Monday, January 20, 2014

How Many Rungs?

You could build a bond ladder that lasts as long as you think you might live, say 35 years. But, should you?

You could buy TIPS bonds, for example, that mature in 2015, 2016 and so on out to 2049. Each year when bonds matured you would spend that principal. That’s a 35-year ladder.
If TIPS returns match their long-term real average of 2%, you could spend 3.9% of the initial value of your total investments in the bond ladder each year and your bond ladder should last exactly 35 years, at which time you would have spent all the interest and all the principal. A 30-year ladder under the same circumstances would have an annual payout of 4.46%1.

In comparison, systematic withdrawal strategies estimate a payout of about 4%, though you might end up with some capital to leave to heirs, and an inflation-protected single-payment fixed annuity currently offers a 65-year old couple with 100% survivor benefits about 4%.

(TIPS bond yields are significantly lower than 2% right now, as the graph below shows, so you can’t do that today. I’m guessing you will be able to again within the next few years as the Fed stops holding rates down. As a matter of fact, purchasing secure future retirement income, or "flooring", either with bonds or annuities, is extremely expensive right now.)

You could also build a rolling ladder of any shorter length. For example, you could build a 10-year ladder with bonds that matured in 2015 through 2024. You could set aside capital to fund living expenses after age 74 in a stock index mutual fund. 

When the 2015 bonds mature, you would spend the principal and interest and purchase 2025 bonds with funds from your stock portfolio, keeping the ladder length at ten years.
The next year, you would spend the interest and principal from the matured 2015 bond and purchase a bond maturing in 2025 with funds from the stock account.

Why build a ladder shorter than the length of life you might live?

Because long bonds are very sensitive to interest rates and behave more like stocks than bonds of shorter maturity and because stocks have a better risk-adjusted return than long bonds.

Let’s look at the short end of the ladder first. You probably want a couple of years of expense money, three at the most, in cash or short term bonds. Inflation isn’t my greatest concern; persistent inflation is. The money I keep in cash or short term bond funds will compensate for inflation in the short term. So, I prefer cash and bond funds for the first three years of the ladder. Individual bonds aren’t as liquid and, frankly, aren't worth the effort.

Now, let’s look at the long end of the ladder.  Long bonds suck. Their return doesn’t reward their extra risk.

A 4% return earned from a small cap growth stock isn't the same as a 4% return from a blue chip stock because you took much more risk to earn the former. We can measure risk-adjusted return with the Sharpe ratio. The higher the Sharpe ratio, the better the investment's returns are relative to the amount of risk taken. Vanguard Small Cap Growth Index has a Sharpe ratio of 1.0, while the S&P 500's is 1.3.

Vanguard Intermediate-Term Bond Index Fund Investor Shares has a Sharpe ratio of 1.24, and Vanguard Short-Term Bond Index Fund Investor Shares sports a Sharpe ratio of 1.64. But, the Sharpe ratio for Vanguard Long Term Bond Index Fund is a measly 0.7. You get a tiny bit more return from long bonds but you take a lot more risk.
As you can see from the table above, the volatility of long-term bonds, as measured by standard deviation of returns, is much closer to the volatility of an S&P 500 stock dividend index fund than to that of an intermediate-term bond fund2.

As the chart below from a recent Wade Pfau paper entitled, "How Do I Build a TIPS Bond Ladder for Retirement Income?" demonstrates, interest rates rise quite rapidly with bond maturity up to about ten years. The return curve flattens out from 10 to 20 years, before becoming quite flat at 20 years. As you can see, the return for a 30-year bond isn’t much higher than that of a 20-year bond.

As Wade points out from his analysis, "One conclusion which does emerge is that there is relatively little additional safety to be gained from extending the bond ladder beyond about 20 years."

The sweet spot appears to be the intermediate range of bonds with maturities longer than 3 years but less than 7 to 10 years. Stocks, on the other hand, rarely lose money if you hold them 10 years or more. I’d prefer to hold my “secure floor capital” in stocks for floors beyond 10 years (though I would also be OK with holding that capital in an intermediate-term bond fund if I needed to do so to maintain my overall portfolio allocation).

As my ladder rolls forward, I will spend the maturing bonds and add an additional rung at the top of the ladder with funds from this stock allocation. 

As I have discussed in recent blogs, TIPS bond ladders are relatively free of interest rate risk if we hold individual bonds to maturity. The problem with this strategy is that we might be forced to sell bonds from the ladder before they mature. If interest rates rise, the value of our bond ladder will decline. Should a medical emergency or the need for long term care, for example, force us to sell bonds we intended to hold to maturity after rates have risen, we might take a loss on the bonds sold.

We have to plan for a long retirement because the results of planning for an average life span and then living a long time could be disastrous. Still, most people won’t live into their nineties and those with long bond ladders who don't live a long life won’t be around to hold those bonds to maturity.

Long bonds are much more sensitive to interest rates than intermediate or short bonds. A long bond might have a duration of 16 years, while an intermediate bond has a duration of 6.7 years and a short bond 2.7 years. That means a 1% increase in overall interest rates might result in a 2.7% decline in the price of a short bond, a 6.7% drop in the price of an intermediate fund and a decline of 16% in the value of a long bond.

The greatest bond risk, then, is at the long end of the ladder and that is also the end that has the lowest risk-adjusted return. The longer your bond ladder, the worse its risk-adjusted return and price volatility, and the greater likelihood that you will be forced to sell long bonds before they mature.

One last idea you might consider. We often have discussions about whether annuities or bond ladders are better, but they aren't mutually exclusive. If fixed annuities interest you, the sweet spot for purchasing them is around age 70 to 72, when mortality credits are higher, making the payouts larger. You could build a TIPS bond ladder to cover your income to age 70 or so and then purchase a fixed annuity.

I like a 10-year ladder with the capital for future rungs held in stocks until needed. That way I avoid the worst interest rate risk and lower risk-adjusted return of long bonds and add some upside potential from the stocks. I keep cash to cover the first year of the ladder and use high-quality, short-term bond funds for years 2 and 3.

There are any number of ways to create a rolling bond ladder, or a single long ladder, or a combination of a ladder and fixed annuity, depending on your resources and your attitude toward risk.

But this is how I roll.

1The present value of a 35-year annuity paying $1.02 a year and discounted at 2% is $25.49. A $1.02 annual payout on a $25.49 investment is 3.9%. A 30-year ladder under the same circumstances would have a payout of 4.46%.

2This doesn't mean you should replace the long bonds in your portfolio with stocks. While long-term bonds may have volatility similar to stocks and a worse risk-adjusted return, bonds have a relatively low correlation to stock returns, which means bonds are still vital to reduce the volatility of your portfolio. My point is that intermediate-term bonds are probably a better bet for maintaining your portfolio allocation than long-term bonds.


  1. Hmmm, I'm trying to wrap my head around your math. Are you sure footnote 1 is correct?

    If I have an annuity that pays $1 (real) at the beginning of each year, for the next 35 years, with discount rate of 2%:

    TimeValue[AnnuityDue[1, 35], 0.02]

    then the present value $25.99, as you stated. The payout rate is:

    1/25.99 = 3.9%, also as you stated.

    However, it we change from 35 years to 30 years, then we have:


    and the present value is $22.84, but that's a payout rate of:

    1/22.84 = 4.38%, which doesn't match the number you gave.

    Can you help me reconcile Mathematica with the tool you're using to make these calculations? (But maybe I'm just misinterpreting what you said.)

    Thanks, Matt

    1. Matt, first of all, I can't reconcile anything with Mathematica, though I try really hard. I think I struggle with it because I am a programmer and it isn't like other languages. Hope I can contact you in the future when I can't get it to work. :-)

      I used 4.46%, which you have to admit isn't far from 4.38%. I get 4.38% when I use my HP-12C and 4.46% when I use Excel. Since Sharpe, et. al used 4.46% in their paper, "A 4% Rule - At What Price?", I elected to go with the Nobel Laureate on this one.

      I think the more important point is that when we're guessing future interest rates with little expected accuracy as the input to these models, focusing on less than a tenth of a percent in the result implies much greater accuracy than we are capable of forecasting.

      Please see your other comment for a link to a spreadsheet.

      It's nice to know people are checking my math! It keeps me motivated to get it right the first time. Thanks!

  2. I'm also trying to wrap my head around the payout ratio. You state that:

    "you could spend 3.9% of your total investments in the bond ladder each year"

    But this is true for every year? I grok that:

    1/25.49 = 3.9%

    but that 25.49 refers to the present value of an annuity (due) that lasts 35 years. But after 1 year, we now have 34 years and so the present value changes to:


    which is 24.99, and to the payout is:

    1/24.99 = 4%

    After the second year, 33 years remain and so the PV is 24.47 and the payout is 4.1%.

    Or am I just totally confused?

    1. Matt, I made two small changes to the text in response to your comments. First, the easy one. Both examples in my footnote referred to 30-year payouts but the first should have said 35.

      Second, when we talk about "payouts", of fixed annuities, safe withdrawal strategies, bond ladders, etc., we are commonly referring to a percentage of the total initial investment, not the remaining balance at any point in time. If I purchase a $100,000 annuity with a 6% payout, I expect a $6,000 annual payment, for example, for as long as I live. Interest rates may change over its life, but the payout (interest plus your own return of capital) doesn't. I changed the explanation to reflect this explicitly. In my example that you quote.

      You could withdraw a constant dollar amount of 3.9% of an initial bond ladder investment of say, $100,000, or $3,900 a year every year for 35 years, at which time the bond account balance would be zero.

      I shared a Google Docs spreadsheet at the following URL to show how it would work. (Notice, once again, Excel says 4% while by trusty HP-12C says 3.9%.)

      Thanks for reading!

  3. Hi Dirk

    When you say that it's best to buy annuities at 70 to 72 because of mortality credits, would it also be the same for a deferred annuity? E.g., buying an annuity at 60 to start paying at 70



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    2. Wade Pfau did some work on this issue at the following link, but he says the issue isn't fully resolved.

  4. I'm confused. Wasn't the objective of the bond ladder to provide a predictable amount of annual real income to fund living expenses in retirement? I can understand why you might elect to purchase only 10 years of bonds for your ladder, but doesn't investing the balance (which could be 60 percent or more of your total portfolio) in stocks introduce unnecessary sequence of returns risk? Isn't this an example of where the pursuit of higher returns could potentially jeopardize your income immunization strategy? Why not simply purchase short maturity (e.g., 1 to 3-year) Treasury notes with the balance instead?

    1. I don't think you are confused at all. As I said, there are many ways to do this. Since stocks would generally recover in most historical 10-year periods, I am personally OK with the extra risk I would take on in exchange for the upside potential of stocks. You might not be.

      Investing that money in bond funds is a reasonable strategy. If you are particularly risk-averse, build a very long ladder. Keep the money in cash. It all depends on your risk tolerance.

      Yes, it will create SOR risk anytime you spend stocks systematically. (Anytime, technically, but especially when you do it frequently.) That's part of the risk I'm aware of and willing to accept.

      Keep in mind that you still need to maintain your portfolio's overall allocation to stocks/bonds/cash, though. In my case, if I don't invest that money in stocks, I can't maintain my overall stock allocation.

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  6. Hi Dirk. Thanks for the post. Would your recommend buying all TIPS "rungs" at retirement (so TIPS maturing in 4, 5, 6, ... years), or buying longer term TIPS in the years leading up to retirement (for instance, buy 2018 TIPS in 2008, 2019 TIPS in 2009, etc)? Thanks, Dave

    1. Dave, there was recently a discussion on this topic at Wade Pfau's blog and I believe the consensus was that little research had been done on this topic. One professor noted that he preferred to buy the bonds before retirement, but conceded that there was little research to support that.

      I have two thoughts on the topic. The first is that people approaching retirement should do so with a more conservative portfolio than they held during the accumulation phase so he or she doesn't get wiped out by a bear market at that most vulnerable time immediately after retirement. Wade Pfau and Michael Kitces have done some preliminary work suggesting that retirees should have limited stock exposure at the beginning of retirement, with growing exposure as they age. If you're going to be shifting from stocks to bonds as you approach retirement, it might be a good time to begin building the ladder.

      My second thought, which maybe should have been my first, is that you want to buy bonds when they are cheapest. That's normally impossible to predict, but with interest rates currently at historical lows, secure future income is quite expensive. The Fed had signaled that it will let rates rise in the future, so locking in today's rates today might not be the best idea.

      So, my answer is that while there isn't much research that answers your question, there's a good chance that "flooring" will be cheaper in the not-distant future than it is today.

      Excellent question. Thanks!

  7. Just one question on the "how I roll" ladder. Looking only at the ladder suggests that by age 68 there are no cash or short term bonds rungs (all rungs are now TIPS). But the paragraphs preceding the ladder give the impression that the bottom three rungs are always in cash and short term bonds as the ladder moves forward through the years. Can you answer whether it is the former or the latter; and if it is the latter, address specifically how the funds move year to year to maintain those lower three rungs?

    1. I think the best answer is that it doesn't much matter. There isn't much difference between a very short TIPS bond and cash. There isn't enough time left until maturity for inflation protection to provide much value. And if the TIPS bond will mature in three years or less, it is a short term bond.

      Your question then becomes one of when to convert short term (TIPS) bonds to cash. You could hold the bonds to maturity and spend the redeemed principal the year they mature, or sell them a year or two earlier and hold the proceeds as cash.

      I don't think it will make any measurable difference either way.

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