Orders of Magnitude

The rebalancing bonus exists because of a misleading definition. It is an illusion. Very often, rebalancing lowers returns.

Returns from individual market slices add or subtract 2% to 3% from the market as a whole.

Variations caused by valuations are huge. At today’s prices, with P/E10=26, the most likely (real) return ten years from now is 1.3%. At historically typical prices, with P/E10=14, the most likely return after ten years is 6.3%. At bargain levels, but well above market bottoms, with P/E10=8, the most likely return after ten years is 14.5%.

The Rebalancing Bonus

The rebalancing bonus is an illusion created by a misleading definition. Gummy (Professor Peter Ponzo) provides an example of what really happens in his tutorial about The Rebalancing Bonus.

Gummy’s (Peter Ponzo’s) Web Site
Gummy's: The Rebalancing Bonus

“Look at Figure 2. Here we have a portfolio with 70% devoted to the S&P 500 and 30% to 5-year Treasuries, from 1950 to 2000. If we rebalance we get an annualized return of 11.3%, but if we just stick 70% of our money into the S&P 500 and the rest into the Treasuries ... and do NOT rebalance ... we'd get an annualized return of 12.4%, so ...”

You are better off NOT rebalancing your portfolio.

Now comes the sleight of hand. The rebalancing bonus compares the weighted average of annualized returns of two investments to a rebalanced portfolio that uses the same weights for allocations.

This is a confusing definition. The key point is that the weighted average of annualized returns differs from two independent (i.e., not rebalanced) portfolios that start out with the same proportions. In the absence of rebalancing, the better performing portfolio becomes a larger percentage of the total.

Continuing with Gummy’s example:

“For the 70% (S&P) + 30% (5-yr T) example, the annualized returns for each (over the period from 1950 to 2000) are 13.1% and 6.2% respectively so the weighted average (with the 70/30 split) is 70% x (13.1) + 30% x (6.2) = 11.0% whereas the actual annualized return, With rebalancing, is ...”

“I get 12.4%, from Figure 2.
No, that's Without rebalancing. With rebalancing, it's 11.3%, the red curve from Figure 2.”

“So the rebalancing bonus is 11.3% - 11.0% = 0.3%, right?
Right.”

You may have heard the rebalancing bonus is 1%. It is less. In the example, it is 0.3%.

Compared to not rebalancing, however, rebalancing can be expensive. If you continue reading, eventually you will see what happens if you do not rebalance. More terms appear. They subtract from the bonus. If you look at the numbers after a decade, the next adjustment is to subtract 3% (assuming reasonable investment returns). After that, you subtract another 1%.

Our anticipated 1% bonus turned out to be a 0.3% bonus. Then, when we compared this to a portfolio without rebalancing, we ended up with a deficit worse than 3% (i.e., the rebalancing bonus = 0.3%-3%-1%).

Even worse, studies seldom include the costs associated with rebalancing.

Market Slices

I located Gummy’s historical database.

Gummy’s (Peter Ponzo's) Database

I calculated annualized, nominal returns for the S&P500 slices.

The annualized return (approximately) equals the average return minus one-half of the standard deviation squared (or one-half of the variance).

Using Gummy’s Historical Returns, the 1928-2000 annualized, nominal returns of the S&P500 and its slices were:

The S&P500 Index 10.7%.
Large Capitalization Growth 9.8%.
Large Capitalization Value 12.2%.
Small Capitalization Growth 8.6%.
Small Capitalization Value 13.7%.

The best slice had an annualized return 3.0% greater than the S&P500. The worst slice had an annualized return 2.1% worse than the S&P500.

Valuations

I used the Stock-Return Predictor.

The Stock Returns Predictor

Variations caused by valuations are huge. At today’s prices, with P/E10=26, the most likely (real) return ten years from now is 1.3%. At historically typical prices, with P/E10=14, the most likely return after ten years is 6.3%. At bargain levels, but well above market bottoms, with P/E10=8, the most likely return after ten years is 14.5%.

With P/E10=26, the most likely (real) return after 20 years is 2.7%. After 30 years, it is 5.4%.

With P/E10=14, the most likely (real) return after 20 years is 6.3%. After 30 years, it is 6.7%.

With P/E10=8, the most likely (real) return after 20 years is 12.1%. After 30 years, it is 9.0%.

Summary

Rebalancing has little to offer except, as we have discovered, when valuations are high and you have no way to discern value.

Individual market slices produce significantly different returns, of the order of 2% to 3% (annualized).

Valuations, as measured by P/E10, have a huge effect. Returning to normal valuations would increase 10 year returns by 5% (annualized). Returning to bargain levels would increase 10 year returns by 13% (annualized).

Have fun.

John Walter Russell
July 24, 2006