Annual Rebalancing Research Articles

Rebalancing Strategies for Creating Efficient Portfolios

This article applies an annual rebalancing strategy to create portfolios of industry leaders and compares the efficiency of these portfolios with the S&P 500 Index and the CRSP market index portfolios. For the last four decades, value-weighted portfolios consisting of as few as eight or nine securities formed from industry leaders are more efficient with annual rebalancing than the S&P 500 and are indistinguishable from the CRSP market index portfolio. The findings suggest important implications for choosing appropriate benchmarks for measuring tracking error.

Rebalancing strategies and the performance of balanced portfolios: 1925–2001

The results of a study of the performance of balanced portfolios in South Africa over the last 77 years are presented. Using the asset classes South African equities, bonds and cash, five portfolios of widely varying composition were formed. In addition two portfolios containing a portion of the equity allocation in the US market were created. Three rebalancing periods of a month, a quarter and a year and a strategy of rebalancing whenever the equity proportion of the portfolio moved more than five percentage points from its target were tested. The compound annual returns of the portfolios were largely unaffected by the choice of rebalancing period. A small increase in portfolio standard deviation was found as the rebalancing period increased. In the absence of transactions costs it appears that an annual rebalancing strategy would have been the best choice. However annual rebalancing resulted in large deviations in the portfolio equity proportions during the rebalancing period, particularly for portfolios with low proportions of equity.

What's the Long-Term Expected Return to Your Portfolio?

Many investors and investment consultants use mean-variance optimizers to select efficient portfolios. Mean-variance optimization is inherently a single-period technique. Most investors use it in a multiyear context by assuming annual rebalancing and independence and stationarity of returns. These assumptions are often reasonable, and they enable investors to estimate a portfolio's future growth rate, or long-term expected return. Investors such as definedbenefit plan sponsors and foundations have a keen interest in the long-term expected returns to their portfolios. Sponsor contributions and foundation budgets are often tied directly to this estimate of the future growth rate of assets. This focus on a future portfolio growth rate appears to lead many practitioners mistakenly to use past growth rates to asset classes as inputs to their mean-variance optimizers. The consequence of this error is an estimated longterm expected return to the portfolio that is likely to be at least 50 basis points lower than the correct estimate. Correct estimation of a portfolio's future multiperiod growth rate is a two-step procedure. First, determine the single-period characteristics of portfolio returns. Then, estimate the multiperiod characteristics of those singleperiod returns. A simple example illustrates this point. From Ibbotson Associates' Stocks, Bonds, Bills, and Inflation 1994 Yearbook, the compound annual growth rates to largecompany stocks and long-term corporate bonds from December 31, 1925, through December 31, 1993, were 10.3 percent and 5.6 percent, respectively. These numbers could be used as estimates of future long-term expected returns to stocks and bonds. To estimate the future growth rate to a portfolio of stocks and bonds, rebalanced annually to 50/50, one might be tempted simply to take the arithmetic average of the stock and bond growth rates. This calculation is quick and easy, and it yields an estimated future portfolio growth rate of 7.9 percent. One might think 7.9 percent is a reasonable estimate, but it is not. Using the two-step procedure outlined in the preceding paragraph, first calculate all 68 annual portfolio returns to stocks and bonds. In the second step, calculate the annual growth rate from these 68 annual portfolio returns. That growth rate is 8.4 percent, 50 basis points higher than the quick and easy estimate of 7.9 percent! The stock/bond version of the erroneous calculation is given in Equation 1. Equation 1 is appropriate for calculating the singleperiod, say annual, expected return to a portfolio, because it holds for actual annual rates of return. Skipping Step 1 by using growth rates in Equation 1 is a mistake, however, because a portfolio growth rate is not a linear combination of the growth rates of the assets in the portfolio. An annualized growth rate calculated from a series of annual returns will be lower than the arithmetic average of the returns because of volatility. A simple approximation of this relationship is given in Equation 4. Use of Equation 1 with long-term expected returns ignores the reduction in volatility coming from diversification between the two assets and yields a long-term expected return that is too low. The more diversified the portfolio, the larger the error. To convince yourself about this, just follow through the details of the stock and bond example below. This is the same example as above, except that Equation 4 is used for Step 2 rather than a calculation of all 68 annual portfolio returns.

The Effects of Rebalancing on Size and Book-to-Market Ratio Portfolio Returns

After adjusting for transaction costs and different rebalancing periods, portfolios of securities selected on the basis of the issuing firm's book-to-market-equity (BE/ME) ratio and size can produce returns superior to those of the the market. Specifically, after adjusting for 1.0 percent transaction costs and annual rebalancing, investors would have outperformed the market by 4.82 percent over the 1963–88 period if they had invested in securities from firms with high BE/MEs and small size. The optimal rebalancing period for long positions in these securities is two years, and the optimal period for portfolios that use the proceeds from short positions in firms with low BE/MEs and large size to purchase firms with high BE/MEs and small size is four years.