4-asset optimization. Max-Sharpe: 6.390. Portfolio: return=159.42%, vol=24.32%. Weights: w_^VIX=0.0786, w_BTC-USD=0.4287, w_SOYB=0.0000, w_XHB=0.4927.

Question:
Assets: ^VIX, BTC-USD, SOYB, XHB
Annualized mean returns: ^VIX:0.0864, BTC-USD:2.9600, SOYB:-0.0975, XHB:0.6466
Covariance matrix (annualized):
[[0.541391, -0.004282, 0.007931, -0.079078], [-0.004282, 0.244388, 0.002383, 0.01366], [0.007931, 0.002383, 0.018947, -0.006405], [-0.079078, 0.01366, -0.006405, 0.047599]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_^VIX=0.0786, w_BTC-USD=0.4287, w_SOYB=0.0000, w_XHB=0.4927

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_^VIX=0.0786, w_BTC-USD=0.4287, w_SOYB=0.0000, w_XHB=0.4927
Portfolio annualized return: 159.42%, volatility: 24.32%
Sharpe ratio: (1.5942 - 0.0400) / 0.2432 = 6.3896


4-asset optimization. Max-Sharpe: -1.666. Portfolio: return=-156.95%, vol=96.59%. Weights: w_^VIX=1.0000, w_LINK-USD=0.0000, w_SCHP=0.0000, w_HAUZ=0.0000.

Question:
Assets: ^VIX, LINK-USD, SCHP, HAUZ
Annualized mean returns: ^VIX:-1.5695, LINK-USD:-0.0990, SCHP:-0.0645, HAUZ:-0.2110
Covariance matrix (annualized):
[[0.932913, -0.056685, 0.013018, -0.071441], [-0.056685, 0.167786, 0.00428, 0.008814], [0.013018, 0.00428, 0.003242, -0.00104], [-0.071441, 0.008814, -0.00104, 0.025204]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_^VIX=1.0000, w_LINK-USD=0.0000, w_SCHP=0.0000, w_HAUZ=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_^VIX=1.0000, w_LINK-USD=0.0000, w_SCHP=0.0000, w_HAUZ=0.0000
Portfolio annualized return: -156.95%, volatility: 96.59%
Sharpe ratio: (-1.5695 - 0.0400) / 0.9659 = -1.6664


4-asset optimization. Max-Sharpe: 0.979. Portfolio: return=19.72%, vol=16.07%. Weights: w_VEA=1.0000, w_BNB-USD=0.0000, w_CPER=0.0000, w_XHB=0.0000.

Question:
Assets: VEA, BNB-USD, CPER, XHB
Annualized mean returns: VEA:0.1972, BNB-USD:-0.1662, CPER:0.0209, XHB:0.0433
Covariance matrix (annualized):
[[0.025815, 0.003956, 0.014241, 0.024284], [0.003956, 0.145347, 0.007925, 0.012046], [0.014241, 0.007925, 0.047706, 0.00309], [0.024284, 0.012046, 0.00309, 0.052514]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_VEA=1.0000, w_BNB-USD=0.0000, w_CPER=0.0000, w_XHB=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VEA=1.0000, w_BNB-USD=0.0000, w_CPER=0.0000, w_XHB=0.0000
Portfolio annualized return: 19.72%, volatility: 16.07%
Sharpe ratio: (0.1972 - 0.0400) / 0.1607 = 0.9785


4-asset optimization. Max-Sharpe: 2.303. Portfolio: return=63.29%, vol=25.75%. Weights: w_XLE=0.0000, w_AVAX-USD=0.1918, w_SLV=0.5328, w_CSHI=0.2754.

Question:
Assets: XLE, AVAX-USD, SLV, CSHI
Annualized mean returns: XLE:-0.1382, AVAX-USD:1.4236, SLV:0.6402, CSHI:0.0680
Covariance matrix (annualized):
[[0.04172, 0.058548, 0.030022, 0.001028], [0.058548, 0.572079, 0.079791, 0.008864], [0.030022, 0.079791, 0.095934, 0.002479], [0.001028, 0.008864, 0.002479, 0.000407]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_XLE=0.0000, w_AVAX-USD=0.1918, w_SLV=0.5328, w_CSHI=0.2754

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLE=0.0000, w_AVAX-USD=0.1918, w_SLV=0.5328, w_CSHI=0.2754
Portfolio annualized return: 63.29%, volatility: 25.75%
Sharpe ratio: (0.6329 - 0.0400) / 0.2575 = 2.3029


4-asset optimization. Max-Sharpe: -0.840. Portfolio: return=-15.29%, vol=22.97%. Weights: w_XLI=0.2500, w_MATIC-USD=0.2500, w_PALL=0.2500, w_SGOV=0.2500.

Question:
Assets: XLI, MATIC-USD, PALL, SGOV
Annualized mean returns: XLI:0.4619, MATIC-USD:-0.1748, PALL:-0.9539, SGOV:0.0553
Covariance matrix (annualized):
[[0.014195, 0.029601, 0.021942, 0.000113], [0.029601, 0.642572, -0.041226, 0.000337], [0.021942, -0.041226, 0.16537, 0.000255], [0.000113, 0.000337, 0.000255, 8e-06]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_XLI=0.2500, w_MATIC-USD=0.2500, w_PALL=0.2500, w_SGOV=0.2500

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLI=0.2500, w_MATIC-USD=0.2500, w_PALL=0.2500, w_SGOV=0.2500
Portfolio annualized return: -15.29%, volatility: 22.97%
Sharpe ratio: (-0.1529 - 0.0400) / 0.2297 = -0.8398


4-asset optimization. Max-Sharpe: 2.130. Portfolio: return=4.57%, vol=0.27%. Weights: w_VTI=0.0000, w_AVAX-USD=0.0000, w_BIL=1.0000, w_XHB=0.0000.

Question:
Assets: VTI, AVAX-USD, BIL, XHB
Annualized mean returns: VTI:-0.1312, AVAX-USD:-1.0294, BIL:0.0457, XHB:-0.5114
Covariance matrix (annualized):
[[0.028229, 0.034535, -6.3e-05, 0.032711], [0.034535, 0.582276, -0.00047, 0.009392], [-6.3e-05, -0.00047, 7e-06, -5.6e-05], [0.032711, 0.009392, -5.6e-05, 0.051496]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_VTI=0.0000, w_AVAX-USD=0.0000, w_BIL=1.0000, w_XHB=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VTI=0.0000, w_AVAX-USD=0.0000, w_BIL=1.0000, w_XHB=0.0000
Portfolio annualized return: 4.57%, volatility: 0.27%
Sharpe ratio: (0.0457 - 0.0400) / 0.0027 = 2.1302


4-asset optimization. Max-Sharpe: 2.456. Portfolio: return=38.73%, vol=14.14%. Weights: w_XLY=1.0000, w_BNB-USD=0.0000, w_BNDX=0.0000, w_HAUZ=0.0000.

Question:
Assets: XLY, BNB-USD, BNDX, HAUZ
Annualized mean returns: XLY:0.3873, BNB-USD:-0.1188, BNDX:0.0595, HAUZ:0.0851
Covariance matrix (annualized):
[[0.019991, 0.012328, 0.001461, 0.012771], [0.012328, 0.228821, 0.006424, 0.021844], [0.001461, 0.006424, 0.001721, 0.00359], [0.012771, 0.021844, 0.00359, 0.025432]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_XLY=1.0000, w_BNB-USD=0.0000, w_BNDX=0.0000, w_HAUZ=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLY=1.0000, w_BNB-USD=0.0000, w_BNDX=0.0000, w_HAUZ=0.0000
Portfolio annualized return: 38.73%, volatility: 14.14%
Sharpe ratio: (0.3873 - 0.0400) / 0.1414 = 2.4565


4-asset optimization. Max-Sharpe: 3.308. Portfolio: return=4.79%, vol=0.24%. Weights: w_EEM=0.0000, w_BNB-USD=0.0000, w_SHV=0.7541, w_CSHI=0.2459.

Question:
Assets: EEM, BNB-USD, SHV, CSHI
Annualized mean returns: EEM:0.1784, BNB-USD:-0.1815, SHV:0.0455, CSHI:0.0554
Covariance matrix (annualized):
[[0.018964, 0.005142, 9.2e-05, 0.000199], [0.005142, 0.168157, 9.8e-05, 6e-06], [9.2e-05, 9.8e-05, 5e-06, 0.0], [0.000199, 6e-06, 0.0, 4.5e-05]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_EEM=0.0000, w_BNB-USD=0.0000, w_SHV=0.7541, w_CSHI=0.2459

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EEM=0.0000, w_BNB-USD=0.0000, w_SHV=0.7541, w_CSHI=0.2459
Portfolio annualized return: 4.79%, volatility: 0.24%
Sharpe ratio: (0.0479 - 0.0400) / 0.0024 = 3.3078


4-asset optimization. Max-Sharpe: 2.949. Portfolio: return=62.11%, vol=19.70%. Weights: w_XLU=0.0000, w_AVAX-USD=0.0718, w_PALL=0.0000, w_ITB=0.9282.

Question:
Assets: XLU, AVAX-USD, PALL, ITB
Annualized mean returns: XLU:-0.1085, AVAX-USD:0.5794, PALL:-0.3711, ITB:0.6243
Covariance matrix (annualized):
[[0.025315, 0.006114, 0.012838, 0.004198], [0.006114, 0.215517, -0.019244, 0.022159], [0.012838, -0.019244, 0.087756, 0.003784], [0.004198, 0.022159, 0.003784, 0.040343]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_XLU=0.0000, w_AVAX-USD=0.0718, w_PALL=0.0000, w_ITB=0.9282

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLU=0.0000, w_AVAX-USD=0.0718, w_PALL=0.0000, w_ITB=0.9282
Portfolio annualized return: 62.11%, volatility: 19.70%
Sharpe ratio: (0.6211 - 0.0400) / 0.1970 = 2.9490


4-asset optimization. Max-Sharpe: -1.614. Portfolio: return=-20.63%, vol=15.26%. Weights: w_XLRE=0.2500, w_AVAX-USD=0.2500, w_SLV=0.2500, w_BIL=0.2500.

Question:
Assets: XLRE, AVAX-USD, SLV, BIL
Annualized mean returns: XLRE:0.1094, AVAX-USD:-1.4947, SLV:0.5097, BIL:0.0502
Covariance matrix (annualized):
[[0.019662, 0.013783, 0.012067, -9.2e-05], [0.013783, 0.20314, 0.017948, 0.00014], [0.012067, 0.017948, 0.062442, -8.6e-05], [-9.2e-05, 0.00014, -8.6e-05, 5e-06]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_XLRE=0.2500, w_AVAX-USD=0.2500, w_SLV=0.2500, w_BIL=0.2500

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLRE=0.2500, w_AVAX-USD=0.2500, w_SLV=0.2500, w_BIL=0.2500
Portfolio annualized return: -20.63%, volatility: 15.26%
Sharpe ratio: (-0.2063 - 0.0400) / 0.1526 = -1.6139


4-asset optimization. Max-Sharpe: 0.679. Portfolio: return=21.67%, vol=26.04%. Weights: w_VTI=0.0000, w_ADA-USD=0.0000, w_CPER=0.0000, w_ITB=1.0000.

Question:
Assets: VTI, ADA-USD, CPER, ITB
Annualized mean returns: VTI:-0.0674, ADA-USD:-0.0492, CPER:-0.1984, ITB:0.2167
Covariance matrix (annualized):
[[0.031328, 0.040937, 0.000736, 0.038373], [0.040937, 0.456838, 0.017983, 0.034458], [0.000736, 0.017983, 0.050848, -0.003099], [0.038373, 0.034458, -0.003099, 0.067796]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_VTI=0.0000, w_ADA-USD=0.0000, w_CPER=0.0000, w_ITB=1.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VTI=0.0000, w_ADA-USD=0.0000, w_CPER=0.0000, w_ITB=1.0000
Portfolio annualized return: 21.67%, volatility: 26.04%
Sharpe ratio: (0.2167 - 0.0400) / 0.2604 = 0.6786


4-asset optimization. Max-Sharpe: 5.321. Portfolio: return=12.23%, vol=1.55%. Weights: w_ACWI=0.0800, w_ETH-USD=0.0222, w_ICSH=0.8978, w_VNQI=0.0000.

Question:
Assets: ACWI, ETH-USD, ICSH, VNQI
Annualized mean returns: ACWI:0.4757, ETH-USD:1.8459, ICSH:0.0482, VNQI:0.1445
Covariance matrix (annualized):
[[0.011627, 0.011521, 9e-05, 0.007927], [0.011521, 0.199064, -9.6e-05, 0.0131], [9e-05, -9.6e-05, 2.1e-05, 0.000196], [0.007927, 0.0131, 0.000196, 0.013898]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_ACWI=0.0800, w_ETH-USD=0.0222, w_ICSH=0.8978, w_VNQI=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_ACWI=0.0800, w_ETH-USD=0.0222, w_ICSH=0.8978, w_VNQI=0.0000
Portfolio annualized return: 12.23%, volatility: 1.55%
Sharpe ratio: (0.1223 - 0.0400) / 0.0155 = 5.3212


4-asset optimization. Max-Sharpe: -0.004. Portfolio: return=3.95%, vol=12.15%. Weights: w_XLB=1.0000, w_XRP-USD=0.0000, w_INDS=0.0000, w_JNK=0.0000.

Question:
Assets: XLB, XRP-USD, INDS, JNK
Annualized mean returns: XLB:0.0395, XRP-USD:-0.6759, INDS:-0.0445, JNK:0.0207
Covariance matrix (annualized):
[[0.014751, 0.018617, 0.014401, 0.003301], [0.018617, 0.217788, 0.031196, 0.008487], [0.014401, 0.031196, 0.039659, 0.008518], [0.003301, 0.008487, 0.008518, 0.002895]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: bull

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_XLB=1.0000, w_XRP-USD=0.0000, w_INDS=0.0000, w_JNK=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLB=1.0000, w_XRP-USD=0.0000, w_INDS=0.0000, w_JNK=0.0000
Portfolio annualized return: 3.95%, volatility: 12.15%
Sharpe ratio: (0.0395 - 0.0400) / 0.1215 = -0.0043


4-asset optimization. Max-Sharpe: 0.987. Portfolio: return=28.06%, vol=24.37%. Weights: w_USMV=0.2319, w_XRP-USD=0.4986, w_SCHP=0.2695, w_VNQ=0.0000.

Question:
Assets: USMV, XRP-USD, SCHP, VNQ
Annualized mean returns: USMV:0.1107, XRP-USD:0.4832, SCHP:0.0519, VNQ:-0.0657
Covariance matrix (annualized):
[[0.02067, 0.021916, 0.006387, 0.025518], [0.021916, 0.209466, -0.000516, 0.027446], [0.006387, -0.000516, 0.006318, 0.008624], [0.025518, 0.027446, 0.008624, 0.049891]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_USMV=0.2319, w_XRP-USD=0.4986, w_SCHP=0.2695, w_VNQ=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_USMV=0.2319, w_XRP-USD=0.4986, w_SCHP=0.2695, w_VNQ=0.0000
Portfolio annualized return: 28.06%, volatility: 24.37%
Sharpe ratio: (0.2806 - 0.0400) / 0.2437 = 0.9872


4-asset optimization. Max-Sharpe: 2.887. Portfolio: return=106.61%, vol=35.54%. Weights: w_FXI=0.5022, w_ETH-USD=0.4978, w_IYR=0.0000, w_DBB=0.0000.

Question:
Assets: FXI, ETH-USD, IYR, DBB
Annualized mean returns: FXI:0.7915, ETH-USD:1.3431, IYR:-0.2601, DBB:-0.0065
Covariance matrix (annualized):
[[0.177558, 0.006674, 0.006158, 0.084717], [0.006674, 0.315446, 0.002822, -0.010345], [0.006158, 0.002822, 0.023664, 0.007721], [0.084717, -0.010345, 0.007721, 0.052034]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_FXI=0.5022, w_ETH-USD=0.4978, w_IYR=0.0000, w_DBB=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_FXI=0.5022, w_ETH-USD=0.4978, w_IYR=0.0000, w_DBB=0.0000
Portfolio annualized return: 106.61%, volatility: 35.54%
Sharpe ratio: (1.0661 - 0.0400) / 0.3554 = 2.8875


4-asset optimization. Max-Sharpe: -2.112. Portfolio: return=-31.00%, vol=16.57%. Weights: w_XLRE=0.2500, w_MATIC-USD=0.2500, w_ICSH=0.2500, w_HAUZ=0.2500.

Question:
Assets: XLRE, MATIC-USD, ICSH, HAUZ
Annualized mean returns: XLRE:0.2946, MATIC-USD:-1.5821, ICSH:0.0613, HAUZ:-0.0138
Covariance matrix (annualized):
[[0.01929, -0.001784, 0.000119, 0.01513], [-0.001784, 0.333866, 0.000725, 0.016101], [0.000119, 0.000725, 1.5e-05, 0.000224], [0.01513, 0.016101, 0.000224, 0.025135]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: bull

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_XLRE=0.2500, w_MATIC-USD=0.2500, w_ICSH=0.2500, w_HAUZ=0.2500

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLRE=0.2500, w_MATIC-USD=0.2500, w_ICSH=0.2500, w_HAUZ=0.2500
Portfolio annualized return: -31.00%, volatility: 16.57%
Sharpe ratio: (-0.3100 - 0.0400) / 0.1657 = -2.1123


4-asset optimization. Max-Sharpe: 0.912. Portfolio: return=18.68%, vol=16.11%. Weights: w_IWM=1.0000, w_AVAX-USD=0.0000, w_HYG=0.0000, w_HAUZ=0.0000.

Question:
Assets: IWM, AVAX-USD, HYG, HAUZ
Annualized mean returns: IWM:0.1868, AVAX-USD:0.0607, HYG:0.0430, HAUZ:-0.1415
Covariance matrix (annualized):
[[0.025954, 0.058108, 0.003242, 0.013151], [0.058108, 0.347913, 0.009667, 0.043534], [0.003242, 0.009667, 0.00104, 0.002489], [0.013151, 0.043534, 0.002489, 0.019066]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_IWM=1.0000, w_AVAX-USD=0.0000, w_HYG=0.0000, w_HAUZ=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_IWM=1.0000, w_AVAX-USD=0.0000, w_HYG=0.0000, w_HAUZ=0.0000
Portfolio annualized return: 18.68%, volatility: 16.11%
Sharpe ratio: (0.1868 - 0.0400) / 0.1611 = 0.9115


4-asset optimization. Max-Sharpe: 1.226. Portfolio: return=5.43%, vol=1.17%. Weights: w_MTUM=0.0864, w_BTC-USD=0.0000, w_ICSH=0.9136, w_GLD=0.0000.

Question:
Assets: MTUM, BTC-USD, ICSH, GLD
Annualized mean returns: MTUM:0.1763, BTC-USD:0.0962, ICSH:0.0428, GLD:0.0016
Covariance matrix (annualized):
[[0.016242, 0.004373, -0.000118, -0.002136], [0.004373, 0.121687, 0.000384, 0.010152], [-0.000118, 0.000384, 4e-05, 0.000392], [-0.002136, 0.010152, 0.000392, 0.018414]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_MTUM=0.0864, w_BTC-USD=0.0000, w_ICSH=0.9136, w_GLD=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_MTUM=0.0864, w_BTC-USD=0.0000, w_ICSH=0.9136, w_GLD=0.0000
Portfolio annualized return: 5.43%, volatility: 1.17%
Sharpe ratio: (0.0543 - 0.0400) / 0.0117 = 1.2259


4-asset optimization. Max-Sharpe: 1.615. Portfolio: return=29.56%, vol=15.83%. Weights: w_VLUE=0.0000, w_LINK-USD=0.0000, w_ITB=0.5284, w_CSHI=0.4716.

Question:
Assets: VLUE, LINK-USD, ITB, CSHI
Annualized mean returns: VLUE:-0.1705, LINK-USD:-2.5193, ITB:0.5211, CSHI:0.0431
Covariance matrix (annualized):
[[0.024914, 0.042995, 0.028895, 0.000871], [0.042995, 0.46203, 0.052583, 0.006003], [0.028895, 0.052583, 0.088916, 0.000376], [0.000871, 0.006003, 0.000376, 0.000214]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_VLUE=0.0000, w_LINK-USD=0.0000, w_ITB=0.5284, w_CSHI=0.4716

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VLUE=0.0000, w_LINK-USD=0.0000, w_ITB=0.5284, w_CSHI=0.4716
Portfolio annualized return: 29.56%, volatility: 15.83%
Sharpe ratio: (0.2956 - 0.0400) / 0.1583 = 1.6149


4-asset optimization. Max-Sharpe: 3.561. Portfolio: return=5.02%, vol=0.29%. Weights: w_^VIX=0.0004, w_ADA-USD=0.0028, w_TLH=0.0000, w_BIL=0.9967.

Question:
Assets: ^VIX, ADA-USD, TLH, BIL
Annualized mean returns: ^VIX:1.0745, ADA-USD:0.5335, TLH:-0.1045, BIL:0.0484
Covariance matrix (annualized):
[[1.506865, -0.213697, 0.027192, 0.000835], [-0.213697, 0.253579, -0.002129, -0.000238], [0.027192, -0.002129, 0.00834, 4.3e-05], [0.000835, -0.000238, 4.3e-05, 7e-06]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_^VIX=0.0004, w_ADA-USD=0.0028, w_TLH=0.0000, w_BIL=0.9967

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_^VIX=0.0004, w_ADA-USD=0.0028, w_TLH=0.0000, w_BIL=0.9967
Portfolio annualized return: 5.02%, volatility: 0.29%
Sharpe ratio: (0.0502 - 0.0400) / 0.0029 = 3.5612


4-asset optimization. Max-Sharpe: 2.055. Portfolio: return=76.66%, vol=35.35%. Weights: w_^VIX=0.0330, w_SOL-USD=0.3588, w_INDS=0.6082, w_PALL=0.0000.

Question:
Assets: ^VIX, SOL-USD, INDS, PALL
Annualized mean returns: ^VIX:0.2152, SOL-USD:1.7355, INDS:0.2249, PALL:-0.5447
Covariance matrix (annualized):
[[0.387122, 0.095463, -0.027779, -0.03489], [0.095463, 0.774742, 0.017296, -0.014704], [-0.027779, 0.017296, 0.043598, 0.023178], [-0.03489, -0.014704, 0.023178, 0.163033]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_^VIX=0.0330, w_SOL-USD=0.3588, w_INDS=0.6082, w_PALL=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_^VIX=0.0330, w_SOL-USD=0.3588, w_INDS=0.6082, w_PALL=0.0000
Portfolio annualized return: 76.66%, volatility: 35.35%
Sharpe ratio: (0.7666 - 0.0400) / 0.3535 = 2.0552


4-asset optimization. Max-Sharpe: 0.454. Portfolio: return=12.71%, vol=19.19%. Weights: w_XLE=0.0000, w_LINK-USD=0.0000, w_ITB=0.0000, w_DBB=1.0000.

Question:
Assets: XLE, LINK-USD, ITB, DBB
Annualized mean returns: XLE:-0.0203, LINK-USD:-0.9224, ITB:-0.5166, DBB:0.1271
Covariance matrix (annualized):
[[0.02745, 0.020146, 0.011577, 0.007979], [0.020146, 0.391625, 0.023145, 0.032381], [0.011577, 0.023145, 0.059735, 0.010214], [0.007979, 0.032381, 0.010214, 0.036821]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_XLE=0.0000, w_LINK-USD=0.0000, w_ITB=0.0000, w_DBB=1.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLE=0.0000, w_LINK-USD=0.0000, w_ITB=0.0000, w_DBB=1.0000
Portfolio annualized return: 12.71%, volatility: 19.19%
Sharpe ratio: (0.1271 - 0.0400) / 0.1919 = 0.4539


4-asset optimization. Max-Sharpe: 3.836. Portfolio: return=102.30%, vol=25.62%. Weights: w_XLP=0.0000, w_DOT-USD=0.0183, w_SLV=0.9817, w_IYR=0.0000.

Question:
Assets: XLP, DOT-USD, SLV, IYR
Annualized mean returns: XLP:0.0472, DOT-USD:0.7284, SLV:1.0285, IYR:0.0153
Covariance matrix (annualized):
[[0.007614, 0.00415, 0.001028, 0.006848], [0.00415, 0.47119, 0.038049, 0.017802], [0.001028, 0.038049, 0.066548, 0.012463], [0.006848, 0.017802, 0.012463, 0.027008]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_XLP=0.0000, w_DOT-USD=0.0183, w_SLV=0.9817, w_IYR=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLP=0.0000, w_DOT-USD=0.0183, w_SLV=0.9817, w_IYR=0.0000
Portfolio annualized return: 102.30%, volatility: 25.62%
Sharpe ratio: (1.0230 - 0.0400) / 0.2562 = 3.8363


4-asset optimization. Max-Sharpe: -3.132. Portfolio: return=-44.86%, vol=15.60%. Weights: w_XLV=0.2500, w_MATIC-USD=0.2500, w_BIL=0.2500, w_GLD=0.2500.

Question:
Assets: XLV, MATIC-USD, BIL, GLD
Annualized mean returns: XLV:0.0580, MATIC-USD:-2.0503, BIL:0.0528, GLD:0.1451
Covariance matrix (annualized):
[[0.011935, 0.00668, -4e-06, 0.004862], [0.00668, 0.317839, 3e-05, 0.005049], [-4e-06, 3e-05, 5e-06, -0.00011], [0.004862, 0.005049, -0.00011, 0.02648]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_XLV=0.2500, w_MATIC-USD=0.2500, w_BIL=0.2500, w_GLD=0.2500

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLV=0.2500, w_MATIC-USD=0.2500, w_BIL=0.2500, w_GLD=0.2500
Portfolio annualized return: -44.86%, volatility: 15.60%
Sharpe ratio: (-0.4486 - 0.0400) / 0.1560 = -3.1324


4-asset optimization. Max-Sharpe: 2.635. Portfolio: return=7.79%, vol=1.44%. Weights: w_EEM=0.0643, w_DOT-USD=0.0000, w_CSHI=0.0000, w_SHV=0.9357.

Question:
Assets: EEM, DOT-USD, CSHI, SHV
Annualized mean returns: EEM:0.5997, DOT-USD:-1.9650, CSHI:0.0429, SHV:0.0420
Covariance matrix (annualized):
[[0.046851, 0.060789, 0.00033, 4.4e-05], [0.060789, 0.483653, 0.000656, 0.000245], [0.00033, 0.000656, 4.4e-05, -3e-06], [4.4e-05, 0.000245, -3e-06, 9e-06]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_EEM=0.0643, w_DOT-USD=0.0000, w_CSHI=0.0000, w_SHV=0.9357

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EEM=0.0643, w_DOT-USD=0.0000, w_CSHI=0.0000, w_SHV=0.9357
Portfolio annualized return: 7.79%, volatility: 1.44%
Sharpe ratio: (0.0779 - 0.0400) / 0.0144 = 2.6349


4-asset optimization. Max-Sharpe: 4.218. Portfolio: return=5.26%, vol=0.30%. Weights: w_EFA=0.0000, w_BTC-USD=0.0022, w_SGOV=0.9978, w_USO=0.0000.

Question:
Assets: EFA, BTC-USD, SGOV, USO
Annualized mean returns: EFA:-0.0547, BTC-USD:0.4520, SGOV:0.0517, USO:-0.5411
Covariance matrix (annualized):
[[0.017845, 0.008515, 3.9e-05, 0.017789], [0.008515, 0.151504, -4.6e-05, 0.012518], [3.9e-05, -4.6e-05, 8e-06, -0.000106], [0.017789, 0.012518, -0.000106, 0.132634]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_EFA=0.0000, w_BTC-USD=0.0022, w_SGOV=0.9978, w_USO=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EFA=0.0000, w_BTC-USD=0.0022, w_SGOV=0.9978, w_USO=0.0000
Portfolio annualized return: 5.26%, volatility: 0.30%
Sharpe ratio: (0.0526 - 0.0400) / 0.0030 = 4.2179


4-asset optimization. Max-Sharpe: -0.920. Portfolio: return=-19.97%, vol=26.05%. Weights: w_EWJ=0.2500, w_AVAX-USD=0.2500, w_UNG=0.2500, w_BIL=0.2500.

Question:
Assets: EWJ, AVAX-USD, UNG, BIL
Annualized mean returns: EWJ:0.1722, AVAX-USD:-0.9342, UNG:-0.0858, BIL:0.0489
Covariance matrix (annualized):
[[0.022325, 0.007726, 0.01979, -8e-06], [0.007726, 0.461561, 0.012062, -0.000284], [0.01979, 0.012062, 0.523683, -0.000144], [-8e-06, -0.000284, -0.000144, 9e-06]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_EWJ=0.2500, w_AVAX-USD=0.2500, w_UNG=0.2500, w_BIL=0.2500

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EWJ=0.2500, w_AVAX-USD=0.2500, w_UNG=0.2500, w_BIL=0.2500
Portfolio annualized return: -19.97%, volatility: 26.05%
Sharpe ratio: (-0.1997 - 0.0400) / 0.2605 = -0.9203


4-asset optimization. Max-Sharpe: 2.232. Portfolio: return=4.98%, vol=0.44%. Weights: w_ACWI=0.0000, w_AVAX-USD=0.0000, w_ICSH=1.0000, w_ITB=0.0000.

Question:
Assets: ACWI, AVAX-USD, ICSH, ITB
Annualized mean returns: ACWI:-0.2501, AVAX-USD:-0.7278, ICSH:0.0498, ITB:-0.8431
Covariance matrix (annualized):
[[0.013745, 0.022461, -5.4e-05, 0.019088], [0.022461, 0.199247, 2.7e-05, 0.043517], [-5.4e-05, 2.7e-05, 1.9e-05, -0.000169], [0.019088, 0.043517, -0.000169, 0.06572]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_ACWI=0.0000, w_AVAX-USD=0.0000, w_ICSH=1.0000, w_ITB=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_ACWI=0.0000, w_AVAX-USD=0.0000, w_ICSH=1.0000, w_ITB=0.0000
Portfolio annualized return: 4.98%, volatility: 0.44%
Sharpe ratio: (0.0498 - 0.0400) / 0.0044 = 2.2324


4-asset optimization. Max-Sharpe: 6.845. Portfolio: return=5.97%, vol=0.29%. Weights: w_FXI=0.0000, w_LINK-USD=0.0031, w_SGOV=0.9957, w_ITB=0.0012.

Question:
Assets: FXI, LINK-USD, SGOV, ITB
Annualized mean returns: FXI:-0.2322, LINK-USD:2.5217, SGOV:0.0518, ITB:0.2944
Covariance matrix (annualized):
[[0.066841, 0.018625, -0.000128, 0.033218], [0.018625, 0.52183, -0.000589, 0.018529], [-0.000128, -0.000589, 7e-06, -5.2e-05], [0.033218, 0.018529, -5.2e-05, 0.081641]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_FXI=0.0000, w_LINK-USD=0.0031, w_SGOV=0.9957, w_ITB=0.0012

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_FXI=0.0000, w_LINK-USD=0.0031, w_SGOV=0.9957, w_ITB=0.0012
Portfolio annualized return: 5.97%, volatility: 0.29%
Sharpe ratio: (0.0597 - 0.0400) / 0.0029 = 6.8453


4-asset optimization. Max-Sharpe: 0.531. Portfolio: return=33.59%, vol=55.71%. Weights: w_XLU=0.0000, w_BTC-USD=1.0000, w_TLT=0.0000, w_CPER=0.0000.

Question:
Assets: XLU, BTC-USD, TLT, CPER
Annualized mean returns: XLU:-0.1693, BTC-USD:0.3359, TLT:-0.1143, CPER:0.0113
Covariance matrix (annualized):
[[0.042468, 0.015332, 0.001338, -0.01211], [0.015332, 0.310341, -0.00102, 0.009915], [0.001338, -0.00102, 0.033041, -0.007284], [-0.01211, 0.009915, -0.007284, 0.048272]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_XLU=0.0000, w_BTC-USD=1.0000, w_TLT=0.0000, w_CPER=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLU=0.0000, w_BTC-USD=1.0000, w_TLT=0.0000, w_CPER=0.0000
Portfolio annualized return: 33.59%, volatility: 55.71%
Sharpe ratio: (0.3359 - 0.0400) / 0.5571 = 0.5311


4-asset optimization. Max-Sharpe: 0.521. Portfolio: return=16.37%, vol=23.73%. Weights: w_FXI=0.0000, w_SOL-USD=0.0803, w_ICSH=0.0000, w_PPLT=0.9197.

Question:
Assets: FXI, SOL-USD, ICSH, PPLT
Annualized mean returns: FXI:-0.2790, SOL-USD:0.0870, ICSH:0.0382, PPLT:0.1704
Covariance matrix (annualized):
[[0.087632, -0.007376, -0.000445, 0.012707], [-0.007376, 0.341919, 0.000157, -0.00661], [-0.000445, 0.000157, 5.2e-05, 0.000229], [0.012707, -0.00661, 0.000229, 0.065106]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_FXI=0.0000, w_SOL-USD=0.0803, w_ICSH=0.0000, w_PPLT=0.9197

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_FXI=0.0000, w_SOL-USD=0.0803, w_ICSH=0.0000, w_PPLT=0.9197
Portfolio annualized return: 16.37%, volatility: 23.73%
Sharpe ratio: (0.1637 - 0.0400) / 0.2373 = 0.5213


4-asset optimization. Max-Sharpe: 2.358. Portfolio: return=60.74%, vol=24.06%. Weights: w_XLB=0.0000, w_AVAX-USD=0.0000, w_ICSH=0.0000, w_MORT=1.0000.

Question:
Assets: XLB, AVAX-USD, ICSH, MORT
Annualized mean returns: XLB:0.0958, AVAX-USD:-0.4983, ICSH:0.0362, MORT:0.6074
Covariance matrix (annualized):
[[0.030918, 0.024772, -0.000252, 0.028488], [0.024772, 0.243117, 0.00031, 0.028603], [-0.000252, 0.00031, 4.4e-05, -0.0], [0.028488, 0.028603, -0.0, 0.057892]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_XLB=0.0000, w_AVAX-USD=0.0000, w_ICSH=0.0000, w_MORT=1.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLB=0.0000, w_AVAX-USD=0.0000, w_ICSH=0.0000, w_MORT=1.0000
Portfolio annualized return: 60.74%, volatility: 24.06%
Sharpe ratio: (0.6074 - 0.0400) / 0.2406 = 2.3581


4-asset optimization. Max-Sharpe: 2.589. Portfolio: return=80.03%, vol=29.37%. Weights: w_XLY=0.0000, w_LINK-USD=0.0000, w_SLV=1.0000, w_EMB=0.0000.

Question:
Assets: XLY, LINK-USD, SLV, EMB
Annualized mean returns: XLY:-0.0265, LINK-USD:-2.2379, SLV:0.8003, EMB:0.0365
Covariance matrix (annualized):
[[0.026856, 0.034647, 0.003245, 0.007849], [0.034647, 0.389665, 0.016028, 0.013923], [0.003245, 0.016028, 0.08626, 0.001416], [0.007849, 0.013923, 0.001416, 0.006824]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_XLY=0.0000, w_LINK-USD=0.0000, w_SLV=1.0000, w_EMB=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLY=0.0000, w_LINK-USD=0.0000, w_SLV=1.0000, w_EMB=0.0000
Portfolio annualized return: 80.03%, volatility: 29.37%
Sharpe ratio: (0.8003 - 0.0400) / 0.2937 = 2.5885


4-asset optimization. Max-Sharpe: 1.949. Portfolio: return=30.66%, vol=13.68%. Weights: w_XLU=0.6672, w_LINK-USD=0.0913, w_CPER=0.2414, w_IYR=0.0000.

Question:
Assets: XLU, LINK-USD, CPER, IYR
Annualized mean returns: XLU:0.2778, LINK-USD:0.6347, CPER:0.2622, IYR:0.0500
Covariance matrix (annualized):
[[0.025088, 0.003974, -0.001734, 0.011172], [0.003974, 0.302645, 0.047316, 0.012109], [-0.001734, 0.047316, 0.051453, -0.001138], [0.011172, 0.012109, -0.001138, 0.015088]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_XLU=0.6672, w_LINK-USD=0.0913, w_CPER=0.2414, w_IYR=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLU=0.6672, w_LINK-USD=0.0913, w_CPER=0.2414, w_IYR=0.0000
Portfolio annualized return: 30.66%, volatility: 13.68%
Sharpe ratio: (0.3066 - 0.0400) / 0.1368 = 1.9495


4-asset optimization. Max-Sharpe: -2.330. Portfolio: return=-50.01%, vol=23.18%. Weights: w_EFA=0.2500, w_SOL-USD=0.2500, w_XHB=0.2500, w_BIL=0.2500.

Question:
Assets: EFA, SOL-USD, XHB, BIL
Annualized mean returns: EFA:-0.1376, SOL-USD:-2.0565, XHB:0.1481, BIL:0.0457
Covariance matrix (annualized):
[[0.025065, 0.029383, 0.028067, -5.2e-05], [0.029383, 0.601283, 0.028611, -0.000449], [0.028067, 0.028611, 0.062077, 3.2e-05], [-5.2e-05, -0.000449, 3.2e-05, 6e-06]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_EFA=0.2500, w_SOL-USD=0.2500, w_XHB=0.2500, w_BIL=0.2500

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EFA=0.2500, w_SOL-USD=0.2500, w_XHB=0.2500, w_BIL=0.2500
Portfolio annualized return: -50.01%, volatility: 23.18%
Sharpe ratio: (-0.5001 - 0.0400) / 0.2318 = -2.3301


4-asset optimization. Max-Sharpe: 9.845. Portfolio: return=9.25%, vol=0.53%. Weights: w_XLY=0.0124, w_SOL-USD=0.0010, w_BIL=0.9761, w_ITB=0.0105.

Question:
Assets: XLY, SOL-USD, BIL, ITB
Annualized mean returns: XLY:1.1777, SOL-USD:6.0071, BIL:0.0516, ITB:2.0580
Covariance matrix (annualized):
[[0.023814, 0.040106, -3.2e-05, 0.029829], [0.040106, 1.420277, 0.000557, 0.072659], [-3.2e-05, 0.000557, 6e-06, -1.9e-05], [0.029829, 0.072659, -1.9e-05, 0.063969]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_XLY=0.0124, w_SOL-USD=0.0010, w_BIL=0.9761, w_ITB=0.0105

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLY=0.0124, w_SOL-USD=0.0010, w_BIL=0.9761, w_ITB=0.0105
Portfolio annualized return: 9.25%, volatility: 0.53%
Sharpe ratio: (0.0925 - 0.0400) / 0.0053 = 9.8448


4-asset optimization. Max-Sharpe: 10.261. Portfolio: return=101.08%, vol=9.46%. Weights: w_MTUM=0.6126, w_BTC-USD=0.1360, w_TLT=0.2241, w_SLV=0.0272.

Question:
Assets: MTUM, BTC-USD, TLT, SLV
Annualized mean returns: MTUM:0.9574, BTC-USD:1.3043, TLT:1.0613, SLV:0.3290
Covariance matrix (annualized):
[[0.016299, -0.016681, 0.003138, 0.001445], [-0.016681, 0.175353, -0.006751, -0.017133], [0.003138, -0.006751, 0.036296, 0.010213], [0.001445, -0.017133, 0.010213, 0.066852]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_MTUM=0.6126, w_BTC-USD=0.1360, w_TLT=0.2241, w_SLV=0.0272

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_MTUM=0.6126, w_BTC-USD=0.1360, w_TLT=0.2241, w_SLV=0.0272
Portfolio annualized return: 101.08%, volatility: 9.46%
Sharpe ratio: (1.0108 - 0.0400) / 0.0946 = 10.2615


4-asset optimization. Max-Sharpe: 5.070. Portfolio: return=62.43%, vol=11.52%. Weights: w_XLV=0.5690, w_DOT-USD=0.0283, w_PALL=0.0000, w_VNQI=0.4027.

Question:
Assets: XLV, DOT-USD, PALL, VNQI
Annualized mean returns: XLV:0.5005, DOT-USD:1.7897, PALL:-0.2708, VNQI:0.7173
Covariance matrix (annualized):
[[0.012051, 0.018779, 0.012123, 0.007647], [0.018779, 0.75239, -0.052408, 0.01939], [0.012123, -0.052408, 0.184705, 0.031163], [0.007647, 0.01939, 0.031163, 0.026064]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_XLV=0.5690, w_DOT-USD=0.0283, w_PALL=0.0000, w_VNQI=0.4027

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLV=0.5690, w_DOT-USD=0.0283, w_PALL=0.0000, w_VNQI=0.4027
Portfolio annualized return: 62.43%, volatility: 11.52%
Sharpe ratio: (0.6243 - 0.0400) / 0.1152 = 5.0697


4-asset optimization. Max-Sharpe: 2.563. Portfolio: return=6.09%, vol=0.82%. Weights: w_VEA=0.0511, w_LINK-USD=0.0029, w_SCHH=0.0000, w_SHV=0.9460.

Question:
Assets: VEA, LINK-USD, SCHH, SHV
Annualized mean returns: VEA:0.3197, LINK-USD:0.4928, SCHH:-0.0469, SHV:0.0456
Covariance matrix (annualized):
[[0.013435, 0.00647, 0.010368, 0.000195], [0.00647, 0.384926, 0.010496, -9e-06], [0.010368, 0.010496, 0.027179, 0.000301], [0.000195, -9e-06, 0.000301, 8e-06]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_VEA=0.0511, w_LINK-USD=0.0029, w_SCHH=0.0000, w_SHV=0.9460

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VEA=0.0511, w_LINK-USD=0.0029, w_SCHH=0.0000, w_SHV=0.9460
Portfolio annualized return: 6.09%, volatility: 0.82%
Sharpe ratio: (0.0609 - 0.0400) / 0.0082 = 2.5628


4-asset optimization. Max-Sharpe: 2.596. Portfolio: return=18.11%, vol=5.43%. Weights: w_FXI=0.0000, w_XRP-USD=0.0000, w_USO=0.0151, w_BNDX=0.9849.

Question:
Assets: FXI, XRP-USD, USO, BNDX
Annualized mean returns: FXI:-0.7491, XRP-USD:-1.0670, USO:0.1672, BNDX:0.1813
Covariance matrix (annualized):
[[0.085991, -0.016309, 0.009207, -7.9e-05], [-0.016309, 0.173684, -0.050082, 0.000622], [0.009207, -0.050082, 0.093842, 0.001266], [-7.9e-05, 0.000622, 0.001266, 0.002982]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_FXI=0.0000, w_XRP-USD=0.0000, w_USO=0.0151, w_BNDX=0.9849

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_FXI=0.0000, w_XRP-USD=0.0000, w_USO=0.0151, w_BNDX=0.9849
Portfolio annualized return: 18.11%, volatility: 5.43%
Sharpe ratio: (0.1811 - 0.0400) / 0.0543 = 2.5964


4-asset optimization. Max-Sharpe: 2.184. Portfolio: return=7.51%, vol=1.61%. Weights: w_XLF=0.0000, w_SOL-USD=0.0127, w_CSHI=0.9732, w_VNQ=0.0140.

Question:
Assets: XLF, SOL-USD, CSHI, VNQ
Annualized mean returns: XLF:0.1364, SOL-USD:1.7974, CSHI:0.0491, VNQ:0.3188
Covariance matrix (annualized):
[[0.026931, 0.03615, 0.000595, 0.029549], [0.03615, 0.952028, 2.6e-05, 0.055591], [0.000595, 2.6e-05, 5.9e-05, 0.000626], [0.029549, 0.055591, 0.000626, 0.05248]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_XLF=0.0000, w_SOL-USD=0.0127, w_CSHI=0.9732, w_VNQ=0.0140

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLF=0.0000, w_SOL-USD=0.0127, w_CSHI=0.9732, w_VNQ=0.0140
Portfolio annualized return: 7.51%, volatility: 1.61%
Sharpe ratio: (0.0751 - 0.0400) / 0.0161 = 2.1840


4-asset optimization. Max-Sharpe: 2.928. Portfolio: return=62.67%, vol=20.04%. Weights: w_XLP=0.0000, w_DOT-USD=0.0000, w_BIL=0.0000, w_DBB=1.0000.

Question:
Assets: XLP, DOT-USD, BIL, DBB
Annualized mean returns: XLP:-0.1398, DOT-USD:-0.2729, BIL:0.0382, DBB:0.6267
Covariance matrix (annualized):
[[0.020454, 0.022362, -0.000108, 0.009738], [0.022362, 0.240995, 0.000273, 0.045209], [-0.000108, 0.000273, 1.1e-05, -6.7e-05], [0.009738, 0.045209, -6.7e-05, 0.040157]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_XLP=0.0000, w_DOT-USD=0.0000, w_BIL=0.0000, w_DBB=1.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLP=0.0000, w_DOT-USD=0.0000, w_BIL=0.0000, w_DBB=1.0000
Portfolio annualized return: 62.67%, volatility: 20.04%
Sharpe ratio: (0.6267 - 0.0400) / 0.2004 = 2.9280


4-asset optimization. Max-Sharpe: 2.895. Portfolio: return=100.00%, vol=33.17%. Weights: w_USMV=0.5442, w_XRP-USD=0.4558, w_TIP=0.0000, w_ICSH=0.0000.

Question:
Assets: USMV, XRP-USD, TIP, ICSH
Annualized mean returns: USMV:0.0697, XRP-USD:2.1108, TIP:-0.0142, ICSH:0.0340
Covariance matrix (annualized):
[[0.008893, -0.003154, 0.000208, -8.1e-05], [-0.003154, 0.524312, 0.000403, -0.000183], [0.000208, 0.000403, 0.000368, 3.1e-05], [-8.1e-05, -0.000183, 3.1e-05, 1.8e-05]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_USMV=0.5442, w_XRP-USD=0.4558, w_TIP=0.0000, w_ICSH=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_USMV=0.5442, w_XRP-USD=0.4558, w_TIP=0.0000, w_ICSH=0.0000
Portfolio annualized return: 100.00%, volatility: 33.17%
Sharpe ratio: (1.0000 - 0.0400) / 0.3317 = 2.8946


4-asset optimization. Max-Sharpe: -1.067. Portfolio: return=-19.25%, vol=21.79%. Weights: w_EFA=0.2500, w_DOT-USD=0.2500, w_GLD=0.2500, w_BIL=0.2500.

Question:
Assets: EFA, DOT-USD, GLD, BIL
Annualized mean returns: EFA:0.0722, DOT-USD:-1.7710, GLD:0.8767, BIL:0.0523
Covariance matrix (annualized):
[[0.011506, 0.032009, 0.002317, 6e-06], [0.032009, 0.606405, 0.025496, 6.3e-05], [0.002317, 0.025496, 0.022066, -4e-06], [6e-06, 6.3e-05, -4e-06, 7e-06]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_EFA=0.2500, w_DOT-USD=0.2500, w_GLD=0.2500, w_BIL=0.2500

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EFA=0.2500, w_DOT-USD=0.2500, w_GLD=0.2500, w_BIL=0.2500
Portfolio annualized return: -19.25%, volatility: 21.79%
Sharpe ratio: (-0.1925 - 0.0400) / 0.2179 = -1.0668


4-asset optimization. Max-Sharpe: 8.248. Portfolio: return=106.61%, vol=12.44%. Weights: w_USMV=0.3627, w_ADA-USD=0.0698, w_INDS=0.1897, w_TLH=0.3777.

Question:
Assets: USMV, ADA-USD, INDS, TLH
Annualized mean returns: USMV:0.5430, ADA-USD:4.0000, INDS:1.4835, TLH:0.8166
Covariance matrix (annualized):
[[0.010465, 0.015544, 0.011276, 0.001503], [0.015544, 0.732192, 0.026769, -0.00554], [0.011276, 0.026769, 0.04816, 0.01768], [0.001503, -0.00554, 0.01768, 0.021712]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_USMV=0.3627, w_ADA-USD=0.0698, w_INDS=0.1897, w_TLH=0.3777

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_USMV=0.3627, w_ADA-USD=0.0698, w_INDS=0.1897, w_TLH=0.3777
Portfolio annualized return: 106.61%, volatility: 12.44%
Sharpe ratio: (1.0661 - 0.0400) / 0.1244 = 8.2478


4-asset optimization. Max-Sharpe: 6.266. Portfolio: return=5.53%, vol=0.24%. Weights: w_VTI=0.0064, w_LINK-USD=0.0000, w_SOYB=0.0023, w_SHV=0.9913.

Question:
Assets: VTI, LINK-USD, SOYB, SHV
Annualized mean returns: VTI:0.2865, LINK-USD:1.0016, SOYB:0.0551, SHV:0.0538
Covariance matrix (annualized):
[[0.029795, 0.076981, -0.002672, -9.1e-05], [0.076981, 0.523328, -0.025418, 7e-06], [-0.002672, -0.025418, 0.033357, -5.4e-05], [-9.1e-05, 7e-06, -5.4e-05, 6e-06]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_VTI=0.0064, w_LINK-USD=0.0000, w_SOYB=0.0023, w_SHV=0.9913

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VTI=0.0064, w_LINK-USD=0.0000, w_SOYB=0.0023, w_SHV=0.9913
Portfolio annualized return: 5.53%, volatility: 0.24%
Sharpe ratio: (0.0553 - 0.0400) / 0.0024 = 6.2656


4-asset optimization. Max-Sharpe: 4.874. Portfolio: return=5.23%, vol=0.25%. Weights: w_IWM=0.0014, w_MATIC-USD=0.0000, w_SHV=0.9736, w_CSHI=0.0250.

Question:
Assets: IWM, MATIC-USD, SHV, CSHI
Annualized mean returns: IWM:0.2644, MATIC-USD:0.0191, SHV:0.0516, CSHI:0.0666
Covariance matrix (annualized):
[[0.047984, 0.061278, 1.2e-05, 0.001495], [0.061278, 0.506421, 7.6e-05, 0.006695], [1.2e-05, 7.6e-05, 6e-06, 2e-06], [0.001495, 0.006695, 2e-06, 0.000403]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_IWM=0.0014, w_MATIC-USD=0.0000, w_SHV=0.9736, w_CSHI=0.0250

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_IWM=0.0014, w_MATIC-USD=0.0000, w_SHV=0.9736, w_CSHI=0.0250
Portfolio annualized return: 5.23%, volatility: 0.25%
Sharpe ratio: (0.0523 - 0.0400) / 0.0025 = 4.8738


4-asset optimization. Max-Sharpe: 1.236. Portfolio: return=4.55%, vol=0.44%. Weights: w_VEA=0.0000, w_XRP-USD=0.0064, w_SHV=0.9834, w_REZ=0.0102.

Question:
Assets: VEA, XRP-USD, SHV, REZ
Annualized mean returns: VEA:0.0374, XRP-USD:0.3973, SHV:0.0423, REZ:0.1329
Covariance matrix (annualized):
[[0.01756, 0.01006, 7.4e-05, 0.009968], [0.01006, 0.200608, -9.2e-05, 0.008176], [7.4e-05, -9.2e-05, 9e-06, -2.7e-05], [0.009968, 0.008176, -2.7e-05, 0.030105]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_VEA=0.0000, w_XRP-USD=0.0064, w_SHV=0.9834, w_REZ=0.0102

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VEA=0.0000, w_XRP-USD=0.0064, w_SHV=0.9834, w_REZ=0.0102
Portfolio annualized return: 4.55%, volatility: 0.44%
Sharpe ratio: (0.0455 - 0.0400) / 0.0044 = 1.2365


4-asset optimization. Max-Sharpe: -0.581. Portfolio: return=-7.27%, vol=19.40%. Weights: w_XLE=1.0000, w_ADA-USD=0.0000, w_XHB=0.0000, w_HYG=0.0000.

Question:
Assets: XLE, ADA-USD, XHB, HYG
Annualized mean returns: XLE:-0.0727, ADA-USD:-0.8953, XHB:-0.6681, HYG:-0.1042
Covariance matrix (annualized):
[[0.037642, 0.014846, 0.003677, 0.001379], [0.014846, 0.104112, 0.025172, 0.007089], [0.003677, 0.025172, 0.049791, 0.010189], [0.001379, 0.007089, 0.010189, 0.003472]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_XLE=1.0000, w_ADA-USD=0.0000, w_XHB=0.0000, w_HYG=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLE=1.0000, w_ADA-USD=0.0000, w_XHB=0.0000, w_HYG=0.0000
Portfolio annualized return: -7.27%, volatility: 19.40%
Sharpe ratio: (-0.0727 - 0.0400) / 0.1940 = -0.5807


4-asset optimization. Max-Sharpe: 0.725. Portfolio: return=9.92%, vol=8.17%. Weights: w_VTI=0.0000, w_BTC-USD=0.0000, w_PDBC=1.0000, w_IEF=0.0000.

Question:
Assets: VTI, BTC-USD, PDBC, IEF
Annualized mean returns: VTI:-0.3080, BTC-USD:-0.4482, PDBC:0.0992, IEF:-0.1947
Covariance matrix (annualized):
[[0.013044, 0.013668, 0.003112, 0.002102], [0.013668, 0.109253, 0.000123, 0.007105], [0.003112, 0.000123, 0.00668, 0.001365], [0.002102, 0.007105, 0.001365, 0.005153]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_VTI=0.0000, w_BTC-USD=0.0000, w_PDBC=1.0000, w_IEF=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VTI=0.0000, w_BTC-USD=0.0000, w_PDBC=1.0000, w_IEF=0.0000
Portfolio annualized return: 9.92%, volatility: 8.17%
Sharpe ratio: (0.0992 - 0.0400) / 0.0817 = 0.7246


4-asset optimization. Max-Sharpe: 0.563. Portfolio: return=11.19%, vol=12.79%. Weights: w_VEA=1.0000, w_AVAX-USD=0.0000, w_VNQI=0.0000, w_ICSH=0.0000.

Question:
Assets: VEA, AVAX-USD, VNQI, ICSH
Annualized mean returns: VEA:0.1119, AVAX-USD:-0.6947, VNQI:-0.0272, ICSH:0.0329
Covariance matrix (annualized):
[[0.016353, 0.016743, 0.016106, -0.000348], [0.016743, 0.243188, 0.024204, -0.000133], [0.016106, 0.024204, 0.024719, -0.000206], [-0.000348, -0.000133, -0.000206, 5.1e-05]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_VEA=1.0000, w_AVAX-USD=0.0000, w_VNQI=0.0000, w_ICSH=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VEA=1.0000, w_AVAX-USD=0.0000, w_VNQI=0.0000, w_ICSH=0.0000
Portfolio annualized return: 11.19%, volatility: 12.79%
Sharpe ratio: (0.1119 - 0.0400) / 0.1279 = 0.5626


4-asset optimization. Max-Sharpe: 1.138. Portfolio: return=15.73%, vol=10.30%. Weights: w_EWJ=0.0000, w_AVAX-USD=0.0000, w_DBC=1.0000, w_INDS=0.0000.

Question:
Assets: EWJ, AVAX-USD, DBC, INDS
Annualized mean returns: EWJ:-0.1213, AVAX-USD:-4.3635, DBC:0.1573, INDS:-0.1235
Covariance matrix (annualized):
[[0.021469, 0.03408, 0.000991, 0.018098], [0.03408, 0.54029, 0.012077, 0.041965], [0.000991, 0.012077, 0.010612, 0.001234], [0.018098, 0.041965, 0.001234, 0.03811]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: bull

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_EWJ=0.0000, w_AVAX-USD=0.0000, w_DBC=1.0000, w_INDS=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EWJ=0.0000, w_AVAX-USD=0.0000, w_DBC=1.0000, w_INDS=0.0000
Portfolio annualized return: 15.73%, volatility: 10.30%
Sharpe ratio: (0.1573 - 0.0400) / 0.1030 = 1.1383


4-asset optimization. Max-Sharpe: -1.220. Portfolio: return=-75.05%, vol=64.81%. Weights: w_XLU=0.0000, w_MATIC-USD=1.0000, w_PALL=0.0000, w_SCHH=0.0000.

Question:
Assets: XLU, MATIC-USD, PALL, SCHH
Annualized mean returns: XLU:-0.3090, MATIC-USD:-0.7505, PALL:-0.0740, SCHH:-0.1278
Covariance matrix (annualized):
[[0.019876, 0.023611, 0.009761, 0.010791], [0.023611, 0.420038, 0.00516, 0.030078], [0.009761, 0.00516, 0.078987, 0.008887], [0.010791, 0.030078, 0.008887, 0.016708]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_XLU=0.0000, w_MATIC-USD=1.0000, w_PALL=0.0000, w_SCHH=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLU=0.0000, w_MATIC-USD=1.0000, w_PALL=0.0000, w_SCHH=0.0000
Portfolio annualized return: -75.05%, volatility: 64.81%
Sharpe ratio: (-0.7505 - 0.0400) / 0.6481 = -1.2198


4-asset optimization. Max-Sharpe: 4.152. Portfolio: return=9.00%, vol=1.21%. Weights: w_XLF=0.0960, w_XRP-USD=0.0000, w_BNDX=0.0000, w_CSHI=0.9040.

Question:
Assets: XLF, XRP-USD, BNDX, CSHI
Annualized mean returns: XLF:0.4318, XRP-USD:0.3184, BNDX:-0.0118, CSHI:0.0538
Covariance matrix (annualized):
[[0.01249, 0.025807, 0.000519, -6.8e-05], [0.025807, 0.928657, 0.016949, 0.002796], [0.000519, 0.016949, 0.001917, 8.5e-05], [-6.8e-05, 0.002796, 8.5e-05, 5.1e-05]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_XLF=0.0960, w_XRP-USD=0.0000, w_BNDX=0.0000, w_CSHI=0.9040

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLF=0.0960, w_XRP-USD=0.0000, w_BNDX=0.0000, w_CSHI=0.9040
Portfolio annualized return: 9.00%, volatility: 1.21%
Sharpe ratio: (0.0900 - 0.0400) / 0.0121 = 4.1518


4-asset optimization. Max-Sharpe: 2.805. Portfolio: return=6.44%, vol=0.87%. Weights: w_QUAL=0.0470, w_BNB-USD=0.0000, w_DBC=0.0000, w_BIL=0.9530.

Question:
Assets: QUAL, BNB-USD, DBC, BIL
Annualized mean returns: QUAL:0.4170, BNB-USD:-1.9528, DBC:-0.3011, BIL:0.0470
Covariance matrix (annualized):
[[0.020429, 0.011789, 0.012192, 0.000218], [0.011789, 0.160987, 0.018248, 7.3e-05], [0.012192, 0.018248, 0.03284, 5.1e-05], [0.000218, 7.3e-05, 5.1e-05, 1.2e-05]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_QUAL=0.0470, w_BNB-USD=0.0000, w_DBC=0.0000, w_BIL=0.9530

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_QUAL=0.0470, w_BNB-USD=0.0000, w_DBC=0.0000, w_BIL=0.9530
Portfolio annualized return: 6.44%, volatility: 0.87%
Sharpe ratio: (0.0644 - 0.0400) / 0.0087 = 2.8049


4-asset optimization. Max-Sharpe: 4.581. Portfolio: return=5.10%, vol=0.24%. Weights: w_EWJ=0.0000, w_DOT-USD=0.0000, w_STIP=0.0200, w_BIL=0.9800.

Question:
Assets: EWJ, DOT-USD, STIP, BIL
Annualized mean returns: EWJ:-0.1524, DOT-USD:-1.0288, STIP:0.0526, BIL:0.0510
Covariance matrix (annualized):
[[0.021025, 0.015202, 0.001143, 3.6e-05], [0.015202, 0.611154, -0.001456, -2.4e-05], [0.001143, -0.001456, 0.000335, -0.0], [3.6e-05, -2.4e-05, -0.0, 6e-06]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_EWJ=0.0000, w_DOT-USD=0.0000, w_STIP=0.0200, w_BIL=0.9800

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EWJ=0.0000, w_DOT-USD=0.0000, w_STIP=0.0200, w_BIL=0.9800
Portfolio annualized return: 5.10%, volatility: 0.24%
Sharpe ratio: (0.0510 - 0.0400) / 0.0024 = 4.5813


4-asset optimization. Max-Sharpe: 0.940. Portfolio: return=14.39%, vol=11.05%. Weights: w_EFA=1.0000, w_BNB-USD=0.0000, w_INDS=0.0000, w_TLH=0.0000.

Question:
Assets: EFA, BNB-USD, INDS, TLH
Annualized mean returns: EFA:0.1439, BNB-USD:0.0524, INDS:-0.1123, TLH:-0.0336
Covariance matrix (annualized):
[[0.012212, 0.006904, 0.01653, 0.005222], [0.006904, 0.172081, 0.001252, 0.00179], [0.01653, 0.001252, 0.039542, 0.013829], [0.005222, 0.00179, 0.013829, 0.012244]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: bull

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_EFA=1.0000, w_BNB-USD=0.0000, w_INDS=0.0000, w_TLH=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EFA=1.0000, w_BNB-USD=0.0000, w_INDS=0.0000, w_TLH=0.0000
Portfolio annualized return: 14.39%, volatility: 11.05%
Sharpe ratio: (0.1439 - 0.0400) / 0.1105 = 0.9398


4-asset optimization. Max-Sharpe: 6.401. Portfolio: return=59.30%, vol=8.64%. Weights: w_XLP=0.7711, w_ADA-USD=0.0742, w_JNK=0.0000, w_PPLT=0.1547.

Question:
Assets: XLP, ADA-USD, JNK, PPLT
Annualized mean returns: XLP:0.4844, ADA-USD:1.3191, JNK:0.1619, PPLT:0.7862
Covariance matrix (annualized):
[[0.009168, -0.012292, 0.002031, -0.001023], [-0.012292, 0.354187, 0.015337, 0.00301], [0.002031, 0.015337, 0.005901, 0.001628], [-0.001023, 0.00301, 0.001628, 0.068754]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_XLP=0.7711, w_ADA-USD=0.0742, w_JNK=0.0000, w_PPLT=0.1547

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLP=0.7711, w_ADA-USD=0.0742, w_JNK=0.0000, w_PPLT=0.1547
Portfolio annualized return: 59.30%, volatility: 8.64%
Sharpe ratio: (0.5930 - 0.0400) / 0.0864 = 6.4008


4-asset optimization. Max-Sharpe: 3.732. Portfolio: return=39.92%, vol=9.63%. Weights: w_VLUE=0.5559, w_DOT-USD=0.0167, w_LQD=0.4274, w_REZ=0.0000.

Question:
Assets: VLUE, DOT-USD, LQD, REZ
Annualized mean returns: VLUE:0.4846, DOT-USD:1.2081, LQD:0.2565, REZ:0.5107
Covariance matrix (annualized):
[[0.017257, 0.02088, 0.003571, 0.020575], [0.02088, 0.916605, 0.007543, 0.051122], [0.003571, 0.007543, 0.008127, 0.007419], [0.020575, 0.051122, 0.007419, 0.03877]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_VLUE=0.5559, w_DOT-USD=0.0167, w_LQD=0.4274, w_REZ=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VLUE=0.5559, w_DOT-USD=0.0167, w_LQD=0.4274, w_REZ=0.0000
Portfolio annualized return: 39.92%, volatility: 9.63%
Sharpe ratio: (0.3992 - 0.0400) / 0.0963 = 3.7315


4-asset optimization. Max-Sharpe: 5.180. Portfolio: return=5.63%, vol=0.32%. Weights: w_IVV=0.0026, w_LINK-USD=0.0000, w_IEF=0.0224, w_BIL=0.9750.

Question:
Assets: IVV, LINK-USD, IEF, BIL
Annualized mean returns: IVV:0.1530, LINK-USD:-0.3484, IEF:0.2610, BIL:0.0514
Covariance matrix (annualized):
[[0.028832, 0.066379, -0.000508, 6e-06], [0.066379, 0.576097, -0.011847, 0.0002], [-0.000508, -0.011847, 0.004285, 4.1e-05], [6e-06, 0.0002, 4.1e-05, 6e-06]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: bull

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_IVV=0.0026, w_LINK-USD=0.0000, w_IEF=0.0224, w_BIL=0.9750

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_IVV=0.0026, w_LINK-USD=0.0000, w_IEF=0.0224, w_BIL=0.9750
Portfolio annualized return: 5.63%, volatility: 0.32%
Sharpe ratio: (0.0563 - 0.0400) / 0.0032 = 5.1796


4-asset optimization. Max-Sharpe: 3.939. Portfolio: return=11.89%, vol=2.00%. Weights: w_VTI=0.0000, w_BTC-USD=0.0254, w_XHB=0.0336, w_CSHI=0.9410.

Question:
Assets: VTI, BTC-USD, XHB, CSHI
Annualized mean returns: VTI:0.2841, BTC-USD:1.2378, XHB:0.8234, CSHI:0.0635
Covariance matrix (annualized):
[[0.033674, 0.037465, 0.039253, 0.000557], [0.037465, 0.138256, 0.041942, 0.00124], [0.039253, 0.041942, 0.065139, 0.000777], [0.000557, 0.00124, 0.000777, 6.6e-05]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_VTI=0.0000, w_BTC-USD=0.0254, w_XHB=0.0336, w_CSHI=0.9410

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VTI=0.0000, w_BTC-USD=0.0254, w_XHB=0.0336, w_CSHI=0.9410
Portfolio annualized return: 11.89%, volatility: 2.00%
Sharpe ratio: (0.1189 - 0.0400) / 0.0200 = 3.9392


4-asset optimization. Max-Sharpe: 0.929. Portfolio: return=19.54%, vol=16.72%. Weights: w_QQQ=1.0000, w_ADA-USD=0.0000, w_SLV=0.0000, w_SCHP=0.0000.

Question:
Assets: QQQ, ADA-USD, SLV, SCHP
Annualized mean returns: QQQ:0.1954, ADA-USD:-0.5192, SLV:0.1504, SCHP:-0.0138
Covariance matrix (annualized):
[[0.027964, 0.039586, 0.024378, 0.004273], [0.039586, 0.488131, 0.046957, 0.016438], [0.024378, 0.046957, 0.067076, 0.010026], [0.004273, 0.016438, 0.010026, 0.003981]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_QQQ=1.0000, w_ADA-USD=0.0000, w_SLV=0.0000, w_SCHP=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_QQQ=1.0000, w_ADA-USD=0.0000, w_SLV=0.0000, w_SCHP=0.0000
Portfolio annualized return: 19.54%, volatility: 16.72%
Sharpe ratio: (0.1954 - 0.0400) / 0.1672 = 0.9293


4-asset optimization. Max-Sharpe: 1.226. Portfolio: return=5.14%, vol=0.93%. Weights: w_EWJ=0.0000, w_DOT-USD=0.0000, w_XHB=0.0000, w_CSHI=1.0000.

Question:
Assets: EWJ, DOT-USD, XHB, CSHI
Annualized mean returns: EWJ:-0.1175, DOT-USD:-1.6393, XHB:-0.3845, CSHI:0.0514
Covariance matrix (annualized):
[[0.022515, 0.011157, 0.018503, 0.000414], [0.011157, 0.105009, 0.01901, 0.000314], [0.018503, 0.01901, 0.053457, 0.000494], [0.000414, 0.000314, 0.000494, 8.7e-05]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_EWJ=0.0000, w_DOT-USD=0.0000, w_XHB=0.0000, w_CSHI=1.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EWJ=0.0000, w_DOT-USD=0.0000, w_XHB=0.0000, w_CSHI=1.0000
Portfolio annualized return: 5.14%, volatility: 0.93%
Sharpe ratio: (0.0514 - 0.0400) / 0.0093 = 1.2264


4-asset optimization. Max-Sharpe: 3.792. Portfolio: return=76.21%, vol=19.04%. Weights: w_XLF=0.1300, w_XRP-USD=0.0000, w_BNO=0.8700, w_SCHP=0.0000.

Question:
Assets: XLF, XRP-USD, BNO, SCHP
Annualized mean returns: XLF:0.1630, XRP-USD:-1.0320, BNO:0.8517, SCHP:-0.1259
Covariance matrix (annualized):
[[0.014732, 0.029337, 0.004898, 0.001655], [0.029337, 1.021827, 0.04342, 0.015384], [0.004898, 0.04342, 0.046108, 0.002887], [0.001655, 0.015384, 0.002887, 0.003663]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_XLF=0.1300, w_XRP-USD=0.0000, w_BNO=0.8700, w_SCHP=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLF=0.1300, w_XRP-USD=0.0000, w_BNO=0.8700, w_SCHP=0.0000
Portfolio annualized return: 76.21%, volatility: 19.04%
Sharpe ratio: (0.7621 - 0.0400) / 0.1904 = 3.7925


4-asset optimization. Max-Sharpe: 5.728. Portfolio: return=5.33%, vol=0.23%. Weights: w_USMV=0.0000, w_XRP-USD=0.0000, w_VCIT=0.0000, w_SGOV=1.0000.

Question:
Assets: USMV, XRP-USD, VCIT, SGOV
Annualized mean returns: USMV:-0.1104, XRP-USD:0.0832, VCIT:-0.2384, SGOV:0.0533
Covariance matrix (annualized):
[[0.008403, 0.000411, 0.003653, -3.5e-05], [0.000411, 0.125621, 0.000678, 2e-05], [0.003653, 0.000678, 0.005195, 5e-06], [-3.5e-05, 2e-05, 5e-06, 5e-06]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_USMV=0.0000, w_XRP-USD=0.0000, w_VCIT=0.0000, w_SGOV=1.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_USMV=0.0000, w_XRP-USD=0.0000, w_VCIT=0.0000, w_SGOV=1.0000
Portfolio annualized return: 5.33%, volatility: 0.23%
Sharpe ratio: (0.0533 - 0.0400) / 0.0023 = 5.7280


4-asset optimization. Max-Sharpe: 5.629. Portfolio: return=60.94%, vol=10.11%. Weights: w_XLY=0.0000, w_DOT-USD=0.0000, w_TLH=0.4427, w_REZ=0.5573.

Question:
Assets: XLY, DOT-USD, TLH, REZ
Annualized mean returns: XLY:-0.2796, DOT-USD:-1.6526, TLH:0.3917, REZ:0.7823
Covariance matrix (annualized):
[[0.070194, 0.058849, -0.002485, 0.011895], [0.058849, 0.286701, -0.018749, 0.032963], [-0.002485, -0.018749, 0.012429, 0.001467], [0.011895, 0.032963, 0.001467, 0.022766]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_XLY=0.0000, w_DOT-USD=0.0000, w_TLH=0.4427, w_REZ=0.5573

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLY=0.0000, w_DOT-USD=0.0000, w_TLH=0.4427, w_REZ=0.5573
Portfolio annualized return: 60.94%, volatility: 10.11%
Sharpe ratio: (0.6094 - 0.0400) / 0.1011 = 5.6291


4-asset optimization. Max-Sharpe: 4.624. Portfolio: return=8.27%, vol=0.92%. Weights: w_XLK=0.0117, w_ETH-USD=0.0150, w_DBB=0.0000, w_ICSH=0.9733.

Question:
Assets: XLK, ETH-USD, DBB, ICSH
Annualized mean returns: XLK:0.4464, ETH-USD:1.8642, DBB:-0.3214, ICSH:0.0508
Covariance matrix (annualized):
[[0.036422, 0.014389, 0.002201, 0.000174], [0.014389, 0.239502, 0.007479, -0.000131], [0.002201, 0.007479, 0.019733, 1.5e-05], [0.000174, -0.000131, 1.5e-05, 2.2e-05]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_XLK=0.0117, w_ETH-USD=0.0150, w_DBB=0.0000, w_ICSH=0.9733

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLK=0.0117, w_ETH-USD=0.0150, w_DBB=0.0000, w_ICSH=0.9733
Portfolio annualized return: 8.27%, volatility: 0.92%
Sharpe ratio: (0.0827 - 0.0400) / 0.0092 = 4.6235


4-asset optimization. Max-Sharpe: 2.058. Portfolio: return=31.39%, vol=13.31%. Weights: w_XLF=1.0000, w_SOL-USD=0.0000, w_CORN=0.0000, w_IGOV=0.0000.

Question:
Assets: XLF, SOL-USD, CORN, IGOV
Annualized mean returns: XLF:0.3139, SOL-USD:-0.7026, CORN:-0.2098, IGOV:-0.1899
Covariance matrix (annualized):
[[0.017722, 0.029116, 0.004333, -0.000355], [0.029116, 0.410599, 0.016091, 0.005022], [0.004333, 0.016091, 0.088735, 0.007974], [-0.000355, 0.005022, 0.007974, 0.008966]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_XLF=1.0000, w_SOL-USD=0.0000, w_CORN=0.0000, w_IGOV=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLF=1.0000, w_SOL-USD=0.0000, w_CORN=0.0000, w_IGOV=0.0000
Portfolio annualized return: 31.39%, volatility: 13.31%
Sharpe ratio: (0.3139 - 0.0400) / 0.1331 = 2.0577


4-asset optimization. Max-Sharpe: 3.390. Portfolio: return=10.87%, vol=2.03%. Weights: w_EFA=0.0000, w_LINK-USD=0.0339, w_DBA=0.0692, w_CSHI=0.8970.

Question:
Assets: EFA, LINK-USD, DBA, CSHI
Annualized mean returns: EFA:-0.0806, LINK-USD:1.3656, DBA:0.1628, CSHI:0.0571
Covariance matrix (annualized):
[[0.016414, 0.017983, 0.003897, 0.000407], [0.017983, 0.247761, -0.007717, 8e-05], [0.003897, -0.007717, 0.010633, 0.000291], [0.000407, 8e-05, 0.000291, 8.9e-05]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_EFA=0.0000, w_LINK-USD=0.0339, w_DBA=0.0692, w_CSHI=0.8970

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EFA=0.0000, w_LINK-USD=0.0339, w_DBA=0.0692, w_CSHI=0.8970
Portfolio annualized return: 10.87%, volatility: 2.03%
Sharpe ratio: (0.1087 - 0.0400) / 0.0203 = 3.3900


4-asset optimization. Max-Sharpe: 2.888. Portfolio: return=46.18%, vol=14.61%. Weights: w_EWJ=0.0000, w_BNB-USD=0.2795, w_DBC=0.7205, w_MORT=0.0000.

Question:
Assets: EWJ, BNB-USD, DBC, MORT
Annualized mean returns: EWJ:0.0736, BNB-USD:0.4855, DBC:0.4525, MORT:-0.0921
Covariance matrix (annualized):
[[0.032273, 0.01505, 0.000638, 0.006664], [0.01505, 0.11918, -0.014959, 0.023971], [0.000638, -0.014959, 0.034769, -0.003208], [0.006664, 0.023971, -0.003208, 0.022821]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_EWJ=0.0000, w_BNB-USD=0.2795, w_DBC=0.7205, w_MORT=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EWJ=0.0000, w_BNB-USD=0.2795, w_DBC=0.7205, w_MORT=0.0000
Portfolio annualized return: 46.18%, volatility: 14.61%
Sharpe ratio: (0.4618 - 0.0400) / 0.1461 = 2.8876


4-asset optimization. Max-Sharpe: 4.289. Portfolio: return=71.10%, vol=15.65%. Weights: w_XLE=0.4423, w_DOT-USD=0.0000, w_TLH=0.0000, w_WEAT=0.5577.

Question:
Assets: XLE, DOT-USD, TLH, WEAT
Annualized mean returns: XLE:0.4224, DOT-USD:-2.0135, TLH:-0.2350, WEAT:0.9399
Covariance matrix (annualized):
[[0.021765, 0.008194, -0.001232, 0.007752], [0.008194, 0.522456, -3e-06, 0.00303], [-0.001232, -3e-06, 0.011817, 0.003234], [0.007752, 0.00303, 0.003234, 0.052717]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_XLE=0.4423, w_DOT-USD=0.0000, w_TLH=0.0000, w_WEAT=0.5577

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLE=0.4423, w_DOT-USD=0.0000, w_TLH=0.0000, w_WEAT=0.5577
Portfolio annualized return: 71.10%, volatility: 15.65%
Sharpe ratio: (0.7110 - 0.0400) / 0.1565 = 4.2888


4-asset optimization. Max-Sharpe: 3.529. Portfolio: return=17.78%, vol=3.91%. Weights: w_QQQ=0.2219, w_XRP-USD=0.0102, w_DBB=0.0000, w_BIL=0.7679.

Question:
Assets: QQQ, XRP-USD, DBB, BIL
Annualized mean returns: QQQ:0.5916, XRP-USD:1.4079, DBB:-0.3365, BIL:0.0419
Covariance matrix (annualized):
[[0.025493, 0.037973, 0.009864, 7.7e-05], [0.037973, 0.693903, 0.021415, -0.00048], [0.009864, 0.021415, 0.028481, 1.8e-05], [7.7e-05, -0.00048, 1.8e-05, 1.2e-05]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_QQQ=0.2219, w_XRP-USD=0.0102, w_DBB=0.0000, w_BIL=0.7679

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_QQQ=0.2219, w_XRP-USD=0.0102, w_DBB=0.0000, w_BIL=0.7679
Portfolio annualized return: 17.78%, volatility: 3.91%
Sharpe ratio: (0.1778 - 0.0400) / 0.0391 = 3.5290


4-asset optimization. Max-Sharpe: 6.623. Portfolio: return=7.99%, vol=0.60%. Weights: w_FXI=0.0116, w_MATIC-USD=0.0000, w_ICSH=0.9752, w_IYR=0.0132.

Question:
Assets: FXI, MATIC-USD, ICSH, IYR
Annualized mean returns: FXI:0.9341, MATIC-USD:0.0441, ICSH:0.0648, IYR:0.4478
Covariance matrix (annualized):
[[0.069414, 0.047225, 2e-06, 0.000356], [0.047225, 0.518682, -0.0, 0.033289], [2e-06, -0.0, 2.1e-05, 0.000121], [0.000356, 0.033289, 0.000121, 0.018925]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_FXI=0.0116, w_MATIC-USD=0.0000, w_ICSH=0.9752, w_IYR=0.0132

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_FXI=0.0116, w_MATIC-USD=0.0000, w_ICSH=0.9752, w_IYR=0.0132
Portfolio annualized return: 7.99%, volatility: 0.60%
Sharpe ratio: (0.0799 - 0.0400) / 0.0060 = 6.6230


4-asset optimization. Max-Sharpe: -0.901. Portfolio: return=-38.24%, vol=46.89%. Weights: w_XLRE=0.0000, w_LINK-USD=1.0000, w_SHV=0.0000, w_HAUZ=0.0000.

Question:
Assets: XLRE, LINK-USD, SHV, HAUZ
Annualized mean returns: XLRE:-0.0702, LINK-USD:-0.3824, SHV:0.0390, HAUZ:-0.0847
Covariance matrix (annualized):
[[0.034597, 0.016196, 1.6e-05, 0.015767], [0.016196, 0.21988, -0.000113, 0.00534], [1.6e-05, -0.000113, 9e-06, -6e-06], [0.015767, 0.00534, -6e-06, 0.022549]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_XLRE=0.0000, w_LINK-USD=1.0000, w_SHV=0.0000, w_HAUZ=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLRE=0.0000, w_LINK-USD=1.0000, w_SHV=0.0000, w_HAUZ=0.0000
Portfolio annualized return: -38.24%, volatility: 46.89%
Sharpe ratio: (-0.3824 - 0.0400) / 0.4689 = -0.9007


4-asset optimization. Max-Sharpe: 5.143. Portfolio: return=5.42%, vol=0.28%. Weights: w_IWM=0.0000, w_LINK-USD=0.0000, w_IEF=0.0196, w_SGOV=0.9804.

Question:
Assets: IWM, LINK-USD, IEF, SGOV
Annualized mean returns: IWM:0.0687, LINK-USD:-0.4407, IEF:0.2025, SGOV:0.0513
Covariance matrix (annualized):
[[0.023923, 0.036532, 0.004861, -6.8e-05], [0.036532, 0.398993, 0.008421, 0.000285], [0.004861, 0.008421, 0.004489, -1e-06], [-6.8e-05, 0.000285, -1e-06, 6e-06]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: bull

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_IWM=0.0000, w_LINK-USD=0.0000, w_IEF=0.0196, w_SGOV=0.9804

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_IWM=0.0000, w_LINK-USD=0.0000, w_IEF=0.0196, w_SGOV=0.9804
Portfolio annualized return: 5.42%, volatility: 0.28%
Sharpe ratio: (0.0542 - 0.0400) / 0.0028 = 5.1430


4-asset optimization. Max-Sharpe: 3.040. Portfolio: return=8.95%, vol=1.63%. Weights: w_VTI=0.0000, w_XRP-USD=0.0372, w_UNG=0.0000, w_ICSH=0.9628.

Question:
Assets: VTI, XRP-USD, UNG, ICSH
Annualized mean returns: VTI:0.1991, XRP-USD:1.3325, UNG:-1.2932, ICSH:0.0416
Covariance matrix (annualized):
[[0.025927, 0.034911, 0.030626, 9.3e-05], [0.034911, 0.190452, 0.055268, -0.000153], [0.030626, 0.055268, 0.672062, -0.000785], [9.3e-05, -0.000153, -0.000785, 1.5e-05]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_VTI=0.0000, w_XRP-USD=0.0372, w_UNG=0.0000, w_ICSH=0.9628

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VTI=0.0000, w_XRP-USD=0.0372, w_UNG=0.0000, w_ICSH=0.9628
Portfolio annualized return: 8.95%, volatility: 1.63%
Sharpe ratio: (0.0895 - 0.0400) / 0.0163 = 3.0400


4-asset optimization. Max-Sharpe: 0.701. Portfolio: return=19.37%, vol=21.93%. Weights: w_VTI=0.0000, w_ADA-USD=0.0000, w_VNQ=0.7344, w_BNO=0.2656.

Question:
Assets: VTI, ADA-USD, VNQ, BNO
Annualized mean returns: VTI:-0.0132, ADA-USD:0.0092, VNQ:0.1875, BNO:0.2108
Covariance matrix (annualized):
[[0.037868, 0.053114, 0.037401, 0.029989], [0.053114, 0.336862, 0.065267, 0.053982], [0.037401, 0.065267, 0.053433, 0.026055], [0.029989, 0.053982, 0.026055, 0.129229]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_VTI=0.0000, w_ADA-USD=0.0000, w_VNQ=0.7344, w_BNO=0.2656

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VTI=0.0000, w_ADA-USD=0.0000, w_VNQ=0.7344, w_BNO=0.2656
Portfolio annualized return: 19.37%, volatility: 21.93%
Sharpe ratio: (0.1937 - 0.0400) / 0.2193 = 0.7008


4-asset optimization. Max-Sharpe: 5.548. Portfolio: return=5.41%, vol=0.25%. Weights: w_EWJ=0.0000, w_BNB-USD=0.0001, w_INDS=0.0000, w_SGOV=0.9999.

Question:
Assets: EWJ, BNB-USD, INDS, SGOV
Annualized mean returns: EWJ:-0.3445, BNB-USD:0.0511, INDS:-0.2928, SGOV:0.0541
Covariance matrix (annualized):
[[0.021074, 0.008261, 0.018404, -6.1e-05], [0.008261, 0.173403, 0.004579, -7e-06], [0.018404, 0.004579, 0.041811, -4.9e-05], [-6.1e-05, -7e-06, -4.9e-05, 6e-06]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: bull

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_EWJ=0.0000, w_BNB-USD=0.0001, w_INDS=0.0000, w_SGOV=0.9999

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EWJ=0.0000, w_BNB-USD=0.0001, w_INDS=0.0000, w_SGOV=0.9999
Portfolio annualized return: 5.41%, volatility: 0.25%
Sharpe ratio: (0.0541 - 0.0400) / 0.0025 = 5.5483


4-asset optimization. Max-Sharpe: 7.233. Portfolio: return=5.71%, vol=0.24%. Weights: w_QUAL=0.0005, w_ADA-USD=0.0000, w_SHV=0.9995, w_DBC=0.0000.

Question:
Assets: QUAL, ADA-USD, SHV, DBC
Annualized mean returns: QUAL:0.1543, ADA-USD:-0.0893, SHV:0.0570, DBC:-0.3902
Covariance matrix (annualized):
[[0.01417, 0.005488, 3e-05, 0.00133], [0.005488, 0.234667, 0.000354, -0.016357], [3e-05, 0.000354, 6e-06, -8.4e-05], [0.00133, -0.016357, -8.4e-05, 0.015189]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_QUAL=0.0005, w_ADA-USD=0.0000, w_SHV=0.9995, w_DBC=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_QUAL=0.0005, w_ADA-USD=0.0000, w_SHV=0.9995, w_DBC=0.0000
Portfolio annualized return: 5.71%, volatility: 0.24%
Sharpe ratio: (0.0571 - 0.0400) / 0.0024 = 7.2332


4-asset optimization. Max-Sharpe: -1.489. Portfolio: return=-37.47%, vol=27.85%. Weights: w_XLY=0.0000, w_ETH-USD=0.0000, w_PALL=1.0000, w_SCHP=0.0000.

Question:
Assets: XLY, ETH-USD, PALL, SCHP
Annualized mean returns: XLY:-0.5264, ETH-USD:-0.6798, PALL:-0.3747, SCHP:-0.2202
Covariance matrix (annualized):
[[0.036472, 0.014082, 0.015496, 0.004154], [0.014082, 0.104726, 0.015452, 0.006876], [0.015496, 0.015452, 0.07755, 0.0061], [0.004154, 0.006876, 0.0061, 0.002852]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_XLY=0.0000, w_ETH-USD=0.0000, w_PALL=1.0000, w_SCHP=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLY=0.0000, w_ETH-USD=0.0000, w_PALL=1.0000, w_SCHP=0.0000
Portfolio annualized return: -37.47%, volatility: 27.85%
Sharpe ratio: (-0.3747 - 0.0400) / 0.2785 = -1.4890


4-asset optimization. Max-Sharpe: -0.434. Portfolio: return=-15.33%, vol=44.59%. Weights: w_EFA=0.0000, w_ETH-USD=0.0000, w_IYR=0.0000, w_UNG=1.0000.

Question:
Assets: EFA, ETH-USD, IYR, UNG
Annualized mean returns: EFA:-0.0789, ETH-USD:-0.7968, IYR:-0.0737, UNG:-0.1533
Covariance matrix (annualized):
[[0.018, 0.024358, 0.008862, 0.006251], [0.024358, 0.112443, 0.015901, -0.010777], [0.008862, 0.015901, 0.016524, 0.007482], [0.006251, -0.010777, 0.007482, 0.198787]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_EFA=0.0000, w_ETH-USD=0.0000, w_IYR=0.0000, w_UNG=1.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EFA=0.0000, w_ETH-USD=0.0000, w_IYR=0.0000, w_UNG=1.0000
Portfolio annualized return: -15.33%, volatility: 44.59%
Sharpe ratio: (-0.1533 - 0.0400) / 0.4459 = -0.4336


4-asset optimization. Max-Sharpe: 4.363. Portfolio: return=42.51%, vol=8.83%. Weights: w_XLV=0.0104, w_BTC-USD=0.2083, w_BNDX=0.5273, w_IAU=0.2540.

Question:
Assets: XLV, BTC-USD, BNDX, IAU
Annualized mean returns: XLV:0.0126, BTC-USD:1.5703, BNDX:0.1118, IAU:0.1532
Covariance matrix (annualized):
[[0.014625, -0.00646, 0.00151, -0.000621], [-0.00646, 0.178575, -0.003994, -0.016025], [0.00151, -0.003994, 0.0031, 0.002496], [-0.000621, -0.016025, 0.002496, 0.017001]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_XLV=0.0104, w_BTC-USD=0.2083, w_BNDX=0.5273, w_IAU=0.2540

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLV=0.0104, w_BTC-USD=0.2083, w_BNDX=0.5273, w_IAU=0.2540
Portfolio annualized return: 42.51%, volatility: 8.83%
Sharpe ratio: (0.4251 - 0.0400) / 0.0883 = 4.3635


4-asset optimization. Max-Sharpe: 5.851. Portfolio: return=5.35%, vol=0.23%. Weights: w_VEA=0.0049, w_ETH-USD=0.0000, w_TLH=0.0000, w_SGOV=0.9951.

Question:
Assets: VEA, ETH-USD, TLH, SGOV
Annualized mean returns: VEA:0.1717, ETH-USD:-1.9891, TLH:0.0370, SGOV:0.0530
Covariance matrix (annualized):
[[0.012913, 0.031417, 0.005315, -1.2e-05], [0.031417, 0.373625, 0.002122, 6e-06], [0.005315, 0.002122, 0.011606, 3e-06], [-1.2e-05, 6e-06, 3e-06, 5e-06]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: bull

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_VEA=0.0049, w_ETH-USD=0.0000, w_TLH=0.0000, w_SGOV=0.9951

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VEA=0.0049, w_ETH-USD=0.0000, w_TLH=0.0000, w_SGOV=0.9951
Portfolio annualized return: 5.35%, volatility: 0.23%
Sharpe ratio: (0.0535 - 0.0400) / 0.0023 = 5.8505


4-asset optimization. Max-Sharpe: 3.111. Portfolio: return=7.47%, vol=1.12%. Weights: w_XLP=0.0000, w_LINK-USD=0.0083, w_CSHI=0.9917, w_LQD=0.0000.

Question:
Assets: XLP, LINK-USD, CSHI, LQD
Annualized mean returns: XLP:-0.1610, LINK-USD:0.5894, CSHI:0.0704, LQD:-0.0183
Covariance matrix (annualized):
[[0.009607, 0.011633, -1.2e-05, 0.000691], [0.011633, 0.258253, -0.00017, 0.007531], [-1.2e-05, -0.00017, 0.000111, -1.6e-05], [0.000691, 0.007531, -1.6e-05, 0.005441]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_XLP=0.0000, w_LINK-USD=0.0083, w_CSHI=0.9917, w_LQD=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLP=0.0000, w_LINK-USD=0.0083, w_CSHI=0.9917, w_LQD=0.0000
Portfolio annualized return: 7.47%, volatility: 1.12%
Sharpe ratio: (0.0747 - 0.0400) / 0.0112 = 3.1111


4-asset optimization. Max-Sharpe: 10.753. Portfolio: return=7.88%, vol=0.36%. Weights: w_VTI=0.0233, w_BTC-USD=0.0038, w_BIL=0.9725, w_PPLT=0.0004.

Question:
Assets: VTI, BTC-USD, BIL, PPLT
Annualized mean returns: VTI:0.8676, BTC-USD:1.3204, BIL:0.0549, PPLT:0.4677
Covariance matrix (annualized):
[[0.014203, -0.004206, -4.2e-05, 0.008955], [-0.004206, 0.167637, -0.000107, -0.016622], [-4.2e-05, -0.000107, 7e-06, -2.6e-05], [0.008955, -0.016622, -2.6e-05, 0.059104]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_VTI=0.0233, w_BTC-USD=0.0038, w_BIL=0.9725, w_PPLT=0.0004

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VTI=0.0233, w_BTC-USD=0.0038, w_BIL=0.9725, w_PPLT=0.0004
Portfolio annualized return: 7.88%, volatility: 0.36%
Sharpe ratio: (0.0788 - 0.0400) / 0.0036 = 10.7528


4-asset optimization. Max-Sharpe: 4.167. Portfolio: return=57.01%, vol=12.72%. Weights: w_XLP=0.4323, w_AVAX-USD=0.0612, w_IYR=0.5065, w_USO=0.0000.

Question:
Assets: XLP, AVAX-USD, IYR, USO
Annualized mean returns: XLP:0.3221, AVAX-USD:1.8081, IYR:0.6321, USO:-0.2884
Covariance matrix (annualized):
[[0.013266, -0.015057, 0.0075, -0.006227], [-0.015057, 0.926494, 0.007446, -0.081093], [0.0075, 0.007446, 0.028382, -0.001456], [-0.006227, -0.081093, -0.001456, 0.097762]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_XLP=0.4323, w_AVAX-USD=0.0612, w_IYR=0.5065, w_USO=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLP=0.4323, w_AVAX-USD=0.0612, w_IYR=0.5065, w_USO=0.0000
Portfolio annualized return: 57.01%, volatility: 12.72%
Sharpe ratio: (0.5701 - 0.0400) / 0.1272 = 4.1671


4-asset optimization. Max-Sharpe: 3.769. Portfolio: return=5.05%, vol=0.28%. Weights: w_XLF=0.0000, w_MATIC-USD=0.0000, w_SHY=0.0000, w_BIL=1.0000.

Question:
Assets: XLF, MATIC-USD, SHY, BIL
Annualized mean returns: XLF:-0.1432, MATIC-USD:-1.8995, SHY:0.0141, BIL:0.0505
Covariance matrix (annualized):
[[0.015154, 0.010094, 0.000507, -6.4e-05], [0.010094, 0.36906, 0.001462, 0.00063], [0.000507, 0.001462, 0.000257, -0.0], [-6.4e-05, 0.00063, -0.0, 8e-06]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_XLF=0.0000, w_MATIC-USD=0.0000, w_SHY=0.0000, w_BIL=1.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLF=0.0000, w_MATIC-USD=0.0000, w_SHY=0.0000, w_BIL=1.0000
Portfolio annualized return: 5.05%, volatility: 0.28%
Sharpe ratio: (0.0505 - 0.0400) / 0.0028 = 3.7685


4-asset optimization. Max-Sharpe: 0.915. Portfolio: return=4.55%, vol=0.60%. Weights: w_VEA=0.0000, w_SOL-USD=0.0000, w_ICSH=1.0000, w_USO=0.0000.

Question:
Assets: VEA, SOL-USD, ICSH, USO
Annualized mean returns: VEA:-0.2773, SOL-USD:-2.6968, ICSH:0.0455, USO:-0.8432
Covariance matrix (annualized):
[[0.024231, 0.02843, -0.000194, 0.01929], [0.02843, 0.578126, 0.001033, 0.019203], [-0.000194, 0.001033, 3.6e-05, -0.000112], [0.01929, 0.019203, -0.000112, 0.101328]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_VEA=0.0000, w_SOL-USD=0.0000, w_ICSH=1.0000, w_USO=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VEA=0.0000, w_SOL-USD=0.0000, w_ICSH=1.0000, w_USO=0.0000
Portfolio annualized return: 4.55%, volatility: 0.60%
Sharpe ratio: (0.0455 - 0.0400) / 0.0060 = 0.9154


4-asset optimization. Max-Sharpe: 7.013. Portfolio: return=5.23%, vol=0.18%. Weights: w_MTUM=0.0061, w_LINK-USD=0.0000, w_REZ=0.0000, w_SGOV=0.9939.

Question:
Assets: MTUM, LINK-USD, REZ, SGOV
Annualized mean returns: MTUM:0.1069, LINK-USD:0.6387, REZ:-0.1674, SGOV:0.0520
Covariance matrix (annualized):
[[0.017227, 0.02053, 0.004062, -9e-05], [0.02053, 0.56401, 0.030458, 0.000368], [0.004062, 0.030458, 0.021359, -1e-05], [-9e-05, 0.000368, -1e-05, 4e-06]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_MTUM=0.0061, w_LINK-USD=0.0000, w_REZ=0.0000, w_SGOV=0.9939

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_MTUM=0.0061, w_LINK-USD=0.0000, w_REZ=0.0000, w_SGOV=0.9939
Portfolio annualized return: 5.23%, volatility: 0.18%
Sharpe ratio: (0.0523 - 0.0400) / 0.0018 = 7.0133


4-asset optimization. Max-Sharpe: 2.209. Portfolio: return=50.55%, vol=21.07%. Weights: w_IWM=0.0000, w_DOT-USD=0.0000, w_BIL=0.0000, w_TLT=1.0000.

Question:
Assets: IWM, DOT-USD, BIL, TLT
Annualized mean returns: IWM:-0.1121, DOT-USD:-0.5433, BIL:0.0352, TLT:0.5055
Covariance matrix (annualized):
[[0.045806, 0.045672, -0.000113, 0.011435], [0.045672, 0.214104, 0.000195, 0.026428], [-0.000113, 0.000195, 9e-06, 7.1e-05], [0.011435, 0.026428, 7.1e-05, 0.044397]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_IWM=0.0000, w_DOT-USD=0.0000, w_BIL=0.0000, w_TLT=1.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_IWM=0.0000, w_DOT-USD=0.0000, w_BIL=0.0000, w_TLT=1.0000
Portfolio annualized return: 50.55%, volatility: 21.07%
Sharpe ratio: (0.5055 - 0.0400) / 0.2107 = 2.2092


4-asset optimization. Max-Sharpe: 4.246. Portfolio: return=5.54%, vol=0.36%. Weights: w_IVV=0.0054, w_XRP-USD=0.0000, w_ICSH=0.9946, w_PALL=0.0000.

Question:
Assets: IVV, XRP-USD, ICSH, PALL
Annualized mean returns: IVV:0.2060, XRP-USD:-0.4016, ICSH:0.0546, PALL:-0.8701
Covariance matrix (annualized):
[[0.013013, 0.02318, 7.3e-05, 0.012644], [0.02318, 0.183627, 0.00086, 0.036753], [7.3e-05, 0.00086, 1.2e-05, 3.8e-05], [0.012644, 0.036753, 3.8e-05, 0.083779]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_IVV=0.0054, w_XRP-USD=0.0000, w_ICSH=0.9946, w_PALL=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_IVV=0.0054, w_XRP-USD=0.0000, w_ICSH=0.9946, w_PALL=0.0000
Portfolio annualized return: 5.54%, volatility: 0.36%
Sharpe ratio: (0.0554 - 0.0400) / 0.0036 = 4.2465


4-asset optimization. Max-Sharpe: -2.502. Portfolio: return=-39.30%, vol=17.31%. Weights: w_FXI=0.2500, w_DOT-USD=0.2500, w_BIL=0.2500, w_HAUZ=0.2500.

Question:
Assets: FXI, DOT-USD, BIL, HAUZ
Annualized mean returns: FXI:-0.3401, DOT-USD:-1.5769, BIL:0.0510, HAUZ:0.2940
Covariance matrix (annualized):
[[0.038916, 0.02054, 2.7e-05, 0.013906], [0.02054, 0.274536, 0.000219, 0.03802], [2.7e-05, 0.000219, 8e-06, 1e-06], [0.013906, 0.03802, 1e-06, 0.020495]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_FXI=0.2500, w_DOT-USD=0.2500, w_BIL=0.2500, w_HAUZ=0.2500

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_FXI=0.2500, w_DOT-USD=0.2500, w_BIL=0.2500, w_HAUZ=0.2500
Portfolio annualized return: -39.30%, volatility: 17.31%
Sharpe ratio: (-0.3930 - 0.0400) / 0.1731 = -2.5017


4-asset optimization. Max-Sharpe: 4.656. Portfolio: return=8.16%, vol=0.89%. Weights: w_XLI=0.0000, w_BTC-USD=0.0130, w_IGOV=0.0000, w_CSHI=0.9870.

Question:
Assets: XLI, BTC-USD, IGOV, CSHI
Annualized mean returns: XLI:0.3355, BTC-USD:1.9067, IGOV:-0.2849, CSHI:0.0575
Covariance matrix (annualized):
[[0.019629, 0.03395, -0.002807, 0.000202], [0.03395, 0.249335, -0.0032, 0.000342], [-0.002807, -0.0032, 0.00774, 2.1e-05], [0.000202, 0.000342, 2.1e-05, 3e-05]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_XLI=0.0000, w_BTC-USD=0.0130, w_IGOV=0.0000, w_CSHI=0.9870

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLI=0.0000, w_BTC-USD=0.0130, w_IGOV=0.0000, w_CSHI=0.9870
Portfolio annualized return: 8.16%, volatility: 0.89%
Sharpe ratio: (0.0816 - 0.0400) / 0.0089 = 4.6556


4-asset optimization. Max-Sharpe: 0.449. Portfolio: return=11.11%, vol=15.85%. Weights: w_XLV=0.0000, w_BNB-USD=0.0000, w_IYR=1.0000, w_SOYB=0.0000.

Question:
Assets: XLV, BNB-USD, IYR, SOYB
Annualized mean returns: XLV:-0.2372, BNB-USD:-0.1879, IYR:0.1111, SOYB:-0.5095
Covariance matrix (annualized):
[[0.014068, 0.009417, 0.008465, 0.000595], [0.009417, 0.1601, 0.007242, -0.009123], [0.008465, 0.007242, 0.025117, 0.002571], [0.000595, -0.009123, 0.002571, 0.014838]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: bull

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_XLV=0.0000, w_BNB-USD=0.0000, w_IYR=1.0000, w_SOYB=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLV=0.0000, w_BNB-USD=0.0000, w_IYR=1.0000, w_SOYB=0.0000
Portfolio annualized return: 11.11%, volatility: 15.85%
Sharpe ratio: (0.1111 - 0.0400) / 0.1585 = 0.4489


4-asset optimization. Max-Sharpe: 1.811. Portfolio: return=25.01%, vol=11.60%. Weights: w_XLV=0.6741, w_SOL-USD=0.0000, w_DBA=0.3259, w_BNDX=0.0000.

Question:
Assets: XLV, SOL-USD, DBA, BNDX
Annualized mean returns: XLV:0.3056, SOL-USD:-2.4684, DBA:0.1352, BNDX:-0.0319
Covariance matrix (annualized):
[[0.022571, 0.089884, 0.005518, 0.003248], [0.089884, 1.796099, 0.028186, 0.012553], [0.005518, 0.028186, 0.007303, -0.000628], [0.003248, 0.012553, -0.000628, 0.003544]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_XLV=0.6741, w_SOL-USD=0.0000, w_DBA=0.3259, w_BNDX=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLV=0.6741, w_SOL-USD=0.0000, w_DBA=0.3259, w_BNDX=0.0000
Portfolio annualized return: 25.01%, volatility: 11.60%
Sharpe ratio: (0.2501 - 0.0400) / 0.1160 = 1.8112


4-asset optimization. Max-Sharpe: 2.852. Portfolio: return=9.59%, vol=1.96%. Weights: w_XLP=0.0569, w_ETH-USD=0.0243, w_CSHI=0.9187, w_INDS=0.0000.

Question:
Assets: XLP, ETH-USD, CSHI, INDS
Annualized mean returns: XLP:0.1923, ETH-USD:0.8193, CSHI:0.0708, INDS:-0.1521
Covariance matrix (annualized):
[[0.011996, 1.7e-05, 0.000396, 0.015509], [1.7e-05, 0.239268, -0.000508, 0.000216], [0.000396, -0.000508, 0.000219, 0.000925], [0.015509, 0.000216, 0.000925, 0.04405]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_XLP=0.0569, w_ETH-USD=0.0243, w_CSHI=0.9187, w_INDS=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLP=0.0569, w_ETH-USD=0.0243, w_CSHI=0.9187, w_INDS=0.0000
Portfolio annualized return: 9.59%, volatility: 1.96%
Sharpe ratio: (0.0959 - 0.0400) / 0.0196 = 2.8519


4-asset optimization. Max-Sharpe: 3.985. Portfolio: return=415.08%, vol=103.16%. Weights: w_XLV=0.0000, w_ADA-USD=1.0000, w_SCHH=0.0000, w_TLT=0.0000.

Question:
Assets: XLV, ADA-USD, SCHH, TLT
Annualized mean returns: XLV:-0.6538, ADA-USD:4.1508, SCHH:-0.5108, TLT:-0.2175
Covariance matrix (annualized):
[[0.013901, 0.019537, 0.008885, 0.005074], [0.019537, 1.064231, 0.035061, 0.009137], [0.008885, 0.035061, 0.026641, 0.014369], [0.005074, 0.009137, 0.014369, 0.022429]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_XLV=0.0000, w_ADA-USD=1.0000, w_SCHH=0.0000, w_TLT=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLV=0.0000, w_ADA-USD=1.0000, w_SCHH=0.0000, w_TLT=0.0000
Portfolio annualized return: 415.08%, volatility: 103.16%
Sharpe ratio: (4.1508 - 0.0400) / 1.0316 = 3.9848


4-asset optimization. Max-Sharpe: 2.436. Portfolio: return=33.76%, vol=12.22%. Weights: w_XLI=1.0000, w_DOT-USD=0.0000, w_PPLT=0.0000, w_IEF=0.0000.

Question:
Assets: XLI, DOT-USD, PPLT, IEF
Annualized mean returns: XLI:0.3376, DOT-USD:-0.4562, PPLT:-0.6438, IEF:-0.1598
Covariance matrix (annualized):
[[0.014928, 0.025367, 0.006609, 0.003171], [0.025367, 0.421966, 0.008821, -0.000561], [0.006609, 0.008821, 0.045184, 0.003082], [0.003171, -0.000561, 0.003082, 0.005486]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_XLI=1.0000, w_DOT-USD=0.0000, w_PPLT=0.0000, w_IEF=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLI=1.0000, w_DOT-USD=0.0000, w_PPLT=0.0000, w_IEF=0.0000
Portfolio annualized return: 33.76%, volatility: 12.22%
Sharpe ratio: (0.3376 - 0.0400) / 0.1222 = 2.4358


4-asset optimization. Max-Sharpe: 5.377. Portfolio: return=483.36%, vol=89.15%. Weights: w_VTI=0.0000, w_SOL-USD=1.0000, w_USO=0.0000, w_INDS=0.0000.

Question:
Assets: VTI, SOL-USD, USO, INDS
Annualized mean returns: VTI:-0.1503, SOL-USD:4.8336, USO:-0.5880, INDS:-0.6068
Covariance matrix (annualized):
[[0.021464, 0.024669, -0.008701, 0.025683], [0.024669, 0.794734, 0.005096, 0.00995], [-0.008701, 0.005096, 0.103478, -0.020409], [0.025683, 0.00995, -0.020409, 0.05108]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_VTI=0.0000, w_SOL-USD=1.0000, w_USO=0.0000, w_INDS=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VTI=0.0000, w_SOL-USD=1.0000, w_USO=0.0000, w_INDS=0.0000
Portfolio annualized return: 483.36%, volatility: 89.15%
Sharpe ratio: (4.8336 - 0.0400) / 0.8915 = 5.3772


4-asset optimization. Max-Sharpe: 3.849. Portfolio: return=6.14%, vol=0.56%. Weights: w_^VIX=0.0025, w_ADA-USD=0.0091, w_IAU=0.0000, w_ICSH=0.9885.

Question:
Assets: ^VIX, ADA-USD, IAU, ICSH
Annualized mean returns: ^VIX:2.0054, ADA-USD:0.4805, IAU:0.0958, ICSH:0.0527
Covariance matrix (annualized):
[[1.060477, -0.059077, 0.036198, 0.00076], [-0.059077, 0.077177, -0.00168, 8.4e-05], [0.036198, -0.00168, 0.014972, 6.4e-05], [0.00076, 8.4e-05, 6.4e-05, 1.6e-05]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_^VIX=0.0025, w_ADA-USD=0.0091, w_IAU=0.0000, w_ICSH=0.9885

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_^VIX=0.0025, w_ADA-USD=0.0091, w_IAU=0.0000, w_ICSH=0.9885
Portfolio annualized return: 6.14%, volatility: 0.56%
Sharpe ratio: (0.0614 - 0.0400) / 0.0056 = 3.8495


4-asset optimization. Max-Sharpe: 6.744. Portfolio: return=6.29%, vol=0.34%. Weights: w_QUAL=0.0171, w_LINK-USD=0.0000, w_IYR=0.0030, w_BIL=0.9799.

Question:
Assets: QUAL, LINK-USD, IYR, BIL
Annualized mean returns: QUAL:0.4064, LINK-USD:-0.0677, IYR:0.4456, BIL:0.0558
Covariance matrix (annualized):
[[0.00824, 0.015124, 0.007506, 2.2e-05], [0.015124, 0.594214, 0.042869, 6.2e-05], [0.007506, 0.042869, 0.030017, -1.5e-05], [2.2e-05, 6.2e-05, -1.5e-05, 8e-06]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_QUAL=0.0171, w_LINK-USD=0.0000, w_IYR=0.0030, w_BIL=0.9799

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_QUAL=0.0171, w_LINK-USD=0.0000, w_IYR=0.0030, w_BIL=0.9799
Portfolio annualized return: 6.29%, volatility: 0.34%
Sharpe ratio: (0.0629 - 0.0400) / 0.0034 = 6.7443


4-asset optimization. Max-Sharpe: 4.458. Portfolio: return=92.85%, vol=19.93%. Weights: w_MTUM=0.0287, w_MATIC-USD=0.0000, w_CPER=0.9713, w_SCHH=0.0000.

Question:
Assets: MTUM, MATIC-USD, CPER, SCHH
Annualized mean returns: MTUM:-0.0516, MATIC-USD:-3.5280, CPER:0.9575, SCHH:-0.3135
Covariance matrix (annualized):
[[0.034159, 0.015238, -0.005227, 0.01035], [0.015238, 0.434116, 0.035699, 0.023376], [-0.005227, 0.035699, 0.042378, 0.003718], [0.01035, 0.023376, 0.003718, 0.029579]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_MTUM=0.0287, w_MATIC-USD=0.0000, w_CPER=0.9713, w_SCHH=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_MTUM=0.0287, w_MATIC-USD=0.0000, w_CPER=0.9713, w_SCHH=0.0000
Portfolio annualized return: 92.85%, volatility: 19.93%
Sharpe ratio: (0.9285 - 0.0400) / 0.1993 = 4.4585


4-asset optimization. Max-Sharpe: 0.747. Portfolio: return=43.83%, vol=53.31%. Weights: w_IVV=0.0000, w_ETH-USD=1.0000, w_WEAT=0.0000, w_MORT=0.0000.

Question:
Assets: IVV, ETH-USD, WEAT, MORT
Annualized mean returns: IVV:-0.0025, ETH-USD:0.4383, WEAT:-0.2728, MORT:-1.2851
Covariance matrix (annualized):
[[0.02929, 0.028126, 0.006816, 0.038732], [0.028126, 0.284233, 0.016942, 0.042759], [0.006816, 0.016942, 0.053719, 0.010052], [0.038732, 0.042759, 0.010052, 0.077195]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

Compute the portfolio weights that maximize the Sharpe Ratio for the above assets.

Answer: w_IVV=0.0000, w_ETH-USD=1.0000, w_WEAT=0.0000, w_MORT=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_IVV=0.0000, w_ETH-USD=1.0000, w_WEAT=0.0000, w_MORT=0.0000
Portfolio annualized return: 43.83%, volatility: 53.31%
Sharpe ratio: (0.4383 - 0.0400) / 0.5331 = 0.7471