*February 6, 2023*

Welcome to another installment of my Safe Withdrawal Rate Series. See the landing page of this series here for an intro and a summary of all posts I’ve written so far. On the menu today is an issue that will impact most retirees: we all likely receive supplemental cash flows in retirement, such as corporate or government pensions, Social Security, etc. Some retirees opt for an annuity, i.e., transform part of their assets into a guaranteed, lifelong cash flow.

Of course, if you are a long-time reader of my blog and my SWR series you may wonder why I would write a new post about this. In my SWR simulation toolkit (see Part 28), there is a feature that allows you to model those supplemental cash flows and study how they would impact your safe withdrawal rate calculations. True, but there are still plenty of unanswered questions. For example: how do I evaluate and weigh the pros and cons of different options, like starting Social Security at age 62 vs. 67 vs. 70 or receiving a pension vs. a lump sum?

Also, you might want to perform those calculations separately from the safe withdrawal rate analysis, from a purely **actuarial point of view**. For example, we may want to calculate net present values (NPVs) and/or internal rates of returns (IRRs) of the different options before us. Clearly, NPV and IRR calculations are relatively simple, especially with the help of Excel and its built-in functions (NPV, PV, RATE, IRR, XIRR etc.). However, the **uncertain lifespan** over which you will receive benefits complicates the NPV and IRR calculations. How do we factor an uncertain lifespan into the NPV calculations? Should I just calculate the NPV of the cash flows up to an estimate of my life expectancy? Unfortunately, the actuarially correct way is more complicated. But Big ERN to the rescue, I have another Google Sheet to help with that, and I share that free tool with you.

Let’s take a look…

### An Actuarial NPV/IRR tool

Let’s start with a simple example: A 55-year-old male early retiree in average health has access to a life-long corporate pension worth $600 a month. Alternatively, he can cash out the pension and receive $100,000. What’s the best choice for this retiree?

There isn’t one unique answer, but we can address several questions to evaluate this lump-sum vs. lifetime annuity tradeoff:

- Considering the average death probabilities from the Life Table used at the U.S. Social Security Administration (SSA) – latest release here – what is the expected internal rate of return of the net cash flows?
- Assuming a fixed target rate of return, what is the net present value (NPV) of this cash flow stream assuming the SSA life tables?
- We can also ignore the life table probabilities and calculate an IRR for an assumed specific time of death. For example, if this retiree believes that he gets benefits exactly until, say, age 84, what would be the IRR in that case?
- And likewise, for that lifespan up to age 84, what would be the NPV under the target IRR?
- Assuming a certain target rate of return, how long does the retiree have to survive to break even from a financial perspective?

Lots of questions. Let’s look for the answers. Here’s the link to the Google Sheet:

### Evaluating Annuity, Pension, Social Security Google Sheet

Notice that you need to save your own sheet in your own Google account first. I can’t give you permission to edit my clean Google Sheet because you’d likely mess it up for everyone else.

In the Google Sheet, the cells in dark orange are the user-provided inputs. The main outputs are in green and the other cells are used for computing. Please change only orange cell inputs! The main inputs are pretty straightforward:

- Enter the age in years and months.
- From the pulldown menu, select either SSA-Male or SSA-Female to use the respective Social Security Administration life table assumptions.
- Since we’re not all average Americans we can also adjust the death probabilities to model longer or shorter life expectancies. For the baseline case, I leave this parameter at 1.00, because the baseline model assumed an average life expectancy. But later we can play with that parameter and see how sensitive our results are.
- We set the Target IRR at 5.00% (nominal), so roughly in line with an investment-grade (BAA) corporate bond yield in early 2023.
- The age for the NPV Calculation. Consider this a case study for when this retiree dies at exactly age 84.
- The cash flows: I assume that the retiree takes the annuity and receives $600 per month starting in month 0. Sometimes your benefits would start a month later, but that wouldn’t make a huge difference here.
- What’s the deal with the month 0 negative cash flow? The $100,000 that you forego is an opportunity cost. If you net that with the first monthly pension income you get -$99,400.

And we can now read off the results:

- The IRR is 4.915% when using the SSA Life Tables.
- If you require a 5% target IRR, then the pension is worth -$872.85, so the future pension payments don’t entirely cover your initial $100,000 outlay.
- If you were to survive until age 84 the pension looks much more attractive. That would generate a 6.112% internal rate of return!
- And likewise, at your target IRR of 5%, your annuity generates a positive NPV of $12k+. Conditional on surviving that long, the future payments more than compensate for the initial $100k opportunity cost.
- At the 5% target IRR, you’ll need to survive up to age 78 years and 1 month to cross over into “positive financial territory,” i.e., recover the initial $100,000 opportunity cost. Again, this uses the 5% annualized discount rate.

### Ignoring the Opportunity Cost

Alternatively, we could have calculated the NPV of the pension itself, ignoring the opportunity cost. That’s what I did in the calculation below: evaluate the $600 monthly cash flows only. Notice that three features in my Google Sheet are no longer usable: The two IRR calculations and the crossover calculation, because we only consider the positive cash flows.

These calculations will be helpful in a scenario where the retiree doesn’t have a cash-out option and/or wants to assign a value to his or her future cash flows. In the base case example, we can still read off the two NPVs: $99,127 and $112,092 for the probability-weighted and the Death at age 84 scenarios, respectively. Notice that those values differ by precisely the $100,000 opportunity cost in the above calculation because that value has a discount factor of 1.0000.

### Side Note: How much of an error do we make when we ignore the survival probabilities?

Since I made such a big issue out of the difference between the actuarially correct way – discounting cash flows with survival probabilities – and the incorrect way of a cash flow from the pension up to the life expectancy, how much of a difference would that be? That’s easy to answer. In the Google Sheet, I set the age for the NPV calculations equal to the life expectancy, 80.69 years in this case, and compared the two different NPV estimates. With a certain death at age 80.69, you get an NPV of $5,773, but with uncertainty around the exact age at death, you get a -$872.85 NPV. That’s a $6,646 difference, which is quite substantial for a pension with a $100,000 cashout value.

Why the significant difference? Very simple, if there is uncertainty around the age at which the retiree dies then you certainly benefit from living longer and you lose from dying earlier. But since the later cash flows are more heavily discounted, the gains will not sufficiently compensate you for the losses from dying earlier, because those cash flows are not as heavily discounted. So, this numerical example shows very nicely how important it is to get the math and the actuarial assumptions right. A $6,000+ difference in the NPV can often make a difference between an attractive and unattractive annuity or pension arrangement!

### Adjusting the life expectancy

What if you’re not the average person? I’m a generally healthy person, with a healthy body mass index, with some of my ancestors living into their late 80s or even 90s. I’m a non-smoker and I don’t do any “stupid things in stupid places with stupid people.” Thus, my life expectancy should be a bit longer than the SSA average. How do I account for that? Glad you asked because I devised a way to scale the death probabilities to generate more realistic life expectancy estimates. So, imagine that our 55-year-old retiree believes that he has a life expectancy of roughly three years longer than the average American male. We can play with the parameter “Death Prob scaling” to accomplish exactly that. For example, if we set this parameter to 0.7 we raise the base life expectancy from 80.69 years to 83.98 years, see the screenshot below. The way I model this is to assume that over the entire life span, this individual has a 30% reduced death probability every single month. So, if your baseline death probability in month zero at age 55 was 0.0612%, your scaled death probability is only 0.0428% or 0.7×0.0612%. Is this a good assumption? I’m sure actuaries have more sophisticated models that let you input a ton of extra demographic information and then would custom-tailor your death vs. survival probabilities. But with my limited time and resources, this is what I ran with. It’s certainly better than working with only the SSA assumptions! If you don’t like my assumptions, please come up with a better model. It takes a model to beat a model!

So, how much of a difference would that make in my calculations? Please see the screenshot below. Notice that the life expectancy is now 3.29 years longer, which raises the expected horizon to just under 29 years. The Survival-probability-weighted numbers are now greatly improved. You raise your IRR to about 5.5% and the NPV to about $5,725 when using a fixed target return rate of 5%. With the improved life expectancy, this pension starts to look quite attractive. Of course, 5.5% is still way behind an expected equity return, but considering the pension as a safe bucket, fixed-income asset, the return looks quite attractive under my assumptions.

### Do I get an 8% return per year for delaying my Social Security?

If you delay Social Security from your normal retirement age of 67 (for most people in or close to my age cohort) to age 70 you raise your benefits by 24%. With compounding, that’s 7.4% p.a.; not quite but pretty close to 8%. Likewise, if you planned to take benefits early, at age 62, but you waited five more years, you would get a 100/70-1 or roughly 43% increase over five years. That’s again a 7.4% compounded annualized increase.

But the 8% return claim is not just wrong due to some bad rounding and confusing arithmetic vs. geometric returns. The 8% figure is nonsensical because by waiting one year you may get 7.4% more benefits but you also lose one year of benefits. To study the tradeoff between claiming at different ages we need to do a lot more than this back-of-the-envelope calculation.

Let’s look at an example where a retiree is 67 years old and could claim Social Security immediately and receive $2,000 a month or wait 36 months and receive 1.24x$2,000 = $2,480 a month. The differential cash flow for delaying benefits by three years is -$2,000 for the first three years and +$480 for all subsequent months. Notice: it’s not +$2,480 but +$480 at age 70+! In other words, we take the $2,480 cash flow starting in month 36 but we also subtract the opportunity cost of not claiming at age 67. Let’s plug that into the toolkit and see what happens, please see the screenshot below. The first observation: your IRRs are much smaller. All the returns here should be considered real, inflation-adjusted returns because the cash flows are all inflation adjusted. So, curb your enthusiasm and accept leaner returns. In the case of this sample retiree, the IRR of delaying benefits is only 1.2%. If you make it to age 87, it’s still “only” 3.286%. A far cry from the 8% estimate floating around on the web. In fact, even if you survived all the way to age 119.9, your IRR wouldn’t get much above a 7% internal rate of return. And finally, to reach a 2.5% real internal rate of return you’d have to survive until at least age 85 plus 7 months!

Why is the implicit return so low? The benefit increases or reductions from delaying or filing early are roughly actuarially fair. They are supposed to factor in a very modest real rate of return, maybe about in line with the long-term average real U.S. Treasury rate. Let’s be real, friends, our federal government wouldn’t shower us regular slobs with an 8% annualized real return. The real generous gifts go to the defense or pharmaceutical industries, but I digress.

### Higher Life Expectancy

What about someone with a higher life expectancy? Let’s go back to a male retiree, age 67, but with a 0.7 death probability scaling. Now we’re making progress. By increasing the life expectancy by 2.7 years, we also increase the IRR to above 2.6%. This, in turn, means that at a target 2.5% discount rate we’re now at a positive $838.75 NPV. Yeah, you get a little bit extra, but in the big scheme, that’s not a large amount. The NPV of Social Security at age 67 (only counting the +$2,000 cash flows) is $355,611.95 when using a 2.5% target IRR, so the improvement in the NPV from delaying benefits of $838.75 is really a drop in the bucket.

### Female retirees with a higher life expectancy

You can get noticeably better outcomes when looking at a **female** retiree. Assuming again the 0.7 scaling applied to the already lower death probabilities of a female retiree, we now get an IRR of 3.59% and an NPV advantage of almost $9,000 when using a 2.5% annual discount rate. Please see the screenshot below. And again, some people will complain that 3.59% is much lower than they can make with their VTSAX. I know, but keep in mind that these are real, inflation-adjusted returns, and they are perfectly safe without any equity volatility. So, for a safe, fixed-income bucket investment, any real return north of 2.5% and certainly 3.5% is a great return. If you have a better-than-average life expectancy, you should undoubtedly delay your Social Security benefits.

### Future research, extensions

Notice that in this simple toolkit, I’ve abstracted from a few other potential benefits of Social Security. First and foremost is **joint spousal retirement planning**. For example, when the older spouse with a shorter life expectancy has higher benefits, it’s often beneficial to claim benefits at age 70. When that older spouse dies, the surviving spouse can then take over the higher benefits. In today’s post, I have ignored the joint spousal benefit calculations, but I may add that all at a later point. There is an excellent tool at opensocialsecurity.com already, so I’m not rushing to add that feature now.

Another benefit of Social Security is the advantageous tax treatment. Only up to 85% of the benefits are taxable. So, maximizing lifetime benefits is essential!

And talking about taxes, here’s another reason to use a very sharp pencil and craft a careful personalized analysis: taking a large lumpsum today might push you into a higher tax bracket, while small future pension payments may not. It’s possible that such tax considerations might make the pension even more attractive than it already is.

### Side note: beware of the “Worst of the Web”

People shall be forgiven when they miss some of the subtleties of actuarial calculations, like calculating IRRs up to the life expectancy vs. using survival-probability-weighted cash flows. Sometimes the differences are not that great, so as a quick-and-dirty first estimate we can certainly just look at the IRR and NPV up to the life expectancy. But I’ve seen much worse out there; mind-blowing examples of financial and mathematical illiteracy that I just wanted to feature here as a warning about how we should take everything floating on the internet with a grain of salt.

The first common mistake is to ignore the time value of money altogether, effectively setting the discount rate to 0%. So in other words, in this context people will often argue that since the $100,000 cash-out value is only worth about 167 monthly premiums, the crossover point occurs before age 69. Compare that to your life expectancy of 80+ and you’re good to go with this pension. Uhm, wrong!

The same funny math is common when gauging the pros and cons of Social Security timing. You’ll be surprised how widespread this error is. I’ve seen this on financial adviser pages. Even reputable major brokerage houses, like Fidelity, publish this nonsense on their website as one of their “Viewpoints.” See this link, comparing lifetime Social Security benefits when claiming benefits at different ages. Note that the future benefits are not discounted but just added up to one fixed age of 95. I want to avoid beating up Fidelity too much because it’s my preferred broker. I’m sure other large brokerages also publish this rubbish written by people with a similar disregard for elementary accounting and finance principles, like the time value of money. But this is the financial misinformation we’re often dealing with out there!

Another error is messing up the time value of money calculations. One fellow FIRE blogger produced results even worse than if he had simply set the discount rate to 0%. Specifically, he makes these two *insane *assumptions:

- Instead of (slightly incorrectly) discounting cash flows up to a specific life expectancy or (correctly) discounting with survival probabilities, this brainiac blogger discounts the future cash flows – and I am not making this up – up to
**INFINITY**! As in**“forever.”**Probably because the geometric sum formula is much simpler when discounting to infinity rather than a set future date. But it’s also wrong and it doesn’t even pass the smell test because a pension or annuity NPV must be different at age 50 vs. 90. - He also discounts future benefits of a pension by the (intermediate-term) U.S. Treasury Rate (e.g., 10-year Treasury, currently at 3.532% as of February 3, 2023). (granted, for corporate pensions, this blogger indeed uses an adjustment factor of 0.95, but that only raises the effective discount rate to 3.72%, still too low compared to IG corporate yields). Not a good idea – actuaries typically prefer an IG corporate bond yield, e.g., somewhere between the AAA at 4.28% and the BAA yield at 5.28% as of early February.

Now take the annual cash flow, say $7,200 in the base case scenario, and divide that by the 10-year Treasury rate (3.532%), and you get $7,200/0.03532=$203,8416. Or $193,658 when applying the 0.95 risk factor. In either case, that’s even “wronger” than just using the life expectancy times benefits: $7,200×25.69=$184,968. Note that the correct NPV was only $99,127, less than half of the infinite-horizon value. I’m going to spare the fellow the embarrassment and not mention him here. But you might already guess who he is; I’ve had a run-in with him before on another issue.

So, I hope that with my little toolkit here I’ve taken away some of the excuses for spreading bad math on the internet. If people bother to read my post and use it…

### Conclusion

Wow, I was able to write an entire blog post without any safe withdrawal rate **simulations**. I wanted to offer this Google Sheet because sometimes folks ask me about my views on annuities and pensions and I like to be able to refer people to a simple tool where they can punch in their numbers and play around themselves. Saves me a lot of time!

I am also planning to write a separate post about how annuities, pensions, and Social Security timing work in the context of my safe withdrawal rate toolkit (see Part 28 for a guide and the link to that Google Sheet). I didn’t want to squeeze those two major topics into one blog post because I’m already past 3,500 words.

Obviously, the guaranteed payments likely look even more attractive in a withdrawal rate analysis because longevity is correlated with running out of money in retirement. Anything that hedges this longevity risk, like an annuity, pension, or Socal Security, will look good when optimizing a failsafe withdrawal rate. But then again, that’s not 100% guaranteed, either. Annuities and pensions are often just nominal, i.e., not CPI-adjusted, so they would not do well in today’s high-inflation environment. Critics could also argue that it’s most important to hedge against sequence risk during the first 5-10 years of retirement, so a safe asset phased out over that short-to-medium term will likely hedge better against Sequence Risk than an annuity that runs your entire life. The annuity payments are stretched too thin over the whole retirement horizon. And they might be too low during the first ten years of retirement when Sequence Risk is a concern and too high later in retirement when you don’t need a Sequence Risk hedge. All interesting issues to be talked about in a future post. Stay tuned!

### Technical Appendix

You might have noticed that the SSA life table uses annual data, but I prefer monthly simulations. How did I go from annual to monthly numbers? Simple. I assumed that the SSA annual numbers refer to the survivors on their birthdays at that age. Then I interpolated the monthly numbers in between with a cubic spline interpolation (interpolate.splev, using the scipy package). I then noticed that the interpolation was whacky for young and very old cohorts. So I transform the annual survival rates to (geometric) monthly rates for ages 0-20 and 100-119. But I kept the cubic spline interpolation for ages 20-100. See the interpolated survivors and death probabilities below:

### Thanks for stopping by today! Please leave your comments and suggestions below! Also, make sure you check out the other parts of the series, see here for a guide to the different parts so far!

Also notice, all the usual disclaimers apply!

*Picture Credit: Pixabay.com*

Hi Ern,

Thanks again for this great post. Although I am not eligible to collect Social Securities, I appreciate the rationale and detailed analysis of all your posts.

Indeed, with so many statements online without proper analysis, and even worse, a total misunderstanding of financial and economical concepts, I sometimes doubt my reasoning and waste too much time trying to understand what they tried to demonstrate.

Glad you helped with my sanity!

Thanks for the kind words! The tool should also work for folks in other countries in case you have similar tradeoffs for claiming government retirement benefits. And pensions and annuities obviously exist elsewhere, too!

Been using your tools and line of thinking since 2018 and am now in year 3 of my ERN. Thanks for all you do!!

I plan on taking SS and my employment annuity as early as possible. I feel that the utility of the money at age 62 makes it more valuable than the increased amounts in my older age.

What are your thoughts on this? How would you add a ‘utility’ factor into your models?

For most folks it’s better to wait, especially if you think you have a higher-than-average life expectancy. And if you have a younger spouse with lower benefits who can take over your benefits after you pass it’s even more profitable to wait. At least in expected NPV terms.

Not enough credits to qualify for SS on my own record. Female spouse just a few months older should outlive me. Both of us should take SS at 67 since my spousal benefit doesn’t increase after that, right?

I would consult with the link I provided: opensocialsecurity.com. Depending on your wife’s and your health status it may still be optimal for her to wait until age 70.

I had thought that for me, it was better to take social security early. Since I’m retired, the extra income I needed either needed to come from social security or IRA.

The way I viewed it was if I took social security later, I was using traditional IRA savings to buy a better paying “annuity” via social security. If I took social security at 62, and only needed 1.8% of savings to live on, I’d be able to take the money I would have used to buy a better gov annuity and still have the principal when I’m gone to leave to family (they’ll need it!).

However, RMDs didn’t figure into that plan.

RMDs and taxes could be a big problem for us. If you know of any planners that allows you to do what-ifs taking into account both social security and RMDs, I’d be interested.

Since you have an extremenly low consumption target, you don’t really need to worry too much about Sequence Risk. So, if you like maximize the expected estate you leave to your heirs you are *probably* better off delaying SS until 70. But it still depends on your personal tax situation, correct.

@Jeremy

Be aware of tax liability when you do this. Too much income can trigger SS taxes.

Agree. One should factor in the tax impact and then do the NPV calculations on an after-tax basis to cover all your bases. But that’s very idiosyncratic, so people should do that for themselves. That’s why I posted the toolkit for folks to enter their own numbers.

I had not factored that into my projections, but your comment made the light bulb come on in my head.

We are getting by paying no taxes by keeping dividend income below the standard deduction and supplementing that with long-term capital gains. If our income increases even moderately we will be taxed on that. This leads me to the conclusion that I should hold off on social security until I am 70. I can increase my withdrawals from long-term capital gains without any additional tax burden.

Now I am off to update Big ERN’s SWR Toolbox and see where I am at.

Thanks ERN!

I just turned 61 so timing of SS Benefits is something I have been thinking out. I would appreciate some thoughts around income tax considerations. For me personally I will be receiving deferred compensation from my former employer for the next 5 years. In fact, I see my income moving from a 35% marginal rate now down to 24% when the deferred compensation ends. As such I am planning on taking SS when the deferred comp runs out, if I take it today it’ll all be in the higher tax bracket, take it later I get a lower marginal rate.

Yeah, I’d wait until at least the end of the deferred comp. The other option is to wait even longer until age 70, and do some Roth conversions along the way.

Again: for folks with a higher-than-average life expectancy, it’s often optimal to defer until age 70. Especially with a younger and lower-income spouse.

Nice post and a very useful tool! As a fellow geek the cubic spline interpolation warmed my heart!

I remember that 0.5% WR post and your rebuttal. Now I wonder what if FS is not a troll at all but just plain incompetent? He calculated some pension values in the seven figures: insane!

Good point! Maybe I was too harsh on Sam. Hanlon’s Razor: don’t attribute to malice what can be explained with incompetence.

Thank you for the great analysis, explanation, and toolkit! Could you help clarify why you chose a 2.5% target rate (presumably real rate) for discounting in your social security examples when current TIPS are running about 1.3-1.4%?

There’s no unique correct rate to use here. But my thinking was as follows. If you use 5% for a

nominalreturn target and you subtract maybe a 2-2.25% expected inflation rate you end up with 2.75-3.00% real. Well, since you also eliminated all of the inflation risks of a nominal bond, maybe I’m willing to reduce my target IRR a little bit further, to 2.5%.Another way would be to use the long-term real return average of 10y Treasuries (2.33% since 1871): 2.33%.

I have a related but slightly different question so I’ll tag it on to this existing thread. Why use the return rate of bonds only? My first inclination was to use the average real return of my 70/30 portfolio, which I calculated as 4.85% real (6.5% equities, 1% bonds). My rationale is/was that if I take SS early what i’ll be doing is not withdrawing that amount of money from my portfolio that has that weighting.

Because bonds are a similar asset class to the annuity. If you discount at too high a rate (say a 70/30 portfolio) you will likely make the annuity too unattractive.

Aloha,

Thanks for the great post and spreadsheet. This must have been fun to create.

Question on the retiree investigating different ages to claim Social Security. Typically the benefit offered changes annually. So, would it be reasonable to enter the first three years of foregone benefits at the respective annual levels, and make subsequent cash flow the difference between the third year and age 70 benefit?

When I use the numbers below, I get a result substantially different than yours. Have I made a flawed assumption or otherwise misused the spreadsheet? I’m just trying to understand this so I can feel confident I have the results I intended.

Thank you so much for your terrific contributions to the body of knowledge in this area!

Hypothetical example:

retiree 67 years old benefit $2,000 / month (months 1-12 -2000 cash flow)

at 68 years old benefit 2000*1.08 = $2160 / month (months 13-24 -2160 cash flow)

at 69 years old benefit 2000*1.16 = $2320 / month (months 25-36 -2320 cash flow)

at 70 years old benefit 2000*1.24 = $2480 / month (months 37 on +160 cash flow)

Once you claim benefits they go up with inflation. They do not go up from 2000->2160->2320->2480 between 67 and 70. In fact, in real terms, the benefits stay constant. That’s what I assumed in my calculations: $2000 in constant $ forever is the opportunity cost. $2480 in constant $ after age 70 is the gain. Exactly as I did in my sheet. If you get different results you did something wrong, yes!

Great article, and your conclusions about SSI withdrawal age match my intuition and results. And like you I’d also like to do some analysis on the impacts to spousal benefits – from those I’ve talked to who are planning to wait to take SSI until 70, the two big reasons are 1) they are still working and don’t want to get pushed into a higher tax bracket any sooner than needed, and 2) they want to maximize the benefits for their spouse.

Haven’t seen that Open Social Security calculator before, I’ll check it out.

For the failed interpolation at ages 0-20 and 100-119, did you consider a higher order polynomial, using something like numpy.polyfit?

Good question. Ages 0-20 don’t make a difference because nobody will claim Social Security or a pension at age 15.

The interpolation past age 100 won’t make a big difference for most retirees in their 50s, 60s, and even 70s. The problem with 100+ is that there are too few survivors and the numbers are so granular, that the survivors past age 105 don’t exactly match the the survivor probabilities from the SSA tables. For men they go from 7 to 3 to 1 to 1 to 0 for ages 109-113. It’s best to use the probabilities and calculate survivor numbers not just in integers but with all the digits behind the decimal. That’s what I approximated. But you can obviously do another round and do the spline interpolation for the monthly probabilities, but that would be overkill. Nothing really changes for the men past age 105 or women past age 110. It’s too remote of a change to make it that long.

Back in 2018, I helped my mom with a similar decision whether to take the lump sum or take the monthly payment. After running through the many what-ifs, in a moment of clarity (frustration) at the end I asked myself that if we took the lump sum, how much cashflow could we presumably get out of it?

At 1/30 (or 30x expenses) it would have come out to about $1,500…per year.

Forfeiting the lump sum and taking the monthly option would yield ~$1,000…per month (~$12,000 per year).

I asked my mom whether she thought she had it in her to live another 4+ years; she said yes. We went with the monthly option.

I know we ignored the time value of money but I didn’t think it was possible (at the time and still do) that the lump sum could sustain a >25% withdrawal rate for the rest of her life.

Thanks for sharing. Your example shows beautifully that you shouldn’t always use crude and naïve rules like 4%/25x or 3.33%/30x. For these kinds of situations, life expectancy is the main determinant. And over relatively short payback periods (e.g. 4 years) discounting isn’t making a big difference. So, yes, intuitively you made the mathematically and actuarially correct decision. I wish your mom a long and happy life! 🙂

Hi ERN!

Your mathematical method is correct. However, I would argue it is correct from the point of view of an eventual heir or maybe a person seeking to extract as many dollars as possible out of the system, but not necessarily for the assumed-rational agent making the decision.

This is because our FIRE-minded decision-maker must decide each year whether to sacrifice One More Year of their life (arguably, their healthiest and most valuable remaining year) working or if they should retire now and accept the risk of SORR. By working OMY, they reduce the risk of outliving their money, but at the cost of the most valuable remaining year of their life. This decision relates to delaying SS, cashing in a pension, buying an annuity, or setting an AA / bond tent that trades retirement income for safety.

Our brokerage accounts go up as we earn money, but our life-opportunity accounts go down in a non-linear way as time passes. That is, the utility of one’s time is greatest now, and the utility of money decreases as one ages (Think about how an 85 year old multi-millionaire is objectively worse off than a broke 65 year old.). The solution is arguably an intersection between these lines which signifies “enough”.

To illustrate the issue, imagine if the return on delaying Social Security was 25% instead of 7.4%, and imagine one could delay SS indefinitely. In such a world it would never make mathematical sense to retire, because there would be such huge gains to be had from working OMY, each and every year. It would be the perfect trap to get certain types of thinkers to work their whole lives away for rewards they’d be too old to enjoy.

Under purely mathematical guidance, our decision-maker might not retire until they had used up the best remaining years of their life. They would sit in a wheelchair in their mansion falling asleep watching Wheel Of Fortune reruns for their last few years while their butler dusts the TV. This would happen after they sacrificed the portion of their lifetime they could have used to travel the world, raise kids/grandkids, nurture more friendships, change the world, etc.

The people enjoying LeanFIRE or BaristaFIRE would see something wrong with this life plan because it prioritizes the late-life mansion, servants, and luxury car over enjoyment of one’s most mobile and mentally sharp years.

There are other solutions to the problem rather than maximizing dollar extraction or maximizing free time. One method might be to assign a dollar value to time, or a time value to dollars. E.g. we could create a table assigning the dollar value we would pay to be retired for one year at each year of our remaining life. Because we can do more stuff at age 45 than we can do at age 85, a year of life at 45 is worth more than a year of life at 85. Similarly, we could convert dollars into time.

There is an “exchange rate” to be established, and it is not simply the rate of pay a person works for, because they arguably have no choice but to save money for retirement.

Thanks for sharing. All valid points. I’m happy that I retired when I did because it gave us plenty of time to travel in 2018 and 2019 before “you-know-what” happened.

The calculations here make no assumptions about when you stop working. So, I certainly urge people to retire as early as they can. But conditional on being retired, when should they claim Social Security? Conditional on being retired, should they claim their corporate pension as a lump-sum or monthly payout? So, none of this calculation is about the important life vs. work tradeoffs you mention. But they are important tradeoffs, for sure. 🙂

But what if the optimal thing to do from a financial-maximization perspective is not the optimal thing to from the time-maximization perspective? The math can only solve for financial maximization, which in some circumstances might persuade people to retire too late. OMY can be a financially good deal, but it’s only the right choice if we factor in the loss one must experience to obtain that good deal.

You are trying to start an argument about a non-existent disagreement. I never said that this post was about retiring early vs. retiring late. This current post, Part 56, is entirely about

timing the cash flows.Not timing theretirement date.I never even claimed that this NPV math here can or should be used to time the retirement date. If that was the impression, then there’s a major misunderstanding and I apologize if people got this wrong impression.

This NPV math here likewise shouldn’t be used to study the aerodynamics of airplanes. I present this math to study the pros/cons of timing cash flows. Not more not less.

Chris B,

All good stuff.

Do you have a simple rules of thumb that quantifies or even bounds “enough”?

Real annuities like Social Security can also perform a risk reduction role by addressing both inflation and longevity risk. This risk reduction might allow a retiree to take greater risks with the remaining portfolio.

Imagine, for example, a couple at age 62 with $70k in mandatory expenses and $30k in expected discretionary expenses (but more is better and less is survivable). If they are entitled to $40k in SS at age 62 and $70k just before age 70, then delaying SS would allow them to invest their entire portfolio based on their risk tolerance for discretionary expenses (while investing conservatively enough to cover all of their mandatory expenses between ages 62 and 70 with sufficient confidence). The additional stock investments post-age 70 could easily have an expected return high enough to offset the lower return on Social Security after risk adjusting the portfolio to reflect SS’s much greater safety.

Exactly. But that needs some careful calculations and simulations. If the drop in the stock market is steep enough during your first 8 years of retirement your portfolio may never recover due to SoRR. So, it’s something that has to be evaluated quantitatively. Qualitatively the tradeoffs are all really obvious.

Complicating the simulation design is the fact that claiming Social Security is an option available throughout the 8 year period.

One possible strategy with intuitive appeal is to start out planning to claim at 70 if all goes well, but to claim earlier if there is a large and sustained stock market drop. That would address most of the SoRR from delaying Social Security since it won’t be delayed in the scenarios where SoRR is most painful.

Simulating this would likely require some experimenting on what definition of “large and sustained” produces the best results for the retiree.

Excellent point. This feels like a dynamic programming problem where you model the claiming as an either/or and a one-way choice, so there’s no going back once you claim SS.

Might be overkill, though! 🙂

I always read this blog with interest. I understand the advantage of a later SS claiming strategy in the scenario of the older partner who is the higher earner, but can you say a few words about the implications of the reverse–younger partner is the higher earner? Thanks.

That’s a situation that has to be plugged into that website I mentioned. It might still mean that the higher earner waits until age 70. If that’s the female (with a high LE) and she’s in good health.

When I think about taking SS early vs. later, I think that taking it early has the effect of protecting oneself against sequence of return risk. By taking it early, one does not have to take as much from one’s investment portfolio, which reduces the negative outcomes if the market were to perform poorly in the initial phase of your retirement. Of course by doing this I am taking on longevity risk by forgoing a larger annuity payout by waiting.

Does this thinking have merit or is am I being overly simplistic?

That is exactly the tradeoff. And you can now appreciate the need for quantitative analysis, right? On the one hand, by claiming earlier you protect your portfolio. But on the other hand, SoRR causes portfolio failure only later in life, likely when you’re way past the age of your initial life expectancy. So, longevity insurance is also important. This decision needs to be custom-tailored!

This recent paper by Pfau and Parrish may be of some interest:

https://www.financialplanningassociation.org/learning/publications/journal/JAN23-which-social-security-claiming-strategy-generates-highest-legacy-value-OPEN?utm_source=ONTRAPORT-email-broadcast&utm_medium=ONTRAPORT-email-broadcast&utm_term=%21General+RR+List&utm_content=Episode+51+is+live%21&utm_campaign=02072023

Good read. I need to do my own research first with my SWR toolkit, but I tentatively agree with this.

Now that we’re suddenly in a world with competitive interest rates on things like CDs, treasuries, and high-rated bonds, I wonder if a more conservative portfolio like a 60/40 or 50/50 has higher odds of success in a moderate-interest-rate regime than they had in a low-interest-rate regime? Portfolios have better odds and lower SWRs when CAPE is low, but what about when interest rates are high?

Obviously, if 30 year treasuries were to hit 6-7% a retiree on a 4% WR might find it makes sense to go 90%+ treasuries, foreclosing on every risk except hyperinflation.

Yes, bonds have become significantly more attractive. But so have equities because the CAPE is down from an all-time high. My adjusted CAPE is down to 23. Elevated but much more comfortable than in early 2022.

Also, keep in mind that real bond yields are still not that attractive. Long-term TIPS (see https://www.bloomberg.com/markets/rates-bonds/government-bonds/us) are at around 1.5% right now. Sure, you can support a 30y retirement and 4% real withdrawals. But with depletion. Not useful for an early retiree.

But directionally you’re right: 60/40 doesn’t look so awful anymore. If I have 70/30 right now, I might move toward 60/40 rather than 80/20. But not sure if many people want to go down to 50/50, though. 😉

New to the site – LOTS to absorb. You mention here ‘My adjusted CAPE’ is at 23 – looking online I see CAPE at about 28 – do you have any additional info on the adjustment?

Right here: https://earlyretirementnow.com/2022/10/05/building-a-better-cape-ratio/

Professor ERN, I wished you published this fine analysis when I was advising my wife in 2017 on whether to convert her Florida Retirement System Investment account to the Pension Fund. Nonetheless, my back of the envelope calculation (what I call my Excel calculation compared to your sophisticated one) resulted in going ahead with the conversion. I had helped her select good low-cost mutual funds which resulted in only having to convert 60% of her Investment Fund to the Pension, leaving 40% in the Investment Fund which has since doubled. The FRS became a semi-Defined Benefit Plan after the Great Recession with the state requiring 3% employee contribution. I added her total contribution MTD to the opportunity cost and those anticipated right up to her early retirement date. This resulted in an IRR for her actuarial life span of over 14%. I ran other scenarios with the same decision result. This coupled with her county school district 403B which she contributes will allow her to join me in early retirement next year.

Thank you again for your outstanding work and education.

Nice move! That sounds like an attractive arrangement. That’s often the case in public retirement funds! Good luck to you and your wife!

Another excellent analysis. But the elephant in the Social Security benefits room is the looming insolvency of the system. Some account for that by discounting their projected benefits by 25% or so. But I say that (minor) cut ignores the likelihood of (more) means testing, which might well reduce benefits to zero for the ants among us. (The grasshoppers will do just fine because they will benefit from the wealth transfer.) How do you quantify this risk? And does it not imply that taking SS early is the smarter play for the one percent?

Yeah, great point!

It depends on how we deal with the inevitable insolvency. Normally, benefits will be adjusted for future generations, not current ones because they are too important a voting block. So, if you’re 62+ you can probably breathe easy. And use the sheet as intended.

The adjustments will certainly hit current contributors aged 40 and under. Likely with a rise in the full benefits age. But that’s not really who’s using the sheet for the timing (yet).

But if you like to be extra cautious, sure, make some adjustments. But that would impact both your current benefits at age 62 and your future benefits at age 70+. It might make the early claiming a bit more attractive because you will have lower benefits spread over a longer time. This can make you less susceptible to means-tested policy changes, i.e., fleece/tax the rich propaganda.

Hi Karsten, Thanks for the spreadsheet. I noticed that the heading of column H is CF*Disc but the values appear to be equal to CF not CF*Disc (i.e. the value of cell Hx = Cx for all x >= 18). This may not matter as I don’t see the values of column H used in the results. Is this a typo or am I missing something?

Good catch. It’s an unused column with an incorrect column header. I erased those values.

Hello Big Ern,

Thank you as always for great tools that are occasionally so advanced that I may be misusing them! 🙂

One project I always struggle with is how to value my US military retirement. It currently pays $10,094 monthly and gets an annual inflation adjustment based on CPI; up 8.7% this year for example.

If I use your spreadsheet tool to estimate my Survival-Prob Weighted NPV, is it reasonable just to fill in 10,094 for all months in column C and assume this will be in “real” dollars? (Or are there inflation adjustments elsewhere in the calculation that I am missing?)

Is it reasonable to use the Target IRR of 5%? (Military retirements do not have a “fund” like SSA; they are paid from a special Treasury bond that the military has to “buy” each year from Dept of Treasury based on actuarial data and number of retirees that year at different ranks/longevities)

Appreciate any thoughts you have regarding if I am thinking about this correctly.

Yes, just enter everything in real USD and then you’ll also need a real discount rate.

5% real is likely a very high discount rate. Maybe start with the 30y TIPS rate (1.50%) and add a little bit of a risk premium (1%) for a total of 2.5%.

Nice interview for the choosefi Karsten. However, in the end it wasn’t clear what your allocation and strategy is. For Fritz it’s clear 70-20-10 but for your strategy, what’s exactly your recommendation in simple terms?

Similar. From my post a while back (https://earlyretirementnow.com/2021/10/18/passive-income-through-option-writing-part-8-2021-update/) I have a roughly 75% risky, 25% diversifying asset allocation.

https://i0.wp.com/earlyretirementnow.com/wp-content/uploads/2021/10/Put-Writing-Part08-Chart02.png?w=911&ssl=1