Basu’s wrong definition of success

In 2007 Basu & Drew published “Portfolio Size and Lifecycle Asset Allocation in Pension Funds”. This was possibly the first paper to look at the actual effects of a declining equity glidepath: that is, where your allocation to stocks decreases over time. This has become something of a de facto standard due to the prevalence of target date, or lifecycle, funds in most 401(k) plans.

Basu & Drew use a bootstrap analysis — that is they start with historical asset returns and randomly shuffle them up. This is a kind of halfway house between Monte Carlo and historical backtesting. Because everything is shuffled up, you lose any reversion to mean or serial correlation from the historical backtesting (which is bad). But you are able to generate and test a lot more scenarios (which is good).

At the end of their paper they decide that a declining equity glidepath is not a good choice — and actually you should have an increasing equity glidepath.

The apparently naïve contrarian strategies which, defying conventional wisdom, switch to risky stocks from conservative assets produce far superior wealth outcomes relative to conventional lifecycle strategies in all but the most extreme cases.

I think this is a good example of how hard it is to define “success” for a portfolio. How did they decide that it will “produce far superior wealth outcomes”?

From Basu & Drew (2007)

This table shows the outcomes at various percentiles for different variants on the strategies. Basu & Drew see this and note that the lifecycle strategy only performs better in the lowest decile. That is, worst case scenarios that only happen one time in ten.

And that’s where I think they go awry. Here’s what they say:

However, it is very unlikely that investors in reality would select lifecycle asset allocation model with the sole objective of minimizing the severity of these extremely adverse outcomes, should they occur, because the cost of such action is substantial in terms of foregone wealth.

I think this makes an assumption about investor loss aversion that probably doesn’t map to reality. To make their case, Basu & Drew talk about a 10th percentile outcome.

For example, if the 10th percentile outcome is confronted at retirement, one could be better off only by about 7% (less than $17,000) by following the lifecycle (20, 20) strategy instead of the contrarian (20, 20) strategy. A difference of this order after 40 years is hardly going to make a difference in the retiree’s lifestyle.

But I don’t think almost-retirees are worried about one-in-ten events. They are worried about one-in-a-hundred events. They are worried that this will be the one time this century when a 67-year old who has worked and saved hard their entire lives will see everything go up in smoke and they’ll never be able to retire and have to work until they drop dead.

And if you look back at Basu & Drew’s table the one-in-a-hundred outcomes can be up to 48% different. That means instead of retiring on $40,000 a year you’ll be retiring on $19,160 a year.

Why would people be willing to give up so much upside? It seems crazy, right? Well, maybe not. That’s where “Behavioral Portfolio Theory” (BPT)comes in. It is a relatively recent contribution (2000) from Shefrin and Statman. BPT starts with a “safety first” approach and then layers in some behavioural economics and finance.

You can probably already guess that when you start with a safety first approach, you’re going to be more worried about 1% outcomes!

BPT has three main features:

  • Investors are seeking to secure a minimal level of final wealth. That is, they’re more interested in guaranteeing a minimum than reaching a theoretical maximum.
  • Investors think of their portfolio as a collection of sub-portfolios, each of which can have different characteristics. You might have a sub-portfolio for basic (but pleasant) retirement, another one for the kids’ college education, another for emergencies, and another for “dream vacations”. You might invest quite differently for each of those sub-portfolios.
  • Investors do not behave rationally; they will be overly optimistic and overly pessimistic. They distort the objective probabilities and replace them with “decision weights”.

All of that sounds like a much more realistic model of real people and how they really invest. And when I look at it through that lens, Basu & Drew are using the wrong decision criteria when throwing out the traditional declining equity glidepath.

On the contrary, I think their paper is evidence for the success of the declining equity glidepath because it is much better at securing a minimal level of final wealth.

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