Brucie bonuses: diversification and rebalancing

Here's a simple thought experiment for you: suppose you have a fund of £100 and you experience a return of +10% in one year and -10% in the next year. How much do you have at the end of the two years? The impulse is to say £100 but this isn’t quite right. If you follow the maths, you have £110 at the end of the first year, which you then lose £11 of in the next year, leaving you with £99. The investor has lost £1 to 'volatility drag'. 

As we explained in a paper a few years ago, volatility drag usually means that the chance of achieving the mean average return is less than 50% and falls over time. This is why many investors prefer to focus on median outcomes that you have a 50/50 chance of beating.

What do points make?

This drag to median outcomes doesn’t sound great. So where do the Brucie bonuses come in? Well, the first type of bonus we consider is called a 'diversification bonus'. This is a boost to median outcomes arising from – you guessed it – diversification. The idea is that assets on their own could be highly volatile and so individually be exposed to high volatility drag. But if you combine the assets in one portfolio the magic of diversification means that the overall volatility drag of the portfolio is lower than you might expect, boosting median outcomes.

The other potential type of boost is from a 'rebalancing bonus.' This has nothing to do with means or medians (you’ll be relieved to hear) but rather is based on the idea that prices can fluctuate around 'fair value'. If this is true, rebalancing can help ensure you buy low and sell high, boosting overall returns.

The price is right?

Unlike diversification bonuses, rebalancing bonuses rely on markets being inefficient because 'buying low' and 'selling high' is only possible if prices move away from fair value. You need to be careful though because with overly frequent rebalancing you could end up 'fighting momentum'. By this we mean you could be selling/buying assets that have a tendency to keep on going up/down in the short term. This would act as a drag on returns rather than a boost and so the rebalancing bonus could be negative (effectively a drag). Shame!

All right, my loves?

Diversification and rebalancing bonuses are often confused. To demonstrate they really are different we considered two uncorrelated assets both with median returns of 3.92% p.a. over 10 years and volatility of 15% p.a. that behaved like pure random walks (with no momentum or reversion at play). We started with a 50/50 mix of assets and then calculated median outcomes over 10 years for two strategies:

Strategy	Median return (pa) after 10 years
No rebalancing	4.47%
Annual rebalancing	4.49%

As you can see, the median outcomes are almost the same. This illustrates that the boost of around 0.6% p.a. over 10 years doesn’t require rebalancing, and rather is a result of diversification. Of course, a bare-minimum degree of rebalancing is needed over the long term to earn diversification bonuses, simply to prevent too much 'drift' in the portfolio (and maintain diversification). But frequent rebalancing is not necessary in general.

Didn’t they do well?

Understanding that frequent rebalancing is not required to earn a diversification bonus is important. For example, holding an illiquid portion of assets in your portfolio that you don’t intend to rebalance (due to the high transaction costs) still helps earn a diversification bonus unless it becomes either a very small or very large part of the portfolio.

We are currently researching some of the interesting trade-offs involved in rebalancing decisions: there can be conflicting aims in terms of staying close to benchmark, making the most of trending or reverting markets and keeping transaction costs down. This research aims to link in with cashflow aware investing, glidepath management and active tilting. Watch this space!