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Fixed income Risk and Return 449 TABLE 24.4 Two Sets of Constraints    


Portfolio 1-Core High -Quality Portfolio 2-Core Plus Duration Index +/- 0.5 years   Index +/- 2.0 years Minimum credit BBB-/Baa3   No minimum quality       High-yield maximum Not allowed   10% Emerging market Not allowed   10% debt maximum       Other sectors Benchmark +/- 20%   No constraint Non-$ bonds Not allowed   Maximum 20%, maximum 10% unhedged There are a number of items to note in the table. You can see that for each strategy, the level of excess return from that strategy is equal to the allocated tracking error multiplied by the information ratio detailed earlier. For example, in the 75 bps tracking error case, the optimization has suggested an allocation of 48.2 bps to the sector allocation strategy, which contributes 19.3 bps of expected excess return (48.2 times the assumed information ratio of 0.4). Also note that while the total portfolio excess return is equal to the sum of the excess returns from each strategy, the total tracking error is much less than the sum of the tracking errors from each strategy. This is because of the benefit of diversifying risk across a number of strategies that are not highly correlated. Another item of note is that the total portfolio information ratio declines as risk increases. This is generally the case for any portfolio optimization given a set of constraints. Lastly, note that while 100 bps was targeted for the optimization in the rightmost column, the total tracking error is only 87.3 bps. This is because the TABLE 24.5 Portfolio 1 Optimization Results     Target Tracking Error   50 75 100 Tracking Error Excess Tracking Excess Tracking Excess Tracking Return Error Return Error Return Error 40 0 0 Duration Yield curve Sector Security- government/ MBS/ABS/agency Security-corporate/ high-yield/EMD Country Currency Total portfolio Information ratio   35 1.1 5.3 2.3 11.3 7.0 35.0 25 5.5 18.2 7.5 25.0 7.5 25.0 50 9.1 22.7 19.3 48.2 20.0 50.0 25 17.5 25.0 17.5 25.0 17.5 25.0 30.4 0.0 0.0 50.0 20.0 0.0 0.0 66.5 0.9 40.0 0.0 0.0 75.0 20.0 0.0 0.0 72.0 0.8 40.0 0.0 0.0 87.3 15.2 0.0 0.0 48.3 1.0