Longevity risk is the risk that a retiree will outlive his or her retirement savings. It develops in four stages as we make decisions about funding retirement.

Let’s consider those risks by imagining a retiree who splits his retirement savings portfolio in half on the day he retires. The first "legacy" portfolio is intended for his heirs and the second “funding” portfolio is intended to fund his retirement expenses.

To simplify the example, let’s assume he invests both identically in the same 40%-equity index fund on the same day. The only difference between the funding portfolio and the legacy portfolio is that he will spend annually from the funding portfolio and then re-balance it to 40% equities. The legacy portfolio will remain untouched to be left to his estate.

A retiree can pretty much avoid longevity risk altogether by purchasing life annuities or TIPS bonds. There are plenty of good reasons to invest at least some of our savings in stocks and bonds, though, and that decision leads to the first risk, known as market risk. Market risk refers to the volatility of stock prices over time. Once we invest in risky assets like stocks, outliving our savings becomes a possibility.

We can mitigate market risk by reducing our equity exposure or we can completely eliminate it, by purchasing life annuities or TIPS bonds. Our imaginary retiree has decided to mitigate market risk in both portfolios by investing only 40% in equities, but he has not avoided market risk altogether.

If this retiree never spends from or saves to either portfolio, those portfolios will have equal values at the end of retirement. We don't know what that value will be, however, because both are exposed to unpredictable market risk. We only know that they will be exposed to identical market risk and that their "terminal value", or value at the end of life, will be the same.

When a retiree begins to spend from her funding portfolio, the outcomes of those two portfolios go their separate ways. No matter how little our retiree spends each year, so long as there is net spending, there is no future in which the terminal value of the legacy portfolio will not be larger than the terminal value of the funding portfolio at the end of retirement for two reasons.

The first cause is obvious – her funding portfolio will be smaller because she is spending some of it – but the second cause, path-dependent risk, can make her legacy portfolio's terminal value larger or smaller. The funding portfolio will always, however, have less value than her legacy portfolio, again because she is spending some wealth and never saving, but path-dependent risk can leave the funding portfolio fatter or thinner than it would have been with no path-dependent risk.

Path dependence refers to the fact that, once we begin spending from a volatile portfolio, the

*order*of market returns can change the portfolio’s value. A buy-and-hold portfolio has no path dependence (“Path dependence” means the outcome depends on the path we take to get there, which in this discussion refers to the order of annual portfolio returns.)

Let me provide a quick example to explain path dependence. Assume that over the next five years, the stock market will provide the following returns in the following order: 5%, -7%, 9%, 3% and 4%. If we invest $1,000 in this market at the beginning and neither buy nor sell additional shares, we will end up with $1,140 five years later, no matter which order those returns occur.

If we spend $30 at the beginning of each of the five years, however, the order of returns

*does*matter. There are 120 different ways (5 factorial) those five returns can be ordered and each will provide a different outcome. The outcomes will range from $966 to $988, but always less than $1,140. Once we spend from or save to a volatile portfolio, the outcome is path-dependent.

Note that in none of these 120 permutations is our account balance depleted. Path dependence isn't the same as risk of ruin and if we are only spending 3% annually ($30), it is very unlikely that we will exhaust our savings.

Some refer to path dependence as “sequence of returns risk” but the term isn’t always used in that way, so I prefer to avoid it whenever possible. If returns are experienced with the highest gains early in retirement and the lowest gains toward the end, this path dependence helps our portfolios over time and if returns are experienced with the worst returns early in retirement, path dependence hurts our portfolio.

The best possible outcome is achieved when our market returns are ordered from best to worst. The worst possible outcome is the reverse. With 30 years of annual market returns over a long retirement, the odds of experiencing the best or worst outcome are literally astronomical (1 in 30

*factorial, each – there are fewer than 30*

*factorial stars in the visible universe).*

The source of path-dependent risk is selling in the spending phase of retirement finance and buying in the accumulation phase. We have no idea what price we will receive for the securities we will sell (or buy) in the future and that price risk is path-dependent. TIPS bond ladders held to maturity and life annuities have no path dependence risk because we know their future values relatively accurately.

(As an aside, savings portfolios during the accumulation phase also have path-dependence risk because we don’t know the future price at which we will

*buy*equities. A lot less attention is paid to path-dependence in the saving phase because it doesn't lead to portfolio ruin. It does, however, greatly impact wealth accumulation.)

So far, our retiree’s legacy and funding portfolios are both exposed to market risk, and the funding portfolio is exposed to additional risk (path-dependent risk) once she starts spending from it. Note that this risk is introduced by the retiree’s decision to sell shares. Path dependent risk is not market risk, cannot be diversified away like market risk, and therefore we can’t be compensated for it. In general, more risk means a greater expected return, but the market doesn’t compensate us for taking path-dependence risk.

Our retiree will make another decision that affects path-dependence risk, how much to spend annually. The more she spends each year, the more she exposes her portfolio to that selling-price risk each year and the more path dependence risk

*and*risk of ruin she accepts. Simply said, a 4% “sustainable withdrawal rate” is riskier than a 3% rate.

The term “sequence of returns risk” is also sometimes used to refer to the probability that a retiree will outlive his savings, which I refer to as "risk of ruin." Path dependence doesn’t cause a retiree’s portfolio to fail, at least it is not the proximate cause. Refusing to reduce spending when our portfolio declines in value causes portfolios to fail is the proximate cause of portfolio failure. This is not a market risk or path-dependence risk, but a poor decision on the part of the retiree. If your portfolio declines significantly in value and you don't start spending less, you risk ruin.

Most spending strategies, like ARVA, constant-percentage spending and "RMD" rarely or never deplete a portfolio because they reduce spending as a portfolio declines in value, lowering the risk of ruin. Constant-dollar spending is the exception.

I wrote a post some time ago entitled, "When You Have Less Money, You Probably Ought to Spend Less", showing that portfolio failure occurs under the (absurd) assumption that a retiree will continue to spend the same amount from his portfolio every year, even when it becomes obvious that the portfolio will soon be depleted. This is an interesting technique to use in research, but it is not a realistic retirement spending strategy. We sometimes refer to this as “constant dollar spending.”

That post also shows that retirees who spend a reasonable constant percentage of remaining portfolio balance each year will not deplete their savings. Their portfolio will eventually recover and spending can increase.

The “RMD” spending strategy avoids ruin, as well, by dividing the remaining portfolio balance by your remaining life expectancy to calculate a safe withdrawal amount, similar to the manner in which the IRS calculates required minimum distributions for IRA's. Waring and Siegel's ARVA strategy (download PDF) does something similar. Both strategies reduce spending when a portfolio is faltering. In fact, constant-dollar spending is the only widely acknowledged spending strategy that results in portfolio ruin under reasonable spending assumptions.

The third layer of risk in the chain of longevity risk is that of portfolio ruin. It is introduced when a retiree decides to keep spending the same amount after significant portfolio losses. Rational, knowledgeable retirees will reduce spending when their portfolio wealth dwindles dangerously low, but they expose themselves to the risk of a permanent reduction of spending if they wait too long to adjust. (This is a key reason I recommend dynamic spending and annual adjustments. Small, annual adjustments are easier to tolerate and help avoid larger, permanent adjustments by limiting damage.)

To summarize, our decisions can lead us down a chain of retirement wealth risk. It begins when we decide to invest some of our savings in equities. We increase risk by allocating more of our portfolio to equities and decrease it by allocating less.

The next step is our decision to spend from our savings portfolio. Spending more raises the risk and spending less lowers it.

The final step in the chain of risk depends on the decisions we make when our portfolio dwindles in value. Path-dependence can lead to portfolio ruin, but it probably won't if we lower spending when our portfolio is stressed.

Each step we take, we add more risk. Except for the final, "overspending" step, these can all be reasonable risks to assume. Understanding them can help retirees understand how much of each risk they should accept.