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This article appears in the June 2020 issue of Advisor’s Edge magazine. Subscribe to the print edition, read the digital edition or read the articles online.

Markets operate in two different modes: random (or “normal,” as it’s known in the Gaussian world) and fractal (non-normal or extreme). My work on the luck factor (i.e., sequence of returns) about 20 years ago indicated that markets are random about 94% of the time. It is fractal for the remaining 6%, split evenly between up and down directions.

In the random mode, well-known strategies such as asset allocation, diversification, rebalancing, dollar-cost averaging and buy-and-hold work perfectly well. The problem is the other 3% of the time, when markets are fractally going down; then these strategies don’t help much. You might say, “Well, it only happens 3% of the time — why worry?” The answer is simple: plans can get ruined. A bad downturn can wipe out 10 years of retirement income.

After a fractal event such as the market response to Covid-19, we all hope for a quick recovery. In the past, central banks jumped in to help — but these recoveries did not come cheaply. The global total debt was US$87 trillion in 2000. Before Covid-19, it was estimated at US$253 trillion, and governments around the world have since introduced unprecedented monetary and fiscal policies in response to the crisis.

Assuming central banks can continue to bail out the economy, how many months or years would it take the portfolio to recover its original value?

This analysis uses actual market history, which we call “aftcasting” (as opposed to “forecasting”). Aftcasting displays the outcome of all historical asset values of all portfolios, on the same chart, since 1900. It gives a bird’s-eye view of all outcomes for a given scenario. It also provides the success and failure statistics with exact historical accuracy because it includes the actual historical equity performance, inflation and interest rate, as well as the actual historical sequencing/correlation of these data sets.

Recovery in an accumulation portfolio

Let’s first look at an accumulation portfolio. Imagine a 30-year-old client named Keith with a portfolio worth $100,000. The asset mix is 70% equities and 30% fixed income. Half of the equities are in Canadian stocks (S&P/TSX composite) and half are in U.S. stocks (S&P 500).

As for the fixed income portion, we use the historical interest on six-month U.S. certificates of deposit plus 0.5% as the net yield. This reflects approximately a bond ladder with an average maturity of five to seven years at current yields, assuming no defaults and no capital gains/losses.

Keith plans to add $4,000 each year to his portfolio. Then a fractal event happens and his portfolio loses 25% of its value; it’s now worth $75,000. Keith wonders when his portfolio will get back to its pre-crash value of $100,000.

Figure 1 displays the aftcast. Each of the grey lines represents one specific starting year since 1900. The blue line represents the median portfolio: half of the grey lines are above it and the other half are below. The green line represents the “lucky” outcome (the top decile, or top 10%, of all outcomes). A lucky outcome can happen when the recovery is described as V-shaped. The red line represents the bottom decile or “unlucky” outcome. An unlucky outcome usually means a multi-year bear market (such as 1929 or 2000) with several aftershocks.


Figure 1: Accumulation portfolio—Keith’s aftcast

It took about 2.8 years for the median line to reach the original portfolio value of $100,000 (the horizontal dashed line). In a V-shaped recovery, it would take about 14 months; in a multi-year bear market, it would take 5.8 years to see the $100,000 mark again, thanks to Keith’s contributions.

Recovery in a retirement portfolio

Our next example is for the retirement stage. Jane, 65, just retired. She has an RRSP portfolio worth $500,000, with an asset mix of 40% equities and 60% fixed income.

Jane needs $15,000 each year from her savings, indexed for inflation. This represents an initial withdrawal rate of 3% ($15,000 / $500,000), a sustainable amount for life.

After the fractal event, Jane’s portfolio is worth $425,000 — a 15% loss. Jane asks: “When will I see my portfolio back at $500,000?” Figure 2 displays the aftcast.

In a V-shaped recovery, Jane would see her portfolio value reach the original $500,000 after about 1.8 years (22 months). The median portfolio comes close but never reaches the $500,000 mark ($490,000 at age 75).

Jane will likely still have lifelong income. However, the chances are more than 50% that her portfolio will never return to $500,000.


Figure 2: Retirement portfolio—Jane’s aftcast

Forecasting the majority of scenarios

In case your clients ask similar questions, I ran a multitude of scenarios. The results are summarized in Figure 3. Let’s work on an example using that chart.

Jeff has a balanced portfolio of $1 million. He does not add any money to it, nor does he need income from it. After an unfortunate market event, his portfolio is down 22%. When can Jeff expect to see his portfolio back at the $1-million mark?

On Figure 3, draw a vertical line (the dashed line on the chart) starting at the 22% initial portfolio loss on the horizontal axis. Continue this line until it reaches the grey 0% accumulation curve. From this point, draw a horizontal line toward the left axis, and read the number: about 4.2 years. This is historically how long it took the median portfolio to reach its pre-loss value.

Jeff might wonder what happens if he gets lucky and the loss comes with a V-shaped recovery, or if he’s unlucky and gets stuck in a multi-year downturn.

For an accurate answer, you need to run an aftcast for each specific scenario. However, here’s a rule that covers the vast majority of situations: to estimate the lucky outcome, divide the median by three; to estimate the unlucky outcome, multiply the median by 2.5.

In our example, the median was 4.2 years. If Jeff is lucky, he will see his portfolio back to $1 million in 1.4 years (calculated as 4.2 / 3). On the other hand, if he’s unlucky, that day may not come for 10.5 years (calculated as 4.2 x 2.5). This assumes Jeff stays invested throughout.


Figure 3: Estimating the time it takes to reach the pre-loss median portfolio value

Your client might ask about the impact of their asset mix. When fractal events happen, asset mix doesn’t make much difference on the recovery time. If the portfolio is heavy in equities, then it loses more but can also recover faster. The main risk is the client’s staying power, which is easier to manage in a V-type recovery.

We’ll discuss asset allocation based on the client’s staying power in a future article. In my analysis here, I used a 40/60 asset mix for decumulation portfolios and 70/30 otherwise.

Keep in mind, these numbers are based on market history and on the assumption that the current borrowing binge can continue indefinitely. Meanwhile, enjoy this recovery.

by Jim C. Otar, M.Eng., a retired certified financial planner and professional engineer; he founded retirementoptimizer.com.