Actuary reveals secret withdrawal rate techniques

Were you expecting an article about a particularly frugal birth-control method? Sorry to disappoint you, but today we’re going to be looking at how much you can safely spend in retirement – the safe withdrawal rate. And in particular I’ve not seen anything on the special secret techniques that Actuaries use to evaluate this.

Last week I saw a tweet that basically said that a popular personal finance blogger was approaching early retirement and confident that a 2% withdrawal rate would be safe. Let’s use some super-secret actuary techniques to tease out whether this really could be safe.

There is an enormous amount of commentary around the FIRE community about the 4% rule of thumb. This is the idea that if you withdraw 4% of your nest egg each year, then you should be able to enjoy that annual income for the remainder of your life. So withdrawing only half that amount of 2%, should be super-duper safe right?

Well here at Actuary Towers we like to put things under the microscope and… hang on, stop! Here we like to do things differently. We should use the microscope backwards, or even throw the microscope away and try analyzing it with different instruments. Perhaps instead of looking at it through a microscope we’ll look at it through some eclipse glasses and see if that gives us some new inspiration…

Come on guys less chatter, we need to get to work!

Testing the Claim

There are essentially three ways to test the credibility of a safe withdrawal claim, one of these methods looks backward, and two look forward.

  1. Back-testing with historical data
  2. Monte Carlo simulations of future scenarios
  3. Financial economics

#1 has been covered numerous times in many great studies, and the result seems to be that over many historical periods a 2% withdrawal rate would be safe.

#2 just gets me all riled up. So let’s leave that until another day as I’ll just get grumpy and you don’t want to read an angry post do you?

#3 is the secret Actuary method. It sounds scary huh? And at this point I’ve now lost half my readers. But for the three of you remaining, if you enjoy this half as much as I do, then you are in for a treat!

Financial Economics

Financial economists say that you don’t need to make up a load of assumptions about risk and return since market pricing will tell you all you need to know. For example you don’t need to estimate the price of a new lawn mower by back-testing previous pricing, or projecting out economic scenarios and developing complex mathematical models to predict lawn mower prices. You simply go to Home Depot and look at the market price. That is the price at which many lawn mower suppliers and many potential lawn mower buyers have agreed is the price at which they are willing to do a deal. You may not agree with that price, and you may claim that due to the Fed the price has been manipulated to unreal proportions – but it is what it is.

It’s the same with the financial markets. If I want to evaluate the risk in providing a 2% per year income, then I need to search Home Depot the financial markets for a financial instrument that pays 2% per year above inflation. I can then look at the risk of that particular security to tell me how risky that income stream is.

Risk Free Return

The starting point in financial economics is to establish the risk-free return. This is the return that you can be certain to achieve. You might think that Berkshire Hathaway stock is risk-free, but it’s not. In fact no stock is risk free, there is always the risk of the company folding. For example only one of the original twelve Dow Jones companies is still in the index. So the risk free return is generally assumed to be the return you can get on Government Bonds, or “Treasuries”.

To achieve a 2% safe withdrawal rate we really need to generate a return of 2% in excess of price inflation, i.e. a real return of 2%. This will preserve the real value of capital and generate sufficient income every year to live on.

So ideally we need  a Government bond that will pay a 2% real return for a lifetime. If only we could find that then we would be done. But it does not exist.

Bond Yields

The nearest security we could consider is the TIPS (Treasury Inflation Protected Security), and I can tell you that a 30 year TIPS is yielding about 0.9%. So if we bought a load of 30 year TIPS bonds with our savings we could generate a real return of 0.9%. So I would say that a 0.9% safe withdrawal rate is super-super-safe. [Your only risk is Government default, and re-investment risk at 30 years.] However I’m not sure that many of you are targeting a safe withdrawal rate of 0.9%, and our target was 2%, so we need to press on.

From Bloomberg, TIPS pricing
Look at the yield on the 30 year TIPS. I don’t make this stuff up you know

We now know that the market is pricing the risk-free long term real return at 0.9%. This is like the lawn mower, we went to the market and they have told us the price. We don’t need to assume anything, it’s there. We may have a different view about what the long term real return should be, but the sum total of all buyers and sellers have determined that 0.9% is the right number.

The trouble is, 0.9% is not enough. We need 2% return – remember?

But Financial Economic can come to the rescue again. If we want more return then we need to take more risk. That’s a basic axiom of finance, and the market accommodates with a whole load of securities across the risk spectrum. So let’s select one that gives us the right return.

More Bonds to Analyze

It is not just the US Treasury that issues bonds to borrow money, most corporations borrow money by issuing bonds. Just like you and me, companies have a credit rating that determines how low an interest rate they can borrow with. The best rating is AAA, but there are not many companies with that rating. The next best rating is AA. This is equivalent to having a credit score in the high 700’s and 800’s.

Now, I can tell you that a 30 year bond issued by a AA-rated company is yielding 1.2% more than Treasuries. With our financial economist glasses on this is telling us that investors are demanding more return for holding a slightly more risky bond. The US Government is generally recognized to be safer than a AA-rated Company and investors have evaluated the risk of investing in a AA company and determined that 1.2% additional return is sufficient compensation. [The 1.2% is called a ‘spread’ if you wanna impress your Wall Street friends]

So I could theoretically generate a 2% real return by buying an inflation linked long bond issued by a AA Company. Since that should yield about 0.9%+1.2%; the risk free rate of 0.9% plus the additional return that compensates us for investing with a AA company. That’s enough return to cover our 2% withdrawal rate – yay!

This ain’t built on a foundation of sand


So we have found a security that provides a 2% long term real return – it’s a long AA inflation protected bond.

We also know the expected default rate for AA companies. It’s miniscule. The default rate for a AA company over one year is practically zero. Unfortunately over a number of decades the probability of default will rise. I don’t have a fancy credit migration default calculator but I’m going to say the chance of a AA company defaulting over a 30 year horizon is low single digits.

In conclusion we’ve found a market instrument that replicates the 2% real return we need. And we’ve found that the market default probability for that is low single digits.

You’re going to struggle to get an actuary to say something is “safe”, but I’m going to stick my neck out and say that a 2% withdrawal would have an extremely low probability of failure in the low single digits. Praise indeed!

How can I use this?

You should use this analysis as a smell test. For example if you want to roughly get an idea how risky a 4% withdrawal rate is, then you first observe the risk free rate is 0.9% (real) and you need to earn another 3.1% on top of that. Given that high yield bonds are yielding 3.5% above the risk free rate, then you can conclude that a 4% withdrawal rate is perhaps a bit less risky than equities. I’m assuming here that high yield bonds are similar in risk to equities (not quite true). So my best guess for a portfolio that currently has the market risk to support a 4% withdrawal rate might be around 70% equities and 30% bonds. Make sense?

Was that crazy technical, too much? Did you find it gibberish or interesting? Let me know whether you want more financial based articles like this.



[Technical notes. I calculated the risk free rate as a 30 year TIPS and then found the spread on a 30 year AA bond. This gave a yield of 0.9%+1.2%, which would fund the 2% withdrawal rate. We then observed that the default rate on 30 year AA bonds is really low and so concluded that a withdrawal rate of 2% is pretty damn safe. You might think that Treasuries are not risk free over a retiree’s lifetime, and you would be right. We could argue about the hair cut, but 10bps might be ok, and that still gives us 2% return. I did look at CDS on US Treasuries, but I don’t think they are a very useful proxy for Treasury default. Since if the Government defaults over 30 years, do you really think the bank will be around to pay out on the CDS? Also note that inflation protected corporate debt does not exist. Let alone over 30 years. But that doesn’t matter since we constructed from first principles what the market would price if it did exist. The biggest hole in this analysis is the re-investment risk. We simply don’t have securities with long enough tenors. So I had to work with 30 year tenors. Are you still reading this… wow! You’re now my best friend.]

32 thoughts on “Actuary reveals secret withdrawal rate techniques”

  1. Wow this was an interesting read to go “behind the scenes” of an actuary’s mind! I myself think the 4% SWR is too high and would prefer to have a never touch your principle approach but I think that would take too long to save up, so good to know that 2% is ok 🙂

    1. GYM – not sure you want to go too deep in an Actuary’s mind, but you emerged unscathed! The issue of not touching principle is a tricky one. On the one hand you want security, but need to be careful that you’re not overly prudent.
      Thanks for commenting.

    1. Eric – that’s great to hear! I’ve got a few more in the pipeline. So maybe by the end of that there will only be you an me left!

  2. Chris @ Keep Thrifty

    I must be a twisted individual as I really enjoyed this walkthrough! I guess I’ve always been a numbers nerd so it shouldn’t surprise me 🙂

    I hadn’t heard of the financial economics approach, but it makes a lot of sense. Embedded in there is an assumption that the market knows how to appropriately price for the long-haul, but that’s where your minimal risk level comes in.

    Thanks for sharing this – definitely has the rusty gears in my head starting to turn!

  3. Excellent piece! The more (like this) the merrier in my opinion.
    What I’d really be interested in would be an analysis of the other extreme:
    How much risk can one take on before there is a >10% chance of a 50%+ drawdown over the next 30 years?
    Are there actuarial tables for this sort of thing?
    I’ve only seen backrest results that give an answer to the above but wonder if it could be derived from first principles as well.
    Also, it would be interesting to note the most efficient ways to take that risk if we have a long time horizon and are relatively indifferent to the path that gets us there?

    1. You’re going to struggle to answer that question with financial economics, simply because of the long time horizons. You could use the pricing of derivatives to answer that question over a few months or perhaps a year. i.e. based on market prices of derivatives you can back-out an implied probability of drawdown. But not over decades.
      So you are really left with back-testing and Monte Carlo simulations.

  4. Good discussion! I am curious what effect this has on your own planned SWR? I lean more toward the 4% range than way down at 2%, mostly because we all use other safeguards that are not affected by the market (like over-saving, side hustles, etc.).

    1. Yep 2% is way too low for me, but if you have enough assets then why not. I’m not very confident about 4% at the current time, so I am triangulating on about 3.5% at the moment. Thanks for visiting Dylan.

  5. This was interesting!

    I think the approaches you mentioned are complementary. There are still some hidden assumptions in the ‘financial economics’ [the term seems redundant, no?] approach, though–e.g. that TIPS, bonds, and other investments are priced appropriately, that the current rate of inflation will hold, etc.

    The hidden assumption is that TIPS are going to stay at about 0.9% is particularly problematic, since there’s a reasonable chance that the Fed is going to raise the interest rate. My understanding is that they’ve wanted to raise it for years now, and haven’t been able to do so.

    I suppose it boils down to this: if you want to know what your withdrawal rate should be if you were to retire tomorrow, or in the next 6 months, or in the next year, then this calculation may be your best move. But if, like me, you’re DECADES away from retirement, then this method may prove next to useless.

    A thought-provoking article! Well-done! And it seems that you have more than 6 readers 🙂

  6. winningpersonalfinance

    Interesting post. It’s good to hear that 2% is safe. However, based on the 4% rule, I’d think that with a more aggressive allocation we would be able to “safely” withdraw more. If I wait until I have enough to live on 2%, I probably ended up trading too much of my time to employment. I’m much more curious about the maximum SWR instead of finding out if 2% is safe.

    1. You’re absolutely right, a 2% rate is very conservative and with a more aggressive allocation you could ramp that up. I was really looking for a “bookend” near the lower end. What might we be able to determine as a safe rate based on today’s market pricing? Once we get the lower end we can tack on more return for more risk. At the end of the post I comment on the type of portfolio that might support a 4% withdrawal.
      Thanks for reading and commenting.

    1. You’re right things get a bit sketchy at the end!

      Basically we determined that the risk free withdrawal rate is a 0.9% real return. But nobody would ever want to go that low!
      We then need to build on 3.1% more return to get to our 4%. So we need to look for market instruments that return 3.1% above the risk free rate. I observed that High Yield bonds (below investment grade) are currently returning 3.5% above Treasuries. So this gives you a guide that to get to our 4% return [0.9%+3.1%] we would need to take risk commensurate with something like a HY bond. We don’t need 100% HY bonds, so I guessed that something like 70% would get us the 3.1%. (I think it might be nearer 90% to actually).
      Given that HY bonds are pretty similar to equities, then you would need a very equity-heavy portfolio to get you to a 4% withdrawal rate.
      Make sense?

      Thanks for the comment.

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  8. Thanks for this post, I enjoy your stuff.

    I’ve been playing around analyzing Harry Browne’s Permanent portfolio. Over the long term (and the short term) this portfolio has performed very well as long as you stick to it and don’t let greed get the better of you. It has delightfully low volatility and predictable return. What’s your opinion of this portfolio v the “bonds” you describe?

    1. Gasem – firstly thanks for the kind words and taking the time to comment.
      I was not aware of this portfolio, so I’m glad you have brought it to my attention. It’s pretty similar to Ray Dalio’s “All Weather” portfolio. You are right, if you stick with it then you will get what you expect, decent returns over most periods with a reasonably low volatility. The main criticism seems to be that behavior prompts people to trade out at the wrong time.

      Personally I don’t love Gold, and having 25% in cash makes me queasy, but I do see the logic of it. Note that cash plus long Treasuries basically equals intermediate Treasuries, which is what is in Dalio’s portfolio. Anyway, I can’t do it justice here, and there is a 72 page Bogleheads discussion here.
      I would be interested in any more thoughts you have on this portfolio.

      Note that the portfolios I discuss in this post are really theoretical constructs to try and establish the market risk of different withdrawal rates. I guess you could put everything in long bonds if you have a sufficiently low withdrawal rate target, but I wouldn’t recommend it. Something more diversified would be better. And what you suggest is certainly a candidate (though probably not for me).

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  10. One quick question, is there an assumption here that the fund is not being run down over the period (I thought the 4% rule was based on 30 years)?

    1. David – good point. I am tacitly assuming that really. I’m really finding a portfolio that would support a 4% yield so as to fund a 4% withdrawal rate. This then does not run down your principal over the period, as you point out.
      Thanks for stopping by!

  11. Actuary, Thank you so much for your contributions to this niche.
    I want to make a point about SORR with respect to investing for college tuition; a short time line of only 15-20 years. Look at the SPY for the years 2000-20013. These were the years that I saved and invested in 529s for our three children. My experience was that as they aged, the losses were locked into progressively more conservative AA. The SORR risk during that decade ravaged any potential for capital gains.
    Please comment on this.

    1. jz thanks for stopping by and your thoughtful comments. You have prompted me to look at 529 investing in particular. That is an under-researched area IMO.

  12. Actuary, to reframe my question. If one’s saving and investment timeline is short, eg. 15 years from a child’s age 5 ( when a parent gets serious about 529 saving) until age 18 -20, is there a AA to best insulate from SORR?

    1. Good questions. I’m going to do some work on shorter investing time periods. Stay tuned for more on this topic and 529 accounts in particular!

  13. The thing missing here is your methodology is based off preservation of capital. But if you don’t care about such things at 2 percent you just need to keep up with inflation provided tour life expectancy is under 50 years.

    1. Yeah good use of math! Although see my other post on life expectancy to see whether 50 years is sufficient….

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