[img width=500]http://s12.postimg.org/azll7vupp/CAGR_factored.png[/img]

I am defining the factor as the amount the PP component (e.g., stocks) grew or shrank; a factor of 2 means that the component doubled or halved in value. So a portfolio of 25/25/25/25 would become 50/25/25/25 or 12.5/25/25/25. In the former, the component that grew has become 40% of the overall portfolio; in the latter it has become 14.29%. Thus, for a factor of 2, the rebalance bands are 40/14.29. Traditional rebalancing at 35/15 corresponds to an upside factor of 1.62 and a downside factor of 1.89 -- that's why I don't consider it "symmetrical."

Since 1/1/1972, a PP with 35/15 rebalancing bands and dividends reinvested has returned a CAGR of 9.29%. That's the benchmark. I wondered whether there was a factored rebalancing strategy that would have beaten this value; the results are in the chart above, which displays the CAGRs and number of rebalancing events for factors ranging from 1 (in essence, rebalancing every day) to 13 (no rebalancing during the 43 years of backtesting).

There are several interesting features in the chart.

- There was a strategy that would have returned an 11.06% CAGR, albeit with only two rebalances. That factor was 12.93, representing bands of 81.17 and 2.51% -- quite extreme!
- A strategy that would have resulted in rebalancing on average every three years (from 13 to 15 times in 43 years) would have had factors from 1.65 (35.48/16.81 bands) to 1.98 (39.76/14.41 bands), but with quite a swing in CAGRs, from a minimum of 9.03% to a maximum of 9.63%. Thus, small changes in rebalance band percentages can have dramatic effects on returns.
- A factor of 3.60 (54.55/8.47 bands) gave a CAGR of 9.71% (4 rebalances), yet a tiny increase in the factor to 3.61 plunged the CAGR down to just 8.91% (2 rebalances). I think that so few rebalances led to data mining effects that skewed the results, which depend on this one particular starting date.
- A factor of 12.97 (81.21/2.51 bands) led to no rebalancing ever; the CAGR was 8.26%. This CAGR is the lowest in the whole chart, meaning that any one of these factored rebalancing strategies defeated the set-and-forget portfolio. In other words, there is definitely a rebalancing bonus.
- It isn't easy finding a factor that would guarantee beating the CAGR of 9.29% for the 35/15 portfolio. Perhaps somewhere between 3.0 (50/10 bands) and 3.5 (53.85/8.70 bands), with just four rebalances, but the drop at 3.6 loses all of those gains. Any factor above 5.5 (64.71/5.71 bands) seems to beat it, but would any of us be happy rebalancing only twice in 43 years? By the way, I don't think there is anything magical about 35/15. I have performed a similar analysis of 25+x/25-x bands and found just as much noise and sensitivity. I'll post those results soon.

[img width=500]http://s28.postimg.org/6f45h3frx/741_fa ... _value.png[/img]