 60\%

b) The stock price declines to \$70 . What is the percentage margin now?
* New~Market~Value = 100~shares \times \$70/share = \$7,000
* The borrowed amount remains \$4,000 .
* Current~Equity = New~Market~Value - Borrowed~Amount = \$7,000 - \$4,000 = \$3,000
* Current~Percentage~Margin = (\$3,000 / \$7,000) \approx 0.4286 = 42.86\%

c) Assuming a Maintenance Margin Requirement (MMR) of 30\% , how far could the stock price fall before the investor gets a margin call?
* Using the margin call formula: Market~Value = Borrowed / (1 - MMR)
* Market~Value~at~Margin~Call = \$4,000 / (1 - 0.30) = \$4,000 / 0.70 \approx \$5,714.29
* To find the stock price per share: \$5,714.29 / 100~shares \approx \$57.14~per~share
* Therefore, if the stock price falls to approximately \$57.14 , the investor will receive a margin call.

Example 2: Rate of Return with and without Borrowing

An investor has \$10,000 and buys stocks at \$100 per share. The stock is expected to increase by 30\% in 1 year (ignoring dividends). The investor also borrows an additional \$10,000 at an interest rate of 9\% .

  • Scenario 1: With Borrowing (Buying on Margin)

    • Total investment amount = \$10,000 (investor's~funds) + \$10,000 (borrowed) = \$20,000
    • Number of shares purchased = \$20,000 / \$100~per~share = 200~shares
    • Stock price after 1 year = \$100 \times (1 + 0.30) = \$130~per~share
    • Value of shares after 1 year = 200~shares \times \$130/share = \$26,000
    • Interest paid on borrowed funds = \$10,000 \times 0.09 = \$900
    • Profit = (Selling~Price~of~Shares - Initial~Purchase~Price~of~Shares) - Interest~Paid
    • Profit = (\$26,000 - \$20,000) - \$900 = \$6,000 - \$900 = \$5,100
    • Investor's initial equity = \$10,000
    • Rate~of~Return = Profit / Investor's~Initial~Equity = \$5,100 / \$10,000 = 0.51 = 51\%

  • Scenario 2: Without Borrowing (Using only own funds)

    • Total investment amount = \$10,000
    • Number of shares purchased = \$10,000 / \$100~per~share = 100~shares
    • Stock price after 1 year = \$130~per~share
    • Value of shares after 1 year = 100~shares \times \$130/share = \$13,000
    • Profit = Selling~Price~of~Shares - Initial~Purchase~Price~of~Shares = \$13,000 - \$10,000 = \$3,000
    • Investor's initial equity = \$10,000
    • Rate~of~Return = Profit / Investor's~Initial~Equity = \$3,000 / \$10,000 = 0.30 = 30\%
    • Conclusion: Using margin amplified returns (from 30\% to 51\% ) because the stock price went up. However, it would also amplify losses if the stock price declined.

3.9 Short Sales

  • Purpose: Short selling allows investors to profit from an anticipated decline in a security's price.
  • Definition: A short sale involves selling shares that the investor does not actually own. Instead, they borrow these shares through their broker and sell them in the market. The investor then hopes to buy the shares back at a lower price in the future to