# CAPE10 Rebalancing

Back in March 2016, Darrow Kirkpatrick published “The Best Retirement Strategies: Digging Deeper”, where he uses CAPE10 as a rebalancing strategy. If the current CAPE10 is above the historical median then sell stocks for your annual withdrawal. If the current CAPE10 is below the historical median then sell bonds for your annual withdrawal.

The CAPE Median strategy — choosing to liquidate stocks or bonds based on Robert Shiller’s Cyclically Adjusted Price-to-Earnings ratio (CAPE) — continues to stand out. Variations on this strategy occupy the top three slots in my results for success rate, and the two top slots for ending portfolio value.

I’m not convinced by his results, so this is my attempt to dig deeper into them and see whether I’m wrong! :)

Our assumptions aren’t identical, so our results differ slightly.

He uses 10 year treasuries for the bonds. I use the intermediate treasury returns from simba’s spreadsheet; these have an average duration of around 5 years. So the bonds we use are fairly different. Most investors don’t use long term government bonds, so I think intermediate term bonds is a better choice when the data is available.

Everything else is the same as far as I can tell.

# Baseline comparison

Kirkpatrick shows three numbers that can help show whether our models are in the same ballpark or not: success rate, median final portfolio value, and average asset allocation over the simulation.

There are differences but they generally aren’t large and — at this point — I’m just going to assume they are because I used intermediate bonds and he used long bonds.

The biggest differences are the success rates at 40/60 and the final portfolio value for 20/80.

So I’m reasonably confident my simulation isn’t totally broken. From here on out, I’m just going to focus on the 50/50 starting asset allocation for the discussion.

# Inflation-adjusted versus nominal numbers

The final portfolio values are mouth watering (who wouldn’t want $8 million, on average, at the ** end** of 30 years of retirement!)

There’s a problem: those are not inflation-adjusted numbers. $1 at the end of the 1970s is very different from $1 at the end of the 1930. Let’s try inflation-adjusting our final portfolio values before taking an average.

`$2,367,587`

That’s a pretty big drop from $8.4 million but it is still pretty respectable.

To make things more accurate, I’ll use inflation-adjusted numbers throughout the rest of this.

# Median vs. mean

Kirkpatrick uses the “historical median CAPE10”. That’s a perfectly fine choice…but why? Why use the median instead of the mean?

The historical CAPE10 median is (at the time of my writing) 16.05 but the historical mean is 16.7. So switching to the mean makes it more likely that you’d sell bonds. (The number is higher, so you’re less likely to think stocks are overvalued.)

Let’s re-run everything using the historical mean instead of the historical median.

`Final portfolio value: +5.04%`

Success rate: (unchanged)

Average Bond: -7.5%

The final portfolio is higher at the expense of even fewer bonds. So we should be using the historical CAPE10 mean instead of the historical CAPE10 median, right?

# Why 1928?

We have CAPE10 data going back to 1881. (Shiller’s data goes back to 1871, then we need to wait 10 years to start having CAPE10 data.) Let’s use that full range, from 1881 onwards, instead of just since 1928.

We’ll go back to using the historical CAPE10 median and compare it to our previous results.

`Final portfolio value: -36%`

Success rate: +1.6%

Average Bond: +10.3%

The final portfolio value has been cut by 1/3rd just by extending our time span. That’s a bit worrying that the results are so sensitive to the time period we choose. But that just means we will need to investigate that more; it isn’t necessarily a deal breaker. After all, the alternative strategies could still perform worse with this longer data set.

(Again, using the mean instead of the median results in higher final portfolio values at the expense of fewer bonds.)

# Anachronism

Of course, an investor in 1927 wouldn’t have been using a historical CAPE10 median of 16.05. That median is based on data from 1871–2015. An investor in 1927 would only have data from 1871–1927 available. Given the data they had available the “historical CAPE10 median” was 15.17 not 16.05.

How do things look if we use “non-anachronistic historical CAPE10 median” data?

`Final portfolio value: -40.77%`

Success rate: +1.6%

Average Bond: +18.6%

Now our final portfolio value has dropped over 40% from where we originally started.

Using non-anachronistic CAPE10 median numbers we see a mean final portfolio value of $1,402,414; a success rate of 98%; and an average bond percentage of 25.27%.

(I’m going to stop mentioning success rates because they rarely change in the scenarios we’re considering.)

# CAPE10 yearly variance

CAPE10 changes on a daily basis. (Admittedly, not by very much.) But over the course of an entire year it can change enough to influence the rebalancing decision. In March it might say “sell bonds” but in October it might say “sell stocks”. How much of a difference does it make? This is the median final portfolio value based on when you do the rebalancing:

`January: $1,328,523`

February: $1,328,523

March: $1,328,523

April: $1,346,302

May: $1,407,954

June: $1,390,638

July: $1,370,847

August: $1,453,536

September: $1,319,258

October: $1,371,764

November: $1,378,733

December: $1,402,414

The lowest mean value is $1,319,258 if you rebalance with CAPE10 in September. The highest mean value is $1,453,536 if you rebalance with CAPE10 in August. That’s a difference of $134,278; a 10% improvement.

You can see a 10% improvement just by doing your CAPE10 rebalancing in August? I don’t really believe that, but it shows how making small changes to the endpoints can result in relatively large changes to the results. It also shows how sensitive a strategy can be. Will picking the wrong time of year to do your rebalancing destroy any gains you might have seen?

Kirkpatrick most likely is using the CAPE10 numbers at the end of each year. That corresponds to the December numbers above, which is one of the “best” months for CAPE10. That introduces a subtle bias favouring the CAPE10 results.

# Back to 60/40

Let’s take a quick look at what a 60/40 portfolio looks like using the full 1881–2015 dataset. It has a median final portfolio value of $931,427. CAPE10 gave us $1,402,414; that’s a 50% improvement, which is quite a lot.

But we’re comparing a portfolio that is 75% equities (on average) to one that is 60% equities. Let’s try an annually rebalanced portfolio that is 75/25 instead: **mean final portfolio value $1,446,031**.

It appears that we can ignore all this CAPE10 stuff

It appears that we can ignore all this CAPE10 stuff and, if we’re okay with the risk that CAPE10 would force on us anyway, just start out with 75/25 portfolio and end up in a better spot.

# Certainty Equivalent Withdrawals

Based on the above, things already look a bit rocky for a CAPE10 strategy. If you’ve read some of my previous blogs, the next step won’t be surprising:

Using Constant Dollar 4% withdrawals is not a real-world strategy. People vary their withdrawals. So let’s run the whole thing through a variable withdrawal strategy (I’ll use VPW) and compare Certainty Equivalent Withdrawals.

A 75/25 portfolio gives you $46,712 (from 1881–2015).

A 60/40 portfolio gives you $45,381 (from 1881–2015).

A historically-accurate CAPE10 strategy gives you $45,120 (from 1881–2015), making it appear to be the worst performer.