A TIPS ladder can be constructed similarly to a Treasury strips ladder, using the same date from the *Wall Street Journal* Market Data Center, which provides a daily report of wholesale prices from the secondary markets for all outstanding TIPS issues.

On January 3, 2017, there were forty outstanding TIPS available, with maturity dates ranging from January 2017 to February 2046. As I’ve mentioned before, there are no TIPS maturing in 2030-31 and 2033-39.

For these years, we buy extra TIPS for the most recent maturing year (i.e., 2029 for 2030-31 and 2032 for 2033-39) to cover the later spending, assuming those proceeds subsequently grow at a 0% real return until they are needed for spending.

TIPS provide coupon payments, which make the calculations a bit more complex than that of strips. To construct a ladder with coupon bonds, we have to work backward from the ladder’s end date.

Our goal is to construct a TIPS ladder that provides $40,000 of inflation-adjusted income for thirty years between 2017 and 2046. Exhibit 1 shows the process for constructing this TIPS ladder.

*Exhibit 1*

*Constructing **a 30-Year TIPS Ladder **on January 3, 2017 for an Annual Real Income of $40,000*

These columns differ from the strips ladder. In particular, we must make the distinction between real and nominal variables for TIPS trading in secondary markets. The ask price is in real terms.

The accrued principal indicates how an original $1,000 has adjusted for subsequent inflation since the TIPS was first issued. Accrued principal is the real value of the bond at the present. Coupon rates are applied to determine coupon amounts, and the current real value of the accrued principal will be returned as the face value at the maturity date.

The nominal ask price combines the ask price with the accrued principal (multiply together and divide by one-hundred) to let a purchaser know how much must be paid today in order to purchase the TIPS on the wholesale market.

This column is relevant for determining the cost of building the TIPS ladder, but it is a nominal number that is not connected to the yield.

The real yield to maturity is provided in inflation-adjusted terms, linking the ask price and accrued principal with the coupon payments and maturity to find the inflation-adjusted rate of return for holding the TIPS.

As mentioned, to construct the ladder, we have to start from the end date. Starting at 2046, we need to buy enough shares of TIPS to give us $40,000 of inflation-adjusted income that year.

This involves buying the TIPS maturing in 2046, which has a coupon of 1%, an asking price of $101.47, a yield of 0.94%, and accrued principal of $1,020.

In real terms based on today’s accrued principal, and with a simplification that the full coupon payment is made once per year instead of twice, on Feb. 15, 2046, this bond will pay *1020 x (1 + 0.01) =* $1,030.20 in real interest and principal.

We want an income of $40,000, so we need to buy *40000/1030.20 =* 38.8274 shares. The nominal price we pay for a share of this TIPS today is $1,034.98. Given the wholesale nominal asking price, these shares cost us 38.8274 x 1034.98 = $40,186 today.

Paying $40,186 today entitles us to $40,000 of real income in 2046, in addition to $396.04, which is 0.01 x 1020 x 38.83 shares of real coupon payments for each of the years before then.

We know the real value based on today’s accrued principal. The nominal amount you actually receive in 2046 will be larger to the extent that we experience inflation over the next thirty years.

Now we move to 2045. We want $40,000 of real income for that year, too. The trick is that we have to account for the fact that the 2046 maturing TIPS we just purchased is going to give us coupon payments of $396.04 of income for that year as well.

We can subtract that from what we need to purchase. We need an additional $39,603.96 of real income in 2045. To review the process, the 2045 TIPS has a coupon rate of 0.75% and accrued principal of $1,026.

A share will provide real income of *1026 x 1.0075 =* $1,033.70 in 2045. We require *39603.96 / 1033.70 = *38.31 shares of the 2045 TIPS.

The ask price is $95.13, so the price we must pay today is *95.13 x 1026 / 100 =* $975.98. The total cost for these shares is $37,393.

This process continues, working backward to the present. In 2017, the ladder provides $17,734 of real income as interest payments for bonds maturing in later years.

This means that we only need to set aside an additional $22,266 for the $40,000 of spending in the first year.

This is the logic behind constructing the TIPS ladder.

Note that to deal with the problem of missing maturities, we bought three years of spending with the 2029 TIPS and eight years of spending with the 2032 TIPS.

It is impossible for a TIPS ladder to have a cumulative cost column that correctly shows the costs for building shorter TIPS ladders in the same manner as we had for Treasury strips.

With the thirty-year ladder shown, part of the income available at earlier dates comes from coupon payments from longer-dated bonds that would not be part of a shorter ladder.

Because the ladder is constructed beginning at its end, we would have to start from scratch if we chose a different end date. This was not the case for strips, since there was no interest income to complicate the calculations for earlier years in the ladder.

The total cost for this TIPS ladder with wholesale pricing is $1.069 million. For the $40,000 inflation-adjusted spending, this represents an initial withdrawal rate of 3.74%.

The real internal rate of return on the cash flows as they are spent is 0.76%. A thirty-year TIPS ladder is as close as we can get to a real-world “safe withdrawal rate” for thirty-years of inflation-adjusted spending.

At current interest rates, 3.74% is the number. A thirty-year TIPS ladder represents the “risk-free” way to support thirty years of real income. Spending more from an investment portfolio is based on a hope that a higher return can justify and sustain a higher spending rate.

This is risky. It is important to note that with this bond ladder, nothing will be left at the end of the thirtieth year. The calculation is “risk-free” for thirty-years, but the possibility of living beyond thirty years must be considered. A TIPS ladder does not hedge longevity risk.

There is also one further relevant point about comparing the TIPS ladder with the strips ladder. The strips ladder was built with a COLA of 2%. Its cost was just slightly less than the TIPS ladder.

Calibrating the two costs can provide us with a breakeven inflation rate between TIPS and strips. A COLA of about 2.17% calibrates the costs for the two ladders.

In terms of which then provides a better performance for retirees, the TIPS ladder provides more income and inflation-protection if realized average annual inflation exceeds 2.17% over the next thirty years, while the strips ladder would be able to match actual inflation and provide surplus (in real terms) should the realized inflation experience fall short of 2.17%.

The choice between ladder types should depend on how you feel about the likelihood of high inflation in the future, as well as a consideration about the impact of different inflation scenarios on your lifestyle.

If your inflation expectations exceed what the market has priced in and/or if high inflation will be more damaging to your lifestyle than low inflation, then this tilts the decision in favor of TIPS over strips.

Conversely, if you are not worried about inflation and high inflation will not have a negative impact on lifestyle, then you might choose to construct your bond ladder with strips using a smaller COLA that allows for the ladder to be purchased more cheaply.