Monday, January 17, 2022

Annually Recalculated Virtual Annuity

A very low risk way to handle your portfolio in retirement is to invest the whole thing in inflation-protected government bonds and choose a spending level that will have your money last for a very long life.  A related idea is the Annually Recalculated Virtual Annuity (ARVA) where you invest as you see fit and choose your retirement spending level as though your portfolio were invested in inflation-protected government bonds.  Then each year you recalculate your spending level based on your new portfolio size, your new age, and prevailing bond interest rates.

The ARVA idea was introduced by Waring and Siegel in their well written and accessible paper The Only Spending Rule Article You Will Ever Need.  Investors who use the ARVA idea will have annual retirement spending “that fluctuates with asset values, but they can never run out of money.”

The ARVA idea is broadly similar to my own retirement spending plan that is designed to adapt my retirement spending as my portfolio fluctuates.  The similarities between mine and ARVA are that they take into account the planned number of years of retirement left, and they use an assumed rate of return to calculate the amount to spend each year that will ultimately deplete the portfolio.  The differences are in the assumed lifespan and how we arrive at the assumed rate of return.

Very low retirement spending

The downside of ARVA is that it is very conservative and will have you spending very little.  One reason for this is low government bond yields.  In Canada, inflation-protected government bonds are called Real-Return Bonds (RRBs), and as I write this their annual yield is 0.21% above inflation.  A second reason is the authors’ retirement duration advice: “Whatever one’s view on the likelihood of living to extreme old age, it seems prudent to provide for oneself to at least age 105 if male or 110 if female.”

Consider the case of a 60-year old woman.  To provide for a 50-year retirement (until she’s 110 years old) making an investment return of only 0.21% above inflation, we can use the PMT spreadsheet function to find that she can only spend 2.1% of her portfolio in her first year of retirement.  This is a far cry from the widely-quoted 4% rule, particularly when we consider that the ARVA strategy adapts to portfolio fluctuations and can lead to future declines in spending.  Usually, when retirees are prepared to accept future reductions in spending (when portfolio returns disappoint), it increases their current safe spending amount.

To arrive at a rate of return assumption, I use 4% above inflation less costs for stocks, and 0% above inflation less costs for bonds.  I adjust my assumed stock returns downward when the blended Cyclically Adjusted Price-Earnings (CAPE) ratio of my stocks exceeds 20.  Unless the CAPE rises crazily, this gives me an assumed return that is higher than current Real Return Bond rates.  For the length of my retirement, I assume my wife and I will live to 100, rather than 110 and 105.

When I apply ARVA to my own portfolio, I find that it reduces my spending level by 34%.  This is a large reduction considering that most experts already find my approach too conservative.  However, many of these experts are financial advisors who feel the pressure from their clients to say that higher spending rates are safe and reasonable.  So, I’m comfortable that I’m not being unreasonably conservative.

Conflicting Desires

The authors observe that “most people are short on retirement savings to begin with and are anxious to convince themselves that their need for more assets to support desired spending is less than it really is.  Even otherwise thoughtful investors seem springloaded to reject out of hand the need to provide for one’s entire life—and yet they do nonetheless worry about the risk of running out of money.”  The ARVA approach appeals to the “worry” side of this contradiction.

Other spending profiles

So far, we’ve been discussing flat retirement spending over time (with inflation adjustments).  However, it is possible “to modify the shape of the payout, the relative amounts spent over time. There is nothing special about equal payments.”  However, it’s possible to take this too far.  If we decide we’ll spend twice as much in our 60s as in our 80s, we’re using the ARVA approach in name only.  When we get to our 80s and find we can’t cut our spending in half, the ARVA promise that we’ll never run out of money falls flat.

Insurance products

In theory, insurance companies should be able to make a profit for themselves and help retirees by pooling longevity risk.  Academics see the poor uptake of annuities as the “annuity puzzle.”  Unfortunately, there is a big gap between academic theory and the practical reality of the products that insurance companies offer.

“In its seemingly boundless desire to offer something—anything—to appeal to longevity risk hedgers without providing safe (properly hedged), simple, transparent, and fairly priced life annuities, the insurance industry has designed a number of strategies that guarantee a lifetime income (subject to the insurer’s continued solvency).”  As an insurance company customer, “it is hard to figure out whether you are getting a fairly priced deal, so you are probably not.”


The ARVA strategy for deciding how much to spend annually from a portfolio will appeal to the most conservative retirees who want to be certain they’ll never run out of money.  However, most retirees will find the ARVA spending level to be far lower than they were hoping for.  My own fairly conservative strategy calls for more than 1.5 times the spending that ARVA permits.


  1. Seems very conservative, but I guess there are folks that will sleep better with this type of approach.

    I'm planning on following the variable percentage withdrawl approach described here:

    Any thoughts on this approach?

    1. Hi Joel,

      The VPW approach is broadly similar to other methods, including my own. The devil is in the details of how you come up with the expected returns that will ultimately dictate your spending level. Looking through the VPW spreadsheet, it seems that they use fixed assumptions about future returns. The Lists tab at B133 and B134 shows assumed investment returns of 5% above inflation for stocks and 1.9% above inflation for bonds. These are correct in the sense of being the long-term average figures, but current conditions are far from average. The bond return is a dream right now. It's hard to imagine even 0% real returns for bonds; 1.9% real won't happen. I think 5% real for worldwide stocks is unrealistic right now as well. Even in more normal times, I prefer to use 4% real to give a small margin in case stocks disappoint. Given today's high stock prices, I choose to go to about 3% real for the long term.

      All this might seem like nitpicking about a small part of the VPW spreadsheet, but these two numbers (5% real for stocks and 1.9% real for bonds) are the heart of the VPW approach.

      When you set up this spreadsheet for your circumstances, try changing the return assumption from 5% and 1.9% to 3% and 0% just to see how it affects everything else. Then you can decide which approach is better for you.

    2. Hi Mike,

      Thanks for the great response! Just updated the spreadsheet with the 3% and 0% return assumptions and luckily the numbers still work :)

      Would be harder if there is a large crash but I think things would still be manageable based on the 'Required Flexibility'.

      Hopefully the 3% and 0% turns out to be very conservative. My wife and I are in our early sixties and still working part-time, not many hours, and our portfolio is closer to 80/20 stocks/bonds at this point. With almost 40 years to go seems like more equities is not that big a risk!

    3. Hi Joel,

      I'm glad to hear your retirement still works with the more conservative assumptions. Best of luck.

  2. Hi Mike,

    I generally agree with most of your discussion but I have a couple of comments and looking for your feedback. As you know I use this as my basic means for withdrawal approximation but I do vary it somewhat so the discussion is beneficial for me as a potential exercise to improving my withdrawal strategy.

    1. I feel there was a cheap shot in your comparison when you said "... This is a far cry from the widely-quoted 4% rule". You’re comparing a 50 year retirement plan for your sample 60 year old vs a 30 year time frame which was the basis of the 4% rule. If you run ARVA with 30 year timeframe you get 3.44%...a lot closer.

    2. "If we decide we’ll spend twice as much in our 60s as in our 80s, we’re using the ARVA approach in name only. When we get to our 80s and find we can’t cut our spending in half, the ARVA promise that we’ll never run out of money falls flat."
    100% agree.
    It seems to me that all of the withdrawal strategies are just playing around with the withdrawal payment curve. Some strategies take more withdrawals at the start, some more evenly across the timeframe, some based on limits, etc. but in all cases there is the possibility that you could not have enough funds later in life to cover your desired expenses. You only have a certain amount of money that you are starting with and that you can use to generate returns. If you use withdraw 6% of your portfolio in your 60’s, isn’t there a chance you may not have enough funds in your 80’s to cover expenses?
    Depends on your expenses, how tight your financial plan is, inflation and market returns. How can any plan guarantee that there will be enough funds to cover your expenses especially if you are starting with barely enough funds? If you have more funds than needed to cover your fixed expenses and are willing to allow the discretionary spending to vary then sure you can take on more risk both in asset allocation, different withdrawal curves, etc..
    If you barely have enough funds to cover your expenses in retirement then the Original ARVA model (real bonds in portfolio) provides a pretty good guarantee that those payments will be met. You’ll probably end up with more than you need later on in life as your expenses drop but at least no worry.

    3. “My own fairly conservative strategy calls for more than 1.5 times the spending that ARVA permits.”
    I assume this is mostly because you are using higher risk portfolio rather than real return bonds rate, right? If instead of using the Real Return Bonds Rate of 0.21% that you used something like 2.5 to 3% for real portfolio return above inflation over the long haul I’d venture to say that the ARVA would be similar to your strategy.

    1. Hi Ed,

      It wasn't my intention to hold up the 4% rule as some sort of gold standard. Because most people are familiar with the 4% rule, I wanted to use it as a comparison to show how conservative ARVA is. Readers can decide for themselves whether they want to be conservative.

      I agree that most plans have some probability of failure. However, when people make plans that involve high spending early on and low spending later, it becomes self-fulfilling. If their portfolio does well, then their plan calls for spending even more while they're young, and they are increasing the odds that they'll end up too short of funds in their 80s. I agree that the ARVA strategy comes close to guaranteeing your money will last your whole life, but that's if you plan a flat spending pattern and actually use RRB rates to choose your spending level.

      It's true that if you use higher return rate assumptions with ARVA, you get something similar to my strategy, and similar to other strategies as well. I treated the use of RRB rates as an essential element of ARVA. Otherwise, what you're doing isn't really ARVA.

      All that said, if you're modifying ARVA to devise a strategy that's very similar to what I use, I could hardly object. If in the end we're doing almost the same thing, then our entire discussion is about the semantics of what is or is not ARVA. I like the idea that, in the end, we're just in violent agreement :-)

    2. This comment has been removed by the author.

    3. All is good. I'm not really following the ARVA approach but just using the PMT function with adjustments for # of years (vs 100 - age for periods) over the life span of the payout.

      How are you approximating your real return numbers?

      I'm using the data from FPSC that are used by financial planners then adjusting those numbers for long term inflation projection and Portfolio MER fees. Ending up with real returns of 0.7% for bonds, 4.2% Cdn Eq., 4.6% US Eq. and 5.2% for foreign equity. From what I understand, these projections from the FPSC are a bit conservative to protect both the financial planner and the client.

      Of course in the short term, 1 to 5 years we may not see these average returns but over a longer period I would assume so.

      Any thoughts or other places to look for real return projections?

    4. Hi Ed,

      I've been using figures that I'm hoping are reasonable for the rest of my retirement. Before stock prices started booming beyond reason, I was using 4% real for my blend of stocks and 0% real for bonds. These are intended to be slightly conservative. Recently, I made a CAPE-based adjustment (see the article link below that describes how I adjust my bond allocation and my return expectations based on my stocks' blended CAPE value). The current effect of this adjustment is that my average stock return expectations for the rest of my life are about 3% real.

  3. Hi Mike,

    Spent a bit of time thinking about this a bit more and doing a a bit of work. Larger amounts taken out earlier result in 2 things that hurt the portfolio in the long run:

    1. You could end up paying higher taxes as the additional withdrawals could cause you to move into a higher tax bracket thus meaning some of them will be taxed higher than if you kept your income below the next tax bracket.

    2. The removal of additional funds early means those funds are not available for growth to supply income later on.

    One other thing to think about is being safe with respect to sequence of returns. I ran my financial plan with 3 scenarios.

    1. Super conservative PMT calculation with Real Return Bonds rate. This withdrawal value just barely covers my needed slightly inflated expenses. In terms of Monte Carlo analysis in the financial plan, should not be a problem at all. That's good news for me and what I based my current plan on so as to be on the safe side.

    2. When I ran both the Conservative PMT calculation with Mike's real returns of 3% and 0% for stocks / bonds, and the higher PMT calculation with my FPSC projections for asset returns the plans where still ok even in the worse case but were closer to running out that the original plan.

    Lucky for me but for others it may not work out as well. Just to say if you can't run the analysis on your financial plan then maybe better to be more on the conservative side with real return numbers.

    Yes Mike we are still in agreement.

    1. Hi Ed,

      In a technical sense, with both ARVA and my own retirement plan, it's impossible to run out of money because the plan scales retirement spending to portfolio size. So, each year, the plan calculations come up with some percentage of the portfolio to spend. If poor returns make the portfolio small, then this percentage will lead to a small dollar amount. The portfolio only fails if you can't spend as little as the plan calls for.

      It's only with plans like the original 4% rule where running out of money is possible. This is because the 4% rule calls for calculating a starting spending amount for the first retirement year, and then it ignores the portfolio size and call for spending the same amount each year (adjusted for inflation).

      Based on your discussion above, it's not clear to me which type of plan you are considering for yourself.

  4. Sorry for the confusion. I'm using the PMT function with changes in the # of years to fund each year to provide more funds up front.

    When I say running out of funds in my financial plan MC analysis, that assumes that I keep meeting my expense projections within the plan. So if my plan said I need $40k withdrawal to cover my expenses and the PMT calculation said I can only take out $25k I still take out the $40k as part of the analysis meaning that at some point I could hit $0 left. Following the PMT calculation you won't ever run out of money but you may not be able to meet your expense payments or you may have to cut back in some areas say for example travel expenses.

    So you either maintain your standard of living and run out of money or you lower your standard of living. That's what is meant by running out of money. Of course with the ARVA style of projection I'll never run of of annual withdrawal amounts.

  5. Let me try again. What I'm doing is explained in the Siegel and Waring paper on page 17, first paragraph. I'm using 110 as my max and always assuming that my expected life will be no less than 10 years.

    1. With basically a 60 / 40 Stk /Bond allocation that increases bond exposure as I get older.

    2. Hi Ed,

      The approach on page 17 appears to give a reasonable final result. I find the way they get there somewhat convoluted. They start with very low inflation-protected government bond rates, and then they tinker with the ending age to get the initial spending higher.

      That said, the resulting spending level is reasonable enough, and the declining real spending shown in Exhibit 2 probably won't happen, because a 60/40 portfolio will probably beat inflation-protected bonds.