Lesson 1, The Trigonometry of Retirement Income

Once again, the two diametrically opposed paths are illustrated in Figure No. 1. All paths earn an average APR of 5 percent over the long run.

So far I have not mentioned withdrawal rates or values from the portfolio. I will get to that in a moment. For now it is important to notice that if you only invested $1 at the start of a cycle (up or down, bullish or bearish) then at the end of a market cycle of 2? (= 6.28) years you would have a compound annual return of 5 percent and the same amount of money, $1.37, in all cases.

I have reached the first of my two main points. When you are buying and holding it doesn't matter what path the market takes as long as you get the 5 percent annualized return! Whether you move up first and then down, or down first and then up, if your compound return is 5 percent you will know exactly where you end up. But the situation is very different when you withdraw money.

Next let's look at what happens when you start retirement with $100 and withdraw $6, $7 or $8 per year on a continuous basis — under fluctuating as opposed to fixed returns. This all scales up to $100,000 with $6,000 withdrawals or a million dollars with $60,000 withdrawals.

I trust you would agree that on any given day, week or month, you don't really know in which direction the market will move over the next few years. It might go north or it might go south. The relevant question is how long your portfolio will last based on the possible starting market cycles. It should be intuitive that your retirement will be worse off if markets go south versus north. But how bad will it be? That's my second point.

Figure No. 2 tells the story and Table No. 1 summarizes the main results. For example, if you are withdrawing $7 per year and you are invested in a relatively volatile asset class that fluctuates between +20 percent and -10 percent, the portfolio can last anywhere between 34.9 years to 18.9 years depending on where — in the cycle — you start retirement. Figure No. 2 is a graphical illustration of the possible range of outcomes.

As you can see from the adjacent table, if you invest in even more volatile (higher amplitude) asset classes that range from +25 percent to -15 percent per year, for example, the dispersion of outcomes is an even wider 17.1 years to 39.6 years.

Another important insight from the table of numbers is the impact of the spending rate itself. Notice that when you are spending $8 per year the gap between the "good" sequence and the "bad" sequence of returns is only 21.3 – 18 = 3.3 years in the first row (low risk) of the table. This same gap is 41.7 – 31.4 = 10.3 years when spending is reduced to $6 per year. At first glance this might seem odd. Why is the sequence-of-returns effect more powerful at lower spending rates? But of course, this is a relative effect. If you spend more (i.e., $8) you will be worse off in terms of sustainability regardless of the sequence. That said, the gap between worst- and best-case scenarios increases the less you spend. This impact becomes more pronounced at greater volatility levels. Starving yourself — i.e., withdrawing less — might push back your date with retirement ruin, but it won't immunize you from a bad initial sequence-of-returns.

In sum, no economist can tell you with any degree of accuracy whether the next few years will be sine-up or sine-down. It only becomes evident over time. The practical implications of all of this? When it comes time to withdraw, don't take sequence-of-returns chances and make sure to protect your nest egg during the fragile first decade of retirement. We will explore this in future lessons. Next month I will examine how income taxes throw another wrench into the retirement dynamics.

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Moshe A. Milevsky, Ph.D., is a finance professor at the Schulich School of Business at York University and is the executive director o the IFID Centre in Toronto, Canada; see www.ifid.ca.