Consider an example, where the retirees want to construct a ladder to 35 years that will provide inflation adjusted income of 4% of the initial portfolio, the TIPS yield is 2.135% which, not entirely coincidentally, will exactly meet that condition (as entering rate(35,4,-100,0,1) in a spreadsheet package will show). A flat yield curve has been assumed and taxes and fees ignored.

However, at the start of retirement there are no TIPS available to cover the 31st to 35th 'withdrawals', so the retirees construct a ladder to 30 years with just under 90% of the portfolio (the payout rate on a 30 year ladder with 2.135% yield is pmt(2.135%,30,-100,0,1)=4.45% and therefore the 'premium' is required income 4.0/4.45=89.82%). The remaining part of the portfolio (10.18% of the initial portfolio) is invested in a 30 years TIPS, which when it matures 30 years later has grown, in real terms, to 19.18% (i.e., 10.18*power(1.02135,30) ) of the initial portfolio value. If the TIPS yield in 30 years time is equal to or exceeds 2.135%, then the retirees can construct the final 5 year portion of their ladder since the number of periods supported will be lat least 5 years (e.g., nper(2.135%,4,-19.18,0,1) ).

The question then becomes how many periods (i.e. years) can the maturing 30 year TIPS support if the reinvestment yield is less than 2.135%? In the following table, the number of periods (NPER) supported is given as a function of (reinvestment yield, Y2)-(original yield, Y1) where Y1 is 2.135%.

Code: Select all

```
Y2-Y1 NPER
0 5.00
-1 4.90
-2 4.81
-5 4.55
-10 4.19
-13 4.00
-20 3.63
```

In other words, in this example, interest rate risk is minimal unless TIPS yields fall to well below those seen historically (and even lower than the equivalent UK inflation linked gilts were a few years ago). It is relatively easy to calculate what happens at other yields or required income rates (I note that the '-13' is a fairly constant threshold though). However, for a longer ladder (e.g., 40 years covering the retirees to 105yo), the interest rate risk is higher (e.g., with Y2-Y1=-5, only 8 rungs out of 10 are filled).

However, there are other risks with this approach (none of which are really quantifiable)

1) The retirees will need to construct the follow up TIPS ladder when they are 95 (which, they may or may not be able to). Doing this earlier, introduces more interest rate risk (of course, doing the reinvestment over a number of years is an alternative to doing it all in one go).

2) TIPS of the relevant maturities may not be available after 30 years.

3) TIPS may not be available at all.

cheers

StillGoing