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The Role of Capital Guaranteed Products in Financial Plans


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The Role of Capital Guaranteed

Products in Financial Plans

May 2008


Important Information

The views expressed in this publication are those of the author(s) and not necessarily those of MLC Investment Management (a division of National Corporate Investment Services Limited), MLC Investments Limited or any other member of the National Australia Group (i.e. National Australia Bank Limited, its related bodies corporate and associated companies and businesses). They are based on the author’s judgement at the time of this publication and are subject to change.

This publication is intended to provide general information only. However where it contains general advice, it has been prepared without taking into account any particular persons’ objectives, financial situation or needs. Accordingly, investors should, before acting on any information in this publication, consider the appropriateness of this information having regard to their own circumstances.

While due care has been taken in preparation of this publication no warranty is given to the accuracy or completeness of the information. Except where under statute, liability cannot be excluded, no liability (whether arising in negligence or otherwise) is accepted by the author(s), National Corporate Investment Services Limited, MLC Investments Limited, or any other member of the National Australia Group for any error or omission or for any loss caused to any person acting on the information contained in this publication. This publication does not constitute an offer or invitation to purchase any investment product. Any offer of an investment product will be made in a disclosure document and applicants will need to complete the

application form attached to that document.



The financial planning challenge for most individuals is the ongoing need to make decisions regarding savings and consumption, investment strategy, borrowing strategy, career, housing, insurance and social security utilisation to satisfy future cash outflows for retirement income and bequeathment. For people with at least modest levels of wealth (or potential wealth through future savings) these cash outflows are generally many years, even decades, into the future. The sensible advice by many financial advisers is to encourage their clients to adopt a disciplined, long term, investment strategy involving growth assets that have a good chance of delivering the returns required over these years, and a low chance that long term returns will be poor or that the individual will live too long for her money. But this approach has a flaw: although the planning horizon is often long term it is only one long term period. A “low chance” of poor returns or living too long will mean that a small proportion of individuals adopting this strategy will, ex post, experience unsatisfactory outcomes and will not benefit from the sharing of risk with most individuals who have met or exceeded their retirement and bequeathment objectives. This paper addresses this issue and examines the types of products that could be offered by insurance companies and other institutions to insure against the low probability that you will be one of those individuals that chance does not favour. These products, by reshaping the return profile and in some cases providing longevity insurance provide an improved match for a retiree’s needs and reduces the risk of a financial plan failing over time.

Keywords: capital guarantees; variable annuities; CPI linked annuities; financial plans; longevity risk.


We thank Wade Matterson of Milliman for providing the economic costs associated with the guaranteed strategies discussed in this paper.



1 Introduction

There is now an extensive literature on variable annuities and modern capital guaranteed products. Most of these have primarily focussed on the manufacturer’s point of view. Much of the discussion is around basic product design, pricing and risk management practices, primarily the hedging of the guarantees and the practical implications of this.

This paper considers these products more from the customer’s point of view. Do these products have a legitimate part in the development of a financial plan? Do they provide a useful tool in financial plans allowing investors to manage the financial risks that they are exposed to over their lives?

The paper looks at the financial risks faced by individuals and considers them in terms of matching assets to future retirement income needs (the present value of which can be considered as “liabilities”), thus drawing out the implications for financial plans.

We then develop a simulation model for a sample investor and compare the outcomes of traditional financial plans which primarily manage the long term risks through exposure to risky assets and those using

guaranteed products. These examples highlight the benefits and costs of using these products to manage the tail risk that individuals are exposed to.

2 Literature Survey

In this paper we have chosen to focus on the role that capital guaranteed products can play in the financial plans of individuals. In acknowledging the narrowness of this focus we note that others have considered broader aspects of the financial planning problem. We mention a few of our favourites here without any pretence that these references are a comprehensive survey of the wealth of writing on personal financial planning.

Ibbotson et al (2007) highlight the importance of individuals considering their whole financial circumstances, including human capital, i.e. the present value of future earned income. Human capital dominates the “wealth” of younger people early in their careers and is a strong reason why people at this stage in their lives can tolerate greater risk in their financial assets (including leverage). But human capital is not riskless, and the ability for people to recover from setbacks in their financial assets diminishes rapidly as people near the end of their working lives. They discuss the role of annuities and the need to manage the risks of longevity. This work covers many aspects of the financial planning problem which are outside the scope of this paper. Another extensive compilation of excellent observations from eminent commentators including Zvi Bodie, Paul Samuelson, Robert Merton, Philip Dybvig, James Poterba, François Gadenne and many others has been published by Research Foundation of CFA Institute (2008) under the title The Future of Life-Cycle Saving and Investing. This compilation covers most of the challenges that face individuals in planning for their retirement. But even here, there are few references to the need to eliminate unacceptable long run outcomes. One exception is Gadenne (on page 86) who suggests that the crucial periods for protecting capital are in the decade or so on either side of retirement:

“Path dependency matters greatly. As a conditional probability statement, the experience of zero returns (let alone negative returns) in the first decade in retirement may be 70–80 percent correlated with portfolio ruin (that is, running out of money before the retiree dies). The


Another important aspect of the financial planning problem is to truly understand, and even adjust, an individual’s expectations. Statman (2002) explores some of the behavioural aspects of financial planning, recognising the powerful human driver of status, and noting that well-being and wealth are not the same thing. How affluent individuals may feel about a significant loss of wealth may be just as important as a driver to their desire to protect it than the practical impact on their standard of living. For example, later in this paper we identify the social security age pension safety net as an “asset”. The “value” of this “asset” will vary to different people depending on their self perception of status etc.

Given the extensive writing on options pricing and hedging strategies in the finance literature, we were surprised to find a relative paucity of papers dealing with how assets with asymmetric payoffs could be used in an individual’s long term financial plan. We suspect that we have missed some important papers; those we found most pertinent are discussed below.

Bodie (1999) conducted some very straightforward modelling that suggests long term investors combining inflation linked securities over one and five year periods with one or five year equity call options can capture much of the upside available from pure equity strategies and remain confident of having wealth accumulation not fall behind inflation. His analysis suggested that using five year options provided better access to

potential equity upside with little downside risk. I believe that Bodie limited his analysis to five year options as longer term options were not available for practical use.

The Bodie results are contrary to expectations and have been disputed by Dert et al (2003), who claim that the strategy of using a five year call option has about the same likelihood of below target outcomes as buying and holding 100% in equities, but considerably lower mean outcome. However, Dert et al do not dismiss the use of well chosen option strategies to outperform in a number of risk-return frameworks, for example as discussed in Carr & Madan (2001).

Carr & Madan (2001) note that arbitrage-free option pricing models are based on replicating option payoffs by dynamically hedging a portfolio that includes the underlying risky asset. This implies that options are not necessary to develop optimal investment strategies as their return distributions can be created by a dynamic strategy involving the underlying assets. This observation is inconsistent with the real world, in which

options are used extensively and are heavily traded. They relax the assumptions of arbitrage-free models by considering agents with different beliefs about return and volatility, and also considering agents with different utility functions, and show that an option will be attractive to different agents in different ways. The

consequence of this is that options will form part of different investment strategies and that trading in options should be frequent. This consequence is consistent with the real world.

Carr & Madan also make the observation that not all investors are able to run dynamic hedging strategies (involving continuous trading) and so are denied option payoffs if their choice of investments is limited to the underlying risky assets. We note that in fact, no agent can trade continuously, but that some agents are better at approximating this than others and will either (a) sell their trading skills to clients either in the form of a guaranteed payoff, or (b) offer their services as an agent acting with delegated authority on behalf of the other less able agents.

An example of the type of dynamic trading strategy this is commonly sold to investors is Constant

Proportions Portfolio Insurance (CPPI). Black and Perold (1992) designed this strategy, which attempts to replicate option payoffs using trading rules on a physical asset. The technique involves a simple rule to “invest a constant multiple of the cushion in risky assets up to the borrowing limit, where the cushion is the difference between wealth and a specified floor”1.


Ledlie et al (2008) give an excellent summary of the product features of Variable Annuities and the actuarial issues arising from them. They give summaries of the main types of guarantees given over variable annuities and give an overview of their development in a number of countries such as the US, Japan and Europe. A number of papers were presented to the IAA Conference in Christchurch last year discussing these products and their potential application in Australia.

Hayman and Hickey (2007) consider the needs of retirees and discuss a range of potential products and financial planning tools, but without detailed modelling. Brennan, Nicholls and Roberts (2007) discussed how modern financial hedging techniques would facilitate the provision of new generation capital guaranteed products in Australia and the attractiveness of these products. Matterson (2007) similarly discussed the variable annuity products, the hedging of investment risks and the capital requirements for manufacturers.

3 The Moving Parts of the Financial Planning Challenge

While financial plans can have many different objectives, we have assumed that their primary purpose is to ensure an adequate standard of living for a person’s entire life.

This means that we need to consider the risk of running out of money by living too long, poor investment performance, or a combination of the two.

We believe that the concept of a personal balance sheet is useful for examining the structure of the financial planning challenge and analysing the risks that individual investors are exposed to.

This then allows us to identify financial and insurance tools that mitigate and eliminate these risks using the classical concepts of asset and liability matching. The analysis allows us to see that traditional financial plans leave many investors exposed to significant tail risks, or conversely over-insure against some risks at an excessive cost.

This personal balance sheet includes a number of items that don’t appear in traditional analyses. These are, nevertheless, real factors in peoples’ financial decision making.

3.1 Liabilities

3.1.1 Home Mortgage

Most people acquire a house by borrowing the money. This is usually their main financial liability for their lives.

For the purposes of this paper we will assume that the mortgage has been paid off.

3.1.2 Investment Loans


3.1.3 Credit Cards etc.

Credit cards are another, expensive, form of debt. Hopefully retirees will have little need for these except as a cash management tool.

3.1.4 Future Living Expenses (Self and Dependants)

The fundamental ‘liability’ that we all have is the necessity to pay for living expenses. The level of these expenses is, of course, discretionary to some extent but we assume for the purposes of financial planning that there is a desired standard of living that is to be funded and that failing to achieve that objective is a failure for the financial plan.

Living expenses covers any dependents who rely on the financial resources of the family.

Living expenses are obviously dependent on how long you live and are influenced by future inflation. The desired level of living expenses is a variable that needs to be squared with the available assets. Too high a desired living standard may require too much risk to be taken to justify it or just ensure that the money will run out.

3.1.5 Future Holidays/Travel etc.

These are more obvious discretionary expenses but they make up a significant part of many people’s retirement objectives.

These expenses are also dependent on how long you live and remain in good health and are influenced by future inflation.

3.1.6 Future Health Expenses

Health expenses include hospital and prescription expenses as well as nursing home and other expenses associated with extreme old age. Some of these expenses are covered by government benefits, such as Medicare and the Pharmaceutical Benefits Scheme, some are covered by health insurance, but others, such as nursing homes are not well covered.

3.1.7 Bequeathment

Most people wish to leave some money to their children or other family members. The level of this desire will affect the amount of risk that investors are prepared to take. There will, of course, be some interaction between desired standard of living (or the amount that people are prepared to spend on living and discretionary expenses) and the targeted legacy. Ibbotson et al (2007) show how the relative preference between income and bequeathment can affect investment strategy.

3.2 Assets

Assets can be divided into two classes:

• Physical assets such as homes, superannuation, other financial assets (including investment properties) and,


3.2.1 Physical Assets Home

The home is a physical asset that also provides for a large component of future living expenses, being a place to live. To the extent that people may be prepared to live in cheaper accommodation then the value of the home could effectively be subdivided into the value of a place to live and an investment asset to pay for future expenses. But this investment value does not generate a return until the home owner takes action such as downsizing, taking in lodgers etc.

Until then, a home owner may continue to live in apparently unnecessarily large house. He or she is

essentially paying a high, but opaque, price for accommodation, being imputed rent. Often these people are fooled by mental accounting cognitive errors, being unable to assess the opportunity cost of not downsizing. But in many cases the emotional utility from remaining independent by living in the family house is very high and such individuals may explicitly or implicitly be prepared to “pay” a considerable price for this.

The value of a house is market dependent, somewhat sensitive to interest rates and also provides some inflation protection as house values tend to go up with inflation. If maintained it will provide accommodation for as long as the owner lives.

Many people want to be able to leave their house as a bequest to their children, which make them reluctant to access their equity in the house.

The house is often thought of as an additional safety net. In the event of a person running out of financial assets or superannuation then they can access some of the house’s value by selling it and downsizing. In essence, this is no more than belt tightening by reducing “imputed rent”. Its attractiveness as a strategy can probably be attributed to mental accounting.

Various equity release products such as reverse mortgages or ‘home pensionisation’ can be used to access home equity while still living in the home. But to the extent that effective downsizing has not occurred, then the home owner continues to pay higher imputed rent than may be necessary.

House sale can also be used to meet nursing home costs and similar health expenses of advanced old age. Superannuation

Superannuation is more of a tax structure than an asset class. However, due to its tax advantages and liquidity disadvantages it is worth considering separately. The risk and return profile of superannuation assets can be tailored to meet the needs of the investor. This is, effectively, one of the key variables in determining the financial plan for an individual.

In the past defined benefit superannuation plans and traditional life insurance products provided

mechanisms where some or all of the market risks were borne by companies rather than the individual. With the demise of these products it is currently difficult for consumers to access assets that are insulated to a greater or lesser extent from market risk. This means that market risks are now being primarily borne by individual investors. Financial Assets


3.2.2 Contingent Assets

A number of assets do not appear on a typical balance sheet, but are, nevertheless, real and should be allowed for in formulating financial strategies. Future Earning Capacity or “Human Capital”

One of the largest assets that a person has is their ability to earn future income. Sometimes this is referred to as human capital. This asset diminishes over time as people approach retirement.

Income from work is usually correlated with inflation and provides a natural hedge against inflation. Retirement dates are often somewhat elastic as retirement can often be deferred if some extra income is needed. Once someone has fully left the workforce, however it is difficult to re-enter it.

Future income also gives the possibility of investing money at lower prices if market prices do fall, allowing assets to be rebuilt over time. This gives a resilience that allows some higher financial risks to be taken in order to achieve investment goals.

The level and volatility of earned income will depend on the skills of a person and the industry that they work in. Someone working in, say, an investment bank with volatile earnings dependent on investment markets is in a different position to someone whose income is largely fixed and is not dependent on markets, for example, a public servant. Ibbotson et al (2007) explore this issue. Social Security

The Australian Social Security system is a very good system which provides a minimal level of income, which increases with inflation and is for life. It is subject to assets and income tests and therefore acts as a cushion for reductions in other asset values, as the pension increases as assets decline over the range between full eligibility to no eligibility.

Many people believe that they won’t need much income at an advanced age and that they will be happy to live on the pension alone at old age. Many people don’t factor in the costs of long term health care at older ages, which can mean that the combination of Medicare and the pension is inadequate at these older ages. Our position is that for most retirees living on the social security pension on its own is a failure of the financial plan. It does, however, offer a real safety net for retirees and can form an important component of a person’s financial plan.

The jury is out regarding the reliability of this “asset” into the future. Certainly many countries with

deteriorating dependency ratios and “cradle to grave” social security systems are, or will need to, significantly reduce old age pensions or increase retirement ages. Arguably Australia is in a better position than most, primarily due to immigration and compulsory superannuation. And the electoral power of the aging baby boomers may be a force to retain the value of social security well into the future. Nevertheless, the quantum of this contingent asset is not certain. Inheritances

Many people can expect to receive some sort of inheritance from their parents. It is interesting to note that many people mentally segregate inheritances and are keen to preserve them for their own children. This means that they can have a different risk and return preference for this part of their assets.


3.3 Summary

The above can be summarised in the following table which looks at the key characteristics of each of the assets and liabilities that make up the Personal Balance Sheet.

We believe that this gives a very useful framework for considering how a financial plan should be structured at various time of life.

Physical or Contin-gent? Market Sensitivity Interest Rate Sensitive?

Time Inflation? Longevity Risk?



Home Mortgage Physical None Yes No No No No

Investment Loans Physical None Yes No No No Yes

Credit Cards etc. Physical None Yes No No No Yes

Living Expenses (self and dependants)

Physical None No Reduces Yes Yes No

Holidays/Travel etc. Physical None No Reduces Yes Yes Yes

Health Expenses Contingent None No Increase Yes Yes No

Bequeathment Contingent None No No Yes Yes Yes


Home Physical Positive Indirect No Yes No n/a

Superannuation Physical Positive ? No ? No n/a

Financial Assets Physical Positive ? No ? No n/a

Future Earning Capacity

Contingent None No Reduces Yes No n/a

Social Security Contingent Negative No Reduces Yes Yes n/a

For the purposes of this paper, we will conduct case studies on individuals aged 50, 65 and 75. These will include earnings over the period to retirement and then on superannuation assets and living costs in retirement. Other elements of the personal balance sheet will be ignored.

We also assume a preference for income over maximising a potential bequest.

The typical financial plan for a retiree will have their superannuation invested in a mix of financial assets such as a Balanced or Growth oriented diversified fund. This will be subject to market risk. They have no financial liabilities; the only “liability” we consider is the value of future retirement income.

We show by way of these simple cases that the typical financial plan leaves investors with a significant asset-liability mismatch, with longevity and inflation risk that isn’t matched by the typical portfolio of financial assets.


considerable risk of their client running out of money and they have no satisfactory tool to meet that risk. They therefore avoid the conversation by not illustrating it. It is this risk that is the focus of our concern in this paper.

4 Attitudes to Risk

Attitudes to risk are both varied and often inconsistent. Spectacular risks, such as being eaten by a shark or an aeroplane crash tend to be overestimated while more mundane risks such as being involved in a motor vehicle accident are ignored.

In financial services many people do not understand the link between risk and returns. Additionally high personal discount rates mean that for many people long term issues and risks tend to pale into


Interestingly attitudes to risk can be affected by how the questions and issues are framed.

McCrae (undated) shows how the framing of questions can influence the responses of clients to financial planners in setting investment objectives and structures.

Brown et al (2008) investigate using surveys how framing annuities as either consumption tools or investment vehicles change the attitude of people to annuities in the US market. Their conclusion states:

“We hypothesize that framing matters for annuitisation decisions: in a consumption frame, annuities are viewed as valuable insurance, whereas in an investment frame, the annuity is a risky asset because the payoff depends on an uncertain date of death. Survey evidence is consistent with our hypothesis that framing matters: the vast majority of individuals prefer an annuity over alternative products when presented in a consumption frame, whereas the majority of individuals prefer non-annuitised products when presented in an investment frame. To the extent that the investment frame is the dominant frame for consumers making financial planning decisions for retirement, this finding may help to explain why so few individuals annuitise.”

We would expect that this would also apply in the Australian market, except more so, as annuities have such a small market presence in the Australian financial planning landscape.

5 Four Strategies

In this section we consider four strategies that may be considered when developing a financial plan. We label them:

1. “Matching”

2. “Long term investment strategy”

3. "Using insurance with embedded guarantees”

4. “Using deferred withdrawal guarantees for life, with uplift”


We discuss each strategy in turn and present the outcomes from simple modelling of investment and longevity risk. In Section 6 we propose some metrics that attempt to describe this risk in a readily

understandable form that could be used by planners with their clients. The values of these metrics for each of these four strategies are then summarised and discussed.

5.1 Strategy 1: Matching

The most obvious way an individual can attempt to remove investment and longevity risk is to set the asset portfolio to have future cash flows that approximately match the desired cash flow stream in retirement. Significant and obvious life uncertainties such as the timing of death and future inflation could conceivably be hedged by inflation linked life annuities, but even here few truly suitable products are available.

Other less obvious uncertainties such as credit risk, inflation basis risk and unforseen lifestyle changes make even these vehicles only approximate matches to retirement income requirements.

Even if the ideal product was available, we observe that few individuals find these products attractive. Perhaps the two most cited reasons are (a) the irrational sense of unfairness of losing capital in the event of early death, and (b) the rational concern that many of these products are too expensive compared to other strategies in which the individual retains some risk.

For example, we understand that $100,000 can buy CPI linked annuities at age 65 of around $4,500 for males and $4,000 for females. We are able to approximately replicate these rates using best estimate annuitant mortality rates with mortality improvement, discounting at a real rate of around 1.3% pa (tax free) less a “spread” of 1% pa, and then adding 25% loading. The spread and loading are intended to make some allowance for the profit, expenses and risk associated with hedging CPI liabilities into the distant future. In this, and the other strategies, we examine the outcomes for three individuals:

• A single male2 aged 50 who planned to work to age 65, save at a rate of $15,000 pa before then and draw a retirement income from this investment of $30,000 and has just sufficient assets at age 50 which, together with savings until retirement, will pay for deferred CPI adjusted annuity to match this retirement income requirement. (All dollar amounts in this paper are expressed in today’s dollars, with rates of return and discount rates expressed in real, after tax3, terms.) The amount required at this age is $344,0194. We do not believe that such deferred CPI annuities are available and have based this purchase price on the above assumptions, which are consistent with observed market prices at age 65. • A single male age 65 just retired with $666,7195 in assets, once again just sufficient to purchase a CPI

annuity providing a real income of $30,000.

• A single male age 75 with $425,685 in assets, just sufficient to purchase a CPI annuity providing a real income of $30,000.

In the following charts we show the value of such annuities to age 95. The lines are very close to each other, but not identical, as the older purchasers do not benefit from the “survivor” benefit of buying these annuities at earlier ages.


50 55 60 65 70 75 80 85 90 95 0 200 400 600 800 1000 1200

Matched strategy; Commencing at age 50

age Wea lt h $0 00

Value of CPI annuity

65 70 75 80 85 90 95 0 200 400 600 800 1000 1200

Matched strategy; Commencing at age 65

age Wea lt h $0 00


75 80 85 90 95 0 100 200 300 400 500 600 700 800

Matched strategy; Commencing at age 75

age Wea lt h $0 00

Value of CPI annuity

One interesting aspect of these lines are that they are mildly convex in retirement, i.e. the value decreases at a decreasing rate. This is due to the fact that an annuity is only paid if you are alive to collect it, and thus survivors benefit from the release of reserves when others in the pool die. This is unlike the paths of median investment assets (see later charts) that tend to diminish at an accelerating rate as assets are drawn to pay retirement income.

One reason why this type of approach to completely matching retirement income is rare may be due to the fact that it can only be relevant to a small subset of individuals with assets not significantly in excess or deficit of that required for the match.

An individual with insufficient assets to match their expected retirement needs will simply lock in misery by adopting a matched strategy. The blandishment to spend less now and save more for tomorrow may help in some circumstances but can often be patronising and insensitive to the immediate financial challenges facing many people. In these circumstances the individual may be best to save what he can, invest sensibly according to his attitude to risk, develop realistic expectations about standards of living and simply rely on social security and fortune for his retirement. Some of the strategies discussed later may be suitable for this investor, but matching will be unlikely to play a role.


5.2 Strategy 2: Long Term Investment Strategy

A more typical approach to setting investment strategy for a long term investor is to estimate the individual’s future cash flows (savings, retirement income and anticipated lumpy cash flows, such as replacing the car, downsizing the family home etc) and demonstrate the range of outcomes that would occur if a particular investments strategy was to be used.

Under this approach the investment strategy is defined in advance. Indeed it will often involve an asset allocation maintained over the individual’s life. Marginally more sophisticated approaches will adjust the asset allocation over time, but in a predefined way, often referred to as a “glide path” that reduces the allocation to risky assets as the individual approaches and moves through retirement. (See section 7.2 for a brief discussion.)

Under this strategy the investment portfolio is not dependent on the path of risky outcomes that have been experienced in the assets (or indeed the liabilities). In reality, individuals using such an approach will modify their investment, savings and consumption choices in response to unfolding conditions over their life, but the strategy itself does not respond in this way.

Armed with projected cash flows (typically deterministic) and assumed stochastic returns (typically annual) derived from long term return and risk assumptions (typically mean-variance) the individual’s adviser is able to demonstrate to the client the range of wealth outcomes that could be expected over time.

For the purpose of illustration, we demonstrate a strategy whereby a risky portfolio of assets is rebalanced annually to an invariant asset allocation (i.e. we do not bother with a glide path). We also assume time invariant economic conditions that are consistent with a mean real rate of net return of 3.6% per annum before retirement (after fees and superannuation tax) and 4.6% per annum in retirement (tax free, after fees). The respective annual standard deviations are 11.9% and 13.6%. We also assume that these rates of return are log normally distributed and are serially independent. These assumptions are clearly simplistic as they do not incorporate (a) time variance of risk premia, (b) long term mean reversion and (c) non-normal return distributions, all of which are evident in many asset prices. Sophisticated models used for real investment strategy should include these attributes, but the simplistic approach outlined above is satisfactory for the demonstration of the issues in this paper.

We plot the median, 1st and 99th percentile outcomes for such a strategy applied to the same individuals described in Section 5.1. We also redraw the value of a strategy matched by a CPI annuity and quantify a metric labelled “probability of running out of money”. Its meaning is self evident, but is formally defined later in the paper.


50 55 60 65 70 75 80 85 90 95 0 200 400 600 800 1000 1200

Risky investment strategy with no guarantees commencing at age 50

age Wea lt h $0 00

Probability of running out of money 13%

Value of CPI annuity Risky strategy: median Risky strategy: percentile 1 Risky strategy: percentile 99

50 55 60 65 70 75 80 85 90 95 0 5 10 15 20 25 30 35

Risky investment strategy with no guarantees; Commencing at age 50


Some observations:

• The median outcome of this strategy allows the individual to virtually live off real investment returns during retirement, leaving a level of wealth at death (at any age) not significantly diminished since retirement.

• The 1st percentile is clearly worse than the matched strategy as the individual runs out of wealth by age 77.

• This is of course, balanced by upside risk, which is demonstrated by wealth growing to very high levels; the 99th percentile goes off the scale used in this chart before retirement.

• Clearly, the investor has choices along the way if extreme outcomes occur (good or bad). Many people unwittingly increase their standard of living when wealth is available and would spend at a higher rate than planned if the means were available. And in the case of bad outcomes, the investor would tighten their belts (at least to some extent) to make their money last longer.

• But the downside risk is clearly evident. The chart shows that there is a 1:100 chance of this individual running out of money by age 77. How he reacts to this risk can be complex, and will involve

considerations of attitudes to relying on social security, relying on family, standards of living etc. • The immediate jumps to $30,000 in the shortfall chart shows the stark consequence of running out of


The outcomes for other cases (commencing at age 65 and 75) for this strategy are set out in the following charts. Once again, we assume that the assets available to such people are those available to purchase a CPI annuity. 65 70 75 80 85 90 95 0 200 400 600 800 1000 1200

Risky investment strategy with no guarantees commencing at age 65

age Wea lt h $0 00

Probability of running out of money 14%


65 70 75 80 85 90 95 0 5 10 15 20 25 30 35

Risky investment strategy with no guarantees; Commencing at age 65

age In c o m e Sh o rtfa ll $ 0 0 0 percentile 99 percentile 95 percentile 75 75 80 85 90 95 0 100 200 300 400 500 600 700 800

Risky investment strategy with no guarantees commencing at age 75

age Wea lt h $0 00

Probability of running out of money 21%


75 80 85 90 95 0 5 10 15 20 25 30 35

Risky investment strategy with no guarantees; Commencing at age 75

age In c o m e Sh o rtfa ll $ 0 0 0 percentile 99 percentile 95 percentile 75

It is easy to take pot shots at the assumptions behind this sort of modelling, but to do so ignores the fact that this approach allows advisers to help their clients understand two key issues:

• the relationship between current wealth levels, planned savings and retirement income expectations • the notion of risk

This paper is not the place to critically evaluate this type of modelling. But it does beg an important question, which can be very difficult to answer: “What happens if my returns experience just happens to be the 1 in 100 chance of falling below the bottom of your range? This modelling tells me I will run out of money and the investment strategy you are proposing does nothing to guarantee that I won’t.”

The two strategies modelled in the following subsections describe some of the solutions that may be made available to deal with this critical issue.

5.3 Strategy 3: Using Insurance with Embedded Guarantees


There are many flavours of such products, including simple versions that underpin asset values during the accumulation phase to those that guarantee a withdrawal benefit for life.

Many of these products have a guaranteed amount that ratchets if, at certain dates such as policy

anniversaries, the underlying asset values exceed the guaranteed amount. These tend to be very popular with clients and their advisers, but do cost more, give more upside, but may not be as cost effective as possible in protecting the downside.

Also, investors and their advisers do not tend to value guarantees that protect inflation. This is one reason why most of these products are expressed in terms of nominal values (i.e. not inflation adjusted). Another reason is that the difficulty for the life office in hedging uncertain future inflation can mean that true inflation protected products are rare.

In this section we model how the use of “popular” insurance products of this type can help to mitigate, the shortfall between available retirement income and desired retirement income. In the next section we devise a potential improvement that may provide more effective protection.

In this section we model:

• An individual in his accumulation phase purchases a Guaranteed Minimum Accumulation Benefit (GMAB) rider for 15 years with a guaranteed amount uplifted by 3% pa to approximate maintaining the real value of this wealth by retirement. This 3% uplift is a proxy for inflation and tends not to be popular (as it is more expensive than guaranteeing nominal account values). This rider is assumed to cost 1.1% per annum of the amount guaranteed6. The rider during this phase has no ratchets. We have assumed that the further savings before retirement are not protected, but real life strategies could include this. • On retirement the individual then purchases a rider that guarantees, to the extent possible, a retirement

income of $30,000 (in today’s dollars) for life by purchasing a Guaranteed Minimum Withdrawal Benefit (GMWB) of 6% for life, with annual ratchets of the nominal balance of the assets in retirement. This is not a guaranteed real income and, in some cases, it will fall short of the desired income. If the real value of assets at retirement are lower than $500,000 (i.e. required to deliver $30,000), a partial guarantee is purchased. We deduct a cost for these products of 1.03% per annum of the amount guaranteed from age 65 and 0.92% from age 75.

For consistency, the same underlying investment strategy as used in Section 5.2 is applied to the underlying investments. The same two charts (wealth and shortfall) are produced for each of the three ages at


50 55 60 65 70 75 80 85 90 95 0 200 400 600 800 1000 1200

Probability of running out of money 23%

GMAB and nominal GMWB with ratchets; Commencing at age 50

age Wea lt h $0 00

Value of CPI annuity

Risky strategy: percentile 99 Risky strategy: percentile 50 Risky strategy: percentile 1

The chart above shows:

• The probability of running out of money in this case is 23%, much higher the 14% for the previous strategy without guarantees. This is due to the cost of the guarantees that are paid out of the assets. • The cost of the guarantees can also be seen in the median wealth outcome, which shows a distinct

droop over time. The bequeathment to the kids will be reduced, but they may not need to financially support their parent in old age.


50 55 60 65 70 75 80 85 90 95 0 5 10 15 20 25 30 35

GMAB and nominal GMWB with ratchets; Commencing at age 50

age In c o m e Sh o rtfa ll $ 0 0 0 percentile 99 percentile 95 percentile 75


50 55 60 65 70 75 80 85 90 95 0 5 10 15 20 25 30 35 40

GMAB and nominal GMWB with ratchets; Commencing at age 50

age In c o m e T o pu p $ 00 0 percentile 99 percentile 95 percentile 75

This additional chart shows the top ups that the insurance company will need to make to meet the

obligations of the insurance contracts. As expected, it has two bumps. The first is at retirement when the guarantees associated with the GMAB kick in. Then after 10 to 15 years in retirement when the GMWB guarantees start to be called upon.


65 70 75 80 85 90 95 0 200 400 600 800 1000 1200

Probability of running out of money 24%

GMAB and nominal GMWB with ratchets; Commencing at age 65

age Wea lt h $0 00

Value of CPI annuity

Risky strategy: percentile 99 Risky strategy: percentile 50 Risky strategy: percentile 1

65 70 75 80 85 90 95 0 5 10 15 20 25 30 35

GMAB and nominal GMWB with ratchets; Commencing at age 65


65 70 75 80 85 90 95 0 5 10 15 20 25 30 35

GMAB and nominal GMWB with ratchets; Commencing at age 65

age In c o m e T o pu p $ 00 0 percentile 99 percentile 95 percentile 75 75 80 85 90 95 0 100 200 300 400 500 600 700 800

Probability of running out of money 29%

GMAB and nominal GMWB with ratchets; Commencing at age 75

age Wea lt h $0 00

Value of CPI annuity


75 80 85 90 95 0 5 10 15 20 25 30 35

GMAB and nominal GMWB with ratchets; Commencing at age 75

age In c o m e Sh o rtfa ll $ 0 0 0 percentile 99 percentile 95 percentile 75 75 80 85 90 95 0 5 10 15 20 25 30

GMAB and nominal GMWB with ratchets; Commencing at age 75


5.4 Strategy 4: Using Deferred Withdrawal Guarantees for Life, with


The third strategy modelled in the previous section shows how popular usage of insurance products provides some protection from investment and longevity risk. In the forth strategy discussed in this section we

propose usage of a different, less popular, type of strategy that provides more efficient protection. The strategy involves a deferred GMWB for life, with annual uplifts with the purpose of maintaining the real value of the protected retirement income in the face of anticipated future inflation. It does not, however, attempt to remove the risk of unanticipated inflation. We have yet to see significant use of GMWBs for life with a protection linked to inflation. These are likely to be expensive as the provider cannot easily hedge the unanticipated inflation risk.

Specifically we model:

• A 50 year old individual purchases (to the extent affordable) a rider that guarantees a retirement income commencing at age 65. The guarantee is based on a deferred GMWB of 5% for life, with 3% per annum uplift. With the assets of $344,019 available at age 50, only $17,201 can be protected. (We do not attempt to use the next 15 years of savings to buy further protection, but this could be done.) This amount is uplifted at the rate of 3% every year. It turns out in the modelling assumptions we use that 3% is higher than the rate of inflation, so the real value of the guarantee marginally improves over time. But the individual retains the risk that inflation is higher than the 3% uplift. We have not attempted to make inflation stochastic (a relatively trivial extension of the model) and do not present this inflation basis risk in this paper. This guarantee is relatively cheap. We have assumed a cost of 0.75%, including allowance for profit, expenses and hedging risk.

• The 65 year old purchases a similar product, but without the deferred period. He has $666,719 at age 65, more than enough for the $600,000 required to purchase $30,000 for life, uplifted at 3% per annum. This is the reason why the results shown in the following charts show that this individual suffers no shortfall. The cost of this protection is 1.05% per annum.

• The 75 year old has $425,685 and can only afford protection of $21,284 for life, uplifted at 3% per annum. The consequent shortfall is shown in the following charts. The cost of this protection is 0.79% per annum, lower than the 65 year old as the remaining life is shorter.


50 55 60 65 70 75 80 85 90 95 0 200 400 600 800 1000 1200

Deferred GMWB with uplift, but no ratchets commencing at age 50

age Wea lt h $0 00

Probability of running out of money 19%

Value of CPI annuity Risky strategy: median Risky strategy: percentile 1 Risky strategy: percentile 99


50 55 60 65 70 75 80 85 90 95 0 5 10 15 20 25 30 35

Deferred GMWB with uplift, but no ratchets; Commencing at age 50

age In c o m e Sh o rtfa ll $ 0 0 0 percentile 99 percentile 95 percentile 75

The kids would also be pleased with the size of the shortfall. As the GMWB has a 3% uplift, the real value of the protection it offers is approximately maintained. (The downward slope of these lines simply


50 55 60 65 70 75 80 85 90 95 0 5 10 15 20 25

Deferred GMWB with uplift, but no ratchets; Commencing at age 50

age In c o m e T o pu p $ 00 0 percentile 99 percentile 95 percentile 75 65 70 75 80 85 90 95 0 200 400 600 800 1000 1200

Deferred GMWB with uplift, but no ratchets commencing at age 65

age Wea lt h $0 00

Probability of running out of money 28%


65 70 75 80 85 90 95 0 5 10 15 20 25 30 35

Deferred GMWB with uplift, but no ratchets; Commencing at age 65

age In c o m e Sh o rtfa ll $ 0 0 0 percentile 99 percentile 95 percentile 75


65 70 75 80 85 90 95 0 5 10 15 20 25 30 35 40 45 50

Deferred GMWB with uplift, but no ratchets; Commencing at age 65

age In c o m e T o pu p $ 00 0 percentile 99 percentile 95 percentile 75 75 80 85 90 95 0 100 200 300 400 500 600 700 800

Probability of running out of money 28%

Deferred GMWB with uplift, but no ratchets; Commencing at age 75

age Wea lt h $0 00

Value of CPI annuity


75 80 85 90 95 0 5 10 15 20 25 30 35

Deferred GMWB with uplift, but no ratchets; Commencing at age 75

age In c o m e Sh o rtfa ll $ 0 0 0 percentile 99 percentile 95 percentile 75 75 80 85 90 95 0 5 10 15 20 25 30

Deferred GMWB with uplift, but no ratchets; Commencing at age 75


6 Definition of Risk

The preceding discussion shows up the inadequacy of defining risk in terms of variance of returns. Even one-sided metrics such as negative volatility or a measure that gives greater weight to negative returns (say squaring negative returns) say nothing about the success in achieving the objectives of a financial plan. Indeed, long term outcomes are also very much affected by the mean of the return distribution, which is the reason why very conservative approaches may have a greater risk (even certainty) than more volatile strategies of not growing assets at a sufficient rate to meet retirement income objectives.

For individuals we believe that the risk metric to apply to a financial plan is related to the risk of a retiree outliving his or her money and therefore not achieving their desired standard of living.

We have already canvassed one simple metric to demonstrate this, i.e. the probability of the invested funds running out while the investor is still alive (“ProbUnfunded”). The definition of this metric is:






when the































x n s x n

This metric can be used as a way to encourage people to consider protecting against long term downside investment risk and longevity risk. But it is not informative when such protection is in place. We have devised two linked metrics that attempt to illustrate this without the adviser needing to delve too deeply into the actuarial conceit of mortality rates. After all, an individual is either alive or dead, and the concept of probability of survival is only really relevant for large pools of independent lives.

We do this by considering the investor’s position at particular ages. In essence, we say: “If you live to (say) 85 years old, what will your circumstances then be?”

The two linked metrics are the probability that the individual will have a shortfall in income by this age, and if he does, the extent of that shortfall. The first gives a sense of likelihood of needing to tighten the belt at and by this age. The second indicates by how much the belt may have to be tightened.

More formally, the two metrics are:

probability of shortfall at age y for someone currently aged x, labelled: “ProbShortfallx,y”

• severity of shortfall, defined as the conditional value of shortfall at age y as a proportion of the present value of future desired retirement income at that age for someone currently age x, labelled:


y x, s y y x all ProbShortf y RetInc PV s everity ShortfallS

≡ ( , ) ) Pr( , SO y Shortfall PV( , ) ∞

= +

s t t y t y t














annuity CPI the of value in the implied spread) (less rate interest after tax real 1+ ≡ v 1 z RetInc Shortfall

cashflowz ≡cash flow(egshortfall" "or retirementincome" ")at age


For a male now aged 50 at age: 75 85 95 Risky investment strategy with no guarantees

Probability of shortfall 0.7% 10.7% 25.1%

Shortfall severity 0.7% 10.6% 24.9%

GMAB and nominal GMWB with ratchets

Probability of shortfall 2.0% 23.0% 42.7%

Shortfall severity 0.9% 10.5% 21.5%

Deferred GMWB with uplift but no ratchets

Probability of shortfall 1.8% 18.7% 36.1%

Shortfall severity 0.6% 5.7% 10.0%

For a male now aged 50 at age: 75 85 95 Risky investment strategy with no guarantees

Probability of shortfall 0.0% 11.0% 33.9%

Shortfall severity 0.0% 10.9% 33.6%

GMAB and nominal GMWB with ratchets

Probability of shortfall 0.1% 21.0% 51.1%

Shortfall severity 0.0% 8.8% 24.3%

Deferred GMWB with uplift but no ratchets

Probability of shortfall 0.0% 0.0% 0.0%

Shortfall severity 0.0% 0.0% 0.0%

For a male now aged 50 at age: 75 85 95 Risky investment strategy with no guarantees

Probability of shortfall 0.0% 3.5% 59.2%

Shortfall severity 0.0% 3.3% 58.6%

GMAB and nominal GMWB with ratchets

Probability of shortfall 0.0% 8.6% 74.0%

Shortfall severity 0.0% 3.3% 34.4%

Deferred GMWB with uplift but no ratchets

Probability of shortfall 0.0% 8.5% 73.1%

Shortfall severity 0.0% 2.0% 15.3%

Some observations can be made about these results:


• On this count, the more efficient guarantees (Strategy 4) generally cost less than for Strategy 3 and have a lower likelihood of a shortfall occurring.

• The severity of the shortfall is considerably reduced when guarantees are available. The efficiency of Strategy 4 over Strategy 3 on this metric is stark.

• It should be noted that we have used the same asset allocation for the ‘with and without guarantee’ comparisons. The presence of guarantees offers the opportunity to use a more aggressive asset allocation, which may give a better upside outcome albeit with a higher risk of shortfall.

7 Other Strategies

A number of other strategies were contemplated, but have not been explicitly modelled. Some brief comments on each follow.

7.1 Matched and Surplus Portfolios

One simple approach to removing some investment and longevity risk is to split the individual’s assets into those required to match an acceptable level of retirement income (the “matching portfolio”), and those in excess of that level (the “surplus portfolio”). The “acceptable” level of retirement income may be lower than the desired level which was matched in the strategy described in Section 5.1.

The investment strategy applied to the matching portfolio is identical to the matching strategy described in Section 5.1. The key requirement of the investment strategy for the surplus portfolio is that it cannot lose more than its capital. Typical investments in stocks, bonds, either directly or via commingled vehicles will easily satisfy this requirement. Even most commingled vehicles with internal leverage will satisfy this requirement provided they have no recourse to the investor. But leverage or shorting activity undertaken in the investor’s own name may well violate this condition.

Assuming that direct leverage or shorting is absent or limited, this approach will allow the investor to be confident that his minimum acceptable level of retirement income will be available. (Subject, of course, to the caveats regarding counterparty risk, inflation basis risk etc described in Section 5.1.)

While this approach does seem to put a floor on the payoffs, it is unlikely to provide the most attractive payoff to the client. In many cases, too much of the client’s wealth is locked up in the matched portfolio. Moreover, the concept of splitting the portfolio into two, devising strategy separately may well give suboptimal


7.2 Lifecycle Approaches


7.3 Constant Proportions Portfolio Insurance

The concept of Constant Proportions Portfolio Insurance is mentioned in the literature survey. Developments on this approach have found their way into many “protected strategies” offered to retail investors. The risky asset in these products often has an attractive story (eg skill of a hedge fund manager, investing in an emerging market), but despite being attractive, is difficult to sell into the retail market as the perceived risks are too high. But packaged with CPPI, the investor can be sold the illusion of participating in the attractive risky opportunity, with the assurance of limited downside.

However, as Wilcox (2003) identified, the size of the multiple of the cushion that is invested in the risky asset needs to quite large to benefit from the option type payoffs promised by CPPI. But this means that many participants who experience an early period of sharply negative returns on the risky asset will be sold out of the risky asset early and will not participate in later higher returns. This is called “cashing out”.

Our concern in this paper is protecting long term returns, and this feature of CPPI is problematic when the technique is applied over a decade or more. The heavy “cost” of this protection is the lost opportunity of participation in the returns of the risky asset. This opportunity cost can be hidden if the risky asset does not have public pricing outside of the bundled CPPI product. This is probably why the technique tends not to be applied to a substantial portion of an investor’s wealth where the risky asset is a diversified fund with public pricing.

7.4 Short Term “Capital Protected” Products

Like CPPI, many risky, narrow-based investment products are combined with some type of short term protection to make the risk tolerable, without appearing to dilute the “hope” of high returns. These products are generally not designed to take into account the investor’s holistic long term goals and thus are generally not efficient in reducing the longevity and long term investment risk that is the focus of this paper.

Having said that, some providers offer a service that rolls a number of medium term (2-5 year) option contracts which adjust the medium term payoff of the investment strategy. These approaches vary in their sophistication, but often use collar strategies that limit the downside with put options, paid for by selling call options that limit the upside.

These strategies are only designed (and sold) as assisting to manage investment risk; longevity risk is outside their scope. It is outside the scope of this paper to further assess such strategies, but we do observe that any overinsurance embedded in the strategies will almost certainly make these approaches less efficient than strategies that look to solve the holistic financial planning problem. (Strategy 4 discussed earlier is closer to this goal.)

8 Conclusion

This paper has developed a model of the personal balance sheet and analysed the risks that people face in solving the retirement planning problem. Traditional financial plans leave investors exposed to a significant risk of outliving their capital and suffering a significant shortfall in their desired standard of living.


Comparing strategies, it appears that a product offering an element of inflation protection provides a superior outcome to one that relies on ratchets. This is because in some cases the ratchets can result in over

insurance. This has a cost that could be redeployed to provide some inflation protection.

This paper is only a first step in the investigation of the retirement savings problem. It has investigated the case of people with ‘just enough’ assets at the outset. There is scope to examine the position of people with higher and lesser amounts of assets. There is also scope to investigate more complex strategies and other financial products.

9 References

Black, F. & Perold, A. 1992, ‘Theory of Constant Proportion Portfolio Insurance’ Journal of Economic Dynamics and Control, 16 (1992), pp 403-884.

Bodie, Z. 1999, ‘The Design and Production of New Retirement Savings Products’ The Journal Of Portfolio Management Winter Vol 25, Number 2.

Brennan, Nicholls and Roberts (2007) A Review of Design and Hedging Strategies for Modern Australian Investment Guarantee Products Institute of Actuaries of Australia

Brown, Kling, Mullainathan, Wrobel, Why Don't the People Insure Late Life Consumption?

A Framing Explanation of the Under-Annuitization Puzzle , American Economic Review Papers and Proceedings 98:2 (2008), forthcoming.

Carr, P. & Madan D. 2001, ‘Optimal Positioning in Derivative Securities’ Quantitative Finance, Vol 1 pp 19-37.

Hayman L. Hickey J. (2007) Innovation In Retirement Incomes Institute of Actuaries of Australia

Ibbotson, R.G., Milevsky, M.A., Chen, P. & Zhu, K.X. 2007, ‘Lifetime Financial Advice: Human Capital, Asset Allocation, and Insurance’, Monograph published by Research Foundation of CFA Institute.

Ledlie M.C., Corry D.P. Finkelstein G.S. Ritchie A.J. Su K. Wilson D.C.E. Variable Annuities Institute of Actuaries, Faculty of Actuaries March 2008

McCrae M. (undated) Behavioural Factors in client risk profiling by financial planners School of Finance and Accounting University of Wollongong.

Matterson W.(2007) Wealth Management or Risk Management – The Future of Retirement Security Institute of Actuaries of Australia

Research Foundation of CFA Institute, 2008, The Future of Life-Cycle Saving and Investing (2nd Edition) edited by Bodie, Z., McLeavey, D., & Siegel, L.B.

Statman, M. 2002, ‘Financial Physicians’, Investment Counseling for Private Clients IV, AIMR (CFA Institute). Wilcox, J. 2002, ‘Harry Markowitz and the Discretionary Wealth Hypothesis’, The Journal of Portfolio



Black and Perold (1992) page 404


Please excuse the apparent sexist approach to modelling only on male mortality. Indeed, given the lower mortality of females, and thus the higher representation of women in older age groups, modelling a female may have been more relevant. Even closer to reality would be to examine the outcomes for the last survivor of a partnership, but this would have involved increased complexity of modelling and assumptions and would have yielded little incremental insight into the issues investigated.


Tax regimes assumed in the modelling: All investments prior to retirement are assumed to be in superannuation, and after as a superannuation pension.


Please excuse the spurious accuracy, but the principle of setting initial assets equal to the value of the CPI annuity aids in maintaining consistency between the models. It would be interesting, but outside the scope of the present paper, to compare these (and other) strategies for individuals who are significantly better or worse funded.


A CPI linked annuity of $30,000 purchased for $666,719 is approximately at the rate of $4,500 for $100,000 which we have observed in the market.



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