Investment Returns: Effects of Stock/Bond Allocation

I was messing around last night in Vanguard’s Portfolio Watch and decided to look at the performance of various very simple portfolios.

These included all possible allocations (in 10% increments) from 0% stocks and 100% bonds to 100% stocks and 0% bonds.

The results, which were based on real world market performance from 1926-2011, were largely as expected. That is, increasing the equity allocation provided higher expected returns, but also produced higher highs and lower lows.

For the record, it’s not entirely clear what benchmarks these expectations are based on. They only say that they’re based on “broad market indexes” — I’m thus assuming that these are based on total market performance, or a close approximation.

Note that the columns below refer to stock vs. bond allocation, the expected annual performance, the best and worst years on record, and the percentage of years during which the specified allocation would have posted a loss.

StocksBondsExpectedBestWorstYrs w/Loss

Fitting a line through the expected performance data (as a function of stock allocation) reveals a very tight fit, with an R^2 value of 0.99 and an increase in expected return of 0.043% per 1% increase in stock allocation.

In other words, for every 10% increase in stock allocation, your expected returns go up by 0.43% — though you’re of course also increasing variability (i.e., risk).

Fitting a line through the percentage of years with a loss reveals another (relatively) tight fit, with an R^2 value of 0.94 and an expected increase of 0.17% for each 1% increase in stocks. Thus, for every 10% increase in stock allocation, you’re increasing the fraction of years that will experience a loss by 1.7%.

One particularly interesting point, however, is that the percentage of years with a loss is actually higher with a 100% bond portfolio than if you were holding 10% (or even 20%) stocks. In other words, a small equity position actually reduces risk while simultaneously increasing (expected) returns.

This latter point is fully consistent with the efficient frontier concept that was introduced by Harry Markowitz and has been championed by William Bernstein (among others). For a good (and accessible) read on the topic, I highly recommend Bernstein’s “The Four Pillars of Investing.”

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