Modelling 2x S&P500 ETF for historical periods before ETF inception

I am trying to model 2x and 3x leveraged ETFs (SSO, UPRO, etc.) to generate historical data before the inception of those funds.

I thought it would be simple: I'm tracking the change to ^GSPC, multiplying it by the factor of x2 and should be getting something close to the actual NAV (or closing price) of SSO before the daily expense fees.

I am seeing something strange: that, for the first years the ideal (no fees) synthetic SSO performs better than the actual fund. However, in more recent years the actual SSO perform way better than the ideal (no fees/expenses) synthetic fund.

How can it be?

How can I model the ETF so it matches the actual fund closely?
 

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I am trying to model 2x and 3x leveraged ETFs (SSO, UPRO, etc.) to generate historical data before the inception of those funds.

I thought it would be simple: I'm tracking the change to ^GSPC, multiplying it by the factor of x2 and should be getting something close to the actual NAV (or closing price) of SSO before the daily expense fees.

I am seeing something strange: that, for the first years the ideal (no fees) synthetic SSO performs better than the actual fund. However, in more recent years the actual SSO perform way better than the ideal (no fees/expenses) synthetic fund.

How can it be?

How can I model the ETF so it matches the actual fund closely?

Here are the graphs demonstrating the results I'm getting
 

Attachments

  • SSO-vs-regression-synth-vs-ideal-synth.PNG
    SSO-vs-regression-synth-vs-ideal-synth.PNG
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I am trying to model 2x and 3x leveraged ETFs (SSO, UPRO, etc.) to generate historical data before the inception of those funds.

I thought it would be simple: I'm tracking the change to ^GSPC, multiplying it by the factor of x2 and should be getting something close to the actual NAV (or closing price) of SSO before the daily expense fees.

I am seeing something strange: that, for the first years the ideal (no fees) synthetic SSO performs better than the actual fund. However, in more recent years the actual SSO perform way better than the ideal (no fees/expenses) synthetic fund.

How can it be?

How can I model the ETF so it matches the actual fund closely?

The second option that comes to mind (the first being asking "that guy"--assuming "that guy" hasn't already explained what he did in that link you posted) would be to plug the data into a machine learning app and letting it figure out the missing data. Keep us posted.
 
The second option that comes to mind (the first being asking "that guy"--assuming "that guy" hasn't already explained what he did in that link you posted) would be to plug the data into a machine learning app and letting it figure out the missing data. Keep us posted.
A very useful response. Surely this super-duper wonder-AI app will model everything for me!
 
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