in only 87.3 bps of tracking error. There is simply no additional risk to take given the portfolio constraints. This is often the case for portfolios that do not allow investments below investment-grade because most high-credit-quality fixed income securities are highly correlated and it is hard for the returns of a diversified portfolio to deviate substantially from the benchmark, with the exception of returns resulting from duration risk. In this example, we limited the duration band to 0.5 years. The tracking error could be raised if that constraint was lifted, but the information ratio would deteriorate meaningfully. Table 24.6 shows the output from the optimization for Portfolio 2. Because of the more flexible investment constraints, the optimization was run at target tracking errors of 50, 100, and 200 basis points. In this case, the maximum tracking error for most of the strategies was higher than for Portfolio 1 because the investment constraints allowed for both larger size and broader types of risk. Notice that at the same level of tracking error, the information ratio is higher for Portfolio 2 than for Portfolio 1. This is because Portfolio 2 allows for more diversified sources of risk. Also, because Portfolio 2 is allowed to trade in more volatile markets such as high-yield, emerging-market debt, and currency, it is able to achieve much higher levels of tracking error if that is what the investor desires. This analysis is just a sample of how this process works. It is portable to any benchmark with any set of constraints. This risk budgeting strategy could also be used to run hedge fund portfolios that exhibit tracking error of 1,000 basis points or more. To be able to achieve such high levels of risk, the manager must be investing exclusively in high-risk markets and/or utilizing leverage to be able to increase the amount of risk taken in the active strategies that are being used. Keep in mind that this is not the end of the investment process. It is merely the beginning. To achieve the return objectives that result from these risk allocations, TABLE 24.6 Portfolio 2 Optimization Results Target Tracking Error 50 100 200 Maximum _____________ _____________ ________ Tracking Excess Tracking Excess Tracking Excess Tracking     Error Return Error Return Error Return Error Duration 140 0.8 4.2 2.1 10.4 7.4 37.0 Yield curve 25 4.3 14.3 7.5 25.0 7.5 25.0 Sector 160 7.1 17.8 17.7 44.3 62.9 157.3 Security-Government/ 25 17.5 25.0 17.5 25.0 17.5 25.0 MBS/ABS/agency               Security-corporate/ 60 11.9 23.8 29.7 59.3 30.0 60.0 high-yield/EMD               Country 25 7.6 19.0 10.0 25.0 10.0 25.0 Currency 70 7.6 19.0 19.0 47.5 28.0 70.0 Total portfolio   56.9 50.0 103.5 100.0 163.3 200.0 Information ratio   1.1   1.0   0.8