What caught my eye this week.
Two diligent bloggers took a run at the subject of rebalancing portfolios this week.
First up – in a tour de force that could give our own @TA a run for his carefully husbanded money – Occam Investing dove deep into the fabled ‘rebalancing bonus’, where investors see extra returns from regularly rejigging their asset allocation.
The post concludes that while such a rebalancing windfall is obviously welcome, the bonus cannot be banked on in the real-world:
Am I personally likely to benefit from the rebalancing bonus over the long term?
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.
Not so well endowed
Funnily enough, this very same week on a A Wealth of Common Sense, Ben Carlson spotted the rebalancing bonus roaming in the wild.
After showing how a simple portfolio of index-tracking ETFs would have beaten the returns of a bunch of sophisticated endowment funds over the past decade, Ben noticed that an investor with an 80/20 stock/bond split across three particular Vanguard tracker funds could have conjured up even higher returns by annually rebalancing:
If you were to simply multiply the weights for the 80/20 portfolio (48% U.S. stocks, 32% int’l stocks, 20% bonds) by [their] returns you would get an overall annual return of 8.9%.
But the actual 10 year annual return for the 80/20 portfolio shows 9.1%.
How could this be?
The difference here is the rebalancing bonus.
Both authors show their workings, and both are well worth a read.
Everything in moderation
While any investor would take bonus returns where they can get them, rebalancing is best thought of as a risk management tool rather than a source of alpha.
You may or may not see a rebalancing bonus in your years as an investor. That’s down to the luck of the historical draw.
But you might well expect to have a lower-risk portfolio if you keep your allocations broadly in-line with where you’ve determined they should be.
As a naughty active investor, my portfolio is to a passive 60/40 set-up what quantum mechanics is to Newtonian physics. Investments pop in and out of existence in my portfolio all the time. Any one of them could affect my returns (for good or ill) much more than the modest impact of annually rebalancing between asset classes.
Nevertheless, these days I too try to ensure nothing grows too far out of whack. This can mean trimming winning positions, which I do knowing full well this can be a behavioural bias and mathematical blunder that curbs long-term returns.
So why do it?
Because you never really see a catastrophic blow-up in investing that doesn’t involve over-exposure to a share, sector, geography, or asset class.
Stay vaguely diversified and the worst you will likely do is relatively poorly.
Of course we all hope to do better than that! But avoiding disaster is the number one rule.
As Warren Buffett’s sidekick Charlie Munger says: “All I want to know is where I’m going to die, so I’ll never go there.”
Amen to that!
The 22 maxims of Sir John Templeton – Monevator
Bond credit risk valuation rule-of-thumb – Monevator
From the archive-ator: How gold is taxed – Monevator
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When I first learned about the rebalancing bonus, in the early 80s, it had a slightly different definition. It used to be the difference between the observed performance of a rebalanced portfolio and the weighted average performance of the constituents. By that definition there is almost always a positive rebalancing bonus over multi-year periods. So if bonds produced 4% over 10 years, equities 10%, you are very likely to have got more than 7% for an annually rebalanced 50/50 portfolio.
There is the entirely separate issue of whether the rebalancing bonus is sufficient to offset the differences in long term performance between the constituents if the portfolio is not rebalanced. For the 50/50 portfolio, not rebalanced, the 10 year performance would have been 7.4%. Would the rebalancing bonus exceed the 0.4% from not rebalancing? Uncertain, but not unlikely. But if the investment period was 40 years, then the performance of the not rebalanced portfolio would have been 8.4%. So over longer timframes, the rebalancing bonus, which cannot be expected to rise with time, will gradually be insufficient to compensate for regularly rebalancing out of the higher performing asset.
The important consequence of almost always having a positive rebalancing bonus, by my old fashioned definition, means that holding bonds/cash and rebalancing hurts portfolio performance less than might be expected purely based on the expected returns of the bonds.
I agree with the Occam’s view on holding the World index instead of rebalancing across equity regions and strongly suspect that Carlson’s observation of improved performance rebalancing between 48% U.S. stocks, 32% int’l stocks, 20% bonds would have been the same, if not better, had the rebalancing been done across 80% World, 20% bonds. I split equities out by geographical region for tax reasons and (historically) to get lower running costs compared to a World tracker, but I hold these funds by FTSE World Index weight and would not attempt to rebalance across them.
It is interesting what you say about “ensuring nothing grows too far out of whack” as this is the opposite of what a World tracker does! A World tracker is the ultimate let your winners run portfolio, no matter how big the Apple’s, Amazon’s, Tesla’s get, there is no attempt to cut them down to mitigate risks. Sometimes this goes wrong (Dot-com, Japan, etc) but on the whole it works well enough.
@Naeclue — Interesting stuff and of course you’re quite right about the constituents of a World Tracker running amok. I almost mentioned it but it would have begun another longer detour.
For an active investor / stock picker, I think a bit of humility is required, versus a World Tracker which is guaranteed to hold nearly all* the (relatively) large/meaningful successful winners. Few/no stock pickers are going to get all the winners, albeit they might also dodge some of the (mathematically less consequential) losers. So the whole strategy IMHO requires a slightly different source of return/strategy.
That is not to say active investors shouldn’t try to run their winners of course, as I mention, even at the expense of some risky overexposure. I let Amazon run from c. 1% to over 10% of my portfolio before finally starting to cull it (partly because my holding was largely outside of tax shelters, which caused all kinds of issues) but I never liked that level of exposure. Yet I know other successful active investors who might have 20% in one company.
If you’re going to be a lucky tosser, you have to do what works for you I guess… 😉
*Caveated as sometimes active investors in individual companies have access to stocks outside of some indices, such as Tesla for a good period.
Really enjoyed the Gold article by @TI linked to from 2015. Somehow hadn’t seen that one before.
Does anyone have thoughts about the BoE bail-in guide published on 22-Jul ?
@TI, at one point I had a very high proportion of our investments (excluding property) in one company. Hard to be precise as the shares were all privately held and only priced when someone wanted an exit, but I would not be surprised if the allocation peaked at around 60%. To make matters worse, I also worked for the company! Frightening in hindsight, but too focussed on work at the time to consider the risk.
Early in 2020 when an equity tracker went down by 26% I was watching it and decided to rebalance some bonds into equities if the dip got to 40%. It never did so I did (even more of) nothing.
The “rebalancing bonus” is a just an aspect of time diversification. Over most of the last 40 years, the impact hasn’t been especially huge given the outsized returns generated by equities and govt bonds. In an environment of falling inflation and falling macro volatility, the trend was your friend. You were better off playing for momentum, not mean-reversion. Just being long and getting longer worked.
That period though was an anomaly, and now in a zero-yield world, when bonds generate 1%, equities perhaps only a few percent, and macro volatility is rising, that rebalancing bonus of 0.5%/annum would be something you cannot afford to miss out on. If returns stagnate, then playing for mean-reversion may actually become a more signficant part of the return. I’m very much of that view. Stagnant returns, higher macro vol with shorter cycles, more liquidity “airgaps”.
@TI, thanks for that Atlantic link even though I have mixed feelings about being labelled a “Bobo”. It explains something I couldn’t understand: why ordinary American workers would so enthusiastically support Donald Trump, a very rich man from a very different world who has a complete disdain for them and everyone else. It seems they do have something in common, an inferiority complex related fear of those that are better educated and more creative.
Back on topic, presumably rebalancing is helpful in toning down the price volatility which scares people about shares. Though I think I have seen it claimed that the last 10 years have seen relatively low volatility anyway compared with the past.
Possibly inadvertently you might have shone light on the second grievance, that of feeling despised. As the Atlantic writer said
On the rebalancing bonus, Bernstein’s paper is worth a look.
The initial equation he proposes helps to explain the underlying mechanism to the apparent magic. To put it in words; the bonus is the product of the asset classes weighting, their std deviations, and (1 minus) the correlation coefficient. In effect its the low correlation and volatility of the assets that are the main actors by enabling more opportunities over time to buy the higher returning asset at a discount.
One thing that falls out of this is that rebalancing with cash wont produce a bonus since its volatility /std dev is next to zero? Unless of course you get lucky.
Bernstein also considers briefly the possibility of gold as a balancing asset, with its distinct correlation and volatility – and indeed the equation could be used to estimate the expected bonus of any asset in the mix – qualitatively at least. I wonder how different bond types would compare for example.
BTDT – and as you say “frightening in hindsight”. Having said that, it worked out well for us. On reflection, I consider us to have been very lucky!
Much more recently, I had a slightly disproportionate (but overall much smaller) former employer holding that has really suffered due to C-19, but for years prior to that, had also done rather well. Time will tell with this one. I guess there are many lessons herein!
How did your scenario play out?
@Calculus. The problem with the rebalancing bonus in any 70/30 or 50/50 is that it’s just a 2-asset portfolio. You simply cannot get enough time diversification to generate a large rebalancing bonus.
As Bernstein shows, with volatility at say 15% and 5% for equities and bonds and a correlation of -0.25, then a 50/50 portfolio generates just 0.24%. Worse, if the bond-equity correlation goes from -0.25 to 0.25, you will need a 30% increase in volatility to offset that.
So the only way to collect a significant amount of rebalancing bonus is to have far more high vol/low correlation strategies in the portfolio, with minimal transaction costs. FX is ideal for this. For example, 4 currencies will give you 6 currency pairs, which creates 6 volatilites and 15 pairwise correlation coeffcients. You can visualize this as a tetrahedron, where the vertices are the currencies and the lengths are the volatilities, and the angles are the correlations. It’s just an extension of the cosine rule to calculate these. With so many more correlation, you collect far more significant returns through this.
Of course this is just active trading. Passive fanatics sustain the cognitive dissonance to believe that perfection is a cap-weighted market portfolio of risky assets but somehow also believe in rebalancing. CAPM denies ever rebalancing.
If your in the accumulation stage do you not get a rebalancing bonus with your regular purchases, especially if the market is going down?
I do like to keep a cheeky wee 50k in premium bonds just for the fun of buying during market panics but otherwise I just maintain 100% global equities. The predicted meagre future returns are plenty for me!
@ZXSpectrum48k. For a number of years I’ve read your comments and scratched my head. You’re a mighty smart man that deserves all you get with respect to wealth and accompanying lifestyle (genuine comment).
Forgiving the stupid expression on my Chevy Chase, you mention “more high vol/low correlation strategies in the portfolio with minimal transaction costs…FX is ideal for this”.
Can you give me an example of what a high vol/low correlation portfolio would look like in your example – particularly the reference to FX? No desire to replicate, just to understand and absorb as much knowledge as possible.
@ZX. Interesting. That sounds like a turbo charged arbitration approach?!
Another ‘asset’ that comes to mind with very high volatility and low correlation to equities (for now) is cryptocurrency, ie BTC or ETH. I’ll leave it there..
@Calculus (incredibly appropriate name ;)) “One thing that falls out of this is that rebalancing with cash wont produce a bonus since its volatility /std dev is next to zero?”
No you absolutely do get an expected rebalancing bonus when rebalancing with cash. If one of the volatilities is zero, the rebalancing formula does not go to zero, it reduces to X1*X2*(SD1-SD2)^2/2. For equities with volatility of say 15%, a 50/50 equities/cash portfolio would be expected to have a rebalancing bonus of about 0.28%.
As for rebalancing with BTC, you would have had stunning results had you done that from the time BTC was a few dollars but not because of the rebalancing bonus 😉 I have come across articles by people touting Gold as a great diversifier with rebalancing bonuses well over 1%. These often have very convenient start and end dates in their back tests…
Bernstein was not the first person to come up with the formula for the rebalancing bonus by the way, although he may have been the first person to use that term. I learnt about in on a stochastic portfolio theory course around 1983.
@ZXSpectrum48k, “As Bernstein shows, with volatility at say 15% and 5% for equities and bonds and a correlation of -0.25, then a 50/50 portfolio generates just 0.24%. Worse, if the bond-equity correlation goes from -0.25 to 0.25, you will need a 30% increase in volatility to offset that.”
Looks like you made the same mistake as @Calculus. The extra term in the formula buys you another 0.12% and if correlation goes from -0.25 to 0.25, you will need a 17% increase in volatility (eg equity volatility up to 17.5%) to get back to 0.36%.
@Al Cam, The scenario played out well enough thanks. Not as well as it would have done had I owned a similar sized chunk of Apple or Microsoft, but much better than if I had owned a stake in Enron 😉
@Naeclue. Thanks – and quite right, I missed the addition of the second term you’ve given above. Im glad someone was paying attention in 1983!
So the second term has no correlation factor but acts on the difference of the volatilities – intriguing, and means as you say cash or very low volatility asset can work quite well indeed.
@Naeclue. Further thought on BTC/v high volatility asset in a rebalancing scheme; as you say if the returns of one asset are much higher than the other then this will make the bonus insignificant. Conversely if it tends towards zero then that will also dominate, in not a good way! However in the (unlikely) event that the returns do roughly align at the end of the period – it appears the high volatility could lead to a very significant bonus.
@Calculus, yes cash or short dated bonds can work well, especially if you end up with terrible stock market returns. During the worst periods for stock markets there is typically higher volatility which leads to a higher rebalancing bonus, so precisely when it is most useful. The reverse is true when stock markets do well, but the rebalancing bonus does not matter so much then anyway.
To get the best result from rebalancing you do typically want investments that give comparable returns over the period and high volatility, but it is also good to have low correlation (from Bernstein’s simplified formula X1X2(Var1/2 + Var2/2 – Covar1,2)). I had a play with portfoliovisualizer.com earlier and tested a 50/50 portfolio of Microsoft/Apple since 1991. I selected the start date in order to get similar annualised returns. Microsoft had a CAGR of 21.92%, Apple 22.26% and the annually rebalanced portfolio 25.31%. The standard deviations were 40% for MSFT and 73% for AAPL. Correlation came out at only 0.4, which meant the covariance was 0.12. From those numbers Bernstein’s formula implies an expected rebalancing bonus of 5.6%. Actual bonus came out at only 3.2%, which is a little disappointing.
The chances of picking precisely 2 stocks like these at the right time is of course totally fanciful!
I know it’s off topic – any views on 45% grade A /A*? Further Maths was 75%.
They’ve had a tough time yes, but give them £500 not artificial rankings v their recent historical peers. Not sure if a 2021 grade A is equivalent to a “C and above” from mid 80s or “D and above”.
Ok, yes I wish I’d got straight A’s!
B (or is it A* now)