Now suppose that the portfolio manager maintains constant weights of 60 percent in stocks and 40 percent in bonds for all five years. This method is called a constant-proportions strategy. Because value is price multiplied by quantity, price fluctuation causes portfolio weights to change. As a result, the constant-proportions strategy requires rebalancing to restore the weights in stocks and bonds to their target levels. Assuming that the portfolio manager is able to accomplish the necessary rebalancing, we can compute the portfolio returns in 2009, 2010, 2011, and 2012 with Equation 4 as follows:

Portfolio return for 2009 = 0.60(34.1) + 0.40(11.0) = 24.9%

Portfolio return for 2010 = 0.60(16.8) + 0.40(6.4) = 12.6%

Portfolio return for 2011 = 0.60(–9.2) + 0.40(8.4) = –2.2%

Portfolio return for 2012 = 0.60(6.4) + 0.40(3.8) = 5.4%

We can now find the time-series mean of the returns for 2008 through 2012 using Equation 3 for the arithmetic mean. The time-series mean total return for the portfolio is (−19.9 + 24.9 + 12.6 − 2.2 + 5.4)/5 = 20.8/5 = 4.2 percent.

Instead of calculating the portfolio time-series mean return from portfolio annual returns, we can calculate the arithmetic mean stock and bond fund returns for the five years and then apply the portfolio weights of 0.60 and 0.40, respectively, to those values. The mean stock fund return is (−33.1 + 34.1 + 16.8 − 9.2 + 6.4)/5 = 15.0/5 = 3.0 percent. The mean bond fund return is (−0.1 + 11.0 + 6.4 + 8.4 + 3.8)/ 5 = 29.5/5 = 5.9 percent. Therefore, the mean total return for the portfolio is 0.60(3.0) + 0.40(5.9) = 4.2 percent, which agrees with our previous calculation.

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