Leveraged ETFs on the S&P 500 such as UPRO are leveraged on a daily basis so to test investment strategies we need daily data

we interpolate by simulating the days in between the month ends. We do this by generating a random walk with the required return and which has the required volatility as determined by fitting an EGARCH model to the monthly figures

simulated the prices for the 3x leveraged ETF UPRO. The UPRO simulation assumes annual fees of 1%. It is clear that the 3x leverage produces 3 times higher volatility and much higher return.

S&P 500 annualised return is 8.4%, UPRO is 20.4%.

Looks like we could have gone up to more than 10x leverage without doing worse than the unleveraged S&P 500. But high leverage is risky - at 5 or more leverage you would have been wiped out by the 1987 crash where the S&P 500 dropped by more than 20% in a day.

peak is in the same place - about leverage = 5.8

If leverage favoured DCA then we would have expected the peak to be at a higher leverage. A bit disappointing