Oops, the upro is based on total return, not price. Bloomberg adjusts upro price history for this payout. So the correct comparison is with the S&P 500 total return index. The cumulative total return of the s&p 500 (25 jun 2009 to 9 feb 2012) is 55.04%. The cumulative total return of holding upro over the same time frame is 159.11%. Three times the S&P return is 165.12%, so the upro lagged the target by 6% or about 2% a year, corresponding to ‘fees and expenses’. The choice of time interval is important. If the market is down or only up modestly over the given interval, the upro will more significantly lag the target of 3 times the S&P 500 total return.

Note this leveraging factor works both ways. The UPRO significantly underperformed the S&P*3 during last years selloff.

To mimic a true triple leveraged investment, you would continually sell some upro over a bull market otherwise your original capital investment would become too highly leveraged. As you gradually withdrew funds in a bull market, your original capital would be returned and therefore not at risk, while you would continue to participate in the upside. When a big selloff occurs, you would buy more upro at the lower price with the cash you have withdrawn and play the game again. A very interesting option to consider.

If you follow Chang and Mandhavan’s (2009) analysis it would suggest that a -3x ETF has a higher expected decay than a 3x ETF as their exponential decay expression has a term -(x^2-x)*sigma^2.

Hi Jev, Thanks for visiting my site. Your Quantum Blog site looks very interesting as well. I’ll try out some of the Matlab code.