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.

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