Here's something I don't understand about the traditional "balanced" portfolio of 60% stocks and 40% bonds: Why is it 60/40? Why isn't it 40/60, or 80/20, or 100/0? Why don't we bring in leverage and make it 120/-20?

When John Bogle conceived of the 60-40 portfolio as a recommended default allocation for every investor, his logic was that stocks provided "growth" and bonds provided "stability". Younger investors could afford to change the portfolio (holding e.g. 80% stocks), and older investors could increase to an even split of stocks and bonds, but 60/40 has always been the classic — and default — portfolio.

Looking the data, I'm not quite sure why. To get our bearings, let's begin by considering the returns on stock and bond indices from 1988 to present:

As expected, stocks have much higher returns and a commensurate higher level of volatility. Since 1988, the S&P500 has returned nearly 11.1% annualized, including dividends, while the Bloomberg Aggregate bond index achieved a 6.5% annualized return. Balanced portfolios, like the 60/40 plotted in navy in Fig. 1, are going to be some convex combination of these two lines in both level (returns) and variance (volatility). Since investors like higher returns and dislike volatility, it is not prima facie obvious which portfolio is optimal.

Fortunately, financial economists have developed a parsimonious way of weighing the risk-return tradeoff, namely, the Sharpe ratio. The Sharpe ratio measures the average excess return per unit of risk (volatility). That is,

$$ Sharpe_p =\frac{\mathbb{E}[R_p - R_f]}{\sigma(R_p)} $$

where $\mathbb{E}[R_p-R_f]$ is the expected return on a given portfolio $p$ net of the risk-free rate $R_f$, and $\sigma(R_p)$ is the standard deviation of the portfolio's returns. Higher Sharpe ratios are better in the sense that they imply higher returns per unit of risk.

This is where the data start to make less sense. To the extent advisors referred to 60/40 as a favorable balance, I had assumed they had meant it with respect to some metric like a Sharpe ratio. That is, perhaps 60/40 was the optimal tradeoff of risk and return that maximized compensation for a given level of volatility.

But this is not the case...and not even close. The figure below plots the Sharpe ratio across different stock-bond allocation weights. The blue line uses data from 1988 onwards (the Bloomberg Aggregate Total Return Index), while the red line uses a different bond index from 2003 onwards (the iShares Core US Aggregate Bond ETF). Despite the difference in time frame and index, both curves suggest the optimal balanced portfolio is something like 20/80!