Bryan Tannenbaum Ben Schultz James Rigos 22 Nov 11 Portfolio Volatility Portfolio Expected Return 0 096928 6 41 Harvard Management Company Portfolio Expected Return Standard DeviationSharpe Ratio Domestic Foreign Emerging Private Abs Ret 0 00 0 47 0 49 0 49 0 49 0 48 0 46 0 49 3 00 4 00 5 00 6 00 7 00 8 00 9 00 6 90 0 01 0 02 0 04 0 06 0 08 0 10 0 13 0 08 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 04 0 07 0 10 0 13 0 17 0 24 0 13 0 00 0 05 0 10 0 15 0 21 0 31 0 44 0 20 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 Portfolio Expected Return Standard DeviationSharpe Ratio Domestic Foreign Emerging Private Abs Ret 0 00 0 20 0 43 0 44 0 43 0 37 0 40 0 43 3 00 4 00 5 00 6 00 7 00 8 00 9 00 6 90 0 05 0 05 0 05 0 05 0 05 0 05 0 15 0 05 0 01 0 01 0 04 0 10 0 17 0 19 0 19 0 16 0 05 0 05 0 06 0 16 0 25 0 25 0 25 0 25 0 12 0 12 0 12 0 12 0 12 0 30 0 32 0 12 0 05 0 05 0 05 0 05 0 05 0 25 0 25 0 05 0 06 0 05 0 05 0 07 0 09 0 14 0 15 0 09 Numbers in red could not achieve the real return Best possible values used from the solver Part I Part II Part III Part IV Expected Return SD Part III SD of Policy Porfolio SD Part II 0 01 0 02 3 00 4 00 0 06 0 05 0 02 Calculation for 6 90 Expected Return of Portfolio Sum Expected Return of Asset Classes x Weight of Assets Classes SUM 065 12 065 05 085 16 095 25 053 05 052 02 053 16 050 15 040 02 040 12 036 14 030 13 690 Sharpe Ratio Portfolio Expected Return Return on Cash Standard Deviation 069 03 09 43 The solver computes the weights on the individual asset classes in order to minimize the standard deviation for each expected rate of return 5 00 6 00 6 90 7 00 8 00 9 00 0 04 0 06 0 08 0 08 0 10 0 13 0 05 0 07 0 09 0 09 0 14 0 15 0 04 0 06 0 08 0 10 0 13 Investment Opportunities n o ti a i v e D d r a d n a t S 0 16 0 14 0 12 0 10 0 08 0 06 0 04 0 02 0 00 Part II Part III Policy Portfo lio 2 00 3 00 4 00 5 00 6 00 Expected Return 7 00 8 00 9 00 10 00 Final Conclusion The optimal portfolio is the Policy Portfolio The constraint optimization Part II shows the allocations across different security classes for HMC Part III tests these constraints and produces higher standard deviations at every potential return This shows which porfolios should carry higher weights in the domestic and foreign equities rather than in untraditional commodities Harvard Management Company High Yield Commod ReEs Dom Bond For Bond Tips Cash 0 00 1 00 0 17 0 53 0 19 0 17 0 21 0 20 0 16 0 50 0 00 0 50 0 00 0 50 0 20 0 50 0 00 0 03 0 07 0 11 0 16 0 07 0 00 0 15 0 00 0 01 0 02 0 04 0 05 0 08 0 05 0 05 0 00 0 02 0 07 0 11 0 15 0 17 0 15 0 14 0 00 0 11 0 23 0 35 0 48 0 58 0 62 0 46 0 00 0 04 0 09 0 13 0 17 0 12 0 00 0 17 High Yield Commod ReEs Dom Bond For Bond Tips Cash 0 17 0 07 0 17 0 07 0 17 0 07 0 17 0 05 0 10 0 13 0 03 0 13 0 03 0 13 0 14 0 13 0 04 0 04 0 16 0 16 0 16 0 16 0 16 0 16 0 13 0 13 0 03 0 01 0 02 0 03 0 07 0 02 0 14 0 14 0 14 0 14 0 12 0 06 0 06 0 12 0 17 0 17 0 09 0 12 0 16 0 16 0 03 0 15 0 20 0 20 0 18 0 09 0 02 0 00 0 00 0 02 Expected Return of Portfolio Sum Expected Return of Asset Classes x Weight of Assets Classes SUM 065 12 065 05 085 16 095 25 053 05 052 02 053 16 050 15 040 02 040 12 036 14 030 13 690 Sharpe Ratio Portfolio Expected Return Return on Cash Standard Deviation 069 03 09 43 The solver computes the weights on the individual asset classes in order to minimize the standard deviation for each expected rate of return security classes for HMC Part III tests these constraints and produces higher standard deviations at every potential return This shows which porfolios should carry higher weights in the domestic and foreign equities rather than in untraditional commodities The constraint optimization Part II shows the allocations across different Expected Return of Portfolio Sum Expected Return of Asset Classes x Weight of Assets Classes SUM 065 12 065 05 085 16 095 25 053 05 052 02 053 16 050 15 040 02 040 12 036 14 030 13 690
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