The basic idea is that if your portfolio gets hit with lousy market returns around the time of your retirement – a.k.a. the risk zone – the funds will not last as long compared to when the returns are earned in a more favorable order. It is rather easy to demonstrate that if you are practicing “safe retirement withdrawals” of say $5 per $100 nest egg adjusted for inflation each year, the funds will last much longer if you can earn a (positive) +10% average in the first decade and (negative) -10% average in the final decade of retirement, as opposed to the other way around.
There are many insightful ways in which to quantify this conditional-probability effect, and the preferred tool really depends on the audience in question. To mathematicians I talk about diffusions driven by Brownian Bridges. For the laymen I use simple binomial modes. Unfortunately – and this is partially my fault – the SOIR effect is often misinterpreted to imply that the order of market returns has no impact at all “during people’s actual saving and accumulation phase” and is only a problem in retirement. This is patently incorrect, so let me now be clear about it. The sequence of investment returns is irrelevant for a lump sum, is important when you DCA but has the greatest impact during retirement. (With hindsight, I didn’t emphasis this enough during a recent interview with Money Magazine.)
For example, think of my favorite investment triplet {27%, 7%, -13%}, with each number representing the investment return over one period. If you start with $100,000 and hold the investment for three periods, the money will grow to $118,224 regardless of which of the six possible triplet combinations are realized during the three periods. This is the irrelevance of SOIR for a lump-sum. However, if you add $100,000 to the account at the start of each year, there are now SIX possible ending values corresponding to the six possible return paths. For those who want to verify this, here they are:
{+27%, +7%, -13%} -> $298,314;
{-13%, +7%, +27%} -> $381,114;
{+7%, -13%, +27%} -> $355,714;
{-13%, +27%, +7%} -> $361,114;
{+7%, +27%, -13%} -> $315,714;
{+27%, -13%, +7%} -> $318,314;
As you can see, the worst $298,314 and $315,714 outcome is realized when the final period return is the lowest -13%. This intuition should be rather obvious. You don’t want to have the bear market around the time you retire, both immediately before and especially immediately afterwards.
Notice that the compound average (geometric mean) of the triplets is roughly 5.74%. Now, if you start retirement with a lump sum of $100,000 and earn 5.74% on investments for an assumed three periods of retirement, you can support spending of approximately $37,231 per period. The present value of this annuity at 5.74% is exactly $100,000. Work this out period by period. At the end of the first period you will have $68,509; at the end of the second period you will have $35,210 and at the end of the third period you will die exactly broke. Not a cent more and not a cent less.
So, what happens if I apply the above investment triplet instead of the constant 5.74%, and spend the same $37,231 per end-of-period?
In this case the outcome is as follows:
{+27%, +7%, -13%} -> $13,945;
{-13%, +7%, +27%} -> $(16,882);
{+7%, -13%, +27%} -> $(7,425);
{-13%, +27%, +7%} -> $(9,435);
{+7%, +27%, -13%} -> $7,467;
{+27%, -13%, +7%} -> $6,499;
In three of the six cases the individual is ruined before the end of the third (and final period) of retirement. This is the most powerful manifestation of the sequence of investment returns effect, which results in a 50% ruin probability (or, more precisely, frequency).
To me the most important point is as follows. When you are still working – and converting human capital into financial capital – you have the valuable option to delay retirement, work longer and thus mitigate the impact of sequence of investment returns. In retirement, the human capital is gone and all you have remaining is financial capital. An early negative sequence of returns is virtually impossible to recover from, unless you are willing to reduce your spending rate. Ergo, my often-quoted statement that a negative early SOIR is worse during retirement.
