# Long Term investment in leveraged ETFs not necessarily bad?

I have conducted very much research about leveraged ETFs lately. Most sources specifically say that these instruments are not meant for long-term investments and that they are very risky due to the daily recalibration. However, judging by the price of some leveraged ETFs like the SPXL it does seem like they have the potential to be good investments. Of course instruments of this kind should only be used in bullish phases. Nevertheless shouldn't a combination of ETFs like the SPXL for bull phases and the SPXS for bear phases yield superior returns? I have tried to estimate potential returns based on random variables in R. The code is as follows:

X = 0

ETF = function(L,r_avg,v,t){

for (i in 1:t)

{ if (i == 1) X = 1 * (1+ L*rnorm(1,r_avg,v))

else {if (i == t) return(X*(1+L* rnorm(1,r_avg,v)) else X = X* norm(1,r_avg,v)}

Given a leverage L, an average daily return r_avg, a volatility/variance v and a time period t, the function calculates the return of an investment under these circumstances. Of course the model is extremely basic. It only considers returns that can be modeled using the normal distribution and does not consider that there are extra fees for leveraged ETFs. However, in this model the leveraged investments generally outcompete non-leveraged versions even when the volatility is very high. This seems strange, since the sources that I have reviewed suggest that when volatility is high the leveraged funds will be bad choices due to the volatility drag. If someone could clear things up that would be great! Can leveraged ETFs really be long term investment vehicles? And if not, then what is wrong with my model?

• Why is the leverage factor $L$ absent in the "else" clause? Isn't leverage present in every period from 1 to t? Why the special cases? – noob2 Oct 9 '17 at 18:10
• Thats true right, was a bit hasty there. However in my R code I have it like that: X = X*(1+L*rnorm(1,r_avg,v)). – A.Pz Oct 9 '17 at 18:16
• @A.Pz What does this ETF do that's different from other leveraged ETFs? – John Oct 9 '17 at 18:25
• How do you mean? – A.Pz Oct 9 '17 at 18:33
• What makes you think you would get the opposite result than 100 other people who have done this simulation correctly? – noob2 Oct 9 '17 at 21:24