How We Can Backtest Leveraged ETFs All the Way Back To 1885
Leveraged ETFs on the S&P 500 are a relatively new phenomenon. ETFs as a whole are.
The first ETF on the S&P 500 was launched in 1993. The SPDR® S&P 500® ETF, also called SPY.
Therefore backtesting levereaged ETFs is much more complicated than it first may seem.
On this page we explain our methodology which allows us to accurately backtest leveraged ETFs all the way back to 1885.
How We Simulate Leveraged ETF Returns
Let's look at results first. The following charts show how our simulations are up to par with real world data. Afterwards we explain our methodology.
Our 2x Leverage Simulation vs Real SSO Data
Our 3x Leverage Simulation vs Real SPXL Data
Our 3x Leverage Simulation vs Real UPRO Data
Our 2x Leverage Simulation vs Real SPUU Data
Our 3x Leverage Simulation vs Real 3USL Data
Inaccurate Simulations for non US based ETFs
Our 2x Leverage Simulation vs Real DBPG Data
Inaccurate Simulations for non US based ETFs
How it all works and why it's not as simple as it seems
Simulating Leveraged ETF Returns
Now that we have a complete dataset for the S&P 500 Total Return Index going back to 1885, we look into how we can simulate the returns of leveraged ETFs.
To do so we need to account for various factors, including:
- daily rebalancing effects
- management fees - Total Expense Ratio (TER)
- borrowing costs
- additional costs such as spread
Daily rebalancing
Leveraged ETFs are rebalanced daily to maintain the leverage ratio. This means that the value of the ETF will fluctuate based on the daily changes in the S&P 500. This sounds very fancy and complicated, but the math is very simple:
leveraged return = 2 * (S&P 500 return)
This means that if the S&P 500 goes up by 1% today, the leveraged ETF will go up by 2%. Then we simply do this for each day in our dataset. For 3x leveraged ETFs we simply replace the 2 with a 3.
Management fees - Total Expense Ratio (TER)
The TER is the management fee that the ETF issuer charges to manage the ETF. It is deducted from the value of the ETF daily and is just a tiny bit more complicated to account for:
leveraged return = ((1 - TER) / trading days per year) * (S&P 500 return)
This means we simply apply the TER to the value of the ETF daily.
But beware: trading days per year vary. Especially if we go back further in time.
We got that covered. Since we have the daily data avaialble, we can simply count the number of trading days for each year from our dataset.
Borrowing costs
Now this is where it gets interesting. We work on the assumption that leveraged ETF providers are able to borrow money at the Fed rate. Or often referred to as the risk-free rate. Luckily, the FRED API has us covered. We can take the historical rates and apply them accordingly. We use the Federal Funds Effective Rate for this.
Additional Costs
There are some additional costs that are not immediately obvious. The biggest impact usually come from the swap agreement fees which are paid to an investment bank such as Goldman Sachs.
To account for that, we apply additional daily costs of ~0.004%. That is about 0.90% per year. The value is then multiplied by the leverage factor to account for increasing costs with higher leverage
We get to this value by reading the ETF's prospectus and then testing different values and comparing the results to real data. We also use a value that slightly "underperforms" the real data to make sure that our backtests are more conservative and trustworthy.
Improving Our Simulations
Since the markets are always changing and delivering new data, we can consistently improve our simulations. This includes recalibrating simulation parameters and cost assumptions to minimize tracking differences. We strive to do so at least once a week.
If you still have questions, feedback or ideas to improve our simulations, please let us know.