Article by: Dr Laura Rusu, Founder & LENSELL | 20/06/2022
In this article we float a hypothesis that challenges the status quo and the traditional portfolio rebalancing approach. That is, we hypothesise that regular optimisation of the asset allocation in a portfolio produces better results than regular rebalancing of the same portfolio to its original asset allocation. Moreover, we hypothesise that regular optimisation of the asset allocation also produces better results than a “buy and hold” approach.
Investment managers explain portfolio rebalancing as “the process of realigning the weightings of a portfolio of assets. Rebalancing involves periodically buying or selling assets in a portfolio to maintain an original or desired level of asset allocation or risk” [2]. We argue that this approach may produce less efficient results than regular portfolio optimisation.
Arguably, the declared goal of rebalancing to the original asset allocation is to minimise the risk for a given level of expected return [3]. However, this approach is not suitable for the investor in an accumulation phase, whose goal is to get a return as high as possible for an acceptable level of risk (depending on their personal risk tolerance level).
This article analyses the two hypotheses above and shows some very interesting results:
- for the test portfolio considered, regular optimisation of asset allocation to an Optimal Portfolio position produces better results overall than a ‘buy and hold’ approach, and
- for the test portfolio used, the ‘buy and hold’ approach produces slightly better results than regular rebalancing to the original weights.
Let’s see how we got to those results.
For this study,
- To avoid selection bias, we picked 5 ETFs from the ‘Top 20 ASX trades in May 2022 from Sharesight users’ [1], that have a share price history of more than 6 years. We shortlisted VAS, VGS, VTS, NDQ and IVV.
- We considered a test portfolio valued $100000 at 31/05/2016, where each ETF was equally weighted, i.e. 20% ($20000) each.
- We made the following working assumptions: a $10 transaction cost applies for each buy/sell transaction required at optimisation / rebalancing time; a min 1% and a max 99% weighting constraints applied on optimal portfolio calculation.
We studied the following 3 scenarios:
Scenario 1 – starting with 1/06/2016 and every 6 months until 1/06/2022, we optimised the asset allocation to the Optimal Portfolio* position. This was performed using the Diversiview application.
Scenario 2 – starting with 1/06/2016 and every 6 months until 1/06/2022, the portfolio was rebalanced to the original asset allocation (i.e. 20% weight for each ETF).
Scenario 3 – starting with 1/06/2016 and until 1/06/2022, no change was made to the original portfolio.
* Optimal Portfolio (OP) is that portfolio position (combination of weights) that minimises the total portfolio risk and maximises the total portfolio return at the same time.
For all three scenarios, the performance was tracked over the 6 years in terms of: total portfolio value, average portfolio return and portfolio volatility.
Figure 1 and Table 1 below show the total portfolio value in each of the 3 scenarios, and some interesting observations can be made:
a) By 1/06/2022 the test portfolio ended up with a total value of $214,130.63 in Scenario 1 (regular optimisation to the Optimal Portfolio position), approx. $27795 more than in Scenario 2 (regular rebalancing to the original asset allocations) where the total portfolio value at 1/06/2022 was $186,334.65.
b) In Scenario 3 (no change to the initial portfolio) the portfolio value at 1/06/2022 was slightly higher than the amount in Scenario 2 (rebalancing to the original asset allocations) by approx. $2000.
Also, portfolio values were almost equal for Scenario 2 and Scenario 3 during the 6 years, which makes them difficult to differentiate on the graph. A slightly higher difference can be noticed after the March 2020 market crash.
Figure 1 Graph of total portfolio value in each of the 3 scenarios
Table 1 Total portfolio value in each of the 3 scenarios, at 6 months intervals.
The first finding, a), can be explained if we consider that the Optimal Portfolio position is that asset allocations that maximise the expected portfolio return and minimise the portfolio risk (volatility) at the same time. That means that the total expected return of the portfolio will be higher for that allocation that for any other allocation.
For example, Figure 2 below shows the portfolio position in Scenario 2 (rebalancing to equal weights) on the left, and the portfolio position in Scenario 3 (optimal portfolio) on the right – as at 1/12/2021. As it can be noticed, at that date the expected return in Scenario 3 was more than 7% higher than in Scenario 2, at the expense of an increase in the expected volatility of around 4%.
Figure 2 Test portfolio’s risk-return position in equal weights scenario (green dot, left) compared with the optimal portfolio scenario (red star, right) as at 1/12/2021
Note: As one might notice, in the optimisation solution (Fig2, right), some ETFs were allocated 1%. That is because we assumed min 1% and max 99% for weighting constraints (see beginning of the article). If other constraints were used, a solution that observes those constraints would have been calculated.
The second finding, b), can be explained if we look at the correlations between individual investments in the portfolio. Four (4) of the 5 ETFs are strongly correlated (see Figure 3), which means that their market prices would have moved up and down pretty much at the same time during the 6 years studied, therefore resulting only in small deviations from the original asset allocations. The largest contribution to deviations from original allocations were likely brought by the pairs of ETFs less correlated, i.e. VTS-VAS and VAS-IVV.
Due to this, the difference in value between portfolio in Scenario 3 (no change) and Scenario 2 (regular rebalancing to original weights) were caused by the transaction fees charged in Scenario 2 at each rebalancing date.
Figure 2 Correlations between the 5 ETFs in the test portfolio. Higher values indicate stronger correlations.
The two findings above are sustained by the average return and volatility results (see Figure 3), where Scenario 1 looks the best and Scenarios 2 and 3 have very similar results.
Figure 3 Average return and volatility for the test portfolio in the 3 scenarios
As it can be noticed in Figure 3, in all scenarios the annualised volatility was higher than the geometric (compounded) average return, with the lowest difference in Scenario 1.
Conclusion & further work:
Our first hypothesis, that ‘regular optimisation of the asset allocation in a portfolio produce better results than regular rebalancing of the same portfolio to its original asset allocation‘, was confirmed in the case of the test portfolio.
Our second hypothesis, that ‘regular optimisation of the asset allocation also produces better results than a “buy and hold” approach‘, was not confirmed. For the test portfolio considered the result was the other way around, as explained above.
One could legitimately argue that these results cannot justify a generalised conclusion due to the inherent limitations of the test portfolio at hand.
We believe that the results supporting the first hypothesis in this case were quite strong, therefore we will continue the research to see whether a more generic conclusion can be reached. We will consider more scenarios, including but not limited to:
- larger portfolios, consisting of mixed investments (stocks, ETFs, bonds etc)
- more diversified portfolios
- longer time duration
- different weighting constraints for optimisation
- different starting weights for the test portfolios
- different frequency for optimisation and rebalancing
- compare a Minimum Risk Portfolio approach instead of the Optimal Portfolio approach, for retired or conservative investors.
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For any questions please contact the LENSELL team at info@lensell.online. References:
References:
[1] https://www.sharesight.com/blog/top-20-asx-trades-by-sharesight-users-may- 2022/
[2] https://www.betashares.com.au/education/strategies-portfolio- construction/portfolio-rebalancing/
[3] https://www.aaii.com/journal/article/best-practices-for-portfolio-rebalancing?
