Leverage Ratio

What is Leverage Ratio?
The leverage ratio refers to the ratio between the market price of the underlying stock and the market price of the warrant required to purchase one share of the stock. The formula is:

Leverage Ratio = Underlying Stock Price ÷ (Warrant Price ÷ Subscription Ratio)

The leverage ratio measures the magnification effect of "using small capital to control larger positions." A higher leverage ratio means higher potential returns for investors, but it also comes with greater potential losses.

The leverage ratio reflects the cost difference between directly buying the underlying stock and buying warrants to "control" one share. For example, if the leverage ratio is 10x, it means that with the capital required to buy one share of the stock, an investor can buy 10 warrants. In other words, investing 1,000 yuan in warrants can control a stock position worth 10,000 yuan. This shows the capital-amplifying ability of warrants but does not directly reflect the actual price movement ratio between warrants and the underlying stock (i.e., the magnification of investment returns). If investors rely solely on the leverage ratio to estimate potential returns, the results may be inaccurate.

Performance of Leverage Ratio
The appeal of warrants lies in their ability to amplify returns with minimal capital. Investors can achieve returns comparable to or even higher than direct stock investments with a smaller initial outlay. However, many investors confuse "leverage ratio" with "effective leverage ratio." What is the difference, and which one should investors focus on?

To test whether these two concepts are confused, consider this question:
Suppose there are two warrants for the same stock—Warrant A has a leverage ratio of 6.42x, and Warrant B has a leverage ratio of 16.2x. If the stock price rises, which warrant will have a larger price increase? Many might choose Warrant B. However, the correct metric to evaluate potential warrant gains is the effective leverage ratio, not the leverage ratio. Since the question lacks sufficient data, no definitive answer can be drawn.

Formula for Leverage Ratio:
Leverage Ratio = Underlying Stock Price ÷ (Warrant Price × Conversion Ratio)

The leverage ratio indicates the cost difference between investing in the stock and the warrant. For example, a leverage ratio of 10x only means the warrant costs one-tenth of the stock, not that a 1% rise in the stock will lead to a 10% rise in the warrant price.

Below are two call warrants with the same expiration date and implied volatility but different strike prices. The table shows that warrants with higher strike prices generally have lower prices and higher leverage ratios. However, if investors use the leverage ratio alone to predict warrant performance, the actual results may disappoint. For instance, when the stock rises by 1%, Warrant A (with a 6.4x leverage ratio) may only rise by 4.2% (not 6.4%), while Warrant B (with a 16.2x leverage ratio) may only rise by 6% (not 16.2%).

Effective Leverage Ratio
To estimate warrant price movements, investors should look at the effective leverage ratio, calculated as:

Effective Leverage Ratio = Delta × Leverage Ratio

The effective leverage ratio helps investors understand how much a warrant’s price may change when the underlying stock moves by 1%. Investors seeking higher returns should focus on this metric. However, it is important to note that the effective leverage ratio assumes other factors (e.g., implied volatility and market conditions) remain unchanged and only reflects short-term price movements. Therefore, investors should not assume that a warrant with a 10x effective leverage will always move 10 times as much as the stock.

Finally, investors should remember that the effective leverage ratio is a double-edged sword—it can amplify profits if the stock moves favorably but also magnify losses if the market moves against the position. Thus, investors should balance potential returns with risk exposure.

Calculating Leverage Ratio
Many investors trade warrants because of their financial leverage, which magnifies the price movements of the underlying stock, allowing investors to achieve returns comparable to or exceeding direct stock investments with less capital.

The formula for leverage ratio is:
Leverage Ratio = Underlying Stock Price ÷ (Warrant Price ÷ Exercise Ratio)

The leverage ratio reflects the cost difference between investing in warrants and directly buying the stock. For example:

• Stock price: 10 yuan

• Strike price: 8.5 yuan

• Call warrant price: 0.2 yuan

• Exercise ratio: 10:1 (numerical value: 0.1)

If an investor buys 1 lot (100 shares) of the stock directly, it costs 1,000 yuan. To control the same position (100 shares) using warrants, the investor must buy 100 × 10 = 1,000 warrants, costing 0.2 × 1,000 = 200 yuan. Upon exercise, the investor will hold 100 shares of the stock. Thus, the leverage ratio = 10 ÷ (0.2 ÷ 0.1) = 5x, meaning the warrant’s initial cost is only one-fifth of the stock’s cost. This shows that investors can control 100 shares with only one-fifth of the capital, which is why the leverage ratio is also called the "control ratio."

What is Leverage?
Leverage generally refers to the ratio of total assets to equity capital on a balance sheet. High leverage means financial institutions can achieve higher returns on equity during economic booms but face greater risks of significant losses when markets decline. Commercial banks, investment banks, and other financial institutions typically operate with leverage. Before the subprime mortgage crisis, U.S. commercial banks had leverage ratios of 10-20x, while investment banks averaged around 30x.