## Earn CE credits

“The design and depletion of retirement portfolios” is eligible for CE credits. See **Accreditation details** for more information.

**Summary:** Graham Westmacott, portfolio manager at PWL Capital, and Susan Daley, investment advisor at PWL Capital, show how retail advisors can use a pension-style approach to optimize clients’ drawdown portfolios.

## Introduction

The facts that are indisputable are that we are living longer and returns from income generating securities such as bonds have fallen to historic lows. This results in an increased focus on making retirement portfolios more efficient at generating income. Retirees must grapple with two uncertainties: future market returns and how long they will live. Remove these uncertainties and it would be straightforward to project a future consumption pattern that uses all the retirement savings while they are alive. We would consider this an efficient depletion strategy.

Our goal is to introduce tools and ideas that have been in the research literature for some years but not readily accessible to retail investors. The focus is pragmatic and uses widely available investment products that are liquid, low-cost and transparent. When retirement constraints are removed, the portfolios should revert to a well-diversified accumulation portfolio.

## The real retirement crisis

The concern expressed most often about retirees is whether they are saving enough. Sun Life’s Canadian Health Index 2014 found 45% of Canadians are worried about outliving their retirement savings. The good news is that most Canadians in, or soon to be in, retirement are well provided for, although younger savers face more of an uphill struggle.

Of more concern is that many investors lack a workable strategy for converting assets into income. The decline of defined-benefit pension plans has shifted responsibility for managing retirement to the individual through defined-contribution pensions (which aren’t really pensions but savings schemes), RRSPs, TFSAs and taxable savings. The individual saver is left to figure out how much to save, which investment vehicles to use, how to invest, how to convert assets into income and how much to spend.

These are difficult questions to answer. Our goal in this course is to show how some of the tools developed by researchers and used by the pension industry can be applied to better design retirement portfolios for individual investors.

## Why are retirement portfolios different?

Consider the situation of Alan and Betsy, both aged 60, who have invested $1 million in a diversified Canadian equity portfolio. Over the past 20 years, such a portfolio has averaged 8.4% annually, so they consider it prudent to withdraw $60,000 per year (6% of the initial investment). Unfortunately, they do not realize that two out every five investors who pursue this strategy are going to run out of money by age 90 and that the likelihood of one of them living beyond 90 is almost 50%.

Alan and Betsy have encountered two problems specific to retirement portfolios. The first is that withdrawing a fixed amount from a portfolio that fluctuates in value can make the portfolio vulnerable to an irreversible decline if it experiences a market downturn. Second, there is uncertainty about how long they will live and for how long the investments have to provide income. In industry jargon, Alan and Betsy are vulnerable to *withdrawal risk* (spending too much) and *longevity risk *(outliving their money).

Both these risks relate to income, so addressing them requires a fundamental shift from a capital appreciation perspective to an income perspective. The conventional view of portfolio performance is that investment decisions are focused on the value of the assets, progress is measured by portfolio returns and risk is measured by the volatility of those returns. The trouble is that these are the wrong measures if the goal is to obtain a reliable future income.

Consider the idealized situation of an initial portfolio value of $100,000 and a constant return of 5% annually. The volatility of the portfolio is zero. Does this mean the portfolio risk is zero? For a retiree who wants to withdrawal $5,000 annually, or less, the risk of running out of money is indeed zero, no matter how long they live. For the retiree who needs more than $5,000 the portfolio will, with certainty, run out of money.

Conversely, the investor may seek to reduce the risk of running out of money by buying an annuity that guarantees a lifetime of income. Longevity risk and liquidity are both zero and so is the potential for outperformance: in this case all potential for capital growth is traded for income security. For the income investor, the riskless investment is not cash but an inflation-adjusted annuity free of default risk.

## Funded status

Let’s get to know a bit more about Alan and Betsy. Say Alan employs a gardener who is paid $50 in cash before he leaves for the day. But one morning Alan looks in his wallet and sees he has only $40.

Another way to put it would be to say that Alan has a future liability of $50 but only $40 of assets to match this liability. Alan’s funded status is $40/$50 = 0.8. Ideally, Alan needs to have a funded status of 1 or more.

We can apply the same concept to retirement planning. A person’s funded status is **the ratio of two numbers: today’s value of all their assets, and today’s value of all their liabilities**. In this instance, assets include everything someone intends to use to fund retirement. This would include today’s value of current savings, future savings, and employer and government pensions. Liabilities include today’s value of all the future expenditures in retirement.

Let’s dig deeper into Alan and Betsy’s situation. Alan has $600,000 in investments and is on the point of retirement. Betsy’s government and company pensions are worth an additional $400,000 at today’s value, meaning they have total assets of $1,000,000. They plan to consume $40,000 each year in retirement. In other words they have a liability of a series of annual payments of $40,000 for as long as they live. We calculate that the present value of this total retirement liability is $893,830 and so their funded status is 1.12 ($1,000,000 divided by $893,830). We would expect Alan and Betsy to have just sufficient funds for their retirement because their funded status is slightly greater than 1.0. Their situation is illustrated below.

Source: PWL Capital

Our simple illustration ignores taxes. Since most people find it easiest to estimate after-tax consumption, we have to gross up this liability to estimate the present value of the pre-tax retirement income. The chart below provides typical average rates for a retired Canadian couple. The first three data points come from estimates from Fred Vettese and Bill Morneau (*The Real Retirement*), the highest income datum comes from PWL experience with tax minimization strategies for higher income clients. StatsCan 2013 data suggest an average tax rate for those over 65 of 15%, but this includes Canadians still in the workforce. For Alan and Betsy, the tax adjustment to the funded status would be minimal. A couple who required an after-tax consumption of $100,000 in retirement would need a gross income of approximately $115,000 (and pay 13% tax), according to the chart.

Source: *The Real Retirement* by F. Vettese and W. Morneau and PWL Capital

What if Alan and Betsy’ had a higher funded status, much greater than one? In this situation, not all their assets would be consumed in retirement and there would be an estate surplus. It would also mean that Alan and Betsy could take more risk with their investment capital if that was their preference. They might do this to boost their retirement consumption or build a larger estate surplus. In doing so, they risk losing capital and decreasing their funded status.

Conversely, if Alan and Betsy were underfunded and had a funded status less than one, then they would either have to postpone retirement or reduce their planned retirement consumption. The temptation is to roll the dice by increasing the equity allocation to increase expected returns, but this risks decreasing their funded status even further.

In the middle are investors who have a funded status in the range 0.9-1.3. This will be a crowded space as many investors will want to adjust their retirement consumption to sit in this range. This is where careful planning and continuous monitoring can have the most impact.

## Funded status vs. financial projections

The calculation of funded status is complementary to more conventional financial planning projections. Financial planning software takes current investment capital and makes assumptions about future market returns to estimate how much an investor can safely withdraw over their expected lifetime.

Usually the plan allows a safety margin by assuming a longer lifespan (say to age 100) than would be expected. Thus the liabilities are specified but the portfolio value at a future time is highly uncertain because market returns are highly variable. The weakness of this approach is that the options available to the investor from financial projections are choices like:

Would you prefer $40,000 per year with a 10% probability of running out of money?

or

Would you prefer $45,000 per year with a 20% probability of running out of money?

In reality, most retirees hate and fear the idea of running out of money and find both unpalatable. The choice is also rather artificial because no-one (we hope) wakes up one day to discover that they have run out of money, but they could easily find, if they are keeping track, that their funded status is getting perilously close to one.

## Calculating Funded Status

Calculating the funded status requires no assumptions about future market returns. Because the goal is to achieve a specified future spending profile with certainty, it makes sense to use a risk-free discount rate to calculate the net present value of the future liabilities.

The net present value of future payments is the summation of the discounted cash flows adjusted for inflation. The equation for the liability is

Where **D _{t}** is the distribution in period t in today’s dollars

**r _{t}** is the yield of a zero coupon treasury from the Bank of Canada

**p _{t}** is the probability that the liability has to be paid. For a single person this is the probability of being alive in the period and for a couple it is the probability of one being alive. Mortality data is available from the

**CPM2014 Mortality Table.**

** i** is the expected rate of inflation.

** R** is the number of years to retirement or 1, if already retired.

Insurance companies use the same calculations when pricing annuities. This leads to an important observation: **If an investor’s funded status stays at greater than or equal to 1, then he or she has sufficient assets, and thus the option, to buy an annuity at any time in the future to ensure a lifetime income.**

Annuities purchased from insurance companies pool longevity risk. This means that some of the annuitants will live longer than their expected mortality and some will not. Those who die early subsidize those who live longer than expected. The net result is that pooling risk reduces the cost of an annuity by an estimated 35% compared to an estimate based on expected mortality. This means that estimates of annuity costs based on expected mortality tables include a margin of safety.

Investors like the idea of annuities (income for life) but hate the idea of making an irreversible commitment to them. The funded status approach keeps the annuity option in the back pocket, available if, or when, required. In doing so, an investor who maintains a funded status greater than one, has removed the fear of outliving their money.

## Spending rules

Much ink has been spilled on how much a client can safely withdraw from a portfolio without running out of money. Perhaps the most familiar is the “4% rule,” which states the portfolio should survive for 30 years based on an initial withdrawal of 4% of the initial portfolio, with subsequent withdrawals adjusted for inflation.

The deficiencies of this type of spending rule are obvious: it takes no account of expected market returns, the varying cost of meeting liabilities, and the age of the retiree. To ensure retirees do not run out of money in all scenarios requires that there is, on average, significant assets remaining at death.

To illustrate, we applied the 4% rule to a $1,000,000 portfolio with 60% equities, 40% fixed income and applied PWL Capital’s 2015 estimates of expected returns and risk. We started the simulations at age 60. On death, assumed to be age 90, nearly one in 10 portfolios ran out of money, yet nearly a quarter had a value in excess of $1,000,000 – money that was saved for retirement but never used.

A **U.S. study** based on historical returns reached similar conclusions: in more than two-thirds of cases, retirees finished with more than double their wealth at the beginning of retirement, and one out of two nearly tripled their original wealth. This is a very inefficient use of resources.

Some have suggested, in light of historic low bond yields, that 3.5% would be a better rule. Sure enough, the probability of running out of money falls to 3% of cases, but the number of portfolios that leave unused assets of over $1,000,000 rises to 36% of all portfolios.

The 4% spending rule does provide constant, inflation-adjusted spending, which is a valuable attribute. The cost for this zero-volatility income stream is the risk of running out of money and, at the same time, a strong probability that the retiree only spends a fraction of his or her retirement savings before death.

Is there a more efficient way of depleting the portfolio to ensure savings are used for their intended purpose? Such a method would take into account not only the portfolio value but also the present value of the future liabilities and the expected longevity of the retirees. Many ideas have been suggested, but we describe a method in the next section that preserves a retiree’s funded status in real terms and in doing so preserves their real income which, for a retiree, is the true measure of wealth.

## Annually Recalculated Virtual Annuities (ARVA)

The ARVA approach, developed by **M. Barton Waring and Laurence B. Siegel**, is efficient at depleting the portfolio to zero over the lifetime of the retiree so all assets are converted to income. The result, on average, is a considerably higher income than suggested by the 4% spending rule. As we shall see, the trade-off is that the volatility in the portfolio is carried over into the income stream, which varies from year to year.

To see how ARVA works, we’ll look at the case of Jacques and Karine, who want a $40,000 annual income from their $1-million portfolio. For our example we will assume the payment is for a fixed period of 20 years.

In an ideal world, Jacques and Karine could buy a ladder of real return bonds that would mature every year, generating a $40,000 payout indexed to inflation. Real interest rates are currently close to zero, so the lump sum annuity that would yield $40,000 annually is simply $40,000 x 20 = $800,000. For a non-zero average real yield, the calculation is only slightly more complex.

Continuing our example with zero real rates, if we measure Jacques and Karine’s wealth by their assets then clearly their wealth declines with time: they start with $800,000 and after the first year they have spent $40,000, leaving $760,000.

From an income perspective, they remain as well off after the first year as when they started: they have maintained their ability to generate an annual income of $40,000 (but now for 19 years). At any stage during the 20 years, they have the option of buying an annuity that would generate the same income.

This sets up Waring and Seigel’s general principle behind ARVA: “Spending in the current period should not exceed the payout that would have occurred in the same period if the investor had purchased, at the beginning of the period, a fairly priced level-payment real fixed-term annuity with a term equal to the investor’s consumption horizon.”

Implementation uses the time value of money formula for a growing fixed-term annuity:

*A* is the annual payout, *PV* is the present value of the capital, *g* is the growth rate of payments, *i* is the nominal interest rate and *n* is the number of payment periods. In our situation we are interested in payments that are inflation-adjusted, so *g* is the rate of inflation. The real interest rate, *r*, is given by:

This allows a simplification of the annual payout formula to:

We illustrate with two examples. The first reproduces a scenario from Waring and Seigel’s paper and assumes a 30-year spending period with a ladder of real return bonds with an average real return of 2%, Inflation is assumed to be 2.5%. The portfolio value is $1 million.

Source: PWL Capital calculations reproducing Figure 1 of Waring and Siegel

In this example, the first year expenditure is $43,774 and rises to $89,590 in the last year. The portfolio is depleted to zero and as a consequence the spending, as a percentage of assets, increases with age. To an income investor, an inflation-linked bond is a riskless asset, so why don’t investors take more advantage of laddered real return bond portfolios? Some reasons are:

- Currently the real interest rate is close to zero. The payout from a 30-year portfolio with 0% real yield is only $33,333 ($1M/30 = $33,333), which would be considered too low for many retirees. (Higher real rates means buying future income costs less now, which means higher income overall from a set portfolio value.)
- There is no potential for a higher income from owning such a portfolio.
- Real return bonds are in limited supply in Canada and not always available for the maturities required.
- Although riskless from an income perspective, real return bonds have equity like price volatility. Investors used to an asset accumulation perspective find the idea of low returns and high (price) volatility unattractive.

Fortunately, the ARVA approach is easily extended to a risky portfolio. The payout in any year depends not only on the real interest rate, but also the investment returns in the prior period. This means that volatility in investment returns translates directly into income volatility.

We illustrate the use of a risky portfolio with historic data for the period 1985-2014. Consider a portfolio of 60% Canadian equities and 40% Canadian bonds (a more globally diversified portfolio would be preferable in practice). We use historic data for portfolio returns and real yields, and assume retirement starts in 1985 at age 65 and continues for 30 years. Real interest rates varied from -0.40% to 10.30% in the period. Both inflation and real yields have been in decline for most of the period.

Sources: Bloomberg, **World Bank**

Source: PWL Capital, using data from Dimensional Fund Advisors

The graphs, below, show a clear contrast between the ARVA withdrawal approach to the 4% withdrawal rule.

The total income from the 4% withdrawal rule, in real dollars, is $1.2 million (30 × $40,000). Total income from ARVA is $2.23 million, an increase of 86%. Achieving the same income using the 4% rule would require a starting portfolio valued at $1.86 million. If it’s assumed this was accumulated over a savings period of 30 years, it would equate to an additional annual return of 2%. Put another way, two investors, one with a portfolio of $1 million the other with $1.86 million, could have the same cumulative retirement income, depending on which spending rule was used.

The assets are fully depleted in the ARVA calculation, but the 4% rule leaves a residual income of $3.1 million. Also, ARVA income varies from a high of $97,000 to a low of $54,000, while income remains constant at $40,000 using the 4% rule (all in today’s dollars).

Source: PWL Capital

Source: PWL Capital

When looking at these historic charts, it seems obvious with hindsight that rising markets would provide an opportunity for a retiree using the 4% rule to spend more as they see their assets grow. If markets had declined over the past 30 years it would be equally obvious the 4% spending rule would have been a disaster and the retiree would have run out of money. ARVA adjusts spending based on varying current market returns and current real rates without the power of hindsight, in a way that the 4% spending rule does not.

Many retirees may balk at the fluctuation in income from ARVA that arises from volatility in portfolio returns and variability in the real rate of return. For an investor entirely focused on portfolio growth, then risk means volatility. Higher expected returns come from higher risk in the form of greater equity exposure. For the investor seeking income, life is not so simple: the combined impact of portfolio volatility and variability in real returns can be difficult to predict. The chart below shows the income from a portfolio starting in 1980 with withdrawals for 30 years with 60%, 40% and 20% equities.

Income is now a function of real rates and portfolio returns so there is no clear relationship between equity allocation and real income. As the table within the chart shows, over the period 1985-2014, an income investor would have seen slightly more real income from a 40% equity portfolio than a riskier 60% equity allocation.

Source: PWL Capital

Notwithstanding our historic example of a lower equity allocation yielding a higher income, it might be tempting to maintain a volatile portfolio in the expectation of higher returns, but to smooth the yearly withdrawals. A three-year moving average of income would be an example. But any attempt to reduce the income volatility without moderating the underlying portfolio volatility, merely introduces the possibility of running out of money before the end of the spending period. The question remains: if portfolios with higher allocations to equities aren’t the source of higher or more stable income in retirement, how should income portfolios be structured?

## Structure of income portfolios

ARVA provides a spending rule given a risky portfolio by matching the changing values of investment assets with the cost of future spending. As noted above, the underlying portfolio volatility flows through to income volatility. Therefore, to provide a particular income level and income variability that is acceptable to the retiree requires consideration of the portfolio asset allocation and how it changes with time.

In many cases, retirees attach a high value to a minimum level of income and a lesser value to additional income that can be used for discretionary expenditure. Prior to retirement, the retiree is motivated to use their savings to secure the minimum required retirement income first, and then focus on additional income for discretionary expenditure. This is a liability-driven strategy. The main difference from a conventional accumulation investment strategy is that cash is no longer the risk free asset but is replaced with a bond ladder that secures future income.

In practice, part of the low-risk income may be covered by a combination of government benefits and a defined-benefit pension plan, with the remainder coming from the investment portfolio.

Following **Merton** and others, the retirement portfolio can be separated into a Security Portfolio, which covers basic future income needs, and a Growth Portfolio, which will deliver additional income but with some variability.

*Total Portfolio (TP) = Security Portfolio (SP) + Growth Portfolio (GP)*

The Security Portfolio consists of laddered bonds (or a bond ETF equivalent). Investor education is required because the Security Portfolio will, for example, typically hold long bonds that have high price volatility but low income risk. In the situation where all the minimum income needs are met from the Security Portfolio, the Growth Portfolio is the portfolio that the investors would choose if they had no income requirements. For the average investor this is the market portfolio, which approximates a 60% equity, 40% bond portfolio. As income needs dwindle, the Security Portfolio is exhausted, leaving only the Growth Portfolio as an estate asset.

The split between the Security and Growth Portfolio is dictated by the income needs of the retiree and their particular circumstances. For example, a couple with a defined-benefit pension plan already has a source of secure income and, all else equal, could allocate a smaller portion of their investment assets to the Security Portfolio than a couple who were totally reliant on their investment assets for retirement income.

The liability driven approach is a dynamic asset allocation strategy; the allocation to the Security Portfolio is driven by future income requirements rather than retirees’ sensitivity to risk as measured by asset price volatility.

To illustrate how the separation of the investment asset into a Security Portfolio and Growth Portfolio might work in practice, consider the example of an investor with $1,000,000 in 1985. He would like a secure income of $30,000 for the next 30 years, indexed to inflation. In 1985 inflation was 3.30% and real interest rates 7.00%. The net present value of this income liability is $398,000, so the rest of his portfolio, $602,000, is allocated to a 60% equity, 40% fixed-income portfolio.

An investor might choose this option if he was worried about a market crash putting even the secure income of $30,000 at risk. Accordingly, we create a market crash in the first three years of retirement (1985-87) by replacing actual market returns with a decline of 20% in each of the three years.

Using ARVA, we examine the income withdrawal with and without the Security Portfolio. The chart below illustrates the impact. With all the assets allocated to the conventional 60% equity, 40% fixed-income mix, the annual income falls to a minimum of $15,100, well below the secure income threshold. The allocation to the Secure Portfolio eliminates this downside risk and provides superior income in the future. Under these extreme conditions, a portfolio using the 4% withdrawal rule would run out of money.

Source: PWL Capital

## Longevity risk

Thus far the discussion has been limited to pre-specified finite time periods. Commercial life annuities guarantee payouts until death by pooling risk, so annuitants who die early fund those still living. For the individual who does not want to buy a life annuity, there is no means of completely hedging their own longevity risk. But that doesn’t mean the risk can’t be reduced.

This is also a problem for spending rules like the 4% rule, which assumed a 30-year payout. As already observed, spending rules aren’t very efficient at generating income because of the significant probability that they leave assets at the end of the payout period. It is a mistake to assume that this provides a margin of safety for retirees who live longer than 30 years. While it is true that a subset of the population has a longer retirement than 30 years, and that a subset of retirees using the 4% rule will not deplete their assets, there is no guarantee that any particular individual will be fortunate enough to belong to both groups.

Pragmatically, a partial hedge of longevity risk is better than none. Rather than assume everyone survives for a fixed period we can use mortality tables to introduce upper and lower bounds to our planning.

A realistic upper bound to income is to use expected mortality. So, for example, the probability of an 80 year old male dying before age 81 is 4.52% and so the expected pension liability is reduced by the same amount. Annuity calculations using expected mortalities provide an upper bound to the income that should be expected. Using expected mortalities also has the impact of shifting income to the early retirement years compared to assuming zero mortality for a fixed period.

No one has enough money to live forever but this is not a great concern: the probability of living to 105 is low (0.357% for women, 0.074% for men). Using annuity calculations for lives capped at 105 seems a reasonable lower bound to the income. Rather than present results with upper and lower bounds, we simplify and use a 50% weighting using expected mortality and an age limit of 105. For the 65 year old used in the examples above, their expected life is about 84 years, less than the 95-year limit used previously, so payouts will rise. Conversely, assuming payouts until age 105 extends the payout period from 25 to 40 years, so the payout will fall.

In the chart below we compare the impact of mortality weighting on the ARVA calculation. The base case is an investor with $1,000,000 in a 60% equity, 40% fixed-income portfolio, starting retirement in 1985. The impact of mortality weighting on income is compared with the example where death occurs at age 95. As can be seen from the chart below, the impact of mortality weighting is primarily in the last decade. This is an agreeable outcome as spending typically falls in the latter years of retirement, so providing additional protection to living beyond the expected lifespan doesn’t make a material impact on spending in the more active early years of retirement.

Source: PWL Capital

## Term structure of the security portfolio

In the section on the Structure of Income Portfolios we discussed the allocation between the Security Portfolio and the Growth Portfolio. Now we look at the structure of the Security Portfolio in more detail. The goal is to have the bonds in the Security Portfolio generating cash flow in the right amount and at the right time to match retirement liabilities.

Large pension firms can justify the cost of building individual bond portfolios or using sophisticated techniques to replicate the cash flows from such a portfolio. Retail investors have a more limited toolbox available. The model we’ve created uses readily available and liquid bond ETFs to match the retirement cash flows. We outline our approach with a simple example using a GIC ladder for the first 5 years, a medium-term corporate ETF and a long-term government bond ETF.

Average YTM, net of fees | Average Duration (yrs) | Weighted Average Term (yrs) | |
---|---|---|---|

1-5 Year GIC ladder | 1.70% | 3.00 | 3.00 |

BMO Mid Corp Bond ETF | 2.25% | 6.06 | 6.92 |

BMO Long Provincial Bond ETF | 2.65% | 14.99 | 22.94 |

Our calculator can either match cash flows or duration. Duration takes into account not only the maturity values but the size and distribution of coupon payments. The merits of each approach are outside the scope of our discussion. Duration matching provides some protection against changing interest rates, provided that the duration of the longest bond or ETF exceeds the duration of the liability.

To show the flexibility of the approach we consider the situation of a retiree who would like to move through retirement always with a 15-year horizon of secure income.

We consider a female investor who wants to create an annual income stream of $50,000 indexed to inflation, assumed to be 2%, that lasts for 15 years. Thus at age 60 the she is 5 years from retirement and the income stream starts in 5 years and lasts for 15 years. At age 65 the income stream starts immediately and lasts for 15 years. At age 70 the income starts immediately and last 15 years, and so on. We assume the yield curve below for calculating the present value of the liabilities.

Source: Bloomberg

We then calculated the allocation to short (1-5 yrs.), medium (5-10 yrs.) and long (10+ yrs.) bond ETFs to match the retirement income liability. We included the impact of mortality so the expected future liability falls as the retiree ages.

Source: PWL Capital

From the above chart we see the total allocation to the Security Portfolio declines, as expected, because of the increasing impact of mortality. Prior to retirement the allocation is entirely in longer duration ETFs, but the portfolio duration declines as the client ages.

Current yields are close to historic lows so buying future income is expensive. Combined with 5 years of rising equity markets encourages a sense of complacency that equities are a better way of matching future liabilities. This raises the question whether pre-retirees, as in this example, would be willing to commit to long-term bonds to secure future income. An equity bias certainly increases the potential for greater upside in portfolio value. The danger is that we forget what Zvi Bodie showed so convincingly in a **1994 paper**: “Stocks are not a hedge against fixed-income liabilities, even in the long run.”

## Integrated case study

We use the ideas developed above to compare the fortunes of two couples, Jacques and Karine and Claire and David, who retire prior to the Great Recession.

The year is 2007. Both couples are age 65 and looking forward to their first year of retirement. Both have $1,000,000 of investment capital.

Jacques and Karine have a portfolio of 60% equities, 40% fixed income and have been advised that the popular 4% withdrawal rule will allow them to withdraw 4% of their initial capital, indexed to inflation at 2%, without running out of money. Thus they expect $40,000 in the first year, rising with inflation. Their advisor had them complete a risk questionnaire that showed they were tolerant of the risk associated with the price fluctuations of a 60% equity portfolio.

Claire and David had a different advisor who listened to the importance they attached to income stability. They also wanted to withdraw $40,000 annually, indexed to inflation, and wanted to make sure that this could be done for 15 years from the start of retirement. Every year as they progressed through retirement, and should circumstances allow, they wanted to maintain that 15-year horizon of secure income.

Fast-forward to February 2009. Jacques and Karine’s portfolio is depicted in the chart below. They have received their monthly payout but their portfolio has suffered badly from the financial crisis and is only worth $670,000, a 33% decline in just over two years. They are facing the real prospect of running out of money. To make their 2009 withdrawal of $42,085 (inflation-indexed) would mean withdrawing 6.3% of the portfolio. They consider some combination of giving themselves a pay cut or reducing their equity exposure to preserve their remaining capital. Getting a part-time job to provide additional income didn’t seem an option in the prevailing economic climate.

Source: PWL Capital calculation based on monthly performance data from Dimensional Fund Advisors

Claire and David have also received the same monthly payout as Jacques and Karine and are also seeing their capital eroded, but to a much lesser extent (their portfolio is worth $838,000, a 16% decline). The chart below shows Claire and David’s portfolio with Jacques and Karine’s as a blue line for comparison. Claire and David are reassured that their payouts are protected for the next 15 years and they can afford to take a long-term view.

Source: PWL Capital calculation based on monthly performance data from Dimensional Fund Advisors

The process used by Claire and David can be summarised as follows:

- The lump sum required to generate 15 years of $40,000 annually, increasing with inflation, is calculated using 2007 interest rates. The result, which is allocated to the Security Portfolio, is $520,000.
- The Security Portfolio allocation is used to purchase a series of bonds which, through their maturity and interest payments, pay $40,000 annually.
- The remaining $480,000 is used to purchase a long-term Growth Portfolio. In this case we chose a globally diversified 60% equity, 40% bond allocation.
- The Security Portfolio provides all the income. Each year the Security Portfolio allocation is recalculated using prevailing interest rates, taking into account the payout, investment returns and any changes in inflation. The calculation also accounts for the possibility of Claire and David dying. Since this probability increases with age, all other things being equal, the Security Portfolio allocation declines in real terms.
- The portfolio is rebalanced every year between the Security Portfolio and the Growth Portfolio, so the Security Portfolio always provides a 15-year horizon of secure income. Every year they check, using the ARVA method, whether their total portfolio is sufficient to generate an annual real income of at least $40,000 over their expected lifespan. This ensures that they always retain sufficient assets to generate $40,000 in real income not just for the next 15 years but for their expected lifespans.

At the start of 2007, the asset allocation for Claire and David’s total portfolio was 73% bonds, 27% equities. It is easy, with hindsight, to see the wisdom of this choice and why it fared better in the 2008 recession.

However, Claire and David made their choice, not because they could forecast the pending market decline, but because they wanted to protect their income in retirement. Had Claire and David been 30 years old and had no need for income they could have adopted the same portfolio as Jacques and Karine and would have been content to hold out for the market recovery. The key message here is that, for retirees, risk no longer means *price* volatility but *income* volatility. Designing a portfolio with the wrong objectives can lead to poor outcomes.

In our example, Jacques and Karine cut back on their income and cashed out most of their equity investments. If they had the stomach to persevere, we know, again with hindsight, that their portfolio would have recovered. In the figure below we plot the recovery for both couple’s portfolios, assuming both portfolios continued to make annual inflation adjusted withdrawals of $40,000. By the end of 2014 both portfolios have similar value, but Claire and David’s is much less volatile.

Source: PWL Capital

To summarize, this example uses liability matching to provide a 15-year horizon of secure income. The ARVA spending rule was used as a check to ensure that Claire and David never reduced their portfolio below what could sustain a real income of $40,000 for their expected lifespan.

## Concluding remarks

Investments are accumulated to be depleted, usually by the same household as part of retirement funding. The financial industry is always exhorting Canadians to save more, but on the topic of depletion strategies it isn’t so vocal. Simple spending rules that ignore longevity and market risk aren’t efficient in using a retiree’s assets for their intended purpose: consumption.

We started with funded status as an overall assessment of whether assets matched spending liabilities. ARVA was introduced as a dynamic spending rule that considered life expectancy, market performance and interest rates. Complete hedging of retirement risks are seldom affordable and often not realizable, but partial hedges are better than none. Given the challenge, already noted, of building a ladder of real return bonds, using nominal bonds or nominal bond ETFs is a more practical alternative for the Security Portfolio. In the event of unexpectedly high inflation, the retiree is then exposed to the risk of diminishing purchasing power from the Security Portfolio. Studies of retirees spending patterns in developed countries (e.g. *The Real Retirement*, by Fred Vettese and Bill Morneau) indicate spending tends to reduce after the mid-70s, so a decline in real income may mirror a decline in real spending.

Longevity risk can’t be pooled without using commercial annuities, but the risk can be capped by differentiating between essential consumption, as represented by the Security Portfolio, and discretionary consumption, sourced from a Growth Portfolio.

The term structure of the Security Portfolio was introduced to provide a dynamic duration match between the assets and liabilities throughout retirement and to reduce interest rate risk.

Retirees have differing consumption profiles and have different abilities and needs to take risks to achieve their consumption. The methods outlined show how retirees can be more deliberate in assessing trade-offs between income volatility, maximizing income and hedging longevity risk. In doing so, they are more likely to enjoy a higher and more certain level of income in retirement.

## Next steps

- Take this testLog in and answer a multiple-choice exam about the material.
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