We are currently working on a version of the calculator to support two assets. Please check back later for updates.
The volatility metric employed in this calculator represents the annualized daily volatility of the underlying asset. This figure is derived by calculating the standard deviation of daily returns and then multiplying it by the square root of 252 (the typical number of trading days in a year) to annualize the value.
It's important to note that this approach to measuring volatility differs from the monthly volatility often displayed on backtesting websites such as portfoliovisualizer.com.
Additionally, the volatility used here is distinct from the VIX index. The VIX measures implied volatility derived from options, which is a different concept from the annualized daily volatility applied in our calculations.
In the context of leveraging, it is important to acknowledge that leverage is not without cost. Leveraged ETFs (LETFs) typically achieve their leverage through total return swaps. Within these swaps, there is an inherent "borrowing rate" that must be considered.
According to the prospectus of various LETFs, the borrowing rate is generally around 0.5% higher than the 3-month Treasury rate. This additional rate accounts for the cost of borrowing in the leverage process.
Furthermore, it appears that the leverage process in LETFs is not entirely efficient. The exposure of LETFs to swap interest rates tends to exceed the actual leverage ratio slightly. For every unit of leverage, the interest rate exposure tends to be marginally higher.
These assumptions about borrowing rates and leverage efficiency are integrated into our calculator. For those interested in a more detailed discussion, a link to an in-depth analysis on the subreddit r/LETFs is provided.
The assumptions used in our calculator regarding the spread and efficiency associated with LETFs have been validated using real data from LETFs that have been in existence for over 15 years.
For the purpose of our calculations, the expense ratio is assumed to be 0% when leverage is at or below 1. This assumption is based on the fact that stocks typically do not carry any expense ratios, and most unlevered ETFs that track popular indices have negligible expense ratios.
As leverage increases, the expense ratio is presumed to rise linearly at a rate of 0.5% for each additional unit of leverage. Consequently, at 2x leverage, the expense ratio is assumed to be 0.5%; at 3x leverage, it increases to 1%; and at 4x leverage, it reaches 1.5%, continuing in this pattern.
This linear increase in the expense ratio with leverage is grounded in the observation that most triple-leveraged ETFs (3x LETFs) maintain expense ratios in the vicinity of 1%. Leverage levels below 3x can typically be achieved by holding a mix of 3x leveraged ETFs and standard ETFs (which have negligible expense ratios).
In the future, we plan to enhance our calculator to allow users to customize expense ratios at different leverage points.
In the context of Leveraged ETFs (LETFs) which utilize total return swaps for achieving leverage, dividends play a significant role.
It is essential to include dividends when calculating the Compound Annual Growth Rate (CAGR) – denoted by red dots in the calculator. This inclusion ensures that the CAGR reflects the total return of the unlevered fund, not just the index return.
Accounting for dividends is particularly important because it provides a more comprehensive view of the investment returns, encompassing both the price appreciation and income generated through dividends. This approach aligns with the total return perspective, which is a more accurate representation of an investor’s actual experience.
The mathematical foundation of our calculator is based on rigorous academic research. Specifically, the methodologies and formulas are derived from a paper and a thesis available at provided links.
It is crucial to note that the authors of these academic works are not affiliated with our website. Their research has been utilized to ensure that the calculations and models employed in our calculator are grounded in sound mathematical principles and academic rigor.