## 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.

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

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

## 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. $$Equity \quad investment = \frac{100,000}{2.5} = 40,000$$ And the remainder has to be borrowed: $$Borrowed \quad amount = 100,000 – 40,000 = 60,000$$ 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: $$Interest \quad paid = 60,000 × 8\% = 4,800$$ Moving on to the profit calculation:  Sale Price$200,000 Purchase Price $100,000 Realized Gain (Loss)$100,000 Purchase commission -$10 Dividend$800 Margin Interest -$4,800 Sale Comission -$10 Return $95,980 To find the total initial equity investment, just take the$40,000 calculated above and tack on the small commission on purchase of $10: $$Equity \quad investment \quad plus \quad commission = 40,000 + 10 = 40,010$$ Finally, we can calculate the rate of return on this trade: $$Rate \quad of \quad return = \frac{95,980}{40,010} = 239.89\%$$ ## 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: $$Margin \quad call \quad price = \frac{Debt}{1-Maintenance quad margin}$$ ### 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:

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

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:

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

## Question

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

A. 4.00

B. 1

C. 2.50

Solution

The correct answer is C.

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

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

Reading 44 LOS 44f:

Calculate and interpret the leverage ratio, the rate of return on margin transaction, and the security price at which the investor would receive a margin call

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