When we launched Acropolis over 22 years ago, I thought understanding optimizations would be the key to our success. If we could just figure out “the” optimal allocation, we would be well ahead of everyone else.

Of course, that’s true, but figuring out “the” optimal allocation wasn’t possible because you can’t tell in advance.

My memory (which could be better) is that the software package we used then suggested a stock portfolio with 60 percent US large-cap value and 40 percent emerging markets stocks.

With the benefit of hindsight, I can say that the optimal portfolio didn’t turn out very well: large-cap value underperformed large-cap growth, and emerging markets underperformed all other major equity asset classes.

But we didn’t have the benefit of hindsight back then and still realized that the optimal portfolio wasn’t optimal. We knew it wasn’t diversified enough because it wasn’t diversified enough with no exposure to US mid- and small-cap or developed international markets.

We used optimization results to tilt our investments towards value over growth and include emerging markets, which we might have excluded.

What I didn’t fully understand then was that the optimization is telling you something pretty simple: buy the asset classes with the highest realized returns and the lowest correlation to each other, which will lower the volatility.

Knowing the asset classes with the highest realized returns doesn’t tell you much about what they will return in the future. Furthermore, the correlations change all the time. Worse for diversification, the correlations are all structurally higher now than 20 years ago.

You can run optimizers with your estimates of future returns, but no matter how confident you feel, those estimates are fuzzy at best.

With the benefit of hindsight, I can see that the optimal portfolio was 63 percent large-cap growth, 28 percent large-cap value, and nine percent US mid-cap stocks.

A few problems with that last paragraph, though.

First, I’m not using much data – I’ve got a free kick-butt optimizer online (which is remarkable given what we paid for it 20 years ago), but the data only goes back to 1995. One major lesson about optimizers is that the output is incredibly sensitive to the inputs.

Second, and far more importantly, that only tells us what was optimal in the past. It still says nothing about what will be optimal in the future. Perhaps large-cap growth will continue to dominate because of artificial intelligence. Perhaps not. We just don’t know, and an optimizer can’t tell us.

I last used optimizers for allocation decisions more than a decade ago. That said, I play around with them online all the time.

The free online optimizers allow me to optimize on all sorts of things besides what we think of as an optimal portfolio – the most return for a given level of volatility. Online, I can create an optimal portfolio on a dozen or so variables (minimized conditional value at risk, maximize information ratio, risk parity, and other fun party tricks!).

Now, I optimize on something Jack Bogle, the founder of Vanguard, said, which was the optimal portfolio is the one you can live with. That’s what I do for myself, and that’s what we at Acropolis do for all of our clients. And, there’s no software for that.