**Q: I’m new to passive investing and am deciding how to allocate between the asset classes. The best split between Canadian equity, international equity, etc. should be determinable based on studies of their past returns, volatility and correlations. Obviously this would vary over time, but approximate weightings should be achievable. Based on this research, how would you weight the individual asset classes? – R.T.**

It would look impressive if I designed my model portfolios based on an analysis of historical volatility, correlation matrices and expected returns based on Shiller CAPE or some other data. But instead I generally recommend a roughly equal allocation to Canadian, US and international stocks. Nice and simple, with no advanced math required. This is isn’t because building a “portfolio optimizer” is difficult: it’s because it’s a useless exercise.

Investors have a tendency to resist simple solutions, and this bias is exploited by fund managers and advisors who use algorithms and models designed to determine the “optimal” asset mix that will maximize returns and minimize volatility, sometimes down to two decimal places. That sounds more sophisticated than simply splitting your equity holdings in three, but there’s no evidence it produces better results.

One of the most fundamental ideas in portfolio design is the so-called efficient frontier—the sweet spot where you’ll enjoy the highest rate of return for each unit of risk. The problem isn’t that the efficient frontier doesn’t exist: the problem is it’s only knowable in hindsight. You can learn what *would have* achieved the highest risk-adjusted return in the past. But if you’re building a portfolio for the next five or 10 or 20 years, you can’t simply punch numbers into a spreadsheet and determine the optimal asset allocation for your target rate of return or level of volatility. That’s because the standard deviation of returns changes over time, as does the correlation between asset classes. And estimating future stock returns, in particular, is notoriously unreliable.

### Optimize this

In a 2013 article called Stop Playing With Your Optimizer, Brad Steiman of Dimensional Fund Advisors offers a dramatic example of what can go wrong. If you wanted to build an “optimal portfolio” of five asset classes—fixed income, Canadian equities, US equities, international equities and emerging markets equities—you could model it with 20 individual inputs. You’d start with the expected return and volatility of each of the five asset classes, and add the correlations of the 10 possible pairs.

In his example, Steiman used historical data for volatility and correlation and then assumed expected returns of 8% for Canadian, US and international stocks, 9.5% for emerging markets, and 5% for fixed income. With those inputs, the model determined the optimal portfolio with a target standard deviation of 12.5% would include an allocation of about 25% to Canadian stocks.

Then he ran the optimizer again, assuming that 19 of the 20 parameters turned out to be precisely accurate, but the expected return on Canadian equities was slightly off. If the return on this asset class was overestimated by just 0.5%, the optimizer increased the allocation to Canadian equities to 45%. And if the estimate was underestimated by 0.5%, the optimizer called for just a 2% allocation. No wonder Steiman calls portfolio optimizers “mistake maximizers.”

Determining an appropriate asset allocation is one of the most important decisions an investor will make. But a portfolio is not a chemical formula: there is no need for each component to be measured with precision. It’s more like a recipe: as long as you use high-quality ingredients and to get the proportions roughly correct, there is a lot of room for flexibility**. **