# Early Retirement and Time Value of Money (Part 2)

This follow-up article keeps exploring Time Value of Money concepts in the context of early retirement. The intent is to find a flexible way to manage one’s portfolio savings and annual spending levels in combination with various types of irregular cash flows while waiting for stable fixed income (e.g. social security, pension) to settle in.

As we have seen in Part 1, a few spreadsheet formulas can go a long way. Such ‘annuitization’ approach involves some extra risks though and this follow-up article will discuss ways to mitigate such risks.

## Expected Rate of Return

Spreadsheet reference: ‘PV Math Blog’ tab, ‘Rate of Return Sensitivity’ section.

The approach described in the first article (Part 1) is centered on applying Time Value of Money principles, based on NPV() and PMT() formulas which take as an input parameter an (expected) real rate of return. Giving the uncertainties of both the stock and the bond markets (notably when expressed in real, inflation-adjusted, terms), choosing the right value for future returns may seem like an impossible task – and it is, to a large extent. The trick though is to understand that there is no need to make an exact prediction, just making a very coarse guess will do. As long as the rate is not unrealistic (e.g. choosing 0% or 10%), the annuitization logic actually displays quite remarkable self-correcting properties.

First off, the NPV/PMT combination of formulas that we applied to cash flows (fixed income, lump sums, etc) has limited sensitivity to the rate parameter, using both formulas in sequence kind of neutralizing the rate being used, to a large extent.

The following table takes the first 20 years of Harry and Sally’s cash flows and performs the NPV/PMT math while applying rates ranging from 1% to 9%. As you can see, the outcomes are very similar, and it takes rather unrealistic rates to get to a relative difference of 2% or more.

Spreadsheet reference: ‘PV Math Blog’ tab, ‘Harry and Sally’s computations’ section.

Next, the PMT formula that we applied to the regular portfolio is remarkably robust against unexpected sequences of returns. For sure, there will be significant variability along the way, but it will always converge to the Final Value and adjust itself to whatever happens to the portfolio balance year over year. Let’s use again our simple backtesting tool, running Harry and Sally’s scenario and checking various historical starting dates. Please note that the happy couple settled on a 60/40 asset allocation for life, following the sound advice of old sage Peter Bernstein.

If we start in 1930 (the great depression), the compound annual growth rate (CAGR) over the full retirement period would have been 4.1%. Starting in 1950, it would have been 5.8%. Starting in 1970 (right before the oil crisis), it would have been 5.1%. Given compounding effects, those are VERY different numbers. Furthermore, the sequences of returns in those 3 cases were very different (spanning all major stock/bond market crises of US history) and inflation (and deflation during the great depression) varied wildly too. Now, let’s look at the trajectory of annual spending budgets in our simulations (as shown by the red line and right vertical axis).

The most important observation is that the red line always hovered between $100k and $150k while staying kind of flattish overall (standard deviation of ~10%). Sure enough, the 1950 scenario was more favorable (average ~ $130k while 1930 and 1970 were closer to $110k on average), but the PMT approach adjusted itself remarkably well in the presence of rather hectic sequences of events (not only market returns, but also the complex sequence of cash flows in Harry and Sally’s case).

The author would encourage the reader to play around with a copy of the reference spreadsheet, using other starting dates and/or other rates of return. A 4% rate (which would possibly be more realistic nowadays) would work ok, slightly skewing the trajectory upwards (as the US rosy history in the 20th century actually delivered more than that), but still keeping it reasonable. An overly conservative value of 3% or an overly aggressive value of 7% or 8% would have been more troublesome, skewing trajectories upwards or downwards a tad too much for comfort, but even such a really bad guess would end up with a manageable trajectory.

The lesson here is that there is no ‘perfect’ rate of return. But any semi-reasonable guess will do the job. Don’t be overly conservative or overly aggressive, try to find some middle ground. The VPW recommendation of using worldwide historical averages, i.e. 5% for stocks (domestic and international) and 2% for bonds, and then weigh the expected return according to one’s asset allocation, seems quite reasonable for the future to come.

## ‘Double whammy’ risks

Spreadsheet reference: ‘PV Math Blog’ tab, ‘Paul and Sofia’s computations’ section.

Harry and Sally’s scenario has a lot of moving pieces, but it benefits from significant cash inflows during the first decade, largely mitigating the effect of a deep crisis during that time. Not everyone will have similar circumstances.

A lack of cash inflows during early retirement (i.e. before stable fixed income settles in, notably when social security is postponed) combined with limited savings to start with can lead to increased risks. The reason is largely due to the pesky sequence of events issue. A regular PMT() formula applied to a regular portfolio definitely mitigates sequence of returns risks by constraining one’s annual budget when the portfolio is going through a deep crisis. But the effect of extra withdrawals due to the NPV/PMT cash flow technique can create a double-whammy effect.

The fundamental issue is that the outcome of the NPV/PMT path is a function of __future__ cash flows. But as an early crisis unfolds, it leads to sell extra shares of the __regular__ portfolio (which is currently depressed) without having actual access to the future income yet. In some cases, this could create undue pressure making the early retirement end up in bankruptcy or at least severely damaging to long-term prospects.

Let’s take an extreme example. Let’s say that a couple (Paul and Sofia) will enjoy a combined annual fixed income of $80,000 in a decade or so (e.g. government pension). In addition, they will receive a $2M inheritance at some point, but not in the short-term. This sounds like very comfortable money, but those are future prospects. If they only have limited savings (say $250,000) and they plan to early retire 10 years before actually starting to receive their fixed income, we don’t need to do much math to see that there is a problem, even without a stock crisis looming.

Now let’s take a similar example, but making it a bit more realistic. Let’s keep the same limited savings ($250,000) and the same fixed income ($80,000 in 10 years). Let’s assume that a lump sum (e.g. house downsizing) will occur in 5 years, freeing $250,000. And let’s eliminate the inheritance. Finally, let’s assume that Paul is a bit nervous about early retirement and found a way to get a part-time consulting gig bringing $10,000 a year, lasting for four years. That’s $540,000 for 10 years. Their reasoning is that they can go by with $50,000 to $60,000 a year for a decade while waiting for the pension, if that is the price to pay for early freedom/retirement. If they were to put such money in a savings account, this would indeed work.

Now let’s check the numbers with our fancy schmancy NPV/PMT model. Say Paul and Sofia retired in 1970 (a few years before the oil crisis struck). See the model above and the chart below… Er… The portfolio dropped two times to zero and the annual spending budget starts way too high, then tanked badly twice before settling back to the $80k pension. This trajectory is clearly not acceptable.

As previously hinted at, the problem is that Paul and Sofia are exclusively living on their (limited) *regular* portfolio. The NPV/PMT math on the *future* income accounts for the pension down the road, increasing the annual spending budget in the early years accordingly, but this isn’t money readily available, so the extra money has to come from the already stretched portfolio. Furthermore, the oil crisis struck, making the portfolio balance drop like a rock. The ‘house downsizing’ lump sum comes too late to save the day, and even assuming that Paul and Sofia somehow made it until then (e.g. maxing out credit cards), the same ‘fall into oblivion’ event occurs again a couple of years later…

One could argue that the scenario is not terribly plausible and anybody with a modicum of common sense would not have played the stock market roulette under such circumstances. But we can easily sense that there must numerous scenarios which are more borderline, where the outcome of the NPV/PMT math might still be too aggressive in presence of a deep crisis while being perfectly fine in a more benign time period. Could we devise a warning system raising an alarm when things are getting troublesome, something suggesting to further constrain the spending budget and/or to revisit sources of income?

## Spending gates: soft gate

Spreadsheet reference: ‘Scenario 2’ tab.

A first line of thinking (dubbed ‘soft gate’) is to separate early retirement (irregular) cash flows from stable retirement (regular/fixed) income.

One could define a stretch goal for the portfolio when stable retirement is planned to start (in the case of Paul and Sofia, this could actually be $0 given their comfortable pension; other people may not have such cozy fixed income cushion and will want their portfolio to help further down the line, possibly defining the stretch goal as 30% of their starting portfolio). In other words, how much of the portfolio is one willing to spend to fill spending gaps during the early years while possibly dealing with various demanding circumstances like a deep crisis.

Note that it is important to truly stretch the goal, setting up such portfolio limit too high would backfire by overly constraining spending in early retirement. Do not make the mistake of counting the same risk twice. For example, one should not assume a deep crisis in early retirement followed right away by a similar deep crisis in regular retirement, i.e. something twice as bad as any known sequence of events in history. Anything higher than 40% or 50% of the starting portfolio is probably not a good setting. The exact choice is HIGHLY dependent on your personal circumstances.

Based on such stretch goal for the portfolio, combined with the expected cash flows in early retirement, we could run another Time Value of Money computation, in two steps. First, let’s calculate the Net Present Value of the expected cash flows during early retirement, a simple matter of using the NPV() function on those cash flows. We get another ‘virtual portfolio’ number (restricted to the early retirement years, so that we’re not betting on distant cash flows 20 years down the road!).

Next, let’s use the current regular portfolio balance plus this ‘virtual’ portfolio as Present Value, while using the stretch goal for the regular portfolio as Future Value, and restricting the time period to the early retirement years. Logic dictates this provides a realistic spending gate for the current (early retirement) year. And then rinse and repeat. Here is an example of such computation.

The ‘Scenario’ tabs (here Scenario 2) are formatted a little differently from the computations we’ve explained so far, but interested readers should quickly find their way. Column C computes the number of years until stable retirement. The following columns are the usual cash flows, summed up by column G. Column H to N perform the usual PMT/NPV math we’ve been using all along, combining future cash flows with the regular portfolio, and ending up with a tentative spending budget in column N. More backtesting logic can be found in the following columns.

The interesting bit starts in column O. Here, we compute the Present Value of the *early retirement* cash flows. Then column P performs the spending gate computation. Cell P4 is the portfolio stretch goal (remember that Paul and Sofia are willing to spend all their -limited- portfolio savings until their pension starts), and the formula in cell P6 and below runs the PMT math centered on early retirement years.

As emphasized by the red color conditional formatting, the spending gate is indeed often lower than the regular spending budget, strongly advising to either constrain the spending budget accordingly and/or… to step back and re-assess their early retirement plan (maybe actively seeking some other source of additional income, e.g. some part-time work, etc).

Assuming the scenario stays unchanged except for Paul and Sofia following the recommendation to constrain spending to the ‘soft gate’, the spending budget trajectory (red line on the chart) is now much more satisfying. Still, Paul and Sofia are skating on very thin ice as their regular portfolio would have been depleted just in time for the ‘home downsizing’ lump sum saving the day and replenishing the portfolio… They should have downsized their house earlier and/or sought other sources of income and/or used more stable financial assets to pay for some of their baseline bills. The spending gate would have provided ample warnings a few years ahead of time though, hence doing its job.

Note: as a case in point, the author will have no qualms canceling plans to postpone social security if a deep stock market drop (e.g. more than 30%) occurs in his mid-60s and the ‘soft gate’ warning gets activated. Remember Mary’s social security computations? The advantage of postponing social security isn’t that large, it is just not worth the double-whammy potential damage…

## Spending gates: hard gate

Spreadsheet reference: ‘Scenario 2’ tab.

The ‘soft gate’ mechanism seems to work pretty well for all plausible scenarios the author experimented with. It is not difficult though to come up with extreme scenarios where such logic might fail too.

The ‘soft gate’ logic might fail because of the NPV() computation on the early retirement cash flows, which still includes a bet on the future, a near future, but maybe the regular portfolio can’t even accommodate going that far.

The reference spreadsheet includes (column Q) an optional ‘hard gate’ mechanism which eliminates any such bet on the future, by simply looking at the current portfolio, the ‘stretch goal’ for such portfolio in the early retirement years, and the cash flow for the __current__ year, no more.

This mechanism makes sense at face value, but it really doesn’t seem plausible that people in such situation would not have figured out on their own how dire their financials are at this stage. Furthermore, using such hard spending gate to constrain spending year over year would lead to overly hectic trajectories. The author wouldn’t recommend its usage besides some sort of last resort sanity check warning system.

## Conclusion

Spreadsheet reference: ‘Simple Example’ tab.

Those spending gates considerations may seem to add unwelcome complications and detract from the elegant simplicity of the approach suggested by the first article (Part 1), plus it can also raise fears and doubts about the overall approach (Liability Matching proponents would probably cringe big time!).

In all fairness though, nobody should early retire without a solid cushion in their regular portfolio. If that is the case, then the regular approach should work fine, even in the presence of deep crises, and without resorting to setting aside 10 to 15 years of expenses in low-return TIPS.

This being said, implementing the formulas for the spending gate (minimally the soft gate) is actually quite simple, and seems like a robust warning and regulating system against human mistakes and unforeseen situations. The author is actually relieved to have identified such mechanism as the ‘double whammy’ risk was wearing a little heavy on his mind.

The brave readers who made it until those final words can check again the ‘Simple Example’ tab of the reference spreadsheet, where the overall approach is presented in the simplest way possible, with just a few concise formulas to run the math for a given year, computing the spending budget and the soft gate. As you can see, this is really quite simple.

Overall, the author would strongly encourage advanced readers to play around with customized versions of the Scenario tabs, test their numbers against historical data, and try various sets of assumptions. The future might not be the same as the past, but the past is all we have to learn lessons, so better make the best out of it.