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## Leverage Ratio

The relation between risk and borrowing can be measured by the leverage ratio. The maximum leverage ratio calculates financial leverage if the trader’s equity position is equal to the initial margin requirement.

$$\text{Leverage ratio} = \frac{ \text{Total value of the position}}{ \text{Equity value of the position}}$$

$$\text{Maximum leverage ratio} = \frac{1}{ \text{Initial margin requirement}}$$

## Return on Margin Transaction

Calculating the rate of return on a margin transaction is the same as calculating the rate of return on an unlevered transaction; it simply involves one extra step to calculate and subtract out the margin interest paid. The rate of return should be calculated based on the initial equity investment, not the total purchase price of assets. Upfront costs such as commission should be included in the initial equity amount.

### Example of a Margin Transaction

A trader purchases $100,000 worth of a highly volatile stock at a leverage ratio of 2.5, receives a special dividend of$800 after six months, and sells the stock exactly one year after purchase at $200,000. The commission is$10 at purchase. The trader is charged 8% interest on the borrowed money.

To get the rate of return, we just have to find the profit (or loss) and divide it by the initial equity investment.

Let’s first calculate the amount of money the trader had to borrow in order to make this transaction.

We can find the equity investment by dividing the full $100,000 purchase by the leverage ratio of 2.5. $$\text{Equity investment} = \frac{100,000}{2.5} = 40,000$$ And the remainder has to be borrowed: $$\text{Borrowed amount} = 100,000 – 40,000 = 60,000$$ The amount that the trader will have to pay in interest over one year is the interest rate on the loan multiplied by the loan amount: $$\text{Interest paid} = 60,000 × 8\% = 4,800$$ Moving on to the profit calculation: $$\begin{array}{lr} \text{Sale Price} & 200,000 \\ \text{Purchase Price} & -100,000 \\ \text{Realized Gain (Loss)} & 100,000 \\ \text{Purchase commission} & -10 \\ \text{Dividend} & 800 \\ \text{Margin interest} & -4,800 \\ \text{Sale commission} & -10 \\ \text{Return} & 95,980 \\ \end{array}$$ To find the total initial equity investment, just take the$40,000 calculated above and tack on the small commission on purchase of $10: $$\text{Equity investment plus commission} = 40,000 + 10 = 40,010$$ Finally, we can calculate the rate of return on this trade: $$\text{Rate of return} = \frac{95,980}{40,010} = 239.89\%$$ ## Margin Call Price A margin call will take place when equity drops below the maintenance margin requirement. After the purchase of a security on margin, any changes in that security’s price will be reflected completely in equity. There is a simple formula that can be used to find the margin call price: $$\text{Margin call price} = \frac{ \text{Debt}}{1- \text{Maintenance quad margin}}$$ ### Example of a Margin Call Price You have been provided the following information: • Purchase price per share:$30
• Leverage ratio: 2.0
• Maintenance margin: 25%

Remember, the equity investment can be found by dividing the total purchase price by the leverage ratio:

$$\text{Equity investment} = \frac{30}{2} = 15$$

So, this trade involves $15 of equity and$15 of debt, and we need to find at what price a margin call would take place:

$$\text{Margin call price} = \frac{15}{1-0.25} = \frac{15}{0.75} = 20$$

## Question

What is a trader’s maximum leverage ratio, given an initial margin requirement of 40%?

1. 1.00
2. 2.50
3. 4.00

Solution

As shown above, the maximum leverage ratio is equal to 1 divided by the initial margin requirement.

$$\text{Maximum leverage ratio} = \frac{1}{0.4} = 2.5$$

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