Sequence risk in decumulation – smaller than you think?

Sequence risk (also known as sequence-of-returns risk) is the idea that changing the order of market returns can result in different outcomes. This can be due to a changing strategy, cashflows paid in or out over the period, or both. For a static strategy with no cashflows, the order returns arrive makes no difference to the overall outcome.

Sequence risk is often thought to be of particular concern during the early years of pension decumulation, when there can be increased sensitivity to returns due to withdrawals, de-risking, or both. Indeed, it’s common to hear people speak of sequence risk as if it is the only investment risk in decumulation.

This is false – some investment return scenarios are less than ideal no matter what order the returns arrive! However, without being able to quantify sequence risk we can’t understand quite how important it is in the context of overall investment risk.

In this blog post, we present our latest thoughts in relation to pension decumulation. The headline findings:

• With only withdrawals or only de-risking at play, sequence risk explains only around 25% of the variance in returns
• A combination of both de-risking and withdrawing bumps this number up to 45% i.e. still less than half of the variance

The fact sequencing risk is not the dominant investment risk in decumulation may come as a surprise to some. So, how did we arrive at these results?

Sequence risk from withdrawals

We ran some tests, initially focusing on a retiree in decumulation with a static multi-asset income drawdown strategy.

To isolate sequence risk, we generated random returns for many potential simulations (as we normally do when modelling investment risk). However, we forced each simulation to achieve the same time-weighted rate of return (TWRR) over a particular period. The TWRR is effectively the return achieved in the absence of cashflows – like what you might see on a fund factsheet. On the other side, the internal rate of return (IRR) accounts for cashflows, and is the return that matters for outcomes.

We found that even after fixing the TWRR, the IRR varies when there are cashflows – this is the sequence risk we want to capture.

Putting this idea into practice, we modelled a scenario of a retiree with an ‘adaptive’ spending policy for their pension pot over a 10-year period. This involves spending broadly 1/10^th of the remaining pot in year one, 1/9^th in year two and so on – spending all the remaining pot in year 10.

To judge the outcomes of our modelling, we calculated the IRR achieved under every simulation in three different cases:

• All investment risk is modelled
• Only sequence risk is modelled¹
• Only non-sequence risk is modelled²

Finally, we looked at dispersion of IRRs across simulations. These were our results:

The standard deviation of all investment risk is less than the sum of the standard deviations of sequence risk and non-sequence risk separately. This is thanks to diversification between sequence and non-sequence risks. However, the variances – which are the squares of the standard deviations – do add up.

The nice thing about having a measure that adds up in this way is that we can meaningfully talk about how much of the risk comes from different sources. Specifically, here we can say that sequence risk explains about a quarter of the variance in returns.

This proportion doesn’t depend on the volatility of the chosen strategy, because if volatility is higher or lower then sequence and non-sequence risk scale up or down by the same factor. Numerically, we also found that the proportion is invariant to the time horizon.

Sequence risk from de-risking

Sequence risk can also arise from changes in the percentage split of assets through time. If we have no cashflows but instead the strategy is de-risked in a linear way, from growth to risk-free assets, we also find that 25% of return variance is explained by sequencing.³ This ties in with a blog post we wrote a couple of years ago that explains how phasing total capital in and out of growth assets damages risk efficiency due to the sequence risk introduced, reducing the Sharpe ratio by 13%.⁴

De-risking and withdrawing

Unsurprisingly, a combination of both withdrawing and de-risking is the worst for sequence risk. If we assume both the linear de-risk and adaptive withdrawals above, we find sequence risk explains 45% of the variance of returns – substantial although still less than half the total. This works out to be equivalent to a 26% haircut to the Sharpe ratio i.e. we suffer double the dent to risk efficiency.

Don’t let your priorities fall out of sequence

Sequence risk can be a useful concept in some circumstances, even if it can mislead in others. However, it is far from all investment risk in decumulation.

Sequence risk is effectively concerned with experiencing a mix of good and bad years, and the order they arrive being unfavourable. This matters, but investors should remember that the worst outcomes are likely to be dominated by poor returns throughout.

Sources

1. Achieved by forcing the TWRR to always be the same number, namely the expected rate of return

2. This involved looking at the difference in modelled returns of the above two cases and adding the difference to the expected rate of return

3. This is perhaps unsurprising with hindsight. As a simpler example in accumulation, consider fixed cashflows into a growth strategy that’s initially empty. Sequence risk can be interpreted as arising from the cashflows. Alternatively, the present value of the cashflows can be thought of as an asset and sequence risk can be understood as resulting from a phasing of total capital (i.e. including that asset), from bonds to growth.

4. To see how they are consistent, note that with non-sequence risk explaining 3/4 of return variance, the variance of returns increases by a factor of 4/3 due to sequence risk. This is equivalent to volatility increasing by a factor of the square root of 3/4, which means the Sharpe ratio gets multiplied by the square root of 3/4 = 0.87 i.e. there’s a 13% haircut.