Stock Margin
Table of Contents
When an investor buys or shorts a stock on margin, they are using money from their broker. Simply stated:
- Buying stock on margin means the investor receives a loan from their broker, with the stock as collateral.
- Shorting stock on margin means the investor receives a loan from their broker, with the cash proceeds from the short as collateral.
What should be clear to you by the end of the presentation, is that the margin loan is very safe. Further, since the average investor doesn't know this, brokers are able to charge interest rates which are too high for their level of risk. Thus, margin lending is a lucrative profit source for brokerages.
Lastly, note market behaves differently in futures and other derivatives markets, and so what follows should only be applied to stock purchases.
1. Calculating Margin Percent
For what follows let:
- \(T\) be the transaction price (initial buy or sell).
- \(C\) be the current stock price.
- \(N\) be the number of shares
- \(IM\) be the initial margin percent.
- \(MM\) be the maintenance margin percent.
Margin percent is defined as:
\[Margin\ \% = \frac{Equity}{Market\ Value}\]
The only difference between a short and long position is how you calculate Equity.
1.1. Buying (Long) Stock
For a long position:
\[Equity = Market\ Value - Loan\]
where
- \(Loan = T * N * (1 - IM)\)
- \(Market\ Value = C * N\).
Substituting the appropriate numerator, we have:
\[Margin\ \% = \frac{(C * N - T * N * (1 - IM))}{C * N}\]
double long_margin_percent(double purchase_price, double number_shares, double initial_margin_percent, double present_price) { double loan_amount = purchase_price * number_shares * (1 - initial_margin_percent); double margin_percent = (present_price * number_shares - loan_amount) / (present_price * number_shares); return margin_percent; } printf("New margin percent is: %.2f\%\n", 100 * long_margin_percent(100, 100, 0.6, 70));
New margin percent is: 42.86%
Long Margin Percent Calculator
| Purchase Price: | |
|---|---|
| Number of Shares: | |
| Initial Margin: | |
| Current Price: |
Current Margin: %
1.2. Shorting (Short) Stock
For a short position we have:
\[Equity = Cash\ from\ Sale + Margin\ Deposit - Market\ Value\]
where:
- \(Cash\ from\ Sale = T * N\)
- \(Margin\ Deposit = T * N * IM\)
We thus have:
\[Margin\ \% = \frac{(T * N + T * N * IM - C * N)}{C * N}\]
double short_margin_percent(double sale_price, double number_shares, double initial_margin_percent, double present_price) { double K = sale_price * number_shares + sale_price * number_shares * initial_margin_percent; double margin_percent = (K - present_price * number_shares) / (present_price * number_shares); return margin_percent; } printf("New margin percent is: %.2f\%\n", 100 * short_margin_percent(100, 100, 0.6, 95));
New margin percent is: 68.42%
2. Margin Call
2.1. Maintenance Margin
To protect their loan, your broker sets a maintenance margin percent. If your percent margin decreases to the maintenance margin, this triggers a margin call. A margin call means you have to put in more cash to increase your margin, or your broker will close your position.
2.2. Calculation
To calculate the price at which we get a margin call, we simply set our margin percent calculations above equal to the maintenance margin, and solve for the new price.
2.2.1. Price Triggering Margin Call (Long)
Doing this for a stock purchase on margin affords:
\[Margin\ \% = \frac{(C * N - T * N * (1 - IM))}{C * N} = MM \Rightarrow\] \[C = \frac{T*N*(1 - IM)}{N(1 - MM)}\]
where C is the highest price at which you would get a margin call. To verify this formula is correct, you should plug the answer bank in to your margin percent calculation and ensure the new margin percent is equal to the maintenance margin.
Long Margin Call Calculator
| Purchase Price: | |
|---|---|
| Number of Shares: | |
| Initial Margin: | |
| Maintenance Margin: |
Margin Call Price: $
2.2.2. Price Triggering Margin Call (Short)
For a short margin position:
\[Margin\ \% = \frac{(T * N + T * N * IM - C * N)}{C * N} = MM \Rightarrow\] \[C = \frac{T*N*(1 + IM)}{N(MM+1)}\]
where C is the lowest price at which you would get a margin call. Again verify this formula is correct, by plugging the answer bank in to your margin percent calculation and ensure the new margin percent is equal to the maintenance margin.
3. Concept Questions:
If we added interest to the above calculations, would the price at which you get a margin call be higher or lower(long or short position)?
When would your brokers lose money?
If a stock has a higher volatility, would your broker would want to set the maintenance margin percent higher or lower?