What is the rebalancing bonus?

For my next post, I’m planning on having a look at how often you should rebalance your portfolio. i.e. how often you should buy or sell your investments to bring them back to your target weights.

But as I was writing, I realised before we can figure out the answer, we first need to understand something called the rebalancing bonus.

What is the rebalancing bonus?

Simply put, the rebalancing bonus represents the difference in returns between a rebalanced and an un-rebalanced portfolio. It’s the extra return you receive for rebalancing your portfolio.

It’s best explained by starting with an example.

Let’s say we have 2 asset classes, Pokémon cards and dinosaur fossils.

If anyone doubts these are investable asset classes, I refer you to the fact that a single Pokémon card can sell up to £200,000, and this Triceratops skull is currently being offered to investors at $25 a share for a valuation of $285,000.  

So here are the fictional returns for these two investments over two years:

They both have the same annualised return of 3.9%, after having one good year and one bad year each.

But look what happens if we have one portfolio which holds a 50/50 split of both assets and doesn’t rebalance, and compare it to the same portfolio which rebalances after one year:

The portfolio which doesn’t rebalance has the same annualised return as the average of the two asset classes – as we’d expect.

But the portfolio which does rebalance after one year has a 1.1% higher annualised return than the average of the asset classes.

The assets haven’t generated any extra performance, it’s a return generated by the act of rebalancing. This is the rebalancing bonus.

And it’s consistent no matter how many years you extrapolate for:

Cumulatively, that 1.1% a year extra return can make a huge difference to your portfolio. Compound that up and your Pokémon card/dinosaur fossil strategy would make you an extremely wealthy nerd.

Now let’s move a bit closer to the real-world.

The rebalancing bonus with stocks and bonds

It’s possible to earn a rebalancing bonus through rebalancing between stocks and bonds.

Let’s say you end up in a situation where your stocks have drifted to a larger weight in your portfolio than you’d like, and you rebalance back to target weights. Then disaster strikes, and there’s a market crash where stocks fall 50%. By having rebalanced back to having a higher weighting in bonds, you were more protected from the crash, and will have generated a higher return then you would’ve had you not rebalanced.

Congratulations, you’ve earned a rebalancing bonus.

That makes sense for that single time period. This is the equivalent of our first Pokémon card/dinosaur fossil example. Our Pokémon cards increased in value, we rebalanced away from them, and we weren’t hurt as much when the great Pokémon crash of Year 2 hit us.

Now the puzzling bit.

If you repeatedly rebalance away from stocks towards bonds over time, as any normal rebalancing method would do, then most of the time you’ll be hamstringing your returns. This is because you’re consistently rebalancing away from the asset class with a higher expected return, towards the asset with the lower expected return.

So where’s the rebalancing bonus there?

There isn’t one.

So why do we get the same rebalancing bonus in our first Pokémon card/stock market crash scenario, but when we extend that thought experiment out longer term, our Pokémon card/dinosaur fossil strategy still earns that 1.1% rebalancing premium, whereas our stock/bond rebalancing strategy results in lower returns?

The answer: a rebalancing bonus only exists under a particular set of circumstances.

To investigate when and why the rebalancing bonus works, we turn to the grandaddy of the rebalancing bonus, William Bernstein.

When do we earn the rebalancing bonus?

Bernstein has two seminal articles on the rebalancing bonus: one titled ‘The Rebalancing Bonus: Theory and Practice’ and a follow-up article titled ‘When Doesn’t It Pay to Rebalance?’.

They’re both excellent articles – crammed with enough stats for me to be confident he knows what he’s talking about, but also with explanations clear enough that I can understand the conclusions.

The first article deals with what the rebalancing bonus is, and how it can be predicted (ex-post, of course – he can’t predict the future) using a formula, if we know the risk and correlation stats for any two assets.

Here’s a brief summary of his findings:

• The amount we can expect to earn from the rebalancing bonus for any asset pair is the difference between its mean variance and covariance. 
• The rebalancing bonus is predictable enough to be approximated by a formula:
  • • The rebalancing bonus = X₁X₂(Var₁/2 + Var₂/2 – Covar₁,₂)
    • Where X = the percentage held of each asset
• In plain English, that means we can expect to earn a higher rebalancing bonus if:
  • • The volatility of the assets is high, and
    • The correlation between the assets is low
• In terms of how often Bernstein found it was best to rebalance in order to capture this bonus, he concluded that “No one rebalancing period dominates. Monthly rebalancing was best in three cases, quarterly in four, and annual in three”.

The second article then tries to figure out under which conditions need to be right in order to benefit from the rebalancing bonus.  

He starts off with an example comparing the rebalancing bonus potential for stocks and bonds – emphasis is mine:

“The annualized return on common stock for the period 1926-94 was 10.19%, and for long term corporate bonds over the same period 5.51%. Rebalancing this portfolio on an annual basis to maintain a 50/50 mixture yields a return of 8.34%. If one had put equal amounts of money into stocks and bonds on January 1, 1926, and had not rebalanced or paid taxes, then the long term return would have been 9.17%. In this instance the nonrebalanced portfolio has a higher return than the rebalanced portfolio.

This is because over the 69 year period studied the significantly higher stock return overwhelms the bond return; for the last 40 years of the period the unrebalanced portfolio consists of greater than 90% stock. Thus the higher return of the unrebalanced portfolio comes at the cost of a much higher risk than the rebalanced one.”

Now we’re making some progress.

We earned a rebalancing premium in our long-term Pokémon/dinosaur fossil example because both assets had the same annualised returns. But stocks and bonds don’t.

Because stocks have a much higher expected return than bonds, our long-term expected rebalancing bonus is negative, because we’re constantly rebalancing away from high-expected-return assets into low-expected-return assets.

So, the question Bernstein then starts digging into is how dissimilar to asset returns have to be before it no longer pays to rebalance?

To save you some reading, the answer is “it depends on how highly correlated the assets are”.

If the two assets have a correlation of zero (i.e. returns for both are random), if they have the same annualised return of just over 10% (0.83% per month), and volatilities of just over 17% (5% per month), then Bernstein found that over 10 years their returns need to diverge by less than 8% annualised in order for a likely rebalancing bonus to be had.

That’s a lot of assumptions, though.  

Here are the breakeven points for varying levels of return/risk assumptions (expressed as monthly return/risk stats – along the top of the table), and time periods (down the side) for two assets with zero correlation:

Source: William Bernstein

Another example from the table to bring home his point – if the return gap between two noncorrelated assets with returns of 1% per month (over 12% a year) and risk of 10% per month (over 34% per year) is less than 5.5% annualized over 50 years, or less than 13% over 20 years, or less than 17% annualised over 10 years then it pays to rebalance. If the return gap is greater, it does not.

Here’s the big question – what happens when the correlation is not zero?

Bernstein’s answer: “A good rule of thumb is that the break even point is decreased by one third by increasing the correlation from 0.0 to 0.5.”

Given the vast majority of assets which have similar returns also have positive (sometimes very positive) correlations, we’ll need to take a chunky haircut on those break even points, meaning the rebalancing bonus becomes more difficult to capture.

One final point Bernstein makes is that transaction costs will result in further downward adjustment, and taxability may completely eliminate any rebalancing benefit at all.

To conclude, the rebalancing bonus of a two asset portfolio is:

1. Increased by the volatility of each asset,
2. Increased by a decreased correlation between each asset,
3. Decreased as the difference in long term returns increases, and
4. Decreased further if this return difference is maintained over a long period of time,
5. Decreased further the higher transaction costs are incurred,
6. Decreased further the higher taxes are incurred.

We’re now at a point where we’ve got a pretty good idea of what the rebalancing bonus is, and why it exists.

But so far this has mostly been theoretical.

Let’s see a real-world example.

Evidence of the rebalancing bonus in the real world

I’m shamelessly plagiarising an example found by the user ‘Vineviz’ on the Boglehead forums here. It’s such a great and unlikely example I couldn’t help but steal it.

Vineviz found that from January 1999 to March 2020, two Vanguard funds investing in very different stocks had identical CAGRs.

The two funds are Vanguard Emerging Markets Stock fund (VEIEX) and Vanguard Small Cap Value Index fund (VISVX), each of which has had a CAGR of 7.10% over the time period and a very low correlation of annual returns with each other (0.52):

Source: Portfolio Visualizer

These two funds are volatile, only loosely correlated, and had exactly the same return. That sounds like ideal circumstances to earn a rebalancing premium to me, and that’s exactly what we see.

If, on 12/31/1998, you put $5,000 into each fund and never rebalanced between them you’d have ended 3/31/2020 with $42,947 in total. That’s a compound annual growth rate (CAGR) of 7.10%, which is (as it must be mathematically) the average CAGR of the two assets.

If, on 12/31/1998, you put $5,000 into each fund and rebalanced annually between them you’d have ended 3/31/2020 with $49,888 in total. That’s a CAGR of 7.86%.

The difference between 7.86% and 7.10% is what Bernstein was referring to as the “rebalancing bonus”.

That’s a great example of what Bernstein was talking about, and shows the rebalancing bonus can exist under the right conditions.

But that last bit of the sentence is key: under the right conditions.

Conditions

In order for us to benefit from the rebalancing bonus, we need to know a few things ahead of time. Or at least be confident enough in them that we’re willing to put our money where our mouth is and construct our portfolios to try and capture some of this rebalancing bonus.

We’d need to have a decent handle on expected volatility, expected correlations, and expected returns. We wouldn’t need to be perfectly accurate, but at least have a reasonable enough idea that it becomes worth our while constructing our portfolio to target the rebalancing bonus.

Another important consideration is that maximising the rebalancing bonus means making a few changes to a standard stock/bond portfolio.

In order to build a portfolio containing asset classes with similar returns (which is necessary for the rebalancing bonus), it means dis-aggregating out the stock element into its constituent parts. Your global tracker should now be split into a US tracker, a UK tracker, a Europe tracker, an EM tracker, etc. Depending on how vigorously you want to pursue this bonus, you could also look at introducing other asset classes like corporate bonds and property.

My quarrel with this approach to portfolio construction is threefold.

Firstly, it makes a portfolio more difficult to administer. Every additional holding means additional research – both up front and ongoing – and additional time spent actually executing trades.

Secondly, it increases trading fees. More holdings means more trades. Costs may well be coming down for trading, but even “free” trading apps cost you money to trade, whether that’s through wider spreads or higher FX fees.

Thirdly, a disaggregated portfolio also raises the risk of tinkering. If I’m holding an emerging markets fund which is down 30% for the year, you can bet I’m going to want to replace it – for no other reason that doing something feels good and it makes it feel like I’m stemming the bleeding.

But if that EM fund was part of a global tracker, I wouldn’t see that -30% return and therefore wouldn’t care. I can quite happily carry on my day without the temptation to interfere with compounding and sabotage my own returns.

So, to earn a long-term rebalancing bonus we need to be confident that:

1. The assets we’re buying are volatile enough to have a decent chance of earning us a bonus,
2. They’re uncorrelated enough, and will remain uncorrelated enough, to earn us a bonus
3. Their returns are similar enough, and likely to remain similar enough, to earn us a bonus
4. Our transaction costs and taxes are low enough not to erode any bonus we earn,
5. The bonus is high enough for it to be worth the additional time spent monitoring and trading caused by a portfolio with a larger number of holdings,
6. The bonus is high enough to exceed the increased behavioural risk of having a larger number of holdings in the portfolio.

Points 5 and 6 are subjective, but are nonetheless factors in my own decision making.

I’m personally not confident enough in points 1-4 that, when combined with the added time investment required and behavioural risks involved from points 5 and 6, I’m willing to bet on earning a rebalancing bonus.

Conclusion

To summarise: the rebalancing bonus does exist, in theory.

You’re likely to earn a rebalancing bonus if you’re rebalancing between assets with similar long-term returns which aren’t perfectly correlated.

The rebalancing bonus is:

• Increased by the volatility of each asset,
• Increased by a decreased correlation between each asset,
• Decreased as the difference in long term returns increases, and
• Decreased further if this return difference is maintained over a long period of time,
• Decreased further the higher transaction costs are incurred,
• Decreased further the higher taxes are incurred.

For a typical balanced portfolio (say, 60% in an equity tracker and 40% in a bond tracker), the rebalancing trade you’ll be doing most of the time will be selling equity and buying bonds. Because equities are likely to return more than bonds, you’ll periodically need to sell equities and buy bonds to maintain a consistent asset allocation.

In these instances, you’re unlikely to earn a long-term rebalancing bonus due to violating points 3 and 4 – the expected returns from stocks are different to the expected returns from bonds. You may receive a rebalancing bonus on occasion – for example, you would’ve received a good returns boost from rebalancing right before the dot-com crash or 2008 (or the Pokémon crash of Year 2). But over time, the odds of achieving a rebalancing bonus from the stock/bond asset pair is very slim.

Because you’re rebalancing away from the high expected return asset (stocks) into the lower expected return asset (bonds), you’re reducing your expected returns in order to maintain an asset allocation in line with your risk profile. Over time, this will likely overwhelm any gains from the rebalancing bonus.

In order for an investor to benefit from the rebalancing bonus over the longer-term, they’d need to be confident in the future levels of volatility, expected correlations, and expected returns of the assets they’re investing in. They’d also need to disaggregate their global equity and bond trackers into smaller rebalanceable parts, so they’re holding as many different asset classes with similar returns as possible.

Am I personally likely to benefit from the rebalancing bonus over the long term?

Probably not.

I’m not confident it’s possible to forecast anything with a great level of accuracy in markets, let alone being able to predict correlations, returns, and volatility. I’m certainly not confident enough to start making my portfolio more complicated by splitting it up, and therefore increasing trading costs, time required for monitoring, and risk of tinkering.

I may be sacrificing a potential rebalancing bonus by investing in a global tracker because I can’t rebalance its constituent parts. But in my view, the benefits of a global tracker are worth it.

Given I’m unlikely to be able to consistently capture the rebalancing bonus anyway, due to the difficulties in being able to forecast correlations/returns/volatility plus the impact of transaction costs, the behavioural returns benefit alone of having a simple, tamper-proof portfolio is worth it. That’s without mentioning the benefit of having to spend less time administering my portfolio.

For me, the primary purpose of rebalancing is to manage risk, not to increase returns. Any return benefit which might come from rebalancing is a benefit.

But as Jack Bogle would say, “Don’t count on it.”