# 4. Selecting default investment strategies

This chapter provides a framework to assist policy makers in selecting default investment strategies for defined contribution retirement savings arrangements. It describes how to use a stochastic model to assess investment strategies with respect to the objective of maximising retirement income, and discusses the key parameters of the stochastic model that need to be considered. It finally provides guidance to assist countries in using the framework.

Default investment strategies are of critical importance to assist people in defined contribution retirement savings arrangements. Defined contribution (DC) arrangements often offer a variety of investment options to plan members. The different investment options may be qualified as conservative, balanced, dynamic, growth, or aggressive. With the growing importance of environmental, social and governance issues, some investment strategies are now labelled ethical or green. This variety confronts individuals with the challenge to choose the investment strategy that best suits their needs and risk preferences. A rational choice requires a thorough understanding of the potential risks and rewards of the investment strategies offered. However, many individuals are unwilling or unable to make investment decisions. Default investment strategies are therefore an option to assist them when they do not make a decision.

There is no consensus around the design of the default investment strategy. In line with the recommendation in the *OECD Roadmap for the Good Design of Defined Contribution Pension Plans*, several countries use life-cycle investment strategies for the default option, reducing the risk exposure as the individual gets closer to retirement (OECD, 2012[1]). However, a myriad of glide paths are possible. Moreover, life-cycle investment strategies are not a panacea, as the reduction of the share of risky assets also reduces expected returns and thereby expected retirement income. Some countries opt for other solutions for the default option, such as conservative or diversified funds. It is therefore a difficult task to select the most appropriate investment strategy for the default option among the diversity of existing investment strategies.

This chapter aims to help policy makers to select default investment strategies. It provides a framework for selecting a default investment strategy that is in line with the objective of maximising retirement income. The chapter describes how a stochastic model can be used to assess investment strategies and discusses the key parameters of the stochastic model that need to be considered. It also provides guidance to assist countries in using the framework.

Selecting an appropriate default investment strategy requires policy makers to solve a trade-off between minimising the downside risk and maximising the upside potential. The objective of the default investment strategy is to maximise the level of retirement income of default members, under the constraints implied by the parameters of the retirement savings arrangement and the level of risk that policy makers are willing to accept due to the existence of uncertainty around retirement outcomes. This risk implies a trade-off between protecting individuals from getting a retirement income much lower than expected and maximising that retirement income. Taking into account this trade-off, selecting a default investment strategy involves pre-selecting the investment strategies to be assessed, assessing these strategies using a stochastic model to reflect the uncertainty of possible outcomes, calculating indicators reflecting their potential riskiness and performance, and defining thresholds for risk indicators that reflect the importance given to the downside risk relative to the upside potential. The investment strategy selected for the default option is the one meeting the thresholds for the risk indicators and maximising the performance indicators. In addition, when designing the stochastic model, policy makers need to carefully define several important parameters, such as the simulation period, the types of risks to be considered, the asset mix, the macro-economic scenario and the stochastic distribution of the different risk variables.

This chapter starts with the description of the framework for selecting a default investment strategy, before exploring in more details the specifications for the stochastic model and the different parameters that policy makers need to consider when designing such models. It then provides guidance for using the framework, describing its possible applications and providing an illustration of the model outcomes. The last section concludes.

This section presents a framework that policy makers could use to assist them in selecting a default investment strategy. It first highlights the fact that policy makers face a trade-off between protecting individuals from low retirement incomes and maximising retirement income. It then describes the steps of the selection process.

### Uncovering the trade-off between downside risk and upside potential

The goal of the default investment option is to provide an investment strategy for people unwilling or unable to make investment choices. In DC retirement savings plans, individuals can usually choose their investment strategy and then bear the consequences of their investment decisions. However, individuals may lack financial knowledge and are prone to various behavioural biases that can have an impact on investment choices. The main issues include choice and information overload, time-inconsistent preferences, heuristic decision-making, framing effects, overconfidence, over-extrapolation, and loss aversion (OECD, 2018[2]). Default investment strategies address the problem that some people lack the knowledge and/or the commitment to design and manage their own portfolio.

The objective of default investment strategies is to maximise the level of retirement income paid to default members under a number of constraints. These constraints relate to the design of the retirement savings arrangement and to the level of uncertainty that policy makers are willing to accept with respect to the level of retirement income (i.e. the risk that retirement income falls short of expectations).

The default investment strategy needs to take into account the parameters of the retirement savings arrangement. These parameters establish the age at which people can join and retire from a pension plan; the mandatory or minimum contribution rate; the maximum fees charged; the tax rules; and the options people can choose from to transform their assets into a retirement income. These parameters are important for the design of the default investment strategy because they determine the flow of money to be invested in the different asset classes over time.

The default investment strategy also needs to take into account the level of uncertainty surrounding the future level of retirement income. Beyond the parameters of the arrangement, retirement income from DC retirement savings plans depends on several uncertain factors or risks. These include financial risks (i.e. investment returns, inflation and interest rates), labour market risks (i.e. career wage-growth profiles and periods of unemployment or inactivity) and demographic risks (i.e. longevity). One of the main implications of these financial, labour, and demographic risks is that the income derived from DC retirement savings plans is uncertain and can take a range of values for any given individual depending on the realisation of these risks. The default investment strategy should account for this heterogeneity and not only deliver good outcomes for the average scenario.

An example of how the parameters of the arrangement and the risk factors influence the design of the default investment strategy is the structure of the pay-out phase. When individuals have to buy an immediate lifetime annuity at retirement, the default investment strategy should deliver the highest possible annuity payments. This implies that the investment strategy needs to account for the interest rate risk as well as the longevity risk. For example, Mantilla-Garcia et al. (2020[3]) argue for the use of investment strategies hedging against changes in the discount rates when the objective is to secure an income stream in retirement. By contrast, when individuals can freely choose their pay-out product and tend to take a lump sum, the interest rate risk and the longevity risk are less relevant, as the role of the default investment strategy is to maximise the lump sum payment. Antolin, Payet and Yermo (2010[4]) show that the relative performance of investment strategies varies with the type of retirement income product.

The existence of this uncertainty on retirement income implies that policy makers face a trade-off when selecting the default investment strategy, between protecting individuals from the risk of receiving a retirement income much lower than expected (downside risk) and helping them to reach the maximum possible retirement income (upside potential). Uncertainty means that an individual may end up with a very high, or on the contrary very low, retirement income depending on the realisation of the risk factors. The trade-off comes from the fact that not a single investment strategy would at the same time maximise the upside potential and minimise the downside risk. For example, conservative funds and life-cycle investment strategies are well suited to manage the downside risk as they reduce the volatility of investment returns and therefore decrease the risk of losing a large portion of the assets already accumulated, in particular when individuals are close to retirement and have little time to recoup any losses. However, this comes at the cost of reducing future retirement income potential, as these strategies reduce the share of the portfolio invested in risky assets, which provide higher expected returns over the long term. Moving to a conservative investment strategy too early in the accumulation phase may therefore be inconsistent with the objective of achieving a high retirement income.

Taking into account this trade-off, policy makers may need to consider the following steps for selecting the default investment strategy. Firstly, pre-select the investment strategies to be assessed; secondly, assess these strategies using a stochastic model to reflect the uncertainty of the outcomes; thirdly, calculate indicators that reflect the potential riskiness and the potential performance of the assessed investment strategies; fourthly, define thresholds for risk indicators that reflect the importance given to the downside risk relative to the upside potential; and finally, select the default investment strategy among the assessed strategies that meet the thresholds for the risk indicators and maximise the performance indicators.

### Pre-selecting the investment strategies to assess

Policy makers first need to pre-select the investment strategies to assess for the default option. The universe of investment strategies to select from for the default option is broad. This requires policy makers to consider the pros and cons of different categories of investment strategies ex-ante and make a pre-selection of the investment strategies to assess for the default option.

Most countries have a life-cycle investment strategy as a default option. There are several categories of investment strategies to consider for the default option. Countries with DC retirement savings arrangements and individual investment choice offer various types of default investment strategies. Table 4.1 shows that most countries offering investment choice to members have a default investment strategy and the most common type of default is a life-cycle investment strategy. This type of default can be found in eleven countries, at least for a segment of the market. In other countries, the default investment strategy is a conservative fund or a diversified fund. A few countries do not have a default option.

There is a wide variety of possible glide paths for life-cycle investment strategies. Life-cycle investment strategies reduce the share of the portfolio invested in risky assets as the individual approaches retirement. For most of them, this reduction is based on the age of the saver only (or equivalently, based on the remaining time until retirement) and can be linear or not. There are also life-cycle investment strategies that reduce the share of risky assets based on both age and the balance of assets in the retirement savings account.1 The different possible glide paths include the following:

Linear decline with age: The share of risky assets declines linearly with age from the beginning of the accumulation phase. For example, with the “100-age” rule, the allocation into risky assets starts at 75% at age 25 and ends at 35% at age 65. Any other combination of starting and ending risky allocation is possible.

Stepwise linear decline with age: The share of risky assets remains constant during the first part of the accumulation phase and then declines linearly with age down to a minimum level. For instance, in Sweden, the default option in the premium pension system invests 100% in the equity fund up to the age of 55 and rebalances linearly towards the fixed income fund from the age of 56 up to the age of 75 until reaching an allocation of 67% in the fixed income fund and 33% in the equity fund.2

Step decline with age: The share of risky assets declines sharply as the individual reaches specific age thresholds. For example, Chile implements a multi-fund strategy, where individuals move to more conservative funds as they reach the ages of 35 and 55, reducing the equity allocation in the default option from 60% to 40% and then from 40% to 20%, respectively. The limitation of such a strategy is that, in case of a sharp drop in equity markets just before reducing the equity share in the portfolio, the individual would materialise the losses by selling equities at bottom prices.3

Gradual decline with age: The share of risky assets declines gradually with age, but not following a linear function. For example, the Danish pension provider PFA offers an investment strategy starting with a 75% allocation in risky assets when members are young and transitioning gradually to 30% between age 50 and age 65.4 Different formulas may be used to gradually reduce the share of risky assets in life-cycle investment strategies (see for example (Khemka, Steffenssen and Warren, 2019[5])).

Step decline with age and account balance: The share of risky assets declines sharply as the individual reaches specific age thresholds, but the decline varies according to whether the balance in the retirement savings account exceeds a certain threshold. For example, the Australian pension fund QSuper implements a multi-fund strategy, where individuals move to more conservative funds as they reach the ages of 40, 50 and 58. However, the decline in the share of risky assets is lower (respectively higher) when the account balance is below (respectively above) a certain threshold.5 The idea is to protect the assets of individuals who have already reached large balances with a higher proportion of safe assets, while giving individuals with low balances a chance to further increase their balance through higher return potential.

Conservative funds as a default are built for the most risk averse individuals but provide low return potential, ultimately reducing the expected retirement income. Default conservative funds may not be allowed to invest in equities at all (e.g. Latvia) or only within certain limits (e.g. New Zealand).6 A conservative fund as a default may be seen as a transitory fund before members select a more appropriate investment strategy. One of the nine default KiwiSaver providers refers to the default conservative fund as “*a temporary parking space [for people] to take the time to think about which fund option is right for [them]*”.7 In Latvia too, this type of default allocation may be seen as transitory before a more active fund selection by members. In both countries, most members actually select an alternative option (OECD, 2018[6]; Financial Market Authority, 2019[7]). However, due to inertia and procrastination, passive members may remain with a conservative investment strategy for the entire accumulation phase, thereby significantly reducing their return potential and ultimately their future retirement income. Recognising this, the default fund setting in New Zealand will change from a conservative to a balanced fund from June 2021.8

By contrast, fixed portfolio strategies in diversified funds (e.g. balanced, dynamic, growth or aggressive funds) are consistent with the objective of maximising retirement income but expose to the risk of experiencing a large fall just before retirement. These investment strategies rebalance the portfolio every year to keep the weights of the different asset classes constant. In Australia for example, 65% of MySuper funds, the default options in the superannuation system, offer a fixed portfolio strategy with a diversified investment. This is usually a portfolio with around 70% invested in higher-risk growth assets (i.e. shares and property) and 30% in lower-risk safe assets (i.e. cash and fixed income). The main issue with diversified funds as a default option is that they do not protect individuals when equity markets experience a large fall just before retirement. Individuals close to retirement with a high investment in equities could lose a large part of their assets in case of a negative shock to equity markets.

Alternatively to life-cycle investment strategies, conservative funds and diversified funds, the default investment strategy could also include investment guarantees and dynamic investment strategies based on mechanisms building reserves.

Default investment strategies could include minimum return guarantees, but such guarantees come at a cost. Investment return guarantees provide some protection against financial market risks by setting a floor on the value of assets accumulated at retirement. They may increase the attractiveness of saving for retirement in DC plans as they overcome people’s fear of losing the nominal value of their contributions. Some countries already have minimum return guarantees for the default option, or more generally for all investment options. For example, providers of the new pan-European personal pension product (PEPP) can design the default option on the basis of a guarantee on the capital, which makes sure that people will get back at least their contributions in nominal terms. In Colombia, pension fund administrators must provide a minimum return guarantee set by the regulator.9 In Chile, pension fund managers must ensure that returns fall within a band that is defined differently depending on the type of fund.10 However, investment return guarantees have to be paid for, and this cost reduces the expected value of benefits from DC plans relative to a situation where there are no guarantees. These costs take the form of explicit or implicit costs to support the security mechanism in place to secure the guarantee provided, as well as opportunity costs due to a reduced capacity for the provider to invest in risky assets (c.f. Chapter 6).

Finally, dynamic investment strategies based on reserves built from contributions or investment returns could also be the default option. Most of the previous investment strategies are deterministic, so they do not adjust the share of risky assets to the market situation. For example, by reducing the share of risky assets following a pre-determined glide path, life-cycle investment strategies may forego good returns in times when equity markets are booming. According to the PEPP Regulation for example, mechanisms dynamically allocating the assets based on reserves built from contributions or investment returns are valid for the default option, as long as their design is consistent with the objective to allow the PEPP saver to recoup nominal contributions.11 The idea of such investment strategies is that the share of risky assets varies with the level of the reserve, which increases (respectively decreases) when the portfolio performs better (respectively worse) than a benchmark return.12 Goecke (2016[8]) shows that investment strategies resulting from mechanisms building reserves from investment returns would systematically have outperformed fixed portfolio strategies invested fully in bonds or in equities, using real market data for Germany from 1955 to 2015.

Given the wide range of possible investment strategies to consider for the default option, a pre-selection is necessary. There is a balance to strike to select the right number of investment strategies for the assessment. On the one hand, it is important to assess as many investment strategies as possible to make sure that a potentially good investment strategy is not excluded from the assessment. On the other hand, assessing too many investment strategies may be inefficient and may make the results hard to interpret. Policy makers may have pre-conceived ideas about the characteristics that the default investment strategy should have. The assessed strategies may also need to be in line with what market participants are able to offer.

### Stochastic model

A stochastic model enables the generation of several possible outcomes from saving for retirement under different investment strategies. The assessment of investment strategies ex-ante for the selection of the default option needs to account for the variety of possible outcomes from saving in a DC plan. A stochastic model simulates different realisations of the world given different values of the uncertain random variables (e.g. investment returns). It derives uncertainty by assuming random-generating processes for each of the variables (or risks) in question. For each of the realisations of the world, the model generates the outcomes needed to calculate the indicators and compare them to the thresholds for each of the investment strategies assessed for the default option. The Monte Carlo simulation is one example of a stochastic model that is well suited to illustrate the impact of risk and uncertainty on a given outcome. The number of simulations needs to be sufficiently large (e.g. 10 000) to cover a wide range of possible outcomes.

The stochastic model needs to reflect the rules of the retirement savings arrangement. In particular, the model should account for the ages at which individuals are more likely to join and exit retirement savings plans, the mandatory, minimum or average contribution rates, the fees charged by pension providers, the mix of asset classes available to invest in (e.g. taking into account any investment restrictions), the tax rules, and the structure of the pay-out phase.

When public and private pensions are interlinked, the model should also simulate the rules to determine public pension entitlements. In some countries, public pensions are means-tested and retirement savings assets are included in the asset test, thereby reducing entitlements to the public pension when they are above a certain threshold. As what matters to individuals is the total income they will get from both sources, the model should include the interaction rules between both schemes and check whether the investment strategies optimise this interaction. For example, the Australian pension fund QSuper reduces investment risk in its default option for individuals with higher balances in their account because the impact of investment risk on retirement income is larger for them, but also because these individuals can rely less on the public non-contributory Age Pension as they exceed the means-test thresholds (Van Wyk, 2015[9]).

There is a trade-off between having a sophisticated or a straightforward stochastic model. A stochastic model using a lot of parameters and sophisticated distributions for the different risk factors may provide a better picture of the different possible outcomes. However, this comes at the cost of potentially lengthy computation times and greater difficulty for different pension providers to replicate the model. Alternatively, a simpler model may be less accurate, but more easily replicable and adjustable to different populations. Policy makers therefore need to carefully assess the potential gains of adding sophistication, and thus complexity, into the model. In particular, adding complexity will only lead to an improvement in accuracy if the additional parameters can be estimated in an accurate way (i.e. having the proper model and the relevant data needed for the calibration). Priority for sophistication may be given to asset classes that are likely to be dominant in the portfolios. Section 4.2 discusses in more detail the parameters that policy makers need to consider when designing the stochastic model.

### Indicators

The stochastic model allows calculating several indicators to assess whether an investment strategy is suitable for the default option. The assessment requires indicators focussing on the potential riskiness of investment strategies, and indicators focussing on their potential performance, so that policy makers and regulators can evaluate the trade-off between downside risk and upside potential.

The following categories of indicators can help to determine the risk profile of investment strategies:

Dispersion: The dispersion reflects the uncertainty of the retirement income. The standard deviation and the inter-quartile range are the most common dispersion indicators. The standard deviation of retirement income represents how much retirement income fluctuates around its average. The inter-quartile range is the difference between the 75

^{th}percentile and the 25^{th}percentile of the distribution of retirement income, indicating the spread of retirement incomes when excluding the 25% best and the 25% worst values. A large dispersion may not translate into bad outcomes for individuals when distributions are skewed towards high values.Unfavourable scenario: The low percentiles of the distribution of retirement income can be used to assess how low retirement income may be in an unfavourable scenario. For example, the 5

^{th}percentile represents the value of the retirement income such that in only 5% of cases would the retirement income be lower. More or less extreme unfavourable scenarios may be selected, e.g. the 1^{st}or the 10^{th}percentiles.Probability that the retirement income falls below a certain level: This is the proportion of simulations where the retirement income is below a certain level. For example, one could calculate the probability that the level of assets accumulated at retirement is lower than the sum of nominal contributions.

Expected shortfall: The expected shortfall represents the expected magnitude of a loss conditional on suffering a loss. For example, one can measure the average difference between the level of assets accumulated at retirement and the sum of nominal contributions in situations where the individual would not recoup the contributions.

The following categories of indicators can be used to measure the potential performance of investment strategies:

Expected retirement income: The mean and the median are the usual indicators to measure expected outcomes. The median is less sensitive to extreme values than the mean.

Favourable scenario: As a mirror to the unfavourable scenario, the high percentiles of the distribution of the retirement income can be used to assess how high retirement income may be in a favourable scenario. For example, the 95

^{th}percentile represents the value of the retirement income that puts 95% of all possible values below it. In case of skewed distributions, high percentiles may represent very unlikely outcomes, however. Choosing between the 70^{th}and the 80^{th}percentiles could represent a more realistic upside potential.

Combining risk and potential performance indicators allows addressing the trade-off between achieving the highest possible retirement income at the lowest risk, and thus selecting the default investment strategy. However, to address the trade-off, there is a need for thresholds for risk indicators.

### Thresholds for risk indicators

Finally, policy makers need to define a threshold for each of the indicators that assess the riskiness of investment strategies. These thresholds represent minimum or maximum values that the indicators need to meet to select an investment strategy as the default option. All investment strategies meeting the thresholds carry an acceptable level of risk, and the one among them that maximises the performance indicators can be selected for the default option.

Thresholds should reflect the respective weight that policy makers give to the downside risk and to the upside potential. If priority is given to the downside risk, the thresholds should be demanding. For example, the threshold for the probability that the level of assets accumulated at retirement is lower than the sum of nominal contributions could be set at 0.5%. This would imply that only investment strategies producing a probability of 0.5% or lower could be selected for the default option, which would lead to very conservative investment strategies. By contrast, if priority is given to the upside potential, the thresholds for indicators measuring risk should be less demanding (e.g. 10% for the probability of not recouping contributions).

Solving the trade-off between upside potential and downside risk requires policy makers to decide which of the two carries more weight and takes priority. Different considerations can help policy makers to define an acceptable level of downside risk and thereby set the thresholds for the risk indicators.

The acceptable level of risk first depends on the role of the retirement savings scheme in the overall pension system of each country. When the retirement savings scheme is mandatory and is expected to provide a large share of income in retirement, the role of the default investment strategy becomes more important than when the retirement savings scheme is voluntary and is expected to provide a small complement to the main public pension scheme. For example, when the retirement savings scheme provides a small complement to the public pension scheme, individuals may be able to take more investment risk – and accept a greater downside risk – as their main source of income in retirement is guaranteed.13 Alternatively, when the retirement savings scheme is the main source of income in retirement, risk taking may be more limited as any reduction in retirement income will affect individuals significantly.

The importance of the downside risk compared to the upside potential also needs to reflect the population’s level of risk aversion. For example, if individuals are concerned about the risk of losing the money they have contributed into the plan, the downside risk takes priority and the default investment strategy may need to include investment guarantees.

The acceptable level of risk also needs to consider the target population for the default investment strategy. Ideally, different individuals would need different default options to cater for their specific needs and characteristics. For example, if low-income earners are already promised an adequate replacement rate from the public pension scheme, one could argue that they could maximise investment risk and accept a higher downside risk. If performance is good, the retirement savings scheme will provide them with a significant complement to the public pension, while if performance is bad, they still have their public pension and only a small part of their overall retirement income is at risk. By contrast, medium to high-income earners may receive significantly less in relative terms from the public pension scheme. They may rely significantly more on the income from the retirement savings scheme and may therefore be less willing to take large investment risk.14 It is not possible to construct a default investment strategy for each individual, however. Still, the default option may vary for different pension funds, as the characteristics of the population covered may differ from one fund to another (e.g. in the case of sectoral or industry pension funds).

Finally, thresholds need to be realistic and consistent with the parameters of the retirement savings arrangement, in particular with the length of the investment period. Investment risk indeed increases for shorter durations, as people have less time to recover following investment losses. Expectations are also different when people do not save for their entire career. The length of the investment period may vary greatly across individuals, in particular in voluntary arrangements where individuals do not necessarily join a retirement savings plan when entering the labour market. The impact of the length of the investment period may vary across indicators. For example, the dispersion of retirement income may be reduced for shorter investment periods (i.e. reducing risk), while retirement income under an unfavourable scenario may decrease (i.e. increasing risk). Different thresholds may therefore need be defined for different lengths of investment. The drawback with different thresholds is that cases may arise where none of the proposed investment strategies would meet the thresholds for all investment durations, or different strategies would qualify for different investment durations. In that case, the investment strategy with the best results over all investment durations could be selected for the default.

This section explores in more detail the specifications for the stochastic model and the different parameters that policy makers need to consider when designing such models. It covers issues related to the simulation period, the risk variables, the asset mix, the macro-economic scenario, and the distribution of the risk variables.

### Simulation period

The simulation period for the stochastic model should be in line with the parameters of the retirement savings arrangement.

The simulation period should reflect the actual savings period in the retirement savings arrangement. Although in theory individuals may save for retirement for 40 years or more, in practice, savings periods tend to be shorter. This may be because individuals do not join a plan immediately when entering the labour market, or because they stop contributing at some point due to periods of unemployment or inactivity. The simulation period of the stochastic model needs to account for the actual savings period in the country, as using 40 years may lead to the selection of a default investment strategy that does not adjust well to shorter savings periods. In addition, the simulation period for the stochastic model may need to account for the pay-out phase on top of the accumulation phase when individuals have to choose between an annuity and a drawdown product at retirement.

However, the savings period may vary significantly across individuals in voluntary arrangements, calling for the model to assess investment strategies over different investment horizons. While savings periods may be more or less homogeneous in mandatory arrangements (e.g. in line with career length), savings periods are more dissimilar in voluntary arrangements. In voluntary arrangements, individuals may start saving at different ages and thereby may have different investment horizons. Shorter investment horizons imply a reduced compound interest effect, as well as potentially less time to recover in case of investment losses. Investment strategies may therefore need to be assessed over different investment horizons because indicators of risk and performance may worsen when the investment horizon is shorter. As discussed earlier, thresholds for the different risk indicators may also need to be adjusted for different investment horizons. As a result, different investment strategies may qualify for the default option depending on the investment horizon. Some countries account for variability in the length of the investment horizon when assessing investment strategies. For example, in Germany, voluntary personal retirement savings products are assessed for four different investment horizons, 12, 20, 30 and 40 years (Korn and Wagner, 2018[10]).

### Types of risks included

The stochastic model should account for all the factors that influence the level of retirement income. Retirement income depends on three factors: the amount of money contributed by the individual and/or the employer, the cumulative net return until retirement of the assets in which the money is invested, and the cost of converting the assets into a stream of payments during retirement. Each of these factors are themselves subject to different risks:

Labour market risks: Labour market risks refer to the risk of being unemployed or inactive, as well as the uncertainty surrounding the income level and the trajectory of career wages. They affect the level and the density of contributions (i.e. how often individuals contribute during the career). Indeed, during episodes of unemployment or inactivity, contributions set aside to finance retirement may be discontinued. Contribution levels also depend on the wage level and the wage-growth profile, which varies for different individuals, notably according to their socio-economic characteristics. Additionally, spells of unemployment or inactivity may also affect wages, as individuals may re-enter the labour market at lower wages than they enjoyed in their previous job. This type of risk may be less relevant for voluntary personal pension plans, where the contribution schedule may be less connected to individuals’ careers.

Financial risks: Financial risks refer to the uncertainty surrounding investment returns, inflation rates and interest rates. Investment returns for the various asset classes have a direct impact on the performance of the portfolio and the level of assets accumulated at retirement. Inflation rates affect both wage levels and investment returns, as well as the purchasing power of retirement income. Interest rates are used to discount future income streams and influence the level of annuity payments an individual can get for a given level of assets.

Longevity risk: Longevity risk has two components. The idiosyncratic longevity risk refers to the uncertainty over how long an individual is going to live after retirement. When selecting a lump sum or a drawdown product at retirement, individuals may outlive their resources in retirement if they underestimate their life expectancy. When selecting a life annuity, that risk is transferred to the insurance company. The systematic longevity risk refers to the uncertainty over how long individuals of a particular age cohort are going to live after retirement. Life insurance companies can reduce this risk by using mortality tables that include future increases in life expectancy, thereby increasing the price of annuities for individuals. Longevity risk does not need to be accounted for when individuals take the value of assets accumulated at retirement as a lump sum.

Behavioural risks: Behavioural risks refer to the uncertainty about individuals’ or employers’ behaviours with respect to saving for retirement. This includes when individuals start and stop saving, their contribution pattern (e.g. whether the contribution rate is constant or varies over time), and whether they make early withdrawals.

All these risks have to be calibrated to the specific population that would benefit from the default investment strategy. Indeed, labour market risks, longevity risks and behavioural risks are likely to be different for the population as a whole, and for members of specific pension funds. For example, wage levels vary greatly across sectors. If the default investment strategy is selected at the fund level, the specific wage structure of the sector covered by the fund should be used to calibrate the stochastic model.

### Asset mix

The stochastic model should simulate the returns of the range of asset classes in which pension funds actually invest. The simplest model would only have two asset classes: equities and bonds. Equities and bonds are the two main asset classes in which retirement savings assets are invested, accounting for more than half of total investment in 32 out of 36 OECD countries at the end of 2018 (OECD, 2019[11]). However, pension providers in most countries invest in a wider range of asset classes to diversify their portfolios. Within bonds, the respective share of government and corporate bonds varies greatly across countries, with government bonds accounting for more than 85% of total direct bond holdings in the Czech Republic and Hungary, but only 25% in Norway and 11% in New Zealand. Cash and deposits also account for a large share of pension assets in some countries, such as the Czech Republic (20%) or France (35%). The importance of alternative asset classes, such as loans, real estate, unallocated insurance contracts, private investment funds and hedging instruments (e.g. derivatives), is usually minor, but still significant in selected countries like Canada, Denmark, Switzerland, and the United Kingdom. Finally, the proportion of assets invested abroad can be significant, in particular for Eurozone members with small domestic capital markets. The asset classes selected for the model therefore need to reflect their current use by pension funds or other institutional investors in the country, to make sure that the benefits of diversification can be replicated for the investment strategies assessed for the default option.

Once the list of asset classes is set, appropriate indices need to be selected in order to extract the moments (mean and standard deviation) for the stochastic distribution of returns. Indices need to be studied carefully before selection, as they cover various regions, currencies, and elements of the return of an asset class. For example, MSCI offers two different global stock indices. The World Index only includes stocks of developed markets, while the All-Country World Index (ACWI) includes stocks in both developed and emerging markets. In addition, indices may be available in various forms (without dividends, with net dividends reinvested, or with gross dividend reinvested) and in different currencies (US dollars, Euros and local currencies). Moreover, all indices may not have the same starting date and frequency (daily, monthly or annual).

Proxies may need to be used when the appropriate index for a given asset class is not available. For small economies, specific indices may not be available for domestic equities or corporate bonds, or historical data may be limited. When that is the case, equivalent indices for other countries may be used, choosing an economy with similar characteristics to the extent possible.

### Macro-economic scenario

There is no consensus regarding which historical period to select in order to calibrate the model and calculate the moments of the different risk variables, especially asset returns, inflation and interest rates. Given the long projection period when simulating retirement savings (potentially 40 years of accumulation plus 20 years of retirement), a common approach is to use the longest historical period possible to reflect the uncertainty of possible outcomes over such a long-term horizon.15 However, recent periods seem to diverge from historical trends. Table 4.2 shows the average return and the standard deviation of World and European equity indices for the period 1969-2018 and for the period 1999-2018. When shortening the calculation period, the average returns fall significantly, while the standard deviations slightly increase. This shorter period reflects an economic and ﬁnancial landscape of low returns that some commentators argue will be here for decades to come and should therefore be used for projections.16 Some analysts even exclude certain periods that they deem to be atypical. For example, Berardi, Tebaldi and Trojani (2019[12]) exclude the period 2012-2017 to avoid extreme interest rate scenarios possibly driven by the European Central Bank’s asset purchase programme.

Historical data could be complemented by expert judgement to estimate some of the parameters of the stochastic model. For example, Graph and Korn (2020[13]) explain that using an expert opinion for the drift term of a geometric Brownian motion is common practice when modelling a stock price. In the Netherlands, a special committee of pension experts advises the Dutch government every five years about assumptions for returns that defined benefit pension funds are allowed to use when setting their contribution rates. It also provides recommendations about the discount rate used to value liabilities.

The assessment of investment strategies needs to be complemented by sensitivity and scenario analyses as the outputs of the stochastic model may be dependent on the historical period used to calibrate the model. For instance, one could stress some of the parameters and analyse whether the values of the risk indicators still meet their threshold. Alternatively, one could look at the impact of a large negative shock to equity markets when individuals are close to retirement, by recalculating the indicators for simulations where equity returns drop by a minimum value in the final years of the accumulation phase.

### Stochastic distributions

A large variety of models exist to simulate financial and labour market risk variables. However, a compromise is needed between practicality and accuracy.

For equity returns, the standard model is the Black-Scholes model (Black and Scholes, 1973[14]). The stock price is modelled as a geometric Brownian motion, $S\left(t\right)=s\left(0\right){e}^{\left(\mu -\frac{{\sigma}^{2}}{2}\right)t+\sigma W\left(t\right)}$, where the Brownian motion W(t) has a normal distribution with mean 0 and variance t; µ is called the drift and measures the average returns;17 and σ is called the volatility and measures the standard deviation of the return distribution. In this model, the returns of the stock index follow a normal distribution.

However, the Black-Scholes model has several shortcomings. First, the distribution of historical equity returns exhibit a higher peak and two heavier tails than those of the normal distribution (Kou, 2007[15]). This means that returns around the mean are more frequent, while extreme returns, both negative and positive, are further away from the mean. Second, the standard deviation of historical equity returns decreases over time more rapidly than what is implied by a normal distribution (Rinaldi and Ceccarelli, 2016[16]). Therefore, the range of outcomes over long periods is larger in the model than what historical data suggest. Third, the normal distribution assumes that all returns are independent from each other. However, observations show that, while returns themselves are uncorrelated, absolute returns (or the square of returns) tend to be positively correlated. In that respect, Mandelbrot (1963[17]) notes that “*large changes tend to be followed by large changes, of either sign, and small changes tend to be followed by small changes*”.

Many alternative models exist to address the shortcomings of the Black-Scholes model, but the increased complexity needs to be weighed against the gains in accuracy. Kou (2007[15]) presents several alternatives to the Black-Scholes model. For example, in the jump-diffusion model of Merton (1976[18]), the stock price is modelled as a geometric Brownian motion (diffusion part) combined with a Poisson process (jump part), where the jump sizes are normally distributed. This means that the stock price follows a geometric Brownian motion on intervals between jump times. Rinaldi and Ceccarelli (2016[16]) suggest generating equity returns using a stochastic process with two components, a term following a log-normal distribution and a second term capturing extreme negative events with a relatively small probability of occurring every year, but occurring almost certainly over a working life. However, the choice of the model has to be a compromise between accuracy and practicality. More complex models mean more parameters, making the calibration more difficult.

Similarly to equities, a variety of models exist for interest rates, which are needed to derive bond returns as well as discount rates. For example, Brigo and Mercurio (2006[19]) review interest rate models, which can be based on one or several factors. One-factor models are relatively easy to calibrate, as they assume that the evolution of the yield curve is completely determined by the evolution of its initial point. Two-factor models lead to more realistic simulations of interest rates, as they allow interest rates of different maturities to react differently to shocks. The calibration is more complex, however. For example, with the G2++ model, one needs to estimate five parameters, which is more than for one-factor models (e.g. three parameters with the Vasicek model).

Many different approaches are also possible to simulate income levels. Models need to account for the probability of being unemployed or inactive at some point during one’s career. All the factors explaining unemployment spells or periods of inactivity should be considered, such as age, gender, sector, educational level, and income. If the model is built at the pension fund level, these factors need to be tailored to the specific population of the fund. The persistence of unemployment could also be taken into account, as someone unemployed in a given year may have a higher probability of being unemployed the following year. Similarly, the model could consider different real-wage growth profiles. Real-wage gains during a career vary across individuals according, notably, to their socio-economic situation (e.g. occupation, educational level and income). Labour market studies document that there are three main career paths for real wages. In general, real wages experience the largest gains during the early part of a person’s career, with lower gains, even negative gains, in the latter part. This pattern results in real-wage paths that for some people reach a plateau at the end of their career, while for others, real wages plateau earlier, around ages 45 to 55, and fall thereafter. A minority experience flat real wages throughout their working lives (Antolin and Payet, 2011[20]).

Finally, the model should assume correlations between key variables. The correlation coefficients ensure that the value of the different risk variables in each simulation are likely to materialise together and form a plausible realisation of the world. For example, international equity returns and domestic equity returns are correlated, as well as yields on government bonds, corporate bonds and inflation. In addition, the risk of unemployment is correlated to the performance of equity markets. The risk of suffering unemployment indeed tends to be lower when the economy is booming, and to increase when the economy slows down or enters into recession, generally with a lag. Moreover, improvements in the economy or higher economic growth may push returns on investment up. Therefore, when the economy is doing well, returns on investments rise and the risk of suffering spells of unemployment falls, reinforcing the positive feedback cycle regarding the accumulation of assets for retirement. The opposite occurs when the economy declines. To take these patterns into account, the model could add a shock to the probability of being unemployed correlated with the performance of equity markets.

### Applications of the framework

This framework can be useful for policy makers and regulators willing to introduce default investment strategies, and for those thinking about changing the default settings. The *OECD Roadmap for the Good Design of Defined Contribution Pension Plans* indicates that policy makers and regulators should establish appropriate default investment strategies for individuals unwilling or unable to make investment choices (OECD, 2012[1]). Some countries offering investment choice in DC retirement savings plans still lack a default investment strategy (e.g. the Czech Republic, Estonia, Korea and the Slovak Republic). This may discourage individuals from joining a retirement savings plan if they do not know which investment strategy to choose. Moreover, countries already having a default investment strategy may want to reconsider the design of that strategy. The framework described in this chapter allows policy makers and regulators to assess whether their current default settings are effectively in line with the objective of maximising retirement income given the parameters of the arrangement and the level of uncertainty that policy makers are willing to accept.

The framework may be used to select a single default investment strategy for the whole population, or to allow pension funds to select their own default investment strategies. The default investment strategy may be designed for the whole retirement savings arrangement, or individually for each pension fund. For example, in Hong-Kong, China, the Mandatory Provident Fund Schemes Authority has defined a single life-cycle default investment strategy that all schemes have to implement. By contrast, in many OECD countries, default investment strategies tend to be fund specific. Defining the default investment strategy at the national level ensures an equal treatment of all participants. Moreover, when the retirement savings arrangement relies on personal pension plans, the characteristics of the population covered by the different pension providers may not diverge much from each other and from the whole population. By contrast, fund-level defaults may be justified in the case of occupational retirement savings arrangements, as the population covered by different pension funds may vary significantly. For example, pension funds for workers in the health or education sectors are more likely to cover women, who tend to have lower earnings and more career breaks than men, and these characteristics could be taken into account for selecting the most appropriate default investment strategy. In the case of fund-level defaults, pension funds need to use harmonised assumptions for the stochastic model to ensure that all participants have access to a default investment strategy selected according to the same quality standards. In particular, all pension providers should use identical specifications for the market indices, the macro-economic scenario and the stochastic distributions.

A national-level default investment strategy could also be selected using this framework to serve as a benchmark for fund-level defaults. When pension funds can freely design their default investment strategy, policy makers may consider selecting a national default investment strategy for benchmarking purposes. Pension funds could be required to communicate to plan members the relative performance of their default investment strategy compared to the one of the national default. Systematic underperformance could then prompt members to switch to a better performing pension fund. This could also encourage pension funds to adopt the national default investment strategy, or to use the same methodological framework to select a potentially better default.

Finally, policy makers should reapply the framework at regular intervals to account for changes in the retirement savings landscape. Significant changes in the labour market, in financial markets, in life expectancy projections or in individuals’ behaviour may justify an update of the stochastic model to check that the selected default investment strategy is still appropriate. Similarly, countries changing the nature of the retirement savings arrangement, for instance by introducing automatic enrolment or compulsion, may need to reassess any existing default investment strategy, as the retirement savings arrangement would have a greater role in retirement income provision, potentially modifying the balance between the downside risk and the upside potential. Policies such as automatic enrolment may also change the characteristics of the population covered by retirement savings plans by reaching new groups of individuals, thereby justifying an update of the stochastic model to make sure that the default investment strategy is also appropriate for these new members. Moreover, regular updates would allow innovative investment strategies to be assessed and to potentially replace less performing investment strategies as a default.

### Illustration of model outcomes

This section provides an illustration of the model outcomes, selecting the default investment strategy for a hypothetical case. In this illustration, policy makers believe that the default option should either be a conservative fund or a life-cycle investment strategy. An investment limit of 20% in equities applies for conservative funds in this hypothetical case, so the model assesses three different conservative funds with no equities, 10% in equities and 20% in equities. For life-cycle investment strategies, the idea is to reduce equity exposure according to a stepwise linear decline with age, but the starting and ending equity allocations, as well as the age at which the linear decline starts need to be determined. Therefore, the model assesses 18 life-cycle investment strategies, with starting equity allocations of 80%, 90% or 100%, ending equity allocations of 0%, 10% or 20%, and the linear decline starting at 45 or 55 years of age. In addition, members are assumed to take a lump sum at retirement, so retirement income is the level of assets accumulated at retirement and is expressed as a percentage of the average sum of nominal contributions.18 Table 4.3 shows the indicators discussed earlier in the chapter calculated for the 21 investment strategies assessed.

Policy makers need to define a threshold for each of the risk indicators to select the default option among the 21 investment strategies assessed. Risk averse policy makers could require that the default option meets the following requirements: a probability that retirement income is lower than the sum of nominal contributions of 0.5% or less; an average loss conditional on not recouping contributions of 8% or less of the average sum of nominal contributions; a retirement income at least equal to 90% of the average sum of nominal contributions for 95% of the population; and a standard deviation of retirement income of 1.3 or less. Seven investment strategies meet the thresholds for the four risk indicators (green numbers), the three conservative funds, and the life-cycle investment strategies with the equity allocation declining linearly at age 45 from 80% to 20%, from 80% to 10%, from 80% to 0% and from 90% to 0%. Among these seven investment strategies, the one maximising the three performance indicators (bold numbers), and therefore the selected default option, is the life-cycle investment strategy with the equity allocation declining linearly at age 45 from 80% to 20% (in bold in the table). Less risk averse policy makers could select another default option among the 21 assessed investment strategies. The thresholds for the risk indicators could be less demanding, allowing for greater choice for the default option among strategies with higher potential performance. For example, policy makers could require the default option to produce a probability that retirement income is lower than the sum of nominal contributions of 2% or less; an average loss conditional on not recouping contributions of 11% or less of the average sum of nominal contributions; a retirement income at least equal to 85% of the average sum of nominal contributions for 95% of the population; and a standard deviation of retirement income of 1.5 or less. In that case, eight additional investment strategies would meet the thresholds for the four risk indicators (orange numbers). Among the fifteen (7+8) investment strategies, the one selected for the default option would be the life-cycle investment strategy with the equity allocation declining linearly at age 45 from 100% to 20% (in bold in the table). This default option offers higher retirement income potential to individuals, but carries a higher level of risk than the previous one.

Policy makers in this hypothetical case are also concerned that many individuals do not save for their entire career. While Table 4.3 shows the indicators assuming a contribution period of 40 years, Table 4.4 assumes a contribution period of 20 years. The results show that the thresholds need to be adjusted when the assessment is done for a shorter contribution period. Using the same thresholds for risk indicators suggested before, none of the assessed investment strategies would qualify for the default option because none of them would produce a retirement income at least equal to 85-90% of the average sum of nominal contributions for 95% of the population. By contrast, all the investment strategies would meet the thresholds for the dispersion indicator (standard deviation below 1.3 or 1.5). The thresholds therefore need to be readjusted to see whether a different investment strategy would be a better default option for a shorter contribution period.

Selecting a default investment strategy for individuals not able or not willing to make investment choices is a challenge for policy makers. While the objective of the default option is to maximise the level of retirement income, there are a number of constraints to consider. First, the parameters of the retirement savings arrangement affect the flow of money to be invested in the different asset classes over time. Second, uncertainty about the future retirement income implies that individuals may end up with a retirement income much lower than expected because of the materialisation of financial, labour or demographic risks. Policy makers therefore face a trade-off between maximising retirement income (upside potential) and limiting the risk of getting a low retirement income (downside risk). This chapter has presented a framework that policy makers could use to select a default investment strategy, taking into account this trade-off.

Given the wide range of potential investment strategies, policy makers need first to decide which ones they would like to assess for the default option.

These strategies should then be assessed using a stochastic model to reflect the uncertainty of outcomes. Several parameters need to be considered to build the stochastic model:

The simulation period: It should reflect how long people save for, in particular in voluntary retirement savings arrangements, and include the pay-out phase whenever individuals need to select an income stream;

The types of risks: All factors influencing the values of the selected indicators should be included, such as financial risks, labour market risks, longevity risk and behavioural risks;

The asset mix: The appropriate market indices should be selected to calculate the moments of the distribution of investment returns for each of the main asset classes that pension funds invest in;

The macro-economic scenario: The historical period selected to calculate the moments of the distribution of investment returns should be as long as possible given data availability, except when policy makers consider that future trends are likely to diverge permanently from past history;

The stochastic distributions: Policy makers should select the models to simulate the different risk variables keeping in mind the compromise between accuracy and practicality.

To have a complete assessment of investment strategies, several indicators reflecting their potential riskiness and performance should be calculated using the stochastic model.

Policy makers should then define thresholds for the risk indicators that reflect the importance they give to the downside risk relative to the upside potential.

The investment strategy selected for the default option is the one meeting the thresholds for the risk indicators and maximising the performance indicators.

This framework could have several applications. Countries providing investment choice in their DC retirement savings arrangement and lacking a default option could use it to select a default, while those already having a default could use the framework to check that this investment strategy is well aligned with the objective of maximising retirement income given the parameters of the arrangement and the level of uncertainty that policy makers are willing to accept. In addition, the framework could be used to select a single, nationwide default investment strategy, or to allow pension funds to select their own default investment strategy accounting for the characteristics of their members. In the latter case, the national default option could serve as a benchmark for fund-level default options.

## References

[20] Antolin, P. and S. Payet (2011), “Assessing the labour, financial and demographic risks to retirement income from defined-contribution pensions”, *OECD Journal: Financial Market Trends*, Vol. 2010/2, https://www.oecd.org/daf/fin/financial-markets/47522586.pdf.

[4] Antolin, P., S. Payet and J. Yermo (2010), “Assessing Default Investment Strategies in Defined Contribution Pension Plans”, *Financial Market Trends*, Vol. 10/1, http://www.oecd.org/finance/private-pensions/45390367.pdf.

[12] Berardi, A., C. Tebaldi and F. Trojani (2019), “Consumer protection and the design of the default option of a pan-European pension product”, *Swiss Finance Institute Research Paper Series* 19-19, https://dx.doi.org/10.2139/ssrn.3142243.

[14] Black, F. and M. Scholes (1973), “The Pricing of Options and Corporate Liabilities”, *Journal of Political Economy*, Vol. 81/3, pp. 637–654, http://dx.doi.org/10.1086/260062.

[19] Brigo, D. and F. Mercurio (2006), *Interest Rate Models - Theory and Practice*, Springer-Verlag Berlin Heidelberg, http://dx.doi.org/10.1007/978-3-540-34604-3.

[22] Damodaran, A. (2020), *Equity Risk Premiums: Determinants, Estimation and Implications - The 2020 Edition*, http://dx.doi.org/10.2139/ssrn.3550293.

[7] Financial Market Authority (2019), *KiwiSaver Annual Report*, http://www.fma.govt.nz/assets/Reports/20191004-FMA-KiwiSaver-Annual-Report-2019.pdf.

[8] Goecke, O. (2016), “Collective defined contribution plans - Backtesting based on German capital market data 1955-2015”, *Forschung am IVW Köln* Band 5, https://www.th-koeln.de/mam/downloads/deutsch/hochschule/fakultaeten/wirtschafts_und_rechtswissenschaften/5_2016_preprint.pdf.

[13] Graph, S. and R. Korn (2020), “A guide to Monte Carlo simulation concepts for assessment of risk-return profiles for regulatory purposes”, *European Actuarial Journal*, http://dx.doi.org/10.1007/s13385-020-00232-3.

[5] Khemka, G., M. Steffenssen and G. Warren (2019), “How sub-optimal are age-based life-cycle investment products?”, *SSRN Electronic Journal*, http://dx.doi.org/10.2139/ssrn.3416265.

[10] Korn, R. and A. Wagner (2018), “Chance-Risk classification of pension products: Scientific concepts and challenges”, in *Innovations in Insurance, Risk- and Asset Management*, World Scientific Publishing, https://www.worldscientific.com/doi/10.1142/9789813272569_0015.

[15] Kou, S. (2007), *Jump-Diffusion Models for Asset Pricing in Financial Engineering*, http://dx.doi.org/10.1016/S0927-0507(07)15002-7.

[17] Mandelbrot, B. (1963), “The Variation of Certain Speculative Prices”, *The Journal of Business*, Vol. 36/4, pp. 394-419, http://www.jstor.org/stable/2350970.

[3] Mantilla-Garcia, D. et al. (2020), *From defined-contribution towards target-income retirement systems*, http://dx.doi.org/10.2139/ssrn.3585154.

[18] Merton, R. (1976), “Option pricing when underlying stock returns are discontinuous”, *Journal of Financial Economics*, Vol. 3, pp. 125–144, http://dx.doi.org/10.1016/0304-405X(76)90022-2.

[23] OECD (2020), *Annual survey of investment regulation of pension funds*, http://www.oecd.org/daf/fin/private-pensions/2020-Survey-Investment-Regulation-Pension-Funds-and-Other-Pension-Providers.pdf.

[11] OECD (2019), *Pension Markets in Focus*, http://www.oecd.org/daf/fin/private-pensions/Pension-Markets-in-Focus-2019.pdf.

[2] OECD (2018), “Improving retirement incomes considering behavioural biases and limited financial knowledge”, in *OECD Pensions Outlook 2018*, OECD Publishing, Paris, https://dx.doi.org/10.1787/pens_outlook-2018-8-en.

[6] OECD (2018), *OECD Reviews of Pension Systems: Latvia*, OECD Reviews of Pension Systems, OECD Publishing, Paris, https://dx.doi.org/10.1787/9789264289390-en.

[1] OECD (2012), *The OECD Roadmap for the Good Design of Defined Contribution Pension Plans*, https://www.oecd.org/finance/private-pensions/50582753.pdf.

[16] Rinaldi, A. and S. Ceccarelli (2016), *Pension Projections and Risk Indicators for Pension Plan Members: Recent Experiences and Policy Issues*, https://www.researchgate.net/profile/Simone_Ceccarelli/publication/322897647_Pension_Projections_and_Risk_Indicators_for_Pension_Plan_Members_Recent_Experiences_and_Policy_Issues/links/5a7491ee0f7e9b20d49234a3/Pension-Projections-and-Risk-Indicators-for-P.

[21] Temocin, B., R. Korn and A. Selcuk-Kestel (2018), “Constant proportion portfolio insurance in defined contribution pension plan management under discrete-time trading”, *Ann Oper Res* 260, pp. 515-544, http://dx.doi.org/10.1007/s10479-017-2638-5.

[9] Van Wyk, B. (2015), *An ALM approach to DC savings*, https://www.actuaries.org.uk/system/files/documents/pdf/a1-alm-approach-dc-savings.pdf (accessed on 10 July 2020).

## Notes

← 1. In addition, the definition of risky assets may also vary (e.g. domestic equities, foreign equities, real estate, corporate bonds).

← 2. https://www.ap7.se/english/ap7-såfa/

← 3. Chile addresses this issue by transferring 20% of the assets per year when changing funds, instead of all at once.

← 4. https://english.pfa.dk/business/products/pfa-plus/

← 5. https://qsuper.qld.gov.au/investments/options/lifetime

← 6. The default conservative fund in the KiwiSaver system in New Zealand shall be invested between 15% and 25% in growth assets (i.e. shares and property) (OECD, 2020[23]).

← 7. https://www.anz.co.nz/personal/investing-kiwisaver/anz-kiwisaver/compare-funds/

← 8. https://www.beehive.govt.nz/release/default-kiwisaver-changes-support-more-responsible-investment

← 9. The minimum guarantee applies to all funds, not just the default. It is a composite of the industry’s average performance and the performance of a reference portfolio.

← 10. Every month, the annualised real return during the previous 36 months cannot be less than the lowest value between i) the average annualised real return over the previous 36 months minus four percentage points for the funds with the higher equity exposure (A and B), or minus two percentage points for the funds with the lower equity exposure (C, D and E); and ii) the average annualised real return over the previous 36 months minus the absolute value of 50% of that return.

← 11. https://eur-lex.europa.eu/legal-content/EN/TXT/?uri=CELEX:32019R1238

← 12. The benchmark return could be a bond return or the expected portfolio return given the current asset allocation, for instance. See Temocin, Korn and Selcuk-Kestel (2018[21]) for examples of mechanisms building reserves from contributions, and Goecke (2016[8]) for examples of mechanisms building reserves from investment returns.

← 13. Greater equity investment in the complementary retirement savings scheme may also be justified to diversify risks, when the drivers determining retirement income are different in the main public scheme.

← 14. Wealthy individuals may still be able to take investment risk if they have other sources of income in retirement.

← 15. However, the historical period may be constrained by the data available for the different indices.

← 16. The COVID-19 crisis may reinforce the perception that returns may continue to exhibit lower averages and higher standard deviations for the years to come.

← 17. The drift term may also be expressed as the interest rate plus an equity risk premium. The equity risk premium may be estimated using historical data, an implied measure (Damodaran, 2020[22]) or expert judgment.

← 18. The level of assets accumulated at retirement is divided by the average (over all simulations) sum of nominal contributions to avoid expressing it in currency units.