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#### Featured Article:

## Value of Rebalancing

### Theory of Rebalancing

Periodic rebalancing of a portfolio is an important method for maintaining proper diversification within a portfolio as your assets appreciate over time. Rebalancing will return your portfolio to your predetermined asset class allocations. This allows the investor to control the relative contribution of each asset class to the overall variance of his portfolio. Without rebalancing, the variance of the portfolio will be skewed towards the highest performing asset class.

Beyond the value in maintaining desired diversification, rebalancing can actually boost portfolio returns. Below we list several of the necessary conditions required for rebalancing to have a positive impact on returns. When other conditions are present, rebalancing can reduce portfolio returns.

#### Conditions that support increased returns

While rebalancing can often lead to lower standard deviation for your annual returns, there are a set of circumstances where rebalancing will actually boost the performance of a portfolio. These conditions include:

**Uncorrelated or negatively correlated assets**– Positively correlation among asset classes will render rebalancing less meaningful**Mean reversion properties**– When assets behave with a tendency to revert to the mean, then it is more likely that the asset will appreciate at a higher rate than its mean if it has underperformed in the past. Rebalancing serves to move investment dollars into underperforming asset classes. Equities appear to demonstrate mean reversion properties for some periods of time while displaying more trending behavior in other periods.**Similar rates of returns for assets**– If one asset class has a significantly higher mean rate of return, then rebalancing can reduce the overall portfolio’s performance. In this case, the rebalancing will move funds away from the fastest growing asset class.

**High variances within individual asset classes**– High variance leads to the situations where asset classes will (1) substantially outperform the portfolio for periods (during which time the rebalancing will take profits out by selling these shares) and (2) substantially underperform the portfolio in other periods (when the rebalancing will buy shares at the reduced price). The net, long-term result of these swings will be higher return for the overall portfolio.

#### Empirical Results

To test the impact of rebalancing on annual returns and portfolio variance, we have constructed some sample portfolios and used historical data to compare an annual rebalancing policy versus a policy of not rebalancing. These portfolios will be constructed from five asset classes (US Large Cap Stock, International Equities, Emerging Markets Equities, REITs, and US Treasuries). The respective indexes used will: S&P 500, MSCI EAFE, S&P IFC Emerging Markets, S&P REIT and Dow Wilshire REIT and US 5-yr Treasury bonds. Data was collected from Index Fund Advisors and the Global Financial Data website. We will analyze the policies over a 30 year (1975-2004), 20 year (1985-2004) and 10 year (1995-2004) horizon. We’re interested in the differences in annual return (geometric mean) and standard deviation.

Our first portfolio consists of 40% US Large stock, 20% International Equities, 20% Emerging Markets and 20% US Treasuries. Below are the results for the three time periods.

Rebalanced | Not Rebalanced | |||
---|---|---|---|---|

Annual Return | Standard Deviation | Annual Return | Standard Deviation | |

30 Years | 11.3% | 14.4% | 10.0% | 13.8% |

20 Years | 12.9% | 13.9% | 11.6% | 12.9% |

10 Years | 10.8% | 9.9% | 9.4% | 9.4% |

The results show a significant gain to rebalancing for all time horizons. A closer look at the underlying data reveals that several of our required characteristics for enhanced returns are satisfied. The asset classes are largely uncorrelated (see the table below), the mean rate of return for each asset class is very similar (a low of 9.0% to a high of 10.7%) and the variances within the asset classes are somewhat large (emerging markets have a standard deviation of over 40%). Note that the annual return of the rebalanced portfolio is actually larger than the return of the best performing asset class. Interestingly, the standard deviation for the rebalanced portfolio is actually higher – so no free lunch in this case.

The table below lists the correlation coefficient of the asset classes with one another over the 30 year period.

US Large | International | Emerging | REIT | Bond | |
---|---|---|---|---|---|

US Large | 1 | X | X | X | X |

International | 0.49 | 1 | X | X | X |

Emerging | 0.35 | 0.34 | 1 | X | X |

REIT | 0.26 | 0.08 | 0.29 | 1 | X |

Bond | 0.08 | 0 | -0.14 | 0.09 | 1 |

Next, to demonstrate the situation where rebalancing will negatively impact a portfolio’s return, we replaced emerging market exposure in the portfolio with REIT exposure. During the 30 year time horizon, REITs had an IRR of 15.2%. This was the best performing asset class by a large margin (the second highest was the emerging market class with an IRR of 10.7%). Thus, rebalancing with REITs in the portfolio should be less likely to generate an incremental return versus the unbalanced portfolio. The table below shows the actual comparison of the two portfolios.

Rebalanced | Not Rebalanced | |||
---|---|---|---|---|

Annual Return | Standard Deviation | Annual Return | Standard Deviation | |

30 Years | 11.4% | 10.5% | 11.6% | 10.9% |

20 Years | 12.2% | 10.1% | 12.1% | 10.5% |

10 Years | 13.4% | 8.5% | 14.7% | 8.7% |

As expected, the rebalanced portfolio generally slightly trails in performance while the variance is slightly lower in the rebalanced portfolio.

Note: All our annual return figures are geometric means (equivalent to IRRs). For the non-rebalanced portfolio, we don’t calculate the Markowitz mean which is not a relative comparison.

### Conclusions

Rebalancing has two potential benefits to your portfolio: variance reduction and return enhancement. The ability to control the contribution of each asset class to the overall portfolio variance is valuable. Additionally, if you believe that your portfolio will satisfy some or all of the necessary conditions for enhanced returns, you should implement a rebalancing policy.

### Useful Links

The Rebalancing Bonus – a study and discussion from William Bernstein of the Efficient Frontier

Diversification, Rebalancing and the Geometric Mean Frontier (PDF) – a more detailed paper by Bernstein and Wilkinson

Portfolio Rebalancing in Theory and Practice (PDF) – a document from Vanguard with a detailed discussion of portfolio rebalancing and some simulation results

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