The pieces on portfolio rebalancing in the September 1996 and January 1997 EF generated a fair amount of comment, much of it along the lines of "Well, that's all very nice, but all the math made my head hurt and I still don't have a good feel for how often I should be doing it, and when it does and does not work."

So, I've decided to approach the problem from a descriptive angle. Instead of throwing a lot of math at you, I'll provide some real world examples, and describe what falls out.


When It Doesn't Work -- the 1926-94 Stock/Bond Model

Believe it or not, sometimes rebalancing bites you. Consider a portfolio consisting of equal parts of stocks (S&P 500 index) and corporate bonds (Ibbotson Long Corporate index), rebalanced each year. Now, the annualized return of this portfolio turns out to be 8.34%, which is 0.49% higher than the average of the long term return of stocks (10.19%) and bonds (5.51%). This 0.49% margin above the 7.85% average annualized return of the two assets is really not an excess return; it is mathematically incorrect to average long term annualized returns when estimating portfolio returns.

Had one not rebalanced, the return would have been 9.17%, since by the end of the period the portfolio would have consisted of 95% stock. (Each dollar invested in bonds grew to $40.51, each dollar in stock, $809.10.) Clearly, the extra return earned by not rebalancing came at the cost of higher risk in the latter part of the study period. From the sole perspective of return, rebalancing was a losing strategy during this period. Why? Firstly, the returns of the assets were so different, and over such a long time period. Secondly, and more importantly, the rebalancing benefit is directly proportional to asset variance, which is the square of the standard deviation. US stocks and bonds are just not volatile enough to generate excess rebalancing return.

When It Pays off Very Well -- Emerging Markets

Let's look at the opposite end of the rebalancing spectrum. Consider a portfolio consisting of 12 emerging markets:

Argentina
Brazil
Chile
India
Korea
Malaysia
Mexico
Philippines
Portugal
Taiwan
Thailand
Turkey

These are wild and crazy assets. The SD of annual returns for 1988-96 is 165.9% for Turkey, and 126.5% for Argentina. The least volatile market was Chile, with an SD of only 33.0%. Compare this with the SD of the S&P for the same period of 13.5%.

Now, let's create a portfolio consisting of equal parts of each of the above markets on 1/1/88, and hold it, untouched, until 12/31/96. The theoretical return for this portfolio would have been 20.72%. (Very theoretical, since it is not possible for foreign investors to own all of the stocks in some of these indexes, and the transactional cost involved is considerable.)

However, had one rebalanced back to equal amounts of each market annually, the theoretical return would have been 25.86%. Admittedly, some of this return would have been lost via the high costs of trading these markets. We can estimate the trading costs mandated by rebalancing by noting that the portfolio typically turned over an average of 21.5% per year. Assuming a 5% trading cost, the 5% rebalancing benefit still greatly outweighs the estimated 1% extra expense generated by rebalancing.

The reason for the large rebalancing benefit is the very high variance/SD of these assets combined with their very low correlations. Even though there were enormous return differences (The highest return market, Argentina, yielded 34.6% annually, while the worst, Portugal, returned -1.11% annually.) the very high asset volatility generated more than enough excess return to overcome this.

The Real World: Regional Indexes in the 1970-96 Period

Neither of the above examples is terribly relevant to the average investor. Very few of us are going to be investing for 69 years, or will be rebalancing annually individual emerging markets portfolios. On the other hand, most of us do have available to us broad portfolios and indexes of regional markets, and will be actively investing for 3 or 4 decades. Accordingly, I've constructed a model which incorporates the following markets for the years 1970-96:

Asset	1970-96 Return(%)	1970-96 SD(%)
US large stocks	12.27	15.85
US small stocks	14.15	22.93
European stocks	13.05	20.95
Pacific Rim stocks	12.26	30.84
Japanese stocks	14.54	33.68
Prec. Met. stocks	13.70	42.99
20 Year Treasuries	9.27	11.89
5 Year Treasuries	9.28	6.80
30 Day Treasuries	6.88	2.67

(Sources: For US Large Stocks (S&P500), US small stocks, and 30 day, 5 year, and 20 year treasury securities, Stocks, Bonds, Bills, and Inflation, 1997 Yearbook. For Japanese, European, and Pacific Rim (MSCI-PACXJ) MSCI Indexes, from Morningstar Principia. The gold equities index consists of the precious metals mutual fund objective return series from Morningstar after 1976. For 1970-75 the return
of the Van Eck Gold Fund is used, courtesy of the Van Eck Group.)

I then constructed the 36 possible 50/50 portfolios for each 2 asset combination, and calculated the difference in return between the rebalanced and nonrebalanced portfolios:

For each stock asset pair, a significant rebalancing benefit is seen, even with the highly correlated S&P/US SM pair. The only asset which produced persistently negative rebalancing effects was the treasury bill, with its very low return and variance/SD.

Let's look at some more realistic portfolios. A portfolio consisting of equal parts of each of the six stock assets had an excess return of 1.92% over the unrebalanced portfolio, and an average annual turnover of 8.5%. A portfolio consisting of equal parts of all of the assets (2/3 stocks and 1/3 bonds) had an excess return of 1.08% over the unrebalanced portfolio and an average annual turnover of 7.8%. Finally, a highly conventional all stock portfolio of 25% each S&P and US SM and 12.5% each PXJ, EAFE-E, Japan and Gold had a return of 1.65% higher than the unrebalanced portfolio and an average annual turnover of 7.6%.

Clearly, then, there is a considerable excess return to be earned rebalancing global portfolios, in the range of 1%-2%. The transactional costs in the tax sheltered environment are minimal -- at a trading cost of 1.5% and average turnover of about 8% only 0.12% is lost to the trading mandated by rebalancing. In the taxable arena the situation is different. Assuming that you are in the 28% capital gains bracket, it can be seen that 8% annual turnover will likely produce a capital gains jolt which can easily exceed the rebalancing benefit.

What rebalancing interval is optimal? In the previous articles it was shown that that depends on the differences between the annualized variances and correlations for each interval for the period considered; the "optimal" rebalancing interval cannot be accurately predicted. It is clear, however, that since rebalancing benefit is roughly linear with variance and turnover is roughly linear with SD, that more frequent rebalancing will likely be less efficient in terms of transactional cost.

copyright (c) 1997, William J. Bernstein