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

or

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

alan morris

Great insight

Thursday, Oct 12, 2017 at 10:33 am

Vevencia L De Vera

Alan and Betsy are on the safe side of their retirement income because the graph shows that they still have a surplus. The statement says the $40,000 per year is as long as they live and their fund status is greater than one.

Saturday, Sep 30, 2017 at 9:20 am