Risk measurement in
Risk measurement in retirement requires metrics beyond the traditional volatility measure. Determining the most appropriate asset allocation in retirement requires a new framework with appropriate risk measures.
When accumulating savings for retirement, the investment objective is unambiguously one of growth. Risk in the accumulation phase is also well-defined in terms of the potential for loss of capital. This is typically described by the volatility of investment returns or related downside risk measures. An individual with a greater tolerance for volatility is therefore able to take on a higher level of investment risk, with the aim of achieving greater wealth to fund their retirement.
Once we enter retirement the risk-return landscape becomes significantly more complex
Once we enter retirement, however, the risk-return landscape becomes significantly more complex. The primary objective in the decumulation phase ceases to be pure growth, but to use the accumulated retirement wealth to sustain a target level of income throughout the retirement period. Similarly, volatility of investment returns is no longer a suitable risk measure as it does not describe the risk of failing to meet this objective. The traditional Markowitz mean-variance framework, a mathematical model to maximise the return for a given level of portfolio volatility, is therefore inappropriate. When designing retirement solutions for decumulation, we need a different risk-return framework within which to evaluate different strategies.
As a simple example, illustrated in Chart 1, we consider a pot of savings that aims to provide a regular income during a retirement period of 25 years. We ignore longevity risk (any income requirement beyond 25 years can be assumed to be met by a later life annuity). Initially, we wish to examine how different portfolio asset allocations between a risky asset (equity) and a defensive asset (bonds) will fare when a regular income of 4% of the initial pot size is drawn. This is a trivial example when considering the primary income objective alone (no investment solution is necessary to withdraw 25 amounts of £4 from an initial pot of £100). However, retirees will typically also be concerned with secondary objectives such as bequest objectives, i.e. leaving a certain amount of wealth at the end of the retirement period. As well as the expected total amount of income withdrawn during the retirement period, we therefore also consider the ’expected total wealth’. This is the sum of the average total income withdrawn and the average final wealth remaining at the end of the 25-year period.
Chart 1: Regular income of 4% of an initial pot size of £100 over 25 years, with risk represented as volatilitySource: Aberdeen Standard Investments (as of May 2019)
Chart 1 illustrates this example in a typical accumulation risk-return framework, using volatility as the risk metric. For a portfolio comprising 20% equity and 80% bonds we can expect, on average, a total income over the 25 years of 100 (25 lots of 4) and approximately a further 100 final wealth remaining at the end of the 25-year period. The chart is telling us that, in order to achieve a higher expected total wealth, we must accept a higher portfolio volatility. However, it tells us nothing in terms of the real risks of failing to achieve the objective in retirement.
A more relevant risk measure in the context of decumulation is the probability of running out of money. That is, income withdrawals deplete the pot before the end of the 25-year retirement period. This captures important dynamics such as the sequence of returns, which can be particularly damaging in decumulation. A large percentage decline in the value of assets earlier in retirement is more difficult to recover from if it occurs while an income is being withdrawn. In addition to the probability of running out of money, other measures that attempt to quantify the amount of income at risk can be considered. These include the average number of years of income that would be lost.
Chart 2 illustrates the same example but using the probability of running out of money as the risk metric. The chart provides much more useful information in terms of helping an individual evaluate different retirement strategies. As previously mentioned, for this particular example, an individual does not need to take investment risk to achieve the desired level of retirement income with no risk of running out of money. We can see from Chart 2, however, that investing in a portfolio with an equity allocation of up to around 40% can give rise to a significant increase in expected total wealth (up to around £225) with minimal increase in the probability of running out of money (less than 0.3%). Raising the equity allocation beyond 40% further improves the expected total wealth, but with increasing risk to the primary income objective.
Chart 2: Regular income of 4% of an initial pot size of £100 over 25 years, with risk represented as the probability of running out of moneySource: Aberdeen Standard Investments (as of May 2019)
If the desired retirement income can be achieved with minimal probability of running out of money, as is the case in the 4% income example, a retiree may choose to accept a higher probability of running out of money for a higher expected total wealth by investing in a portfolio with a larger allocation to risky assets. Alternatively, the retiree may seek to target a larger regular income at the expense of the level of expected total wealth, as long as the probability of running out of money can be contained to an acceptable level.
Chart 3 incorporates simulation results for a 5% income withdrawal rate, alongside the previous 4% income example. It illustrates the interplay between these various factors, and why it is crucial to help an individual make the difficult decisions they face as they enter retirement. It can be seen, for example, that if a retiree is willing to accept no more than a 5% probability of running out of money, they can withdraw a 4% annual income from a portfolio that holds up to around 65% of risky assets. At the same time, they can expect significant residual wealth of around one and a half times their initial pot size, on average (points marked ‘A’ in Chart 3). For the same risk of running out of money, the same retiree could instead withdraw a larger 5% annual income. However, they would need to restrict their allocation to risky assets to around 35% and would expect roughly half as much residual wealth on average (points marked ‘B’ in Chart 3).
Chart 3: Regular incomes of 4% and 5% of an initial pot size of £100 over 25 years, with risk represented as the probability of running out of moneySource: Aberdeen Standard Investments (as of May 2019)
In the examples considered so far, we have looked at risk through the single lens of the probability of running out of money before the end of the 25-year period. In reality, risk in retirement is multi-dimensional. An individual retiree may have multiple goals, with a different level of importance attached to each. For example, an individual with other sources of retirement income such as a defined benefit pension or rental income may be less reliant on the regular income from their accumulated savings. Thus, they might attach more importance to maintaining/growing their wealth for ad-hoc or unforeseen expenditures, or to leave a bequest. An individual’s risk aversion in retirement will therefore be defined by a holistic view of their retirement goals, and the risks to those goals across all scenarios that could play out during their retirement.
To simplify the problem, we can use the concept of a utility function to describe the relative importance a retiree attaches to generating excess wealth versus falling short of their target income. For example, for a retiree whose clear priority is to secure a regular income, scenarios where there is a shortfall in income will be heavily penalised in comparison with the modest positive weighting attached to favourable scenarios. In this way, a particular retiree’s attitude to these different risks is linked together into a single measure of risk aversion. For a given shape of utility function, Chart 4 illustrates the optimal portfolio allocation to risky assets for different income withdrawal rates and different levels of risk aversion.
Chart 4: Optimal equity allocations for different income withdrawal rates and levels of risk aversionSource: ThomsonReutres DataStream, Bloomberg, internal calculations Aberdeen Standard Investments (as of April 2019)
In conclusion, risk measurement in a retirement context requires metrics beyond the traditional volatility measure. Volatility may be useful to give a sense of the stability of the value of accessible savings during retirement. However, it does not help in evaluating the most appropriate solution for meeting an individual’s key retirement goals. Typically, more than one risk measure is necessary, with multiple stochastic scenarios required to truly appreciate the risks inherent with each solution. Finally, the traditional mean-variance framework used in accumulation to map an individual’s risk aversion level to a proposed asset allocation becomes much less relevant in decumulation. Determining the most appropriate asset allocation in retirement requires a new framework with appropriate risk measures.
Once we enter retirement the risk-return landscape becomes significantly more complex