Simulating Historical Returns Of Leveraged ETFs

by: Greg Hudson

Everyone hates leveraged ETFs over the long term.

But few have actually simulated their historical returns.

I have, and I'll show you how and what I've learned.

In my last article, I used a 30+ year historical simulation to demonstrate that leveraged ETFs can perform well over the long term, if they’re part of a balanced portfolio. For simplicity’s sake, I showed the impressive results of a simulated 50/50 mix of the ProShares UltraPro S&P 500 ETF (NYSEARCA:UPRO) and Direxion Daily 30-Year Treasury Bull 3x Shares ETF (NYSEARCA:TMF) (tl;dr 26% annual return over 30+ years with 65% max drawdown).

For whatever reason, I can’t find anyone else simulating the returns of leveraged ETFs over long time horizons. Most authors just look at their actual performance since inception, and the oldest leveraged ETFs started after the financial crisis, so everything looks rosy. Every blue moon, I find someone who has gone further back (cheers to Double Digit Numerics and RHS Financial!), but they are few and far between.

I’ve spent way too much time simulating the historical performance of a portfolio of leveraged ETFs, which will be the basis of further posts on the subject, but first I’d like to just lay out my approach so that no one is taking me on faith (also I'll offer a bit of candy at the end of this medicine). Also, it’s not that hard, and others should actually look at the historical facts before either decrying leveraged ETFs as unsuitable for the long term based on thought experiments and cherry-picked data or pumping them based on unsustainable performance during a bull market.

Let’s take the example (from my previous article) of simulating a 50/50 portfolio of UPRO and TMF. Each of these seek daily investment results, before fees and expenses, of 300% of the performance of their underlying indices (the S&P 500 and the ICE Treasury 20+ Year Bond index, respectively). Those fees and expenses are .94% and 1.05% respectively, although it’s not entirely clear if those are just management fees or include interest and transaction fees.

To simulate historical performance, we first need to identify proxies for these indices going back a long ways. Good old Vanguard has given us the Vanguard S&P 500 ETF Index Fund (MUTF:VFINX) and Vanguard Long Term Treasury Fund (MUTF:VUSTX), and we can download historical adjusted prices from Yahoo! Finance back to 5/19/1986 for both. To replicate the performance of UPRO and TMF, all we have to do is triple the daily returns and then subtract the daily expense ratios for UPRO and TMF (the annual expense ratios divided by 252 annual trading days).

Folks paying close attention may have noticed that I never tried to strip out the expense ratios these old mutual funds already levied against their indices. Effectively I just tripled their expense ratios and then also added the expense ratios for UPRO and TMF on top of that. This is partly because I’m lazy (expenses for these mutual funds have changed over time), but mostly because I want to be conservative, especially if there are hidden costs that UPRO and TMF don’t tell you about (primarily interest and transaction fees).

For what it’s worth, it doesn’t look like UPRO and TMF are hiding a mountain of fees outside their expressed expense ratios. From inception, both UPRO and TMF have outperformed my simulations by about 1% per year, which indicates the cushion I gave from tripling proxy expense ratios has been more than enough. I’m happy with that and the conservative estimates produced by my simulations.

Moreover, the few simulated portfolios of leveraged ETFs that exist generally assume daily rebalancing between components (in this case, UPRO and TMF). Daily rebalancing is not something I’ll ever do, partly because trading fees may ruin you, and partly because I don’t want to recalculate my balances every day. I’ve back-tested multiple strategies for rebalancing, but generally I’ve found that with a 3x leveraged portfolio, the benefits of rebalancing start to fade around 6-8 times per year. That’s still a lot compared to what’s required with an unlevered portfolio, but if you’re using Robinhood there are no trading fees, and if you’re using Motif, in which rebalancing is simpler and IRA’s are supported, you’re only looking at a $10 fee per rebalancing. Unless otherwise stated, my simulations are based on an initial $10,000 investment with rebalancing 8 times/year, each costing $10.

I promised some candy at the end of this article, so here it is. While a 50/50 portfolio of UPRO and TMF would have performed quite well over the last 30 years, one could do better (if they had perfect “future vision”).

Whether you optimize for Sharpe or Sortino, the best risk-adjusted portfolio of UPRO and TMF since 1986 was:

35% UPRO, 65% TMF

CAGR 25.4%
Max Drawdown 46.1%
Sharpe 1.04
Sortino 1.735

Not so risky for a 3x leveraged portfolio when you consider that the max drawdown was 46% (in 2009) compared with a 55% drawdown for the S&P 500 in that same year.

For a variety of reasons, my portfolio doesn't look like this. I'm scared about the great bond bull market ending, and I also don't like my returns being dominated by treasuries--it's psychologically hard to not participate in what everyone is talking about. That said, those are the historical facts! Do with them what you will. Stay tuned for future posts where I expand my aperture to other leveraged ETFs.

Disclosure: I am/we are long UPRO, TMF. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.

Additional disclosure: Historical returns are not predictive of future returns. My simulations use data from Yahoo! Finance, which contains errors.