Rebalancing Act

A first key finding that we have in the paper, is actually very consistent with what we see here from the adviser community. The key finding is that tolerance band approaches, do tend to be a little bit better, be a little bit more efficient at facilitating rebalancing than pure set frequency calendar based approaches. So very good to see here that the findings of the paper seem to be consistent with what a nine out of 10 responding firms here seem to be doing in practice already. It's good to begin with a framework and the framework that we think is appropriate for rebalancing decisions, essentially boils down to a cost benefit analysis. And the costs essentially arise from the nature of rebalancing as a transaction, right? So if equities fall sufficiently far below my targeted equity allocation, well, I have to buy back into equities and sell something else. Maybe sell bands to offset the equity purchase. Conversely, if equities exceed my specified tolerance, well, I have to sell equities and buy bands. So there's a transaction element which translates into costs that can take different forms for different investors. And then of course, what are you getting for the cost that you're incurring? There are benefits. And the key benefit of rebalancing is that you keep your portfolio on track. So the goal or the tool of rebalancing can be used for making sure that your portfolio stays aligned with what it's intended to do for you. So with your goals, with your risk tolerance, with your preferences. And that extent to which the alignment is, or isn't there, we measure it by looking at the tracking error of a given portfolio, given rebalancing method relative to the target portfolio. But you see here if you just compare the steady 60% target line in the middle to where the teal or turquoise line is, at any point in time that at least up until August or so, your portfolio did in fact look quite different from what you were targeting 60/40, or maybe what you thought you were holding the 60/40 portfolio. So let's bring in the first rebalancing choice or method that does rebalance as opposed to the one that we just had, which didn't rebalance over the course of 2020. And this is a method that rebalances every month. So in some ways the other extreme here, we're using monthly data. So, each one of these arrows symbolizes a rebalancing event. So here for example, you would have also of course had the equity market downturn, the decrease in your equity weight, but at each month end, you rebalance back to 60% in equities and you see that over the course of the year that yellow line, so my effective weight and equities under monthly rebalancing, would have stayed quite a bit closer to target. What would have happened in 2020 with that same 60/40 portfolio, under a 5% tolerance band. And that's the orange line I'm showing here. So again, equities would have trended down, the equity weight in the portfolio would have also fallen as low as 53%. But at that point it would have exceeded on the downside, my 5% tolerance, which specifies that if equities fall below 55% of the portfolio, so five percentage points from the target of 60%, I take things back to target. I rebalance, and again, this is symbolized here illustrated by this arrow. And then you see one other rebalancing transaction on the other end on the upside, where after a couple of good equity market months, you could say, equities exceeded 65% of the overall portfolio. So again, deviated by more than the stipulated 5% of the tolerance. And so I am selling out of equities and buying into bands and thinking things back to target here a second time. And so what you see here is a slightly higher deviations. Again, if you compare the orange line here to the target of 60% and to some of the other approaches, but a lower rebalancing cost. Right, so again, it's that trade-off and action only to rebalancing events as opposed to 12 with monthly rebalancing. But on the other hand, or the other side of that, is that you at times did look quite a bit different from the targeted 60/40 allocation. Something that pops out when you look at the orange line here, right? It's, you know, in some ways with hindsight this looks like it did adjust right, all right? You bought back into equities at the end of March and then sold out here after a couple of good equity months maybe sold high, bought low. But in the paper, and this is a second key finding. We do not find a reliable link between different rebalancing methods and expected returns. So in other words, rebalancing to us based on the study that we just published not a tool to increase expected returns, but instead a tool to, again, keep your portfolio aligned with your goals, with your intended allocation. What happens when I exceed my tolerance? So what type of rebalancing is triggered when I exceed my tolerance band? And the two main types that we study are one rebalancing back to targets. So here a again, hypothetical example suppose my equity allocation in that 60/40 portfolio the equity weight went up to 67%. Time to rebalance, if I have a 5% tolerance band. And in rebalancing to target very simple as the name implies I'm taking things back to 60%, which is my target 60/40. So I'm moving 7% of weight here, 7% turnover. And alternative way that we study in the paper and also here today, is to rebalance to bound. Which means we rebalance back, not all the way to target but instead only to the nearest edge of the tolerance band which in this case would be 65%. That's a 5% tolerance where at 67, the nearest edge of that tolerance band is 65. In which case I'm moving 2%, of turnover two percentage points. The yellow observations here. So the two target we rebalancing approaches that use tolerance band, sit to the bottom to the left of the calendar based approaches, right? So for a given turnover, given costs, I tend to incur less tracking deviation with the tolerance band approaches. Conversely for given tracking error I tend to incur less costs lower turnover for the tolerance band approaches and that's an efficiency gain. Okay, and then let's bring up the last set of candidates here. Rebalancing methods that again, specify tolerance bands but now rebalance to bound. And what we see here, seen through this lens of the trade-off between turnover costs and tracking error is that the set of orange dots here. So these were balanced to bound rules are a little bit more efficient still. So allow for cost mitigation a little bit further even than is the case for the target tolerance bands or conversely allow for tracking error mitigation for given costs a little bit further. And again, we see that because as a group, these orange observations sit to the bottom and to the left. So closer to this optimal bottom left point here then to target tolerance bands. What I'm showing you here is all the 14 rules that we just plotted. So 4 calendar based ones and in 5 each for the two target and two bound tolerance bands. Returns average monthly returns. Over the 40 years that we study 1979 to 2019. And yeah, what jumps out here I think is that all of these bars are basically very similar, right? Very similar returns here. No really discernible difference all in the neighborhood of 87, 88 basis points per month on average. And that ties back to what I mentioned earlier. No reliable link, no evidence for a reliable relation between these different rebalancing methods and expected returns. Let's take a look and expand the asset allocation as you mentioned, Aaron to a global asset allocation. And not only global, but also containing more than the two components that we studied in case study one. So what we have here in particular are six components. Four on the equity side, and then four are bands fixed income we split it into government and credit in equal proportion. If you add these percentage up here, you get the 60/40. And then the second thing we're doing is that we're also studying one additional way of specifying these tolerance bands and that we call that way the tiered rebalancing approach. But then there's a second tier that kicks in. If the equity fixed split is not out of balance. And that is to look separately within equities and within fixed income to check whether anything within these portfolio parts or sleeves is out of balance. And if so, rebalance only in those portfolio parts. And to illustrate here and a similar manner to how we illustrated for case study one the difference between rebalancing to target and to bound let's take a look at how it works. The second tier, again kicks in if there's no full rebalancing. So suppose you're at 64% inequities. So within your 5% tolerance. So it could be the case, for example, that let's say within equities, small caps outperformed large caps but to some extent that's an offsetting movement, it may not be enough to move your equity allocation to move the equity fixed split out of balance. But what happens is that you're not overweight small caps relative to your target and underweight large caps relative to your target. So you might wanna think about addressing that imbalance specifically. And to illustrate that in the bottom right here, hypothetically we're looking at just two equity components for now two equity components at 50 50 each. And one of them, in my example that might've been small caps for example, is now at 57%. So within equities, it's exceeding that 5% tolerance. In which case I can then rebalance either all the way back to target 50% or 55% to bounce. We see a similar trade-off emerge between approaches that rebalance less frequently. Like annual here, for example for the calendar-based rules and more frequently like monthly between turnover and tracking error. And then as before, and we see that the tolerance bands are a little bit more efficient, they sit to the bottom to the left. and then let's bring up our new set of candidates here. The new set of rules, tiered rebalancing. And we pick up a specific example here, the 10%/10% rule. So this would be a rule that says I have a 10% tolerance around my equity fixed split but then if that's not the case, I'm also checking within equities and separately within fixed income if anything is off by more than 10%, and if so, I rebalance just that part of the portfolio. And we see an additional efficiency gain. You can kind of see it two ways here, one is that again, the set of orange observation sits to the bottom, to the left of the other methods here. The tiered rules do seem to be the ones that give you that best trade-off between tracking error and turnover. Good, time to summarize Yes, yes. Some key findings here. Great key points. So the first one is, again, that trade-off I think is the key trade-off, a key framework between tracking error on the one hand. So how different does my portfolio look? And what's my comfort zone around that. And then the cost it takes to maintain that alignment to keep the portfolio in track. We then had the first finding that a calendar bend rules can be convenient of course, easy, simple, and convenient. But do tend to be the least efficient when evaluated through that lens of tracking error versus turnover costs. And then we saw that within different tolerance bands certain specifications tend to work a little better still than let's say, simple to target choices. In particular, we consider two boundary balancing and we completed at, yeah, looking both across asset classes as well as within asset classes. So these tiered approaches. And then we looked at rebalancing choices and their interaction with asset allocations just now. And finally also, yeah. I think a common theme that is not just about rebalancing or common question, but where rebalancing can have an impact is that choice between having an integrated solution investment solution versus one that has many components.