Rebalancing and Returns.indd - Dimensional Fund Advisors

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10 Dimensional Fund Advisors Panel C shows the amount by which the portfolio return exceeds the return on a portfolio with weights held constant at the average allocation, computed as the difference between Panel A and Panel B. Rebalancing with frequent monitoring and a 15%-20% band yielded weights that were positively correlated to returns in this sample, boosting realized returns by 15 to 19 basis points relative to a constant-weight portfolio with the same average allocation. While this difference might be due to skillful rebalancing, it is impossible to distinguish it from random noise with just nine years of returns data. I try to address this issue later in this paper by using a longer sample of historical returns. Components or Core Suppose, for a moment, that the (1, 20%) or the (5, 20%) strategies increase expected returns through skillful rebalancing. The natural question that follows is whether one can achieve higher returns by rebalancing across more asset classes. Daryanani argues that the answer is yes, because “rebalancing benefits can be increased by using more uncorrelated assets, [thus increasing] the number of buy-low/sell-high opportunities.” If this were the case, a core equity strategy would underperform an optimally rebalanced components strategy. To test this claim, I consider a core strategy portfolio that invests 45% in the Russell 3000 Index and a components strategy that invests 45% in a combination of the Russell 1000 Growth Index, the Russell 1000 Value Index, the Russell 2000 Growth Index, and the Russell 2000 Value Index. 6 The remainder of the portfolio has 40% in bonds, 10% in REITs, and 5% in commodities, as in the previous analysis. Trading costs are still assumed to be flat at $20 per trade and the initial investment is $1 million. Table 4 displays the net annualized arithmetic average returns for the core and component strategies over the period February 1996-December 2004. For 37 of the 42 rebalancing strategies, the core portfolio has higher returns than the component strategy. Rebalancing across a greater number of asset classes using the components did not deliver higher returns even with the (1, 20%) strategy, which is the strategy that is supposed to produce the greatest rebalancing benefits. Except in the extreme case of rebalancing to target on a daily or weekly basis where the core strategy clearly dominates the components strategy, none of the return differences between the core and component strategies is statistically significant. Notice that the (1, 20%) strategy no longer produces the highest returns, despite having an identical sampling period and a very similar allocation as the previous analysis. For the core strategy, the best three rebalancing strategies in the sample period are the (5, 25%), the (1, 25%), and the (125, 20%). For the component strategy, the top three are the (20, 25%), the (125, 25%) and the (250, 25%) strategies. 6. The target weights of the Russell components are set equal to their average weight in the Russell 3000 in the year prior to portfolio formation, from February 1995 to January 1996. Specifically, the Russell 1000 Value weight was 39.61%; Russell 1000 Growth, 45.85%; Russell 2000 Value, 5.81%; and Russell 2000 Growth, 8.73%. These weights are then scaled to sum to 45%.
Rebalancing and Returns 11 Table 4 Core vs. Component Strategies February 1996-December 2004 Panel A: Core Portfolio Net Arithmetic Average Returns Look Interval (market days) Rebalance Band 1 5 10 20 60 125 250 0% 8.06 9.30 9.39 9.47 9.49 9.53 9.67 5% 9.61 9.59 9.58 9.60 9.58 9.60 9.73 10% 9.76 9.73 9.74 9.72 9.69 9.70 9.79 15% 9.80 9.77 9.79 9.78 9.78 9.78 9.81 20% 9.76 9.73 9.78 9.79 9.79 9.83 9.76 25% 9.85 9.86 9.71 9.77 9.79 9.66 9.61 100% 9.33 9.33 9.33 9.33 9.33 9.33 9.33 Panel B: Components Portfolio Net Arithmetic Average Returns Look Interval (market days) Rebalance Band 1 5 10 20 60 125 250 0% 6.62 8.94 9.15 9.31 9.40 9.48 9.67 5% 9.43 9.47 9.45 9.46 9.50 9.54 9.71 10% 9.55 9.58 9.57 9.62 9.63 9.67 9.74 15% 9.67 9.71 9.72 9.72 9.70 9.74 9.76 20% 9.74 9.74 9.72 9.77 9.72 9.71 9.74 25% 9.78 9.78 9.76 9.80 9.76 9.79 9.79 100% 9.18 9.18 9.18 9.18 9.18 9.18 9.18 Standard Deviation Look Interval (market days) Rebalance Band 1 5 10 20 60 125 250 0% 9.14 9.11 9.09 9.06 8.98 8.93 8.90 5% 9.14 9.11 9.08 9.05 8.98 8.94 8.94 10% 9.16 9.13 9.10 9.10 9.04 9.00 8.99 15% 9.17 9.13 9.17 9.15 9.10 9.06 9.08 20% 9.28 9.28 9.25 9.23 9.25 9.16 9.23 25% 9.30 9.29 9.33 9.32 9.30 9.37 9.47 100% 10.10 10.10 10.10 10.10 10.10 10.10 10.10 Standard Deviation Look Interval (market days) Rebalance Band 1 5 10 20 60 125 250 0% 9.25 9.22 9.19 9.15 9.04 8.97 8.95 5% 9.25 9.21 9.17 9.13 9.04 8.98 8.99 10% 9.25 9.21 9.19 9.17 9.07 8.99 9.04 15% 9.20 9.16 9.18 9.14 9.09 9.05 9.13 20% 9.18 9.15 9.16 9.18 9.12 9.13 9.23 25% 9.19 9.19 9.19 9.18 9.20 9.21 9.28 100% 10.21 10.21 10.21 10.21 10.21 10.21 10.21 Panel C: Core – Components Return Difference Look Interval (market days) Rebalance Band 1 5 10 20 60 125 250 0% 1.44 0.36 0.24 0.16 0.09 0.06 0.01 5% 0.18 0.12 0.13 0.14 0.09 0.06 0.02 10% 0.20 0.15 0.17 0.10 0.06 0.03 0.05 15% 0.13 0.06 0.06 0.06 0.08 0.04 0.05 20% 0.01 -0.01 0.06 0.01 0.07 0.13 0.02 25% 0.07 0.09 -0.05 -0.03 0.03 -0.14 -0.19 100% 0.15 0.15 0.15 0.15 0.15 0.15 0.15 T-Statistic Look Interval (market days) Rebalance Band 1 5 10 20 60 125 250 0% 7.12 1.77 1.21 0.82 0.51 0.36 0.04 5% 0.83 0.58 0.62 0.69 0.47 0.36 0.15 10% 0.86 0.68 0.77 0.47 0.33 0.18 0.33 15% 0.56 0.27 0.28 0.27 0.39 0.22 0.31 20% 0.06 -0.03 0.27 0.06 0.34 0.73 0.10 25% 0.34 0.42 -0.24 -0.16 0.13 -0.62 -0.82 100% 0.69 0.69 0.69 0.69 0.69 0.69 0.69
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