Does threshold rebalancing work with leveraged funds?

Heard something that caught my ear which launched me onto a bit of a deep dive with Tesfolio this evening. Thought I would share here.

I’ve long been wondering about the best rebalancing strategy for different portfolios, and a recent question from John on Risk Parity Radio really kicked this question into gear. Here is the clip, if you want to listen, from Episode #445. FYI: it is cued up here for Mary reading the question, which has two parts though I’m interested here in just the first. Frank’s answer finishes by 28:35.

The gist of the question is that John was messing around with leveraged funds on Tesfolio and wondering what the right rebalancing strategy was for a portfolio with leveraged funds in it. Using one with a 6% allocation to a simulated version of TQQQ (more on that later), he found that a yearly rebalancing schedule was better than a 20% relative band strategy (aka “threshold” strategy). This was contrary to his expectations. John referenced a paper by Gobind Daryanani which, incidentally, has been in my “must-read” list for months after I saw it referenced in this article by Michael Kitces about rebalancing strategies.

Anyway, Daryanani finds that a 20% tolerance band was the best in his tests; John found that yearly rebalancing worked best, better than the 20% band, and better than other tolerance bands he tested. John concludes by proposing that a 20% tolerance band may work best for non-leveraged assets but that leveraged funds could be better on a calendar-based approach.

My Hunch

That got me thinking. My hunch: what if the 20% tolerance band is just too frequent? Perhaps what is happening here is that TQQQ is getting “knee-capped” too often, and sold off in pieces even as it climbs. We’ve been in a great market for TQQQ and UPRO since they were launched - has the 20% band just meant that its momentum has been cut off too early?

Of course, I had to see myself, and I love how John (and Frank) shared the link to the Testfol.io results.

TL;DR: Looks like John found a particular example where annual rebalancing was better, but it looks like an event, not a pattern.

My Investigation

John’s test is here and was my first stop. John’s right - compared to the 20% tolerance band rebalancing, yearly rebalancing resulted in 118 basis points of out-performance in terms of CAGR, lower max drawdowns and a lower Ulcer Index. It’s a pretty good sized data set (back to 1995), all things considered and indeed, the results for the 60/40 portfolio tilt more in favor of the tolerance band approach. Ooooh… intriguing.

Going to the rebalancing stats, the difference in number of rebalancing events really stands out: 30 for the yearly rebalancing and 286 times (!!!) for the tolerance band approach. So, I’m thinking, yes, that’s just kneecapping the portfolio, and the longer time between events gives the yearly rebalancing approach more time to grow.

However, and in keeping with John’s point, if you put up the tolerance band to a higher number to bring the number of rebalancing events closer to 30, you see some improvement, but it is still worse than annually. After some trial and error, I found that a tolerance band of 68% resulted in 30 rebalancings, as well. Again, the annual plan was better, and surprisingly, the 68% band did worse than the 20. This means my hunch about knee-capping the leveraged fund wasn’t borne out here. Interesting asides: at the 68%, 29 of the 30 rebalancings were because the leveraged fund hit the threshold, whereas with the annual rebalancing, mostly the leveraged fund is out of whack, but not always. Also, 13 of the rebalancings in this case were between 1999 and 2002, and the pace has been slower in the past decade or so.

Next Steps

Then, I really started playing with the test.

Noticed first off that John is using a simulated version of TQQQ (QQQSIM?L=3&SW=1.2&E=0.9, iykyk). I wondered if the parameters used to replicate TQQQ to give it a longer back test made a difference.

Indeed, they do. When I just put in the actual TQQQ for John’s replicated version, I got a different story. In this version, the 20% tolerance band rebalanced was better than the annual strategy - by just a little bit, but still. Putting in the actual TQQQ did truncate the test by 15 years, so back to 2010 only.

Perhaps, this is then really just a question of the timeframe we are looking at. So, I went back to John’s simulated version of TQQQ and set a more recent backtest, just back to August of 2015. In this test, I added in another portfolio, with a 50% tolerance band so that I could get the number of rebalancing events to equal the ten in the annual plan. Interesting here: the 20% strategy was the best, followed by the 50% plan, with the annual plan the worst of the three. Not by much, but still.

Hmmm, but if that’s the way it was from 2015, what about another ten year period, from 1995 to 2005? In this one, the annual plan won hands down. The 50% band proved to not be very strict in this period - there were 24 rebalancing (and all of them due to the simulated TQQQ being out of whack). What about 2005 to 2015? Another win for the annual rebalancing strategy. Seems like whatever was going on with the leveraged fund to make more frequent rebalancing sub-optimal has to do with the performance in those early years.

Lastly, I just wondered if this was about leveraged funds, or just the idiosyncratic behavior of TQQQ. I then substituted “VNQ” for “QQQ” in the code for the asset in order to replicate the fund DRN, a 3x leveraged real estate fund analogous to TQQQ’s relationship to QQQ. This turned out to be an interesting test - the portfolio with the 3X leveraged version of VNQ was better when rebalanced according to the 20% tolerance band, though in the same time period (back to 2004), the 3X leveraged version of QQQ was better when rebalanced annually. That tells me it's not such a leveraged fund phenomenon, but rather the specific path that the simulated QQQ took over the years.

Wrapping Up

It doesn’t look like my hunch was correct, but other tests revealed some reasons to be cautious before assuming that a tolerance band strategy can’t work with leveraged funds. First, it looks like it could be about how you set up the conditions of a simulated leveraged fund - the test looked one way with a simulated TQQQ and another way with the actual TQQQ. Of course, using the actual TQQQ changed the time period, leading to the second observation: it may really just depend on the time period. It worked one way from 1995 to 2015, but has worked differently from 2015 until now. Third, it seems like these results could be true for a leveraged version of QQQ, but not for other leveraged funds, like by a simulated version of VNQ. In that case, we should be circumspect about generalizing for all leveraged funds.

Another big thing to consider: it’s one thing to see these results in hindsight, but another to say definitively what to do in the future. Seems like the whole topic is a bit too murky to see anything clearer ahead.