4-asset optimization. Max-Sharpe: 3.421. Portfolio: return=117.97%, vol=33.32%. Weights: w_XLRE=0.1985, w_XRP-USD=0.0000, w_BNO=0.8015, w_SHY=0.0000.

Question:
Assets: XLRE, XRP-USD, BNO, SHY
Annualized mean returns: XLRE:0.5735, XRP-USD:0.3507, BNO:1.3298, SHY:0.0042
Covariance matrix (annualized):
[[0.070366, 0.031833, 0.047398, -0.000348], [0.031833, 0.178387, 0.031221, 3.5e-05], [0.047398, 0.031221, 0.144981, 5.3e-05], [-0.000348, 3.5e-05, 5.3e-05, 2.1e-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_XLRE=0.1985, w_XRP-USD=0.0000, w_BNO=0.8015, w_SHY=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLRE=0.1985, w_XRP-USD=0.0000, w_BNO=0.8015, w_SHY=0.0000
Portfolio annualized return: 117.97%, volatility: 33.32%
Sharpe ratio: (1.1797 - 0.0400) / 0.3332 = 3.4209


4-asset optimization. Max-Sharpe: 1.711. Portfolio: return=39.68%, vol=20.86%. Weights: w_EWJ=0.0000, w_BTC-USD=0.0000, w_CORN=1.0000, w_INDS=0.0000.

Question:
Assets: EWJ, BTC-USD, CORN, INDS
Annualized mean returns: EWJ:-0.7728, BTC-USD:-0.6268, CORN:0.3968, INDS:-1.3083
Covariance matrix (annualized):
[[0.037885, 0.068032, 0.002789, 0.028338], [0.068032, 0.298551, 0.004222, 0.052892], [0.002789, 0.004222, 0.043497, 0.003832], [0.028338, 0.052892, 0.003832, 0.054414]]
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_BTC-USD=0.0000, w_CORN=1.0000, w_INDS=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EWJ=0.0000, w_BTC-USD=0.0000, w_CORN=1.0000, w_INDS=0.0000
Portfolio annualized return: 39.68%, volatility: 20.86%
Sharpe ratio: (0.3968 - 0.0400) / 0.2086 = 1.7106


4-asset optimization. Max-Sharpe: 0.636. Portfolio: return=18.51%, vol=22.80%. Weights: w_QUAL=1.0000, w_BNB-USD=0.0000, w_BIL=0.0000, w_REZ=0.0000.

Question:
Assets: QUAL, BNB-USD, BIL, REZ
Annualized mean returns: QUAL:0.1851, BNB-USD:-0.6001, BIL:0.0349, REZ:-0.1625
Covariance matrix (annualized):
[[0.051994, 0.093514, -0.000207, 0.041601], [0.093514, 0.654099, -0.000215, 0.097088], [-0.000207, -0.000215, 8e-06, -7e-05], [0.041601, 0.097088, -7e-05, 0.059504]]
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=1.0000, w_BNB-USD=0.0000, w_BIL=0.0000, w_REZ=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_QUAL=1.0000, w_BNB-USD=0.0000, w_BIL=0.0000, w_REZ=0.0000
Portfolio annualized return: 18.51%, volatility: 22.80%
Sharpe ratio: (0.1851 - 0.0400) / 0.2280 = 0.6363


4-asset optimization. Max-Sharpe: 2.896. Portfolio: return=7.87%, vol=1.34%. Weights: w_XLV=0.0000, w_ADA-USD=0.0000, w_VNQ=0.0102, w_TIP=0.9898.

Question:
Assets: XLV, ADA-USD, VNQ, TIP
Annualized mean returns: XLV:-0.0023, ADA-USD:-2.5478, VNQ:0.1421, TIP:0.0780
Covariance matrix (annualized):
[[0.022051, 0.004165, 0.014349, 0.000752], [0.004165, 0.578859, 0.007012, 0.004307], [0.014349, 0.007012, 0.029507, 0.00017], [0.000752, 0.004307, 0.00017, 0.000176]]
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=0.0000, w_VNQ=0.0102, w_TIP=0.9898

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLV=0.0000, w_ADA-USD=0.0000, w_VNQ=0.0102, w_TIP=0.9898
Portfolio annualized return: 7.87%, volatility: 1.34%
Sharpe ratio: (0.0787 - 0.0400) / 0.0134 = 2.8962


4-asset optimization. Max-Sharpe: 3.901. Portfolio: return=65.35%, vol=15.73%. Weights: w_VLUE=0.2872, w_BTC-USD=0.0000, w_XHB=0.7128, w_BNO=0.0000.

Question:
Assets: VLUE, BTC-USD, XHB, BNO
Annualized mean returns: VLUE:0.5247, BTC-USD:-0.2991, XHB:0.7054, BNO:0.1035
Covariance matrix (annualized):
[[0.018947, 0.011985, 0.019784, 0.025707], [0.011985, 0.152226, 0.006782, 0.039714], [0.019784, 0.006782, 0.029666, 0.017843], [0.025707, 0.039714, 0.017843, 0.143406]]
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=0.2872, w_BTC-USD=0.0000, w_XHB=0.7128, w_BNO=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VLUE=0.2872, w_BTC-USD=0.0000, w_XHB=0.7128, w_BNO=0.0000
Portfolio annualized return: 65.35%, volatility: 15.73%
Sharpe ratio: (0.6535 - 0.0400) / 0.1573 = 3.9007


4-asset optimization. Max-Sharpe: 6.380. Portfolio: return=357.47%, vol=55.41%. Weights: w_XLRE=0.0000, w_XRP-USD=0.2581, w_TLH=0.0000, w_HAUZ=0.7419.

Question:
Assets: XLRE, XRP-USD, TLH, HAUZ
Annualized mean returns: XLRE:-0.1864, XRP-USD:13.2014, TLH:-0.0422, HAUZ:0.2262
Covariance matrix (annualized):
[[0.009494, 0.006866, 0.000922, 0.000801], [0.006866, 4.404893, 0.032226, 0.00842], [0.000922, 0.032226, 0.003022, -0.002712], [0.000801, 0.00842, -0.002712, 0.018869]]
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_XRP-USD=0.2581, w_TLH=0.0000, w_HAUZ=0.7419

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLRE=0.0000, w_XRP-USD=0.2581, w_TLH=0.0000, w_HAUZ=0.7419
Portfolio annualized return: 357.47%, volatility: 55.41%
Sharpe ratio: (3.5747 - 0.0400) / 0.5541 = 6.3797


4-asset optimization. Max-Sharpe: 3.774. Portfolio: return=41.83%, vol=10.02%. Weights: w_XLV=0.7067, w_BNB-USD=0.0000, w_IAU=0.0000, w_VNQ=0.2933.

Question:
Assets: XLV, BNB-USD, IAU, VNQ
Annualized mean returns: XLV:0.4146, BNB-USD:-1.2228, IAU:-0.2653, VNQ:0.4274
Covariance matrix (annualized):
[[0.011729, -0.015577, 0.002319, 0.005657], [-0.015577, 0.874152, -0.025795, -0.011115], [0.002319, -0.025795, 0.014326, 0.005824], [0.005657, -0.011115, 0.005824, 0.02145]]
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=0.7067, w_BNB-USD=0.0000, w_IAU=0.0000, w_VNQ=0.2933

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLV=0.7067, w_BNB-USD=0.0000, w_IAU=0.0000, w_VNQ=0.2933
Portfolio annualized return: 41.83%, volatility: 10.02%
Sharpe ratio: (0.4183 - 0.0400) / 0.1002 = 3.7742


4-asset optimization. Max-Sharpe: 2.728. Portfolio: return=199.01%, vol=71.49%. Weights: w_XLV=0.0000, w_XRP-USD=0.4254, w_VNQI=0.0000, w_DBB=0.5746.

Question:
Assets: XLV, XRP-USD, VNQI, DBB
Annualized mean returns: XLV:-0.0012, XRP-USD:4.2566, VNQI:-0.3826, DBB:0.3119
Covariance matrix (annualized):
[[0.014539, 0.071824, 0.009558, 0.010384], [0.071824, 2.439892, 0.080343, 0.116748], [0.009558, 0.080343, 0.015891, 0.013103], [0.010384, 0.116748, 0.013103, 0.037576]]
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_XRP-USD=0.4254, w_VNQI=0.0000, w_DBB=0.5746

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLV=0.0000, w_XRP-USD=0.4254, w_VNQI=0.0000, w_DBB=0.5746
Portfolio annualized return: 199.01%, volatility: 71.49%
Sharpe ratio: (1.9901 - 0.0400) / 0.7149 = 2.7278


4-asset optimization. Max-Sharpe: -0.966. Portfolio: return=-80.65%, vol=87.59%. Weights: w_XLI=0.0000, w_ADA-USD=1.0000, w_SCHP=0.0000, w_HAUZ=0.0000.

Question:
Assets: XLI, ADA-USD, SCHP, HAUZ
Annualized mean returns: XLI:-0.0506, ADA-USD:-0.8065, SCHP:-0.1065, HAUZ:-0.4370
Covariance matrix (annualized):
[[0.059629, 0.0651, 0.005909, 0.039923], [0.0651, 0.767273, 0.004939, 0.05987], [0.005909, 0.004939, 0.006082, 0.003893], [0.039923, 0.05987, 0.003893, 0.036371]]
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_ADA-USD=1.0000, w_SCHP=0.0000, w_HAUZ=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLI=0.0000, w_ADA-USD=1.0000, w_SCHP=0.0000, w_HAUZ=0.0000
Portfolio annualized return: -80.65%, volatility: 87.59%
Sharpe ratio: (-0.8065 - 0.0400) / 0.8759 = -0.9664


4-asset optimization. Max-Sharpe: 3.407. Portfolio: return=40.44%, vol=10.70%. Weights: w_FXI=0.0000, w_BNB-USD=0.0000, w_SOYB=0.0370, w_TLH=0.9630.

Question:
Assets: FXI, BNB-USD, SOYB, TLH
Annualized mean returns: FXI:-0.9559, BNB-USD:-1.2499, SOYB:0.1898, TLH:0.4126
Covariance matrix (annualized):
[[0.060448, 0.001847, 0.006105, -0.004229], [0.001847, 0.896444, -0.024247, 0.003463], [0.006105, -0.024247, 0.056695, 0.002708], [-0.004229, 0.003463, 0.002708, 0.012045]]
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_BNB-USD=0.0000, w_SOYB=0.0370, w_TLH=0.9630

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_FXI=0.0000, w_BNB-USD=0.0000, w_SOYB=0.0370, w_TLH=0.9630
Portfolio annualized return: 40.44%, volatility: 10.70%
Sharpe ratio: (0.4044 - 0.0400) / 0.1070 = 3.4065


4-asset optimization. Max-Sharpe: 5.272. Portfolio: return=546.06%, vol=102.82%. Weights: w_VLUE=0.0000, w_AVAX-USD=0.5210, w_BNO=0.4790, w_ICSH=0.0000.

Question:
Assets: VLUE, AVAX-USD, BNO, ICSH
Annualized mean returns: VLUE:-0.0795, AVAX-USD:10.1597, BNO:0.3491, ICSH:0.0028
Covariance matrix (annualized):
[[0.017919, 0.052018, 0.022755, 2e-06], [0.052018, 3.754839, 0.036544, 0.000228], [0.022755, 0.036544, 0.086128, 1.5e-05], [2e-06, 0.000228, 1.5e-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_VLUE=0.0000, w_AVAX-USD=0.5210, w_BNO=0.4790, w_ICSH=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VLUE=0.0000, w_AVAX-USD=0.5210, w_BNO=0.4790, w_ICSH=0.0000
Portfolio annualized return: 546.06%, volatility: 102.82%
Sharpe ratio: (5.4606 - 0.0400) / 1.0282 = 5.2717


4-asset optimization. Max-Sharpe: 4.119. Portfolio: return=72.00%, vol=16.51%. Weights: w_XLRE=0.0000, w_BTC-USD=0.2200, w_IAU=0.7800, w_INDS=0.0000.

Question:
Assets: XLRE, BTC-USD, IAU, INDS
Annualized mean returns: XLRE:0.0839, BTC-USD:1.5039, IAU:0.4989, INDS:0.1181
Covariance matrix (annualized):
[[0.046259, 0.014502, 0.002225, 0.050777], [0.014502, 0.223831, 0.012105, 0.016519], [0.002225, 0.012105, 0.020169, 0.002934], [0.050777, 0.016519, 0.002934, 0.059305]]
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_BTC-USD=0.2200, w_IAU=0.7800, w_INDS=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLRE=0.0000, w_BTC-USD=0.2200, w_IAU=0.7800, w_INDS=0.0000
Portfolio annualized return: 72.00%, volatility: 16.51%
Sharpe ratio: (0.7200 - 0.0400) / 0.1651 = 4.1187


4-asset optimization. Max-Sharpe: -0.297. Portfolio: return=-19.27%, vol=78.38%. Weights: w_QUAL=0.0000, w_DOT-USD=1.0000, w_BNO=0.0000, w_XHB=0.0000.

Question:
Assets: QUAL, DOT-USD, BNO, XHB
Annualized mean returns: QUAL:-0.2155, DOT-USD:-0.1927, BNO:-0.3513, XHB:-0.3002
Covariance matrix (annualized):
[[0.046546, 0.105096, 0.006668, 0.056599], [0.105096, 0.614322, 0.075989, 0.150025], [0.006668, 0.075989, 0.149097, 7.7e-05], [0.056599, 0.150025, 7.7e-05, 0.086897]]
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=0.0000, w_DOT-USD=1.0000, w_BNO=0.0000, w_XHB=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_QUAL=0.0000, w_DOT-USD=1.0000, w_BNO=0.0000, w_XHB=0.0000
Portfolio annualized return: -19.27%, volatility: 78.38%
Sharpe ratio: (-0.1927 - 0.0400) / 0.7838 = -0.2969


4-asset optimization. Max-Sharpe: 5.276. Portfolio: return=47.59%, vol=8.26%. Weights: w_XLRE=0.0000, w_MATIC-USD=0.0387, w_MORT=0.9613, w_ICSH=0.0000.

Question:
Assets: XLRE, MATIC-USD, MORT, ICSH
Annualized mean returns: XLRE:-0.1922, MATIC-USD:1.6358, MORT:0.4292, ICSH:0.0247
Covariance matrix (annualized):
[[0.013557, -0.011018, 0.002705, 4.3e-05], [-0.011018, 0.702993, -0.00234, 6.6e-05], [0.002705, -0.00234, 0.006434, -1.9e-05], [4.3e-05, 6.6e-05, -1.9e-05, 1.4e-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_XLRE=0.0000, w_MATIC-USD=0.0387, w_MORT=0.9613, w_ICSH=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLRE=0.0000, w_MATIC-USD=0.0387, w_MORT=0.9613, w_ICSH=0.0000
Portfolio annualized return: 47.59%, volatility: 8.26%
Sharpe ratio: (0.4759 - 0.0400) / 0.0826 = 5.2763


4-asset optimization. Max-Sharpe: 2.816. Portfolio: return=61.21%, vol=20.32%. Weights: w_FXI=1.0000, w_BNB-USD=0.0000, w_BIL=0.0000, w_STIP=0.0000.

Question:
Assets: FXI, BNB-USD, BIL, STIP
Annualized mean returns: FXI:0.6121, BNB-USD:-0.7284, BIL:0.0000, STIP:0.0075
Covariance matrix (annualized):
[[0.041289, 0.009694, 2.8e-05, 9.1e-05], [0.009694, 0.466563, 0.000251, 0.001748], [2.8e-05, 0.000251, 2e-06, 2e-06], [9.1e-05, 0.001748, 2e-06, 0.000122]]
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=1.0000, w_BNB-USD=0.0000, w_BIL=0.0000, w_STIP=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_FXI=1.0000, w_BNB-USD=0.0000, w_BIL=0.0000, w_STIP=0.0000
Portfolio annualized return: 61.21%, volatility: 20.32%
Sharpe ratio: (0.6121 - 0.0400) / 0.2032 = 2.8155


4-asset optimization. Max-Sharpe: 2.578. Portfolio: return=39.57%, vol=13.80%. Weights: w_USMV=0.7592, w_BTC-USD=0.0000, w_TLT=0.2408, w_PPLT=0.0000.

Question:
Assets: USMV, BTC-USD, TLT, PPLT
Annualized mean returns: USMV:0.4390, BTC-USD:-0.1119, TLT:0.2593, PPLT:-0.1904
Covariance matrix (annualized):
[[0.02754, 0.058913, 0.001861, 0.012725], [0.058913, 0.413985, -0.005317, 0.07911], [0.001861, -0.005317, 0.042855, 0.004037], [0.012725, 0.07911, 0.004037, 0.072547]]
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=0.7592, w_BTC-USD=0.0000, w_TLT=0.2408, w_PPLT=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_USMV=0.7592, w_BTC-USD=0.0000, w_TLT=0.2408, w_PPLT=0.0000
Portfolio annualized return: 39.57%, volatility: 13.80%
Sharpe ratio: (0.3957 - 0.0400) / 0.1380 = 2.5783


4-asset optimization. Max-Sharpe: 0.289. Portfolio: return=8.18%, vol=14.49%. Weights: w_XLK=0.0000, w_ADA-USD=0.0035, w_SCHH=0.9965, w_ICSH=0.0000.

Question:
Assets: XLK, ADA-USD, SCHH, ICSH
Annualized mean returns: XLK:-0.0031, ADA-USD:0.0651, SCHH:0.0819, ICSH:0.0372
Covariance matrix (annualized):
[[0.038422, 0.011605, 0.00757, -0.000122], [0.011605, 0.74862, 0.010022, -0.000634], [0.00757, 0.010022, 0.021062, -6.3e-05], [-0.000122, -0.000634, -6.3e-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_XLK=0.0000, w_ADA-USD=0.0035, w_SCHH=0.9965, w_ICSH=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLK=0.0000, w_ADA-USD=0.0035, w_SCHH=0.9965, w_ICSH=0.0000
Portfolio annualized return: 8.18%, volatility: 14.49%
Sharpe ratio: (0.0818 - 0.0400) / 0.1449 = 0.2886


4-asset optimization. Max-Sharpe: 0.486. Portfolio: return=11.85%, vol=16.14%. Weights: w_XLB=1.0000, w_LINK-USD=0.0000, w_BNO=0.0000, w_BIL=0.0000.

Question:
Assets: XLB, LINK-USD, BNO, BIL
Annualized mean returns: XLB:0.1185, LINK-USD:-0.1930, BNO:-0.1014, BIL:0.0187
Covariance matrix (annualized):
[[0.026064, -0.032653, 0.007988, 5.4e-05], [-0.032653, 0.602569, -0.071004, 3.6e-05], [0.007988, -0.071004, 0.108047, -9.2e-05], [5.4e-05, 3.6e-05, -9.2e-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_XLB=1.0000, w_LINK-USD=0.0000, w_BNO=0.0000, w_BIL=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLB=1.0000, w_LINK-USD=0.0000, w_BNO=0.0000, w_BIL=0.0000
Portfolio annualized return: 11.85%, volatility: 16.14%
Sharpe ratio: (0.1185 - 0.0400) / 0.1614 = 0.4859


4-asset optimization. Max-Sharpe: 6.496. Portfolio: return=210.57%, vol=31.80%. Weights: w_FXI=0.0000, w_ETH-USD=0.2981, w_MORT=0.0000, w_SLV=0.7019.

Question:
Assets: FXI, ETH-USD, MORT, SLV
Annualized mean returns: FXI:-0.0184, ETH-USD:2.0441, MORT:-0.0518, SLV:2.1318
Covariance matrix (annualized):
[[0.065454, 0.048781, 0.02268, 0.02747], [0.048781, 0.19627, 0.058497, 0.056405], [0.02268, 0.058497, 0.14168, 0.044457], [0.02747, 0.056405, 0.044457, 0.12193]]
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_ETH-USD=0.2981, w_MORT=0.0000, w_SLV=0.7019

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_FXI=0.0000, w_ETH-USD=0.2981, w_MORT=0.0000, w_SLV=0.7019
Portfolio annualized return: 210.57%, volatility: 31.80%
Sharpe ratio: (2.1057 - 0.0400) / 0.3180 = 6.4961


4-asset optimization. Max-Sharpe: 1.272. Portfolio: return=27.29%, vol=18.31%. Weights: w_XLE=0.0000, w_BTC-USD=0.2199, w_INDS=0.7801, w_CPER=0.0000.

Question:
Assets: XLE, BTC-USD, INDS, CPER
Annualized mean returns: XLE:-0.7462, BTC-USD:0.5444, INDS:0.1964, CPER:-0.5867
Covariance matrix (annualized):
[[0.032369, -0.012024, 0.002013, 0.012016], [-0.012024, 0.309634, 0.005759, -0.002928], [0.002013, 0.005759, 0.027224, 0.001236], [0.012016, -0.002928, 0.001236, 0.030518]]
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_BTC-USD=0.2199, w_INDS=0.7801, w_CPER=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLE=0.0000, w_BTC-USD=0.2199, w_INDS=0.7801, w_CPER=0.0000
Portfolio annualized return: 27.29%, volatility: 18.31%
Sharpe ratio: (0.2729 - 0.0400) / 0.1831 = 1.2722


4-asset optimization. Max-Sharpe: 2.201. Portfolio: return=22.43%, vol=8.37%. Weights: w_USMV=1.0000, w_ADA-USD=0.0000, w_SGOV=0.0000, w_XHB=0.0000.

Question:
Assets: USMV, ADA-USD, SGOV, XHB
Annualized mean returns: USMV:0.2243, ADA-USD:-2.9859, SGOV:-0.0001, XHB:-0.3418
Covariance matrix (annualized):
[[0.007012, 0.017281, 1.4e-05, 0.007221], [0.017281, 1.637473, -8e-06, 0.028598], [1.4e-05, -8e-06, 1e-06, 4e-06], [0.007221, 0.028598, 4e-06, 0.033262]]
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=1.0000, w_ADA-USD=0.0000, w_SGOV=0.0000, w_XHB=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_USMV=1.0000, w_ADA-USD=0.0000, w_SGOV=0.0000, w_XHB=0.0000
Portfolio annualized return: 22.43%, volatility: 8.37%
Sharpe ratio: (0.2243 - 0.0400) / 0.0837 = 2.2011


4-asset optimization. Max-Sharpe: 3.362. Portfolio: return=292.76%, vol=85.88%. Weights: w_XLE=0.0000, w_LINK-USD=1.0000, w_SLV=0.0000, w_VNQI=0.0000.

Question:
Assets: XLE, LINK-USD, SLV, VNQI
Annualized mean returns: XLE:0.0459, LINK-USD:2.9276, SLV:-0.3958, VNQI:-0.4173
Covariance matrix (annualized):
[[0.026262, 0.009059, 0.015833, 0.010774], [0.009059, 0.737619, 0.038093, 0.038926], [0.015833, 0.038093, 0.035561, 0.010266], [0.010774, 0.038926, 0.010266, 0.016321]]
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=1.0000, w_SLV=0.0000, w_VNQI=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLE=0.0000, w_LINK-USD=1.0000, w_SLV=0.0000, w_VNQI=0.0000
Portfolio annualized return: 292.76%, volatility: 85.88%
Sharpe ratio: (2.9276 - 0.0400) / 0.8588 = 3.3622


4-asset optimization. Max-Sharpe: 2.383. Portfolio: return=153.42%, vol=62.72%. Weights: w_^VIX=0.0000, w_SOL-USD=0.6851, w_ICSH=0.0000, w_INDS=0.3149.

Question:
Assets: ^VIX, SOL-USD, ICSH, INDS
Annualized mean returns: ^VIX:-2.6371, SOL-USD:2.1811, ICSH:-0.0218, INDS:0.1270
Covariance matrix (annualized):
[[1.569319, -0.490206, -0.001418, -0.160048], [-0.490206, 0.816531, 0.000859, 0.013323], [-0.001418, 0.000859, 3.8e-05, 0.000356], [-0.160048, 0.013323, 0.000356, 0.043778]]
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=0.0000, w_SOL-USD=0.6851, w_ICSH=0.0000, w_INDS=0.3149

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_^VIX=0.0000, w_SOL-USD=0.6851, w_ICSH=0.0000, w_INDS=0.3149
Portfolio annualized return: 153.42%, volatility: 62.72%
Sharpe ratio: (1.5342 - 0.0400) / 0.6272 = 2.3826


4-asset optimization. Max-Sharpe: 4.966. Portfolio: return=261.75%, vol=51.90%. Weights: w_VLUE=0.8097, w_MATIC-USD=0.1903, w_PPLT=0.0000, w_SHV=0.0000.

Question:
Assets: VLUE, MATIC-USD, PPLT, SHV
Annualized mean returns: VLUE:0.2564, MATIC-USD:12.6613, PPLT:-0.0843, SHV:0.0000
Covariance matrix (annualized):
[[0.020143, 0.033146, 0.014383, 1.1e-05], [0.033146, 6.788353, 0.067552, -0.000355], [0.014383, 0.067552, 0.057897, -2e-06], [1.1e-05, -0.000355, -2e-06, 1e-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_VLUE=0.8097, w_MATIC-USD=0.1903, w_PPLT=0.0000, w_SHV=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VLUE=0.8097, w_MATIC-USD=0.1903, w_PPLT=0.0000, w_SHV=0.0000
Portfolio annualized return: 261.75%, volatility: 51.90%
Sharpe ratio: (2.6175 - 0.0400) / 0.5190 = 4.9665


4-asset optimization. Max-Sharpe: 5.424. Portfolio: return=45.23%, vol=7.60%. Weights: w_USMV=0.4333, w_BTC-USD=0.0036, w_DBC=0.3143, w_IGOV=0.2488.

Question:
Assets: USMV, BTC-USD, DBC, IGOV
Annualized mean returns: USMV:0.3315, BTC-USD:-0.0762, DBC:0.8056, IGOV:0.2240
Covariance matrix (annualized):
[[0.007179, -0.004885, 0.001692, 0.001845], [-0.004885, 0.040788, 0.001257, -0.000215], [0.001692, 0.001257, 0.030983, 0.001017], [0.001845, -0.000215, 0.001017, 0.005868]]
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=0.4333, w_BTC-USD=0.0036, w_DBC=0.3143, w_IGOV=0.2488

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_USMV=0.4333, w_BTC-USD=0.0036, w_DBC=0.3143, w_IGOV=0.2488
Portfolio annualized return: 45.23%, volatility: 7.60%
Sharpe ratio: (0.4523 - 0.0400) / 0.0760 = 5.4239


4-asset optimization. Max-Sharpe: 2.944. Portfolio: return=44.28%, vol=13.68%. Weights: w_FXI=0.0000, w_LINK-USD=0.0000, w_USO=0.1645, w_SCHH=0.8355.

Question:
Assets: FXI, LINK-USD, USO, SCHH
Annualized mean returns: FXI:-0.2288, LINK-USD:-4.9805, USO:0.5170, SCHH:0.4282
Covariance matrix (annualized):
[[0.044173, 0.009497, 0.009403, 0.007561], [0.009497, 1.737457, -0.013104, -0.001881], [0.009403, -0.013104, 0.074371, 0.011888], [0.007561, -0.001881, 0.011888, 0.019255]]
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=0.0000, w_USO=0.1645, w_SCHH=0.8355

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_FXI=0.0000, w_LINK-USD=0.0000, w_USO=0.1645, w_SCHH=0.8355
Portfolio annualized return: 44.28%, volatility: 13.68%
Sharpe ratio: (0.4428 - 0.0400) / 0.1368 = 2.9441


4-asset optimization. Max-Sharpe: 4.313. Portfolio: return=31.98%, vol=6.49%. Weights: w_QUAL=0.3980, w_XRP-USD=0.0000, w_TLT=0.4919, w_CORN=0.1101.

Question:
Assets: QUAL, XRP-USD, TLT, CORN
Annualized mean returns: QUAL:0.2721, XRP-USD:-1.3730, TLT:0.3162, CORN:0.5087
Covariance matrix (annualized):
[[0.01308, -0.012125, -0.0037, 0.000966], [-0.012125, 0.417503, 0.014232, -0.015302], [-0.0037, 0.014232, 0.011152, 0.001297], [0.000966, -0.015302, 0.001297, 0.054779]]
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=0.3980, w_XRP-USD=0.0000, w_TLT=0.4919, w_CORN=0.1101

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_QUAL=0.3980, w_XRP-USD=0.0000, w_TLT=0.4919, w_CORN=0.1101
Portfolio annualized return: 31.98%, volatility: 6.49%
Sharpe ratio: (0.3198 - 0.0400) / 0.0649 = 4.3125


4-asset optimization. Max-Sharpe: 1.192. Portfolio: return=22.28%, vol=15.34%. Weights: w_XLF=0.0000, w_SOL-USD=0.0197, w_VNQ=0.9803, w_SHV=0.0000.

Question:
Assets: XLF, SOL-USD, VNQ, SHV
Annualized mean returns: XLF:0.0945, SOL-USD:0.5776, VNQ:0.2157, SHV:-0.0011
Covariance matrix (annualized):
[[0.029667, -0.036589, 0.010583, 4.1e-05], [-0.036589, 3.110099, 0.008181, 0.000214], [0.010583, 0.008181, 0.022898, 1.2e-05], [4.1e-05, 0.000214, 1.2e-05, 2e-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_SOL-USD=0.0197, w_VNQ=0.9803, w_SHV=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLF=0.0000, w_SOL-USD=0.0197, w_VNQ=0.9803, w_SHV=0.0000
Portfolio annualized return: 22.28%, volatility: 15.34%
Sharpe ratio: (0.2228 - 0.0400) / 0.1534 = 1.1921


4-asset optimization. Max-Sharpe: 4.549. Portfolio: return=227.01%, vol=49.03%. Weights: w_VEA=0.5536, w_ETH-USD=0.4464, w_BIL=0.0000, w_TLT=0.0000.

Question:
Assets: VEA, ETH-USD, BIL, TLT
Annualized mean returns: VEA:0.3789, ETH-USD:4.6151, BIL:-0.0007, TLT:-0.4164
Covariance matrix (annualized):
[[0.020546, 0.056335, -2.1e-05, -0.005005], [0.056335, 1.034648, -9.4e-05, -0.015236], [-2.1e-05, -9.4e-05, 2e-06, -2e-06], [-0.005005, -0.015236, -2e-06, 0.01033]]
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=0.5536, w_ETH-USD=0.4464, w_BIL=0.0000, w_TLT=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VEA=0.5536, w_ETH-USD=0.4464, w_BIL=0.0000, w_TLT=0.0000
Portfolio annualized return: 227.01%, volatility: 49.03%
Sharpe ratio: (2.2701 - 0.0400) / 0.4903 = 4.5488


4-asset optimization. Max-Sharpe: 0.545. Portfolio: return=29.89%, vol=47.48%. Weights: w_EWJ=0.0000, w_BNB-USD=0.6022, w_WEAT=0.3978, w_SHY=0.0000.

Question:
Assets: EWJ, BNB-USD, WEAT, SHY
Annualized mean returns: EWJ:-0.1204, BNB-USD:0.4300, WEAT:0.1004, SHY:0.0037
Covariance matrix (annualized):
[[0.010777, -0.002299, 0.009443, -0.000239], [-0.002299, 0.552108, 0.017838, 0.000138], [0.009443, 0.017838, 0.105208, -3.2e-05], [-0.000239, 0.000138, -3.2e-05, 3.8e-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_EWJ=0.0000, w_BNB-USD=0.6022, w_WEAT=0.3978, w_SHY=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EWJ=0.0000, w_BNB-USD=0.6022, w_WEAT=0.3978, w_SHY=0.0000
Portfolio annualized return: 29.89%, volatility: 47.48%
Sharpe ratio: (0.2989 - 0.0400) / 0.4748 = 0.5453


4-asset optimization. Max-Sharpe: -0.666. Portfolio: return=-36.22%, vol=60.38%. Weights: w_XLK=0.0000, w_ETH-USD=1.0000, w_XHB=0.0000, w_BIL=0.0000.

Question:
Assets: XLK, ETH-USD, XHB, BIL
Annualized mean returns: XLK:-1.0907, ETH-USD:-0.3622, XHB:-0.8919, BIL:0.0227
Covariance matrix (annualized):
[[0.090174, 0.09012, 0.081724, -3.9e-05], [0.09012, 0.364571, 0.081461, -0.000172], [0.081724, 0.081461, 0.119924, -2.6e-05], [-3.9e-05, -0.000172, -2.6e-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_XLK=0.0000, w_ETH-USD=1.0000, w_XHB=0.0000, w_BIL=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLK=0.0000, w_ETH-USD=1.0000, w_XHB=0.0000, w_BIL=0.0000
Portfolio annualized return: -36.22%, volatility: 60.38%
Sharpe ratio: (-0.3622 - 0.0400) / 0.6038 = -0.6661


4-asset optimization. Max-Sharpe: -1.182. Portfolio: return=-45.47%, vol=41.86%. Weights: w_EWJ=0.0000, w_ADA-USD=0.0000, w_ITB=1.0000, w_GLD=0.0000.

Question:
Assets: EWJ, ADA-USD, ITB, GLD
Annualized mean returns: EWJ:-0.4551, ADA-USD:-4.4031, ITB:-0.4547, GLD:-0.2874
Covariance matrix (annualized):
[[0.043408, 0.140775, 0.062967, 0.007193], [0.140775, 1.466556, 0.227686, 0.006235], [0.062967, 0.227686, 0.175225, -0.007958], [0.007193, 0.006235, -0.007958, 0.022779]]
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_ADA-USD=0.0000, w_ITB=1.0000, w_GLD=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EWJ=0.0000, w_ADA-USD=0.0000, w_ITB=1.0000, w_GLD=0.0000
Portfolio annualized return: -45.47%, volatility: 41.86%
Sharpe ratio: (-0.4547 - 0.0400) / 0.4186 = -1.1818


4-asset optimization. Max-Sharpe: 5.756. Portfolio: return=43.74%, vol=6.90%. Weights: w_VTI=0.0914, w_XRP-USD=0.0000, w_IAU=0.2153, w_LQD=0.6933.

Question:
Assets: VTI, XRP-USD, IAU, LQD
Annualized mean returns: VTI:0.6679, XRP-USD:0.4811, IAU:0.3598, LQD:0.4311
Covariance matrix (annualized):
[[0.050124, 0.029784, -0.006841, 0.006378], [0.029784, 0.189205, 0.016422, 0.006978], [-0.006841, 0.016422, 0.016482, 0.001317], [0.006378, 0.006978, 0.001317, 0.005515]]
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=0.0914, w_XRP-USD=0.0000, w_IAU=0.2153, w_LQD=0.6933

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VTI=0.0914, w_XRP-USD=0.0000, w_IAU=0.2153, w_LQD=0.6933
Portfolio annualized return: 43.74%, volatility: 6.90%
Sharpe ratio: (0.4374 - 0.0400) / 0.0690 = 5.7560


4-asset optimization. Max-Sharpe: 3.503. Portfolio: return=20.57%, vol=4.73%. Weights: w_XLI=0.2364, w_BNB-USD=0.0075, w_SCHP=0.7131, w_SOYB=0.0430.

Question:
Assets: XLI, BNB-USD, SCHP, SOYB
Annualized mean returns: XLI:0.4111, BNB-USD:0.3200, SCHP:0.1332, SOYB:0.2604
Covariance matrix (annualized):
[[0.01943, -0.010048, 0.000447, 0.004073], [-0.010048, 0.424056, 0.003071, 0.01779], [0.000447, 0.003071, 0.001546, 0.000621], [0.004073, 0.01779, 0.000621, 0.033404]]
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=0.2364, w_BNB-USD=0.0075, w_SCHP=0.7131, w_SOYB=0.0430

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLI=0.2364, w_BNB-USD=0.0075, w_SCHP=0.7131, w_SOYB=0.0430
Portfolio annualized return: 20.57%, volatility: 4.73%
Sharpe ratio: (0.2057 - 0.0400) / 0.0473 = 3.5033


4-asset optimization. Max-Sharpe: 2.190. Portfolio: return=166.29%, vol=74.09%. Weights: w_EWJ=0.0000, w_BTC-USD=1.0000, w_IAU=0.0000, w_IYR=0.0000.

Question:
Assets: EWJ, BTC-USD, IAU, IYR
Annualized mean returns: EWJ:-0.8051, BTC-USD:1.6629, IAU:-0.0281, IYR:-0.7983
Covariance matrix (annualized):
[[0.0907, 0.089988, 0.00118, 0.091191], [0.089988, 0.548985, 0.036143, 0.092049], [0.00118, 0.036143, 0.048676, 0.011067], [0.091191, 0.092049, 0.011067, 0.134885]]
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_BTC-USD=1.0000, w_IAU=0.0000, w_IYR=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EWJ=0.0000, w_BTC-USD=1.0000, w_IAU=0.0000, w_IYR=0.0000
Portfolio annualized return: 166.29%, volatility: 74.09%
Sharpe ratio: (1.6629 - 0.0400) / 0.7409 = 2.1904


4-asset optimization. Max-Sharpe: 5.819. Portfolio: return=135.38%, vol=22.58%. Weights: w_XLY=0.0000, w_BTC-USD=0.4549, w_BNDX=0.4452, w_REZ=0.0999.

Question:
Assets: XLY, BTC-USD, BNDX, REZ
Annualized mean returns: XLY:0.1382, BTC-USD:2.8989, BNDX:0.0525, REZ:0.1170
Covariance matrix (annualized):
[[0.031895, 0.016109, 0.000227, 0.022356], [0.016109, 0.243874, 0.001002, -0.004503], [0.000227, 0.001002, 0.000675, -0.002711], [0.022356, -0.004503, -0.002711, 0.062504]]
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_BTC-USD=0.4549, w_BNDX=0.4452, w_REZ=0.0999

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLY=0.0000, w_BTC-USD=0.4549, w_BNDX=0.4452, w_REZ=0.0999
Portfolio annualized return: 135.38%, volatility: 22.58%
Sharpe ratio: (1.3538 - 0.0400) / 0.2258 = 5.8187


4-asset optimization. Max-Sharpe: -1.777. Portfolio: return=-62.40%, vol=37.36%. Weights: w_XLY=1.0000, w_ETH-USD=0.0000, w_CORN=0.0000, w_SHY=0.0000.

Question:
Assets: XLY, ETH-USD, CORN, SHY
Annualized mean returns: XLY:-0.6240, ETH-USD:-4.3754, CORN:-0.0013, SHY:-0.0029
Covariance matrix (annualized):
[[0.139579, 0.150231, 0.008641, -0.000445], [0.150231, 0.480855, 0.021282, -6.7e-05], [0.008641, 0.021282, 0.047984, 0.000642], [-0.000445, -6.7e-05, 0.000642, 0.000459]]
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_ETH-USD=0.0000, w_CORN=0.0000, w_SHY=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLY=1.0000, w_ETH-USD=0.0000, w_CORN=0.0000, w_SHY=0.0000
Portfolio annualized return: -62.40%, volatility: 37.36%
Sharpe ratio: (-0.6240 - 0.0400) / 0.3736 = -1.7772


4-asset optimization. Max-Sharpe: 1.264. Portfolio: return=5.34%, vol=1.06%. Weights: w_XLY=0.0000, w_ADA-USD=0.0000, w_CSHI=1.0000, w_PDBC=0.0000.

Question:
Assets: XLY, ADA-USD, CSHI, PDBC
Annualized mean returns: XLY:-0.7139, ADA-USD:-1.0907, CSHI:0.0534, PDBC:0.0485
Covariance matrix (annualized):
[[0.095651, 0.114904, 0.001638, 0.031672], [0.114904, 0.565591, 0.000925, 0.057591], [0.001638, 0.000925, 0.000112, 0.001204], [0.031672, 0.057591, 0.001204, 0.052926]]
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_ADA-USD=0.0000, w_CSHI=1.0000, w_PDBC=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLY=0.0000, w_ADA-USD=0.0000, w_CSHI=1.0000, w_PDBC=0.0000
Portfolio annualized return: 5.34%, volatility: 1.06%
Sharpe ratio: (0.0534 - 0.0400) / 0.0106 = 1.2641


4-asset optimization. Max-Sharpe: 3.124. Portfolio: return=74.79%, vol=22.66%. Weights: w_VLUE=0.0235, w_MATIC-USD=0.0000, w_MORT=0.9765, w_LQD=0.0000.

Question:
Assets: VLUE, MATIC-USD, MORT, LQD
Annualized mean returns: VLUE:0.4512, MATIC-USD:-0.9383, MORT:0.7550, LQD:-0.0245
Covariance matrix (annualized):
[[0.028267, 0.041736, 0.029867, 0.001434], [0.041736, 0.768061, 0.059615, -0.003739], [0.029867, 0.059615, 0.052401, 0.000234], [0.001434, -0.003739, 0.000234, 0.004092]]
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=0.0235, w_MATIC-USD=0.0000, w_MORT=0.9765, w_LQD=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VLUE=0.0235, w_MATIC-USD=0.0000, w_MORT=0.9765, w_LQD=0.0000
Portfolio annualized return: 74.79%, volatility: 22.66%
Sharpe ratio: (0.7479 - 0.0400) / 0.2266 = 3.1238


4-asset optimization. Max-Sharpe: 0.056. Portfolio: return=4.99%, vol=17.71%. Weights: w_EFA=0.0000, w_ADA-USD=0.0000, w_SCHH=1.0000, w_ICSH=0.0000.

Question:
Assets: EFA, ADA-USD, SCHH, ICSH
Annualized mean returns: EFA:-0.1739, ADA-USD:-0.7958, SCHH:0.0499, ICSH:0.0179
Covariance matrix (annualized):
[[0.035535, 0.072366, 0.022087, 2.3e-05], [0.072366, 0.452358, 0.034836, -0.000355], [0.022087, 0.034836, 0.031381, -4e-05], [2.3e-05, -0.000355, -4e-05, 1.7e-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_EFA=0.0000, w_ADA-USD=0.0000, w_SCHH=1.0000, w_ICSH=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EFA=0.0000, w_ADA-USD=0.0000, w_SCHH=1.0000, w_ICSH=0.0000
Portfolio annualized return: 4.99%, volatility: 17.71%
Sharpe ratio: (0.0499 - 0.0400) / 0.1771 = 0.0561


4-asset optimization. Max-Sharpe: 2.616. Portfolio: return=369.50%, vol=139.73%. Weights: w_IWM=0.0000, w_MATIC-USD=1.0000, w_IYR=0.0000, w_LQD=0.0000.

Question:
Assets: IWM, MATIC-USD, IYR, LQD
Annualized mean returns: IWM:-1.0724, MATIC-USD:3.6950, IYR:-0.9343, LQD:0.0155
Covariance matrix (annualized):
[[0.198703, 0.375445, 0.164928, 0.022344], [0.375445, 1.952418, 0.2646, 0.055121], [0.164928, 0.2646, 0.169139, 0.022354], [0.022344, 0.055121, 0.022354, 0.022346]]
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_MATIC-USD=1.0000, w_IYR=0.0000, w_LQD=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_IWM=0.0000, w_MATIC-USD=1.0000, w_IYR=0.0000, w_LQD=0.0000
Portfolio annualized return: 369.50%, volatility: 139.73%
Sharpe ratio: (3.6950 - 0.0400) / 1.3973 = 2.6158


4-asset optimization. Max-Sharpe: 3.522. Portfolio: return=11.60%, vol=2.16%. Weights: w_XLP=0.1257, w_DOT-USD=0.0035, w_STIP=0.8708, w_BIL=0.0000.

Question:
Assets: XLP, DOT-USD, STIP, BIL
Annualized mean returns: XLP:0.2883, DOT-USD:0.2050, STIP:0.0907, BIL:-0.0013
Covariance matrix (annualized):
[[0.009387, -0.015714, 0.000455, -3.5e-05], [-0.015714, 1.107488, -0.001049, 3.6e-05], [0.000455, -0.001049, 0.000295, -3e-06], [-3.5e-05, 3.6e-05, -3e-06, 2e-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_XLP=0.1257, w_DOT-USD=0.0035, w_STIP=0.8708, w_BIL=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLP=0.1257, w_DOT-USD=0.0035, w_STIP=0.8708, w_BIL=0.0000
Portfolio annualized return: 11.60%, volatility: 2.16%
Sharpe ratio: (0.1160 - 0.0400) / 0.0216 = 3.5218


4-asset optimization. Max-Sharpe: -0.381. Portfolio: return=-4.72%, vol=22.90%. Weights: w_XLY=0.0000, w_BTC-USD=0.0000, w_DBC=1.0000, w_BIL=0.0000.

Question:
Assets: XLY, BTC-USD, DBC, BIL
Annualized mean returns: XLY:-0.6826, BTC-USD:-3.9679, DBC:-0.0472, BIL:0.0066
Covariance matrix (annualized):
[[0.153522, 0.175207, 0.023093, 0.000157], [0.175207, 0.439555, 0.02967, 0.000225], [0.023093, 0.02967, 0.052458, 0.000124], [0.000157, 0.000225, 0.000124, 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_XLY=0.0000, w_BTC-USD=0.0000, w_DBC=1.0000, w_BIL=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLY=0.0000, w_BTC-USD=0.0000, w_DBC=1.0000, w_BIL=0.0000
Portfolio annualized return: -4.72%, volatility: 22.90%
Sharpe ratio: (-0.0472 - 0.0400) / 0.2290 = -0.3807


4-asset optimization. Max-Sharpe: -0.106. Portfolio: return=-8.80%, vol=120.79%. Weights: w_QUAL=0.0000, w_MATIC-USD=1.0000, w_XHB=0.0000, w_CPER=0.0000.

Question:
Assets: QUAL, MATIC-USD, XHB, CPER
Annualized mean returns: QUAL:-0.5731, MATIC-USD:-0.0880, XHB:-0.6380, CPER:-0.0276
Covariance matrix (annualized):
[[0.036541, 0.132548, 0.04303, 0.020815], [0.132548, 1.459015, 0.164924, 0.083199], [0.04303, 0.164924, 0.077617, 0.022463], [0.020815, 0.083199, 0.022463, 0.04781]]
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=0.0000, w_MATIC-USD=1.0000, w_XHB=0.0000, w_CPER=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_QUAL=0.0000, w_MATIC-USD=1.0000, w_XHB=0.0000, w_CPER=0.0000
Portfolio annualized return: -8.80%, volatility: 120.79%
Sharpe ratio: (-0.0880 - 0.0400) / 1.2079 = -0.1060


4-asset optimization. Max-Sharpe: 1.998. Portfolio: return=77.18%, vol=36.62%. Weights: w_XLK=0.8793, w_SOL-USD=0.1207, w_GLD=0.0000, w_VNQ=0.0000.

Question:
Assets: XLK, SOL-USD, GLD, VNQ
Annualized mean returns: XLK:0.5124, SOL-USD:2.6606, GLD:0.0269, VNQ:0.0071
Covariance matrix (annualized):
[[0.073055, 0.185162, 0.016968, 0.031113], [0.185162, 2.630035, 0.089191, 0.025102], [0.016968, 0.089191, 0.034042, 0.012944], [0.031113, 0.025102, 0.012944, 0.047832]]
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=0.8793, w_SOL-USD=0.1207, w_GLD=0.0000, w_VNQ=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLK=0.8793, w_SOL-USD=0.1207, w_GLD=0.0000, w_VNQ=0.0000
Portfolio annualized return: 77.18%, volatility: 36.62%
Sharpe ratio: (0.7718 - 0.0400) / 0.3662 = 1.9981


4-asset optimization. Max-Sharpe: 2.840. Portfolio: return=67.47%, vol=22.35%. Weights: w_XLE=0.6230, w_BNB-USD=0.1956, w_TLH=0.0000, w_INDS=0.1814.

Question:
Assets: XLE, BNB-USD, TLH, INDS
Annualized mean returns: XLE:0.7958, BNB-USD:0.7731, TLH:-0.4650, INDS:0.1530
Covariance matrix (annualized):
[[0.099132, -0.01153, 0.005345, -0.000103], [-0.01153, 0.318924, 0.004525, 0.013818], [0.005345, 0.004525, 0.023919, 0.001037], [-0.000103, 0.013818, 0.001037, 0.034478]]
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=0.6230, w_BNB-USD=0.1956, w_TLH=0.0000, w_INDS=0.1814

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLE=0.6230, w_BNB-USD=0.1956, w_TLH=0.0000, w_INDS=0.1814
Portfolio annualized return: 67.47%, volatility: 22.35%
Sharpe ratio: (0.6747 - 0.0400) / 0.2235 = 2.8398


4-asset optimization. Max-Sharpe: 2.101. Portfolio: return=55.01%, vol=24.27%. Weights: w_EFA=0.0000, w_BTC-USD=0.0990, w_WEAT=0.9010, w_ICSH=0.0000.

Question:
Assets: EFA, BTC-USD, WEAT, ICSH
Annualized mean returns: EFA:-0.0668, BTC-USD:1.0929, WEAT:0.4904, ICSH:-0.0029
Covariance matrix (annualized):
[[0.01494, 0.023675, 0.006367, -6.9e-05], [0.023675, 0.506169, 0.07934, 0.000305], [0.006367, 0.07934, 0.04902, 0.000114], [-6.9e-05, 0.000305, 0.000114, 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=0.0000, w_BTC-USD=0.0990, w_WEAT=0.9010, w_ICSH=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EFA=0.0000, w_BTC-USD=0.0990, w_WEAT=0.9010, w_ICSH=0.0000
Portfolio annualized return: 55.01%, volatility: 24.27%
Sharpe ratio: (0.5501 - 0.0400) / 0.2427 = 2.1015


4-asset optimization. Max-Sharpe: 0.691. Portfolio: return=45.67%, vol=60.27%. Weights: w_QQQ=0.0000, w_BTC-USD=1.0000, w_ITB=0.0000, w_IEF=0.0000.

Question:
Assets: QQQ, BTC-USD, ITB, IEF
Annualized mean returns: QQQ:-0.3175, BTC-USD:0.4567, ITB:-1.1780, IEF:-0.3050
Covariance matrix (annualized):
[[0.10008, 0.105074, 0.095198, -0.002539], [0.105074, 0.363216, 0.08123, -0.002792], [0.095198, 0.08123, 0.142077, 0.002675], [-0.002539, -0.002792, 0.002675, 0.00954]]
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=0.0000, w_BTC-USD=1.0000, w_ITB=0.0000, w_IEF=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_QQQ=0.0000, w_BTC-USD=1.0000, w_ITB=0.0000, w_IEF=0.0000
Portfolio annualized return: 45.67%, volatility: 60.27%
Sharpe ratio: (0.4567 - 0.0400) / 0.6027 = 0.6913


4-asset optimization. Max-Sharpe: 6.853. Portfolio: return=30.94%, vol=3.93%. Weights: w_USMV=0.3198, w_ADA-USD=0.0135, w_REZ=0.0343, w_IEF=0.6324.

Question:
Assets: USMV, ADA-USD, REZ, IEF
Annualized mean returns: USMV:0.6770, ADA-USD:0.1100, REZ:0.7359, IEF:0.1046
Covariance matrix (annualized):
[[0.019097, -0.024038, 0.012731, -0.004054], [-0.024038, 0.707789, -0.050341, 0.000375], [0.012731, -0.050341, 0.032075, -0.000788], [-0.004054, 0.000375, -0.000788, 0.002671]]
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=0.3198, w_ADA-USD=0.0135, w_REZ=0.0343, w_IEF=0.6324

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_USMV=0.3198, w_ADA-USD=0.0135, w_REZ=0.0343, w_IEF=0.6324
Portfolio annualized return: 30.94%, volatility: 3.93%
Sharpe ratio: (0.3094 - 0.0400) / 0.0393 = 6.8530


4-asset optimization. Max-Sharpe: 1.379. Portfolio: return=30.60%, vol=19.29%. Weights: w_XLV=0.5919, w_LINK-USD=0.0000, w_PALL=0.0000, w_XHB=0.4081.

Question:
Assets: XLV, LINK-USD, PALL, XHB
Annualized mean returns: XLV:0.2562, LINK-USD:-0.6070, PALL:0.1377, XHB:0.3781
Covariance matrix (annualized):
[[0.032497, 0.052826, 0.023414, 0.027006], [0.052826, 0.977643, 0.063301, 0.043783], [0.023414, 0.063301, 0.125688, 0.020404], [0.027006, 0.043783, 0.020404, 0.076768]]
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=0.5919, w_LINK-USD=0.0000, w_PALL=0.0000, w_XHB=0.4081

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLV=0.5919, w_LINK-USD=0.0000, w_PALL=0.0000, w_XHB=0.4081
Portfolio annualized return: 30.60%, volatility: 19.29%
Sharpe ratio: (0.3060 - 0.0400) / 0.1929 = 1.3787


4-asset optimization. Max-Sharpe: 6.055. Portfolio: return=441.47%, vol=72.25%. Weights: w_XLP=0.0000, w_LINK-USD=1.0000, w_MORT=0.0000, w_BIL=0.0000.

Question:
Assets: XLP, LINK-USD, MORT, BIL
Annualized mean returns: XLP:0.2537, LINK-USD:4.4147, MORT:-0.3277, BIL:-0.0016
Covariance matrix (annualized):
[[0.04304, 0.047231, 0.037274, 1.6e-05], [0.047231, 0.522015, 0.119467, -0.00025], [0.037274, 0.119467, 0.269379, 4.7e-05], [1.6e-05, -0.00025, 4.7e-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_XLP=0.0000, w_LINK-USD=1.0000, w_MORT=0.0000, w_BIL=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLP=0.0000, w_LINK-USD=1.0000, w_MORT=0.0000, w_BIL=0.0000
Portfolio annualized return: 441.47%, volatility: 72.25%
Sharpe ratio: (4.4147 - 0.0400) / 0.7225 = 6.0550


4-asset optimization. Max-Sharpe: 3.915. Portfolio: return=56.12%, vol=13.31%. Weights: w_XLK=0.4874, w_XRP-USD=0.0000, w_GLD=0.5126, w_HYG=0.0000.

Question:
Assets: XLK, XRP-USD, GLD, HYG
Annualized mean returns: XLK:0.8301, XRP-USD:-0.2342, GLD:0.3054, HYG:0.1681
Covariance matrix (annualized):
[[0.056884, 0.016748, -0.001686, 0.017793], [0.016748, 0.095232, 0.014846, 0.006018], [-0.001686, 0.014846, 0.019208, -0.003648], [0.017793, 0.006018, -0.003648, 0.011552]]
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=0.4874, w_XRP-USD=0.0000, w_GLD=0.5126, w_HYG=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLK=0.4874, w_XRP-USD=0.0000, w_GLD=0.5126, w_HYG=0.0000
Portfolio annualized return: 56.12%, volatility: 13.31%
Sharpe ratio: (0.5612 - 0.0400) / 0.1331 = 3.9152


4-asset optimization. Max-Sharpe: 8.834. Portfolio: return=89.67%, vol=9.70%. Weights: w_XLK=0.3695, w_MATIC-USD=0.0059, w_VNQI=0.0197, w_SOYB=0.6048.

Question:
Assets: XLK, MATIC-USD, VNQI, SOYB
Annualized mean returns: XLK:0.6693, MATIC-USD:2.6114, VNQI:0.7148, SOYB:1.0248
Covariance matrix (annualized):
[[0.025585, 0.010079, 0.008168, -0.004576], [0.010079, 1.027993, 0.003661, 0.030298], [0.008168, 0.003661, 0.025091, 0.006404], [-0.004576, 0.030298, 0.006404, 0.020165]]
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=0.3695, w_MATIC-USD=0.0059, w_VNQI=0.0197, w_SOYB=0.6048

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLK=0.3695, w_MATIC-USD=0.0059, w_VNQI=0.0197, w_SOYB=0.6048
Portfolio annualized return: 89.67%, volatility: 9.70%
Sharpe ratio: (0.8967 - 0.0400) / 0.0970 = 8.8341


4-asset optimization. Max-Sharpe: 8.746. Portfolio: return=18.88%, vol=1.70%. Weights: w_ACWI=0.1532, w_MATIC-USD=0.0082, w_CORN=0.0000, w_VCIT=0.8387.

Question:
Assets: ACWI, MATIC-USD, CORN, VCIT
Annualized mean returns: ACWI:0.2642, MATIC-USD:3.7547, CORN:-0.0985, VCIT:0.1403
Covariance matrix (annualized):
[[0.012219, 0.00479, 0.003767, -0.001758], [0.00479, 1.07587, -0.006485, -0.002729], [0.003767, -0.006485, 0.017844, -0.00068], [-0.001758, -0.002729, -0.00068, 0.00058]]
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=0.1532, w_MATIC-USD=0.0082, w_CORN=0.0000, w_VCIT=0.8387

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_ACWI=0.1532, w_MATIC-USD=0.0082, w_CORN=0.0000, w_VCIT=0.8387
Portfolio annualized return: 18.88%, volatility: 1.70%
Sharpe ratio: (0.1888 - 0.0400) / 0.0170 = 8.7464


4-asset optimization. Max-Sharpe: 3.215. Portfolio: return=73.36%, vol=21.57%. Weights: w_MTUM=0.7761, w_MATIC-USD=0.0000, w_BIL=0.0000, w_BNO=0.2239.

Question:
Assets: MTUM, MATIC-USD, BIL, BNO
Annualized mean returns: MTUM:0.6724, MATIC-USD:-0.0311, BIL:0.0000, BNO:0.9455
Covariance matrix (annualized):
[[0.042593, 0.023086, 6.7e-05, 0.041877], [0.023086, 0.293227, 0.000366, 0.02673], [6.7e-05, 0.000366, 2e-06, 6.3e-05], [0.041877, 0.02673, 6.3e-05, 0.126195]]
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=0.7761, w_MATIC-USD=0.0000, w_BIL=0.0000, w_BNO=0.2239

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_MTUM=0.7761, w_MATIC-USD=0.0000, w_BIL=0.0000, w_BNO=0.2239
Portfolio annualized return: 73.36%, volatility: 21.57%
Sharpe ratio: (0.7336 - 0.0400) / 0.2157 = 3.2151


4-asset optimization. Max-Sharpe: 5.776. Portfolio: return=54.29%, vol=8.71%. Weights: w_FXI=0.0000, w_MATIC-USD=0.0615, w_IAU=0.2811, w_VCIT=0.6574.

Question:
Assets: FXI, MATIC-USD, IAU, VCIT
Annualized mean returns: FXI:-0.8455, MATIC-USD:4.5616, IAU:0.5386, VCIT:0.1690
Covariance matrix (annualized):
[[0.069821, 0.072418, -0.010128, -0.000526], [0.072418, 0.959807, 0.023478, 0.003886], [-0.010128, 0.023478, 0.01978, 0.000779], [-0.000526, 0.003886, 0.000779, 0.002261]]
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_MATIC-USD=0.0615, w_IAU=0.2811, w_VCIT=0.6574

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_FXI=0.0000, w_MATIC-USD=0.0615, w_IAU=0.2811, w_VCIT=0.6574
Portfolio annualized return: 54.29%, volatility: 8.71%
Sharpe ratio: (0.5429 - 0.0400) / 0.0871 = 5.7763


4-asset optimization. Max-Sharpe: 4.435. Portfolio: return=28.58%, vol=5.54%. Weights: w_USMV=1.0000, w_XRP-USD=0.0000, w_MORT=0.0000, w_IAU=0.0000.

Question:
Assets: USMV, XRP-USD, MORT, IAU
Annualized mean returns: USMV:0.2858, XRP-USD:-1.8030, MORT:0.0564, IAU:-0.1171
Covariance matrix (annualized):
[[0.003072, 0.015904, 0.000632, 0.002102], [0.015904, 0.99218, 0.00711, 0.008771], [0.000632, 0.00711, 0.005642, 0.000128], [0.002102, 0.008771, 0.000128, 0.009378]]
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=1.0000, w_XRP-USD=0.0000, w_MORT=0.0000, w_IAU=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_USMV=1.0000, w_XRP-USD=0.0000, w_MORT=0.0000, w_IAU=0.0000
Portfolio annualized return: 28.58%, volatility: 5.54%
Sharpe ratio: (0.2858 - 0.0400) / 0.0554 = 4.4346


4-asset optimization. Max-Sharpe: 5.703. Portfolio: return=243.92%, vol=42.07%. Weights: w_IVV=0.7832, w_DOT-USD=0.2168, w_BIL=0.0000, w_BNDX=0.0000.

Question:
Assets: IVV, DOT-USD, BIL, BNDX
Annualized mean returns: IVV:0.4387, DOT-USD:9.6654, BIL:0.0000, BNDX:-0.0606
Covariance matrix (annualized):
[[0.019456, 0.065336, 8e-06, 0.00055], [0.065336, 3.038468, 0.000444, 0.011433], [8e-06, 0.000444, 1e-06, 3e-06], [0.00055, 0.011433, 3e-06, 0.000423]]
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=0.7832, w_DOT-USD=0.2168, w_BIL=0.0000, w_BNDX=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_IVV=0.7832, w_DOT-USD=0.2168, w_BIL=0.0000, w_BNDX=0.0000
Portfolio annualized return: 243.92%, volatility: 42.07%
Sharpe ratio: (2.4392 - 0.0400) / 0.4207 = 5.7033


4-asset optimization. Max-Sharpe: 2.617. Portfolio: return=363.76%, vol=137.46%. Weights: w_XLRE=0.0000, w_XRP-USD=1.0000, w_REZ=0.0000, w_LQD=0.0000.

Question:
Assets: XLRE, XRP-USD, REZ, LQD
Annualized mean returns: XLRE:0.0037, XRP-USD:3.6376, REZ:0.1044, LQD:-0.1366
Covariance matrix (annualized):
[[0.032289, 0.073385, 0.032437, 0.00105], [0.073385, 1.889566, 0.073498, 0.00445], [0.032437, 0.073498, 0.036122, 0.001808], [0.00105, 0.00445, 0.001808, 0.001519]]
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_XRP-USD=1.0000, w_REZ=0.0000, w_LQD=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLRE=0.0000, w_XRP-USD=1.0000, w_REZ=0.0000, w_LQD=0.0000
Portfolio annualized return: 363.76%, volatility: 137.46%
Sharpe ratio: (3.6376 - 0.0400) / 1.3746 = 2.6171


4-asset optimization. Max-Sharpe: 3.614. Portfolio: return=24.10%, vol=5.56%. Weights: w_VLUE=0.0000, w_BTC-USD=0.1003, w_HYG=0.8362, w_SLV=0.0635.

Question:
Assets: VLUE, BTC-USD, HYG, SLV
Annualized mean returns: VLUE:0.1580, BTC-USD:0.2099, HYG:0.2291, SLV:0.4471
Covariance matrix (annualized):
[[0.016389, -0.005667, 0.00639, -0.001277], [-0.005667, 0.043678, -0.002975, 0.011373], [0.00639, -0.002975, 0.003698, 0.001828], [-0.001277, 0.011373, 0.001828, 0.056595]]
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_BTC-USD=0.1003, w_HYG=0.8362, w_SLV=0.0635

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VLUE=0.0000, w_BTC-USD=0.1003, w_HYG=0.8362, w_SLV=0.0635
Portfolio annualized return: 24.10%, volatility: 5.56%
Sharpe ratio: (0.2410 - 0.0400) / 0.0556 = 3.6143


4-asset optimization. Max-Sharpe: 0.898. Portfolio: return=30.82%, vol=29.88%. Weights: w_USMV=0.0000, w_BNB-USD=0.0000, w_SGOV=0.0000, w_XHB=1.0000.

Question:
Assets: USMV, BNB-USD, SGOV, XHB
Annualized mean returns: USMV:-0.0302, BNB-USD:-0.3552, SGOV:0.0092, XHB:0.3082
Covariance matrix (annualized):
[[0.034052, 0.069748, -7e-06, 0.044995], [0.069748, 0.462509, 0.000176, 0.120569], [-7e-06, 0.000176, 3e-06, -1.9e-05], [0.044995, 0.120569, -1.9e-05, 0.089293]]
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_BNB-USD=0.0000, w_SGOV=0.0000, w_XHB=1.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_USMV=0.0000, w_BNB-USD=0.0000, w_SGOV=0.0000, w_XHB=1.0000
Portfolio annualized return: 30.82%, volatility: 29.88%
Sharpe ratio: (0.3082 - 0.0400) / 0.2988 = 0.8975


4-asset optimization. Max-Sharpe: 3.390. Portfolio: return=32.41%, vol=8.38%. Weights: w_IVV=0.6119, w_BTC-USD=0.0552, w_SCHH=0.3120, w_CPER=0.0208.

Question:
Assets: IVV, BTC-USD, SCHH, CPER
Annualized mean returns: IVV:0.1970, BTC-USD:1.2266, SCHH:0.4305, CPER:0.0725
Covariance matrix (annualized):
[[0.004568, -0.00585, 0.004436, 0.001232], [-0.00585, 0.525455, 0.0114, 0.015968], [0.004436, 0.0114, 0.020621, -0.005945], [0.001232, 0.015968, -0.005945, 0.049027]]
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=0.6119, w_BTC-USD=0.0552, w_SCHH=0.3120, w_CPER=0.0208

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_IVV=0.6119, w_BTC-USD=0.0552, w_SCHH=0.3120, w_CPER=0.0208
Portfolio annualized return: 32.41%, volatility: 8.38%
Sharpe ratio: (0.3241 - 0.0400) / 0.0838 = 3.3901


4-asset optimization. Max-Sharpe: 4.726. Portfolio: return=41.35%, vol=7.90%. Weights: w_EWJ=0.1650, w_MATIC-USD=0.0162, w_REZ=0.3393, w_DBA=0.4795.

Question:
Assets: EWJ, MATIC-USD, REZ, DBA
Annualized mean returns: EWJ:0.2216, MATIC-USD:3.1548, REZ:0.3779, DBA:0.4120
Covariance matrix (annualized):
[[0.012282, -0.020127, 0.002504, 0.001013], [-0.020127, 3.500313, -0.011594, 0.005435], [0.002504, -0.011594, 0.021359, -0.003801], [0.001013, 0.005435, -0.003801, 0.015129]]
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=0.1650, w_MATIC-USD=0.0162, w_REZ=0.3393, w_DBA=0.4795

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EWJ=0.1650, w_MATIC-USD=0.0162, w_REZ=0.3393, w_DBA=0.4795
Portfolio annualized return: 41.35%, volatility: 7.90%
Sharpe ratio: (0.4135 - 0.0400) / 0.0790 = 4.7263


4-asset optimization. Max-Sharpe: 1.120. Portfolio: return=41.57%, vol=33.54%. Weights: w_FXI=0.0000, w_BTC-USD=1.0000, w_BIL=0.0000, w_SCHH=0.0000.

Question:
Assets: FXI, BTC-USD, BIL, SCHH
Annualized mean returns: FXI:-0.2545, BTC-USD:0.4157, BIL:-0.0027, SCHH:-0.4334
Covariance matrix (annualized):
[[0.067297, 0.028613, 0.000139, 0.019488], [0.028613, 0.112506, 0.000195, 0.001867], [0.000139, 0.000195, 6e-06, 5e-06], [0.019488, 0.001867, 5e-06, 0.02264]]
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_BTC-USD=1.0000, w_BIL=0.0000, w_SCHH=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_FXI=0.0000, w_BTC-USD=1.0000, w_BIL=0.0000, w_SCHH=0.0000
Portfolio annualized return: 41.57%, volatility: 33.54%
Sharpe ratio: (0.4157 - 0.0400) / 0.3354 = 1.1202


4-asset optimization. Max-Sharpe: 5.120. Portfolio: return=193.71%, vol=37.05%. Weights: w_XLY=0.0000, w_ETH-USD=0.0000, w_BNDX=0.0000, w_USO=1.0000.

Question:
Assets: XLY, ETH-USD, BNDX, USO
Annualized mean returns: XLY:-1.1463, ETH-USD:-0.3818, BNDX:-0.1929, USO:1.9371
Covariance matrix (annualized):
[[0.104743, 0.163009, -0.003046, -0.039157], [0.163009, 0.6567, -0.007545, -0.025161], [-0.003046, -0.007545, 0.003488, 0.003933], [-0.039157, -0.025161, 0.003933, 0.137293]]
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_BNDX=0.0000, w_USO=1.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLY=0.0000, w_ETH-USD=0.0000, w_BNDX=0.0000, w_USO=1.0000
Portfolio annualized return: 193.71%, volatility: 37.05%
Sharpe ratio: (1.9371 - 0.0400) / 0.3705 = 5.1200


4-asset optimization. Max-Sharpe: 6.941. Portfolio: return=68.46%, vol=9.29%. Weights: w_VEA=0.7040, w_XRP-USD=0.0321, w_MORT=0.2639, w_ICSH=0.0000.

Question:
Assets: VEA, XRP-USD, MORT, ICSH
Annualized mean returns: VEA:0.3751, XRP-USD:11.5354, MORT:0.1917, ICSH:0.0166
Covariance matrix (annualized):
[[0.005176, 0.027259, -0.000128, 2.4e-05], [0.027259, 4.45663, -0.031415, 0.00072], [-0.000128, -0.031415, 0.011848, -9.3e-05], [2.4e-05, 0.00072, -9.3e-05, 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_VEA=0.7040, w_XRP-USD=0.0321, w_MORT=0.2639, w_ICSH=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VEA=0.7040, w_XRP-USD=0.0321, w_MORT=0.2639, w_ICSH=0.0000
Portfolio annualized return: 68.46%, volatility: 9.29%
Sharpe ratio: (0.6846 - 0.0400) / 0.0929 = 6.9410


4-asset optimization. Max-Sharpe: -1.118. Portfolio: return=-103.87%, vol=96.48%. Weights: w_XLB=0.0000, w_ETH-USD=1.0000, w_ICSH=0.0000, w_VNQ=0.0000.

Question:
Assets: XLB, ETH-USD, ICSH, VNQ
Annualized mean returns: XLB:-0.4002, ETH-USD:-1.0387, ICSH:0.0251, VNQ:-0.4320
Covariance matrix (annualized):
[[0.023841, 0.025403, 2.5e-05, 0.007619], [0.025403, 0.930784, -0.001197, 0.051617], [2.5e-05, -0.001197, 1.4e-05, -4.4e-05], [0.007619, 0.051617, -4.4e-05, 0.020424]]
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_ETH-USD=1.0000, w_ICSH=0.0000, w_VNQ=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLB=0.0000, w_ETH-USD=1.0000, w_ICSH=0.0000, w_VNQ=0.0000
Portfolio annualized return: -103.87%, volatility: 96.48%
Sharpe ratio: (-1.0387 - 0.0400) / 0.9648 = -1.1181


4-asset optimization. Max-Sharpe: 0.956. Portfolio: return=16.60%, vol=13.18%. Weights: w_XLP=0.6713, w_ADA-USD=0.0000, w_VNQI=0.3287, w_SGOV=0.0000.

Question:
Assets: XLP, ADA-USD, VNQI, SGOV
Annualized mean returns: XLP:0.1681, ADA-USD:-1.3184, VNQI:0.1617, SGOV:0.0008
Covariance matrix (annualized):
[[0.019193, 0.038277, 0.014508, 1.4e-05], [0.038277, 0.793076, 0.041717, -0.000261], [0.014508, 0.041717, 0.021405, -2.1e-05], [1.4e-05, -0.000261, -2.1e-05, 1e-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_XLP=0.6713, w_ADA-USD=0.0000, w_VNQI=0.3287, w_SGOV=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLP=0.6713, w_ADA-USD=0.0000, w_VNQI=0.3287, w_SGOV=0.0000
Portfolio annualized return: 16.60%, volatility: 13.18%
Sharpe ratio: (0.1660 - 0.0400) / 0.1318 = 0.9564


4-asset optimization. Max-Sharpe: 6.039. Portfolio: return=90.17%, vol=14.27%. Weights: w_XLRE=0.0000, w_ETH-USD=0.1272, w_IYR=0.1741, w_DBB=0.6987.

Question:
Assets: XLRE, ETH-USD, IYR, DBB
Annualized mean returns: XLRE:0.2643, ETH-USD:2.1711, IYR:0.3972, DBB:0.7962
Covariance matrix (annualized):
[[0.034058, -0.005477, 0.036282, 0.00385], [-0.005477, 0.322598, -0.003032, 0.014078], [0.036282, -0.003032, 0.039638, 0.002756], [0.00385, 0.014078, 0.002756, 0.022323]]
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_ETH-USD=0.1272, w_IYR=0.1741, w_DBB=0.6987

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLRE=0.0000, w_ETH-USD=0.1272, w_IYR=0.1741, w_DBB=0.6987
Portfolio annualized return: 90.17%, volatility: 14.27%
Sharpe ratio: (0.9017 - 0.0400) / 0.1427 = 6.0390


4-asset optimization. Max-Sharpe: 3.379. Portfolio: return=364.65%, vol=106.73%. Weights: w_XLV=0.0000, w_ADA-USD=1.0000, w_VNQI=0.0000, w_ICSH=0.0000.

Question:
Assets: XLV, ADA-USD, VNQI, ICSH
Annualized mean returns: XLV:0.0668, ADA-USD:3.6465, VNQI:-0.0362, ICSH:0.0038
Covariance matrix (annualized):
[[0.010654, 0.012571, 0.000918, -2e-06], [0.012571, 1.139043, 0.051623, 0.000235], [0.000918, 0.051623, 0.015986, 1.3e-05], [-2e-06, 0.000235, 1.3e-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_XLV=0.0000, w_ADA-USD=1.0000, w_VNQI=0.0000, w_ICSH=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLV=0.0000, w_ADA-USD=1.0000, w_VNQI=0.0000, w_ICSH=0.0000
Portfolio annualized return: 364.65%, volatility: 106.73%
Sharpe ratio: (3.6465 - 0.0400) / 1.0673 = 3.3792


4-asset optimization. Max-Sharpe: 4.452. Portfolio: return=40.88%, vol=8.29%. Weights: w_MTUM=0.8636, w_ETH-USD=0.0333, w_HYG=0.0000, w_PPLT=0.1031.

Question:
Assets: MTUM, ETH-USD, HYG, PPLT
Annualized mean returns: MTUM:0.3875, ETH-USD:0.8068, HYG:0.0869, PPLT:0.4593
Covariance matrix (annualized):
[[0.007201, 0.000476, 0.001697, 0.002256], [0.000476, 0.40804, -0.001596, 0.002679], [0.001697, -0.001596, 0.001599, 0.004126], [0.002256, 0.002679, 0.004126, 0.055922]]
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=0.8636, w_ETH-USD=0.0333, w_HYG=0.0000, w_PPLT=0.1031

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_MTUM=0.8636, w_ETH-USD=0.0333, w_HYG=0.0000, w_PPLT=0.1031
Portfolio annualized return: 40.88%, volatility: 8.29%
Sharpe ratio: (0.4088 - 0.0400) / 0.0829 = 4.4517


4-asset optimization. Max-Sharpe: 0.927. Portfolio: return=141.07%, vol=147.86%. Weights: w_^VIX=1.0000, w_BNB-USD=0.0000, w_SLV=0.0000, w_ICSH=0.0000.

Question:
Assets: ^VIX, BNB-USD, SLV, ICSH
Annualized mean returns: ^VIX:1.4107, BNB-USD:-1.9999, SLV:-0.7037, ICSH:0.0089
Covariance matrix (annualized):
[[2.186389, -0.597379, -0.148526, -0.001155], [-0.597379, 0.656945, 0.038695, -0.000215], [-0.148526, 0.038695, 0.06211, 0.000317], [-0.001155, -0.000215, 0.000317, 2.8e-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_^VIX=1.0000, w_BNB-USD=0.0000, w_SLV=0.0000, w_ICSH=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_^VIX=1.0000, w_BNB-USD=0.0000, w_SLV=0.0000, w_ICSH=0.0000
Portfolio annualized return: 141.07%, volatility: 147.86%
Sharpe ratio: (1.4107 - 0.0400) / 1.4786 = 0.9270


4-asset optimization. Max-Sharpe: 6.533. Portfolio: return=262.66%, vol=39.59%. Weights: w_XLF=0.0000, w_LINK-USD=0.3602, w_XHB=0.4884, w_STIP=0.1514.

Question:
Assets: XLF, LINK-USD, XHB, STIP
Annualized mean returns: XLF:0.6091, LINK-USD:4.1291, XHB:2.3124, STIP:0.0651
Covariance matrix (annualized):
[[0.152136, 0.1122, 0.158861, 0.002626], [0.1122, 0.541371, 0.107998, 0.000359], [0.158861, 0.107998, 0.201479, 0.002692], [0.002626, 0.000359, 0.002692, 0.000526]]
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_LINK-USD=0.3602, w_XHB=0.4884, w_STIP=0.1514

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLF=0.0000, w_LINK-USD=0.3602, w_XHB=0.4884, w_STIP=0.1514
Portfolio annualized return: 262.66%, volatility: 39.59%
Sharpe ratio: (2.6266 - 0.0400) / 0.3959 = 6.5331


4-asset optimization. Max-Sharpe: -0.238. Portfolio: return=-2.30%, vol=26.54%. Weights: w_XLB=1.0000, w_MATIC-USD=0.0000, w_SCHP=0.0000, w_MORT=0.0000.

Question:
Assets: XLB, MATIC-USD, SCHP, MORT
Annualized mean returns: XLB:-0.0230, MATIC-USD:-5.5276, SCHP:-0.0217, MORT:-0.1959
Covariance matrix (annualized):
[[0.070424, 0.136374, 0.006394, 0.050013], [0.136374, 1.189562, -0.003155, 0.121211], [0.006394, -0.003155, 0.006252, 0.007313], [0.050013, 0.121211, 0.007313, 0.06841]]
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=1.0000, w_MATIC-USD=0.0000, w_SCHP=0.0000, w_MORT=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLB=1.0000, w_MATIC-USD=0.0000, w_SCHP=0.0000, w_MORT=0.0000
Portfolio annualized return: -2.30%, volatility: 26.54%
Sharpe ratio: (-0.0230 - 0.0400) / 0.2654 = -0.2376


4-asset optimization. Max-Sharpe: 0.381. Portfolio: return=10.34%, vol=16.65%. Weights: w_XLU=0.0000, w_XRP-USD=0.0000, w_WEAT=1.0000, w_VNQ=0.0000.

Question:
Assets: XLU, XRP-USD, WEAT, VNQ
Annualized mean returns: XLU:-0.0911, XRP-USD:-1.0646, WEAT:0.1034, VNQ:-0.0288
Covariance matrix (annualized):
[[0.009631, -0.003232, -0.000657, 0.006619], [-0.003232, 0.23571, 0.010835, 0.004342], [-0.000657, 0.010835, 0.027737, -0.001421], [0.006619, 0.004342, -0.001421, 0.011497]]
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_XRP-USD=0.0000, w_WEAT=1.0000, w_VNQ=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLU=0.0000, w_XRP-USD=0.0000, w_WEAT=1.0000, w_VNQ=0.0000
Portfolio annualized return: 10.34%, volatility: 16.65%
Sharpe ratio: (0.1034 - 0.0400) / 0.1665 = 0.3805


4-asset optimization. Max-Sharpe: 2.224. Portfolio: return=151.36%, vol=66.26%. Weights: w_XLU=0.0000, w_BNB-USD=0.0323, w_UNG=0.9677, w_VNQI=0.0000.

Question:
Assets: XLU, BNB-USD, UNG, VNQI
Annualized mean returns: XLU:-0.0622, BNB-USD:0.3223, UNG:1.5533, VNQI:-0.1269
Covariance matrix (annualized):
[[0.022373, 0.039182, 0.012794, 0.003266], [0.039182, 0.70979, 0.063234, 0.044922], [0.012794, 0.063234, 0.463805, 0.022259], [0.003266, 0.044922, 0.022259, 0.015972]]
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_BNB-USD=0.0323, w_UNG=0.9677, w_VNQI=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLU=0.0000, w_BNB-USD=0.0323, w_UNG=0.9677, w_VNQI=0.0000
Portfolio annualized return: 151.36%, volatility: 66.26%
Sharpe ratio: (1.5136 - 0.0400) / 0.6626 = 2.2239


4-asset optimization. Max-Sharpe: 4.835. Portfolio: return=74.74%, vol=14.63%. Weights: w_XLB=0.6619, w_SOL-USD=0.0451, w_DBB=0.2930, w_ITB=0.0000.

Question:
Assets: XLB, SOL-USD, DBB, ITB
Annualized mean returns: XLB:0.7615, SOL-USD:2.2242, DBB:0.4887, ITB:0.2488
Covariance matrix (annualized):
[[0.03261, -0.053316, 0.009051, 0.009973], [-0.053316, 2.437223, -0.028675, -0.009596], [0.009051, -0.028675, 0.030303, 0.002758], [0.009973, -0.009596, 0.002758, 0.067486]]
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=0.6619, w_SOL-USD=0.0451, w_DBB=0.2930, w_ITB=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLB=0.6619, w_SOL-USD=0.0451, w_DBB=0.2930, w_ITB=0.0000
Portfolio annualized return: 74.74%, volatility: 14.63%
Sharpe ratio: (0.7474 - 0.0400) / 0.1463 = 4.8347


4-asset optimization. Max-Sharpe: 3.281. Portfolio: return=47.04%, vol=13.12%. Weights: w_IWM=0.0000, w_BNB-USD=0.1310, w_HAUZ=0.8690, w_BIL=0.0000.

Question:
Assets: IWM, BNB-USD, HAUZ, BIL
Annualized mean returns: IWM:-0.1406, BNB-USD:2.1530, HAUZ:0.2167, BIL:0.0243
Covariance matrix (annualized):
[[0.031189, -0.006348, 0.010189, 3.8e-05], [-0.006348, 0.649662, -0.000734, -0.000294], [0.010189, -0.000734, 0.008242, 2.3e-05], [3.8e-05, -0.000294, 2.3e-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_IWM=0.0000, w_BNB-USD=0.1310, w_HAUZ=0.8690, w_BIL=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_IWM=0.0000, w_BNB-USD=0.1310, w_HAUZ=0.8690, w_BIL=0.0000
Portfolio annualized return: 47.04%, volatility: 13.12%
Sharpe ratio: (0.4704 - 0.0400) / 0.1312 = 3.2812


4-asset optimization. Max-Sharpe: 1.124. Portfolio: return=32.98%, vol=25.79%. Weights: w_FXI=1.0000, w_ADA-USD=0.0000, w_REZ=0.0000, w_LQD=0.0000.

Question:
Assets: FXI, ADA-USD, REZ, LQD
Annualized mean returns: FXI:0.3298, ADA-USD:-2.9842, REZ:-0.8640, LQD:-0.2173
Covariance matrix (annualized):
[[0.06653, 0.140831, 0.018987, 0.001664], [0.140831, 2.650544, 0.044397, 0.003871], [0.018987, 0.044397, 0.038782, 0.003055], [0.001664, 0.003871, 0.003055, 0.002079]]
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=1.0000, w_ADA-USD=0.0000, w_REZ=0.0000, w_LQD=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_FXI=1.0000, w_ADA-USD=0.0000, w_REZ=0.0000, w_LQD=0.0000
Portfolio annualized return: 32.98%, volatility: 25.79%
Sharpe ratio: (0.3298 - 0.0400) / 0.2579 = 1.1235


4-asset optimization. Max-Sharpe: 3.718. Portfolio: return=42.77%, vol=10.43%. Weights: w_VEA=0.9882, w_ETH-USD=0.0118, w_ICSH=0.0000, w_DBC=0.0000.

Question:
Assets: VEA, ETH-USD, ICSH, DBC
Annualized mean returns: VEA:0.4333, ETH-USD:-0.0436, ICSH:0.0259, DBC:0.1384
Covariance matrix (annualized):
[[0.011259, -0.007932, -0.000116, 0.003638], [-0.007932, 0.466974, 0.000355, -0.001453], [-0.000116, 0.000355, 1.5e-05, -3.9e-05], [0.003638, -0.001453, -3.9e-05, 0.019212]]
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=0.9882, w_ETH-USD=0.0118, w_ICSH=0.0000, w_DBC=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VEA=0.9882, w_ETH-USD=0.0118, w_ICSH=0.0000, w_DBC=0.0000
Portfolio annualized return: 42.77%, volatility: 10.43%
Sharpe ratio: (0.4277 - 0.0400) / 0.1043 = 3.7178


4-asset optimization. Max-Sharpe: 0.689. Portfolio: return=20.28%, vol=23.64%. Weights: w_XLK=0.0000, w_BNB-USD=0.1980, w_BIL=0.0000, w_DBC=0.8020.

Question:
Assets: XLK, BNB-USD, BIL, DBC
Annualized mean returns: XLK:-0.1046, BNB-USD:0.6165, BIL:0.0232, DBC:0.1006
Covariance matrix (annualized):
[[0.083463, 0.04406, -0.000101, 0.018343], [0.04406, 1.014901, -0.000705, -0.003798], [-0.000101, -0.000705, 4e-06, -7.7e-05], [0.018343, -0.003798, -7.7e-05, 0.026882]]
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=0.0000, w_BNB-USD=0.1980, w_BIL=0.0000, w_DBC=0.8020

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLK=0.0000, w_BNB-USD=0.1980, w_BIL=0.0000, w_DBC=0.8020
Portfolio annualized return: 20.28%, volatility: 23.64%
Sharpe ratio: (0.2028 - 0.0400) / 0.2364 = 0.6886


4-asset optimization. Max-Sharpe: 2.749. Portfolio: return=36.30%, vol=11.75%. Weights: w_FXI=0.0000, w_ETH-USD=0.0573, w_EMB=0.0000, w_VNQI=0.9427.

Question:
Assets: FXI, ETH-USD, EMB, VNQI
Annualized mean returns: FXI:-0.8310, ETH-USD:1.1620, EMB:-0.0315, VNQI:0.3145
Covariance matrix (annualized):
[[0.078836, 0.095537, 0.016302, 0.014777], [0.095537, 0.596494, 0.018706, 0.014616], [0.016302, 0.018706, 0.01246, 0.005161], [0.014777, 0.014616, 0.005161, 0.01156]]
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_ETH-USD=0.0573, w_EMB=0.0000, w_VNQI=0.9427

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_FXI=0.0000, w_ETH-USD=0.0573, w_EMB=0.0000, w_VNQI=0.9427
Portfolio annualized return: 36.30%, volatility: 11.75%
Sharpe ratio: (0.3630 - 0.0400) / 0.1175 = 2.7487


4-asset optimization. Max-Sharpe: 2.677. Portfolio: return=59.93%, vol=20.89%. Weights: w_XLE=0.6063, w_MATIC-USD=0.1203, w_TLH=0.2734, w_ICSH=0.0000.

Question:
Assets: XLE, MATIC-USD, TLH, ICSH
Annualized mean returns: XLE:0.3157, MATIC-USD:3.4388, TLH:-0.0216, ICSH:0.0248
Covariance matrix (annualized):
[[0.03529, 0.02613, -0.011068, -0.000123], [0.02613, 2.084108, -0.005222, -0.00173], [-0.011068, -0.005222, 0.009253, 8.4e-05], [-0.000123, -0.00173, 8.4e-05, 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_XLE=0.6063, w_MATIC-USD=0.1203, w_TLH=0.2734, w_ICSH=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLE=0.6063, w_MATIC-USD=0.1203, w_TLH=0.2734, w_ICSH=0.0000
Portfolio annualized return: 59.93%, volatility: 20.89%
Sharpe ratio: (0.5993 - 0.0400) / 0.2089 = 2.6774


4-asset optimization. Max-Sharpe: 3.053. Portfolio: return=13.50%, vol=3.11%. Weights: w_MTUM=0.1492, w_DOT-USD=0.0000, w_VCIT=0.8508, w_SGOV=0.0000.

Question:
Assets: MTUM, DOT-USD, VCIT, SGOV
Annualized mean returns: MTUM:0.2030, DOT-USD:-3.7062, VCIT:0.1231, SGOV:0.0006
Covariance matrix (annualized):
[[0.021697, -0.00243, -0.001851, 1.3e-05], [-0.00243, 1.333543, 0.002291, -0.000237], [-0.001851, 0.002291, 0.00132, -4e-06], [1.3e-05, -0.000237, -4e-06, 1e-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=0.1492, w_DOT-USD=0.0000, w_VCIT=0.8508, w_SGOV=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_MTUM=0.1492, w_DOT-USD=0.0000, w_VCIT=0.8508, w_SGOV=0.0000
Portfolio annualized return: 13.50%, volatility: 3.11%
Sharpe ratio: (0.1350 - 0.0400) / 0.0311 = 3.0527


4-asset optimization. Max-Sharpe: -1.639. Portfolio: return=-37.65%, vol=25.41%. Weights: w_VEA=0.0000, w_BTC-USD=0.0000, w_VNQ=1.0000, w_BIL=0.0000.

Question:
Assets: VEA, BTC-USD, VNQ, BIL
Annualized mean returns: VEA:-0.3857, BTC-USD:-2.8933, VNQ:-0.3765, BIL:0.0020
Covariance matrix (annualized):
[[0.045186, 0.080823, 0.041756, 0.000123], [0.080823, 0.329571, 0.068732, 0.000386], [0.041756, 0.068732, 0.064591, 0.00012], [0.000123, 0.000386, 0.00012, 3e-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=0.0000, w_BTC-USD=0.0000, w_VNQ=1.0000, w_BIL=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VEA=0.0000, w_BTC-USD=0.0000, w_VNQ=1.0000, w_BIL=0.0000
Portfolio annualized return: -37.65%, volatility: 25.41%
Sharpe ratio: (-0.3765 - 0.0400) / 0.2541 = -1.6389


4-asset optimization. Max-Sharpe: 4.614. Portfolio: return=64.20%, vol=13.05%. Weights: w_FXI=0.0000, w_BNB-USD=0.0755, w_REZ=0.9245, w_SHV=0.0000.

Question:
Assets: FXI, BNB-USD, REZ, SHV
Annualized mean returns: FXI:-0.5440, BNB-USD:1.9595, REZ:0.5345, SHV:0.0184
Covariance matrix (annualized):
[[0.037642, 0.007047, 0.006021, -0.000177], [0.007047, 0.895193, -0.014369, -2.6e-05], [0.006021, -0.014369, 0.016293, 8e-06], [-0.000177, -2.6e-05, 8e-06, 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_FXI=0.0000, w_BNB-USD=0.0755, w_REZ=0.9245, w_SHV=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_FXI=0.0000, w_BNB-USD=0.0755, w_REZ=0.9245, w_SHV=0.0000
Portfolio annualized return: 64.20%, volatility: 13.05%
Sharpe ratio: (0.6420 - 0.0400) / 0.1305 = 4.6144


4-asset optimization. Max-Sharpe: 2.193. Portfolio: return=42.75%, vol=17.67%. Weights: w_EWJ=0.6970, w_DOT-USD=0.0000, w_BIL=0.0000, w_VNQI=0.3030.

Question:
Assets: EWJ, DOT-USD, BIL, VNQI
Annualized mean returns: EWJ:0.4261, DOT-USD:-0.5321, BIL:0.0345, VNQI:0.4306
Covariance matrix (annualized):
[[0.033025, 0.05584, -5.7e-05, 0.0267], [0.05584, 0.495696, -0.000313, 0.056779], [-5.7e-05, -0.000313, 8e-06, 5.3e-05], [0.0267, 0.056779, 5.3e-05, 0.042431]]
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=0.6970, w_DOT-USD=0.0000, w_BIL=0.0000, w_VNQI=0.3030

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EWJ=0.6970, w_DOT-USD=0.0000, w_BIL=0.0000, w_VNQI=0.3030
Portfolio annualized return: 42.75%, volatility: 17.67%
Sharpe ratio: (0.4275 - 0.0400) / 0.1767 = 2.1930


4-asset optimization. Max-Sharpe: 1.888. Portfolio: return=43.02%, vol=20.67%. Weights: w_IWM=0.0000, w_MATIC-USD=0.0000, w_XHB=1.0000, w_SGOV=0.0000.

Question:
Assets: IWM, MATIC-USD, XHB, SGOV
Annualized mean returns: IWM:-0.2201, MATIC-USD:0.1035, XHB:0.4302, SGOV:-0.0004
Covariance matrix (annualized):
[[0.036007, 0.025534, 0.025766, 1.8e-05], [0.025534, 1.756695, 0.049887, 2.8e-05], [0.025766, 0.049887, 0.042707, 1.6e-05], [1.8e-05, 2.8e-05, 1.6e-05, 1e-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_IWM=0.0000, w_MATIC-USD=0.0000, w_XHB=1.0000, w_SGOV=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_IWM=0.0000, w_MATIC-USD=0.0000, w_XHB=1.0000, w_SGOV=0.0000
Portfolio annualized return: 43.02%, volatility: 20.67%
Sharpe ratio: (0.4302 - 0.0400) / 0.2067 = 1.8879


4-asset optimization. Max-Sharpe: -0.521. Portfolio: return=-5.98%, vol=19.16%. Weights: w_USMV=1.0000, w_DOT-USD=0.0000, w_SCHP=0.0000, w_SOYB=0.0000.

Question:
Assets: USMV, DOT-USD, SCHP, SOYB
Annualized mean returns: USMV:-0.0598, DOT-USD:-3.5975, SCHP:-0.1250, SOYB:-0.1996
Covariance matrix (annualized):
[[0.03672, 0.078958, 0.003636, 0.002679], [0.078958, 0.867643, 0.002498, 0.022068], [0.003636, 0.002498, 0.006155, -0.00163], [0.002679, 0.022068, -0.00163, 0.051056]]
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=1.0000, w_DOT-USD=0.0000, w_SCHP=0.0000, w_SOYB=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_USMV=1.0000, w_DOT-USD=0.0000, w_SCHP=0.0000, w_SOYB=0.0000
Portfolio annualized return: -5.98%, volatility: 19.16%
Sharpe ratio: (-0.0598 - 0.0400) / 0.1916 = -0.5207


4-asset optimization. Max-Sharpe: 5.616. Portfolio: return=108.27%, vol=18.56%. Weights: w_ACWI=0.0000, w_LINK-USD=0.1819, w_VNQI=0.0000, w_LQD=0.8181.

Question:
Assets: ACWI, LINK-USD, VNQI, LQD
Annualized mean returns: ACWI:-0.0197, LINK-USD:5.5858, VNQI:-0.0782, LQD:0.0814
Covariance matrix (annualized):
[[0.013239, 0.020757, 0.007616, -1e-06], [0.020757, 0.998698, 0.028359, 0.002019], [0.007616, 0.028359, 0.007061, 0.000252], [-1e-06, 0.002019, 0.000252, 0.001223]]
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_LINK-USD=0.1819, w_VNQI=0.0000, w_LQD=0.8181

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_ACWI=0.0000, w_LINK-USD=0.1819, w_VNQI=0.0000, w_LQD=0.8181
Portfolio annualized return: 108.27%, volatility: 18.56%
Sharpe ratio: (1.0827 - 0.0400) / 0.1856 = 5.6163


4-asset optimization. Max-Sharpe: 3.344. Portfolio: return=33.53%, vol=8.83%. Weights: w_ACWI=0.4294, w_BNB-USD=0.0231, w_HAUZ=0.3694, w_CORN=0.1781.

Question:
Assets: ACWI, BNB-USD, HAUZ, CORN
Annualized mean returns: ACWI:0.3058, BNB-USD:0.7326, HAUZ:0.2568, CORN:0.5177
Covariance matrix (annualized):
[[0.010199, 0.008973, 0.005779, 0.001678], [0.008973, 0.473328, 0.005871, 0.007569], [0.005779, 0.005871, 0.006173, 0.004646], [0.001678, 0.007569, 0.004646, 0.056171]]
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=0.4294, w_BNB-USD=0.0231, w_HAUZ=0.3694, w_CORN=0.1781

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_ACWI=0.4294, w_BNB-USD=0.0231, w_HAUZ=0.3694, w_CORN=0.1781
Portfolio annualized return: 33.53%, volatility: 8.83%
Sharpe ratio: (0.3353 - 0.0400) / 0.0883 = 3.3436


4-asset optimization. Max-Sharpe: 2.449. Portfolio: return=36.46%, vol=13.25%. Weights: w_USMV=0.5028, w_XRP-USD=0.0323, w_HYG=0.0000, w_DBB=0.4649.

Question:
Assets: USMV, XRP-USD, HYG, DBB
Annualized mean returns: USMV:0.2857, XRP-USD:0.5572, HYG:0.1630, DBB:0.4366
Covariance matrix (annualized):
[[0.023064, 0.029047, 0.015756, 0.001638], [0.029047, 0.244344, 0.024503, 0.011814], [0.015756, 0.024503, 0.014872, 0.00183], [0.001638, 0.011814, 0.00183, 0.043576]]
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=0.5028, w_XRP-USD=0.0323, w_HYG=0.0000, w_DBB=0.4649

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_USMV=0.5028, w_XRP-USD=0.0323, w_HYG=0.0000, w_DBB=0.4649
Portfolio annualized return: 36.46%, volatility: 13.25%
Sharpe ratio: (0.3646 - 0.0400) / 0.1325 = 2.4494


4-asset optimization. Max-Sharpe: 3.230. Portfolio: return=49.26%, vol=14.01%. Weights: w_XLI=0.9281, w_LINK-USD=0.0719, w_ITB=0.0000, w_SHV=0.0000.

Question:
Assets: XLI, LINK-USD, ITB, SHV
Annualized mean returns: XLI:0.3523, LINK-USD:2.3049, ITB:-0.1148, SHV:0.0184
Covariance matrix (annualized):
[[0.013435, 0.014971, 0.010193, 1.4e-05], [0.014971, 1.173784, 0.043734, 0.000266], [0.010193, 0.043734, 0.041851, 5.9e-05], [1.4e-05, 0.000266, 5.9e-05, 1e-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=0.9281, w_LINK-USD=0.0719, w_ITB=0.0000, w_SHV=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLI=0.9281, w_LINK-USD=0.0719, w_ITB=0.0000, w_SHV=0.0000
Portfolio annualized return: 49.26%, volatility: 14.01%
Sharpe ratio: (0.4926 - 0.0400) / 0.1401 = 3.2303


4-asset optimization. Max-Sharpe: 0.474. Portfolio: return=7.16%, vol=6.66%. Weights: w_VTI=1.0000, w_ADA-USD=0.0000, w_LQD=0.0000, w_BIL=0.0000.

Question:
Assets: VTI, ADA-USD, LQD, BIL
Annualized mean returns: VTI:0.0716, ADA-USD:-0.7236, LQD:-0.0813, BIL:0.0171
Covariance matrix (annualized):
[[0.00444, 0.024873, 0.000332, -5.3e-05], [0.024873, 0.968858, -0.000442, 0.00033], [0.000332, -0.000442, 0.001395, -3e-06], [-5.3e-05, 0.00033, -3e-06, 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_VTI=1.0000, w_ADA-USD=0.0000, w_LQD=0.0000, w_BIL=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VTI=1.0000, w_ADA-USD=0.0000, w_LQD=0.0000, w_BIL=0.0000
Portfolio annualized return: 7.16%, volatility: 6.66%
Sharpe ratio: (0.0716 - 0.0400) / 0.0666 = 0.4738


4-asset optimization. Max-Sharpe: -0.767. Portfolio: return=-86.23%, vol=117.65%. Weights: w_XLI=0.0000, w_LINK-USD=1.0000, w_INDS=0.0000, w_LQD=0.0000.

Question:
Assets: XLI, LINK-USD, INDS, LQD
Annualized mean returns: XLI:-0.2907, LINK-USD:-0.8623, INDS:-0.0585, LQD:-0.0971
Covariance matrix (annualized):
[[0.018475, 0.048406, 0.007068, 0.001208], [0.048406, 1.384123, 0.072922, 0.025035], [0.007068, 0.072922, 0.019734, 0.002136], [0.001208, 0.025035, 0.002136, 0.003359]]
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_LINK-USD=1.0000, w_INDS=0.0000, w_LQD=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLI=0.0000, w_LINK-USD=1.0000, w_INDS=0.0000, w_LQD=0.0000
Portfolio annualized return: -86.23%, volatility: 117.65%
Sharpe ratio: (-0.8623 - 0.0400) / 1.1765 = -0.7670


4-asset optimization. Max-Sharpe: 3.935. Portfolio: return=653.43%, vol=165.02%. Weights: w_XLU=0.0000, w_DOT-USD=1.0000, w_IYR=0.0000, w_BIL=0.0000.

Question:
Assets: XLU, DOT-USD, IYR, BIL
Annualized mean returns: XLU:-0.0655, DOT-USD:6.5343, IYR:0.0164, BIL:-0.0005
Covariance matrix (annualized):
[[0.027411, 0.099714, 0.015505, 3e-06], [0.099714, 2.723183, 0.074875, 0.000593], [0.015505, 0.074875, 0.025411, 1.9e-05], [3e-06, 0.000593, 1.9e-05, 2e-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_XLU=0.0000, w_DOT-USD=1.0000, w_IYR=0.0000, w_BIL=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLU=0.0000, w_DOT-USD=1.0000, w_IYR=0.0000, w_BIL=0.0000
Portfolio annualized return: 653.43%, volatility: 165.02%
Sharpe ratio: (6.5343 - 0.0400) / 1.6502 = 3.9355


4-asset optimization. Max-Sharpe: 5.317. Portfolio: return=167.10%, vol=30.68%. Weights: w_XLF=0.3818, w_BTC-USD=0.2718, w_REZ=0.3464, w_IEF=0.0000.

Question:
Assets: XLF, BTC-USD, REZ, IEF
Annualized mean returns: XLF:0.7633, BTC-USD:4.4262, REZ:0.5098, IEF:-0.1887
Covariance matrix (annualized):
[[0.041218, 0.079067, 0.013012, -0.00398], [0.079067, 0.769032, 0.040062, -0.007407], [0.013012, 0.040062, 0.032467, 0.000867], [-0.00398, -0.007407, 0.000867, 0.001428]]
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=0.3818, w_BTC-USD=0.2718, w_REZ=0.3464, w_IEF=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLF=0.3818, w_BTC-USD=0.2718, w_REZ=0.3464, w_IEF=0.0000
Portfolio annualized return: 167.10%, volatility: 30.68%
Sharpe ratio: (1.6710 - 0.0400) / 0.3068 = 5.3168


4-asset optimization. Max-Sharpe: 1.967. Portfolio: return=51.92%, vol=24.37%. Weights: w_XLP=0.1075, w_ADA-USD=0.0000, w_SHV=0.0000, w_PALL=0.8925.

Question:
Assets: XLP, ADA-USD, SHV, PALL
Annualized mean returns: XLP:0.0931, ADA-USD:-0.5896, SHV:-0.0002, PALL:0.5705
Covariance matrix (annualized):
[[0.020207, 0.041375, 3.7e-05, 0.004943], [0.041375, 0.769753, -1e-05, 0.027152], [3.7e-05, -1e-05, 1e-06, -4.6e-05], [0.004943, 0.027152, -4.6e-05, 0.07305]]
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=0.1075, w_ADA-USD=0.0000, w_SHV=0.0000, w_PALL=0.8925

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLP=0.1075, w_ADA-USD=0.0000, w_SHV=0.0000, w_PALL=0.8925
Portfolio annualized return: 51.92%, volatility: 24.37%
Sharpe ratio: (0.5192 - 0.0400) / 0.2437 = 1.9667


4-asset optimization. Max-Sharpe: 3.568. Portfolio: return=51.99%, vol=13.45%. Weights: w_XLP=0.8354, w_DOT-USD=0.0031, w_BNO=0.1615, w_BNDX=0.0000.

Question:
Assets: XLP, DOT-USD, BNO, BNDX
Annualized mean returns: XLP:0.4563, DOT-USD:0.3363, BNO:0.8522, BNDX:-0.2204
Covariance matrix (annualized):
[[0.025665, 0.006348, -0.035743, -0.000635], [0.006348, 0.491176, 0.026839, 0.005391], [-0.035743, 0.026839, 0.374015, 0.008535], [-0.000635, 0.005391, 0.008535, 0.003421]]
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=0.8354, w_DOT-USD=0.0031, w_BNO=0.1615, w_BNDX=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLP=0.8354, w_DOT-USD=0.0031, w_BNO=0.1615, w_BNDX=0.0000
Portfolio annualized return: 51.99%, volatility: 13.45%
Sharpe ratio: (0.5199 - 0.0400) / 0.1345 = 3.5682


4-asset optimization. Max-Sharpe: -0.682. Portfolio: return=-40.50%, vol=65.21%. Weights: w_VEA=0.0000, w_ADA-USD=0.0000, w_UNG=1.0000, w_BNDX=0.0000.

Question:
Assets: VEA, ADA-USD, UNG, BNDX
Annualized mean returns: VEA:-0.4051, ADA-USD:-1.2452, UNG:-0.4050, BNDX:-0.2312
Covariance matrix (annualized):
[[0.036246, 0.071994, 0.031292, 0.005116], [0.071994, 0.400236, 0.023969, 0.00958], [0.031292, 0.023969, 0.425283, 0.005322], [0.005116, 0.00958, 0.005322, 0.004049]]
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_ADA-USD=0.0000, w_UNG=1.0000, w_BNDX=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VEA=0.0000, w_ADA-USD=0.0000, w_UNG=1.0000, w_BNDX=0.0000
Portfolio annualized return: -40.50%, volatility: 65.21%
Sharpe ratio: (-0.4050 - 0.0400) / 0.6521 = -0.6823


4-asset optimization. Max-Sharpe: -0.004. Portfolio: return=3.88%, vol=27.25%. Weights: w_IWM=1.0000, w_BNB-USD=0.0000, w_SHV=0.0000, w_DBA=0.0000.

Question:
Assets: IWM, BNB-USD, SHV, DBA
Annualized mean returns: IWM:0.0388, BNB-USD:-1.2155, SHV:0.0038, DBA:-0.7333
Covariance matrix (annualized):
[[0.074248, 0.081567, 8.9e-05, 0.008823], [0.081567, 0.415878, 0.000507, -0.007523], [8.9e-05, 0.000507, 1e-05, -3.6e-05], [0.008823, -0.007523, -3.6e-05, 0.030322]]
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_BNB-USD=0.0000, w_SHV=0.0000, w_DBA=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_IWM=1.0000, w_BNB-USD=0.0000, w_SHV=0.0000, w_DBA=0.0000
Portfolio annualized return: 3.88%, volatility: 27.25%
Sharpe ratio: (0.0388 - 0.0400) / 0.2725 = -0.0044


4-asset optimization. Max-Sharpe: 6.361. Portfolio: return=24.81%, vol=3.27%. Weights: w_IVV=0.1359, w_SOL-USD=0.0184, w_BIL=0.0000, w_IEF=0.8457.

Question:
Assets: IVV, SOL-USD, BIL, IEF
Annualized mean returns: IVV:0.4669, SOL-USD:5.2318, BIL:0.0000, IEF:0.1046
Covariance matrix (annualized):
[[0.036925, 0.040061, 5.4e-05, -0.00421], [0.040061, 1.546695, 0.000138, -0.0085], [5.4e-05, 0.000138, 2e-06, 3e-06], [-0.00421, -0.0085, 3e-06, 0.001254]]
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=0.1359, w_SOL-USD=0.0184, w_BIL=0.0000, w_IEF=0.8457

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_IVV=0.1359, w_SOL-USD=0.0184, w_BIL=0.0000, w_IEF=0.8457
Portfolio annualized return: 24.81%, volatility: 3.27%
Sharpe ratio: (0.2481 - 0.0400) / 0.0327 = 6.3611


4-asset optimization. Max-Sharpe: 0.565. Portfolio: return=10.90%, vol=12.22%. Weights: w_IVV=0.0000, w_BTC-USD=0.0000, w_WEAT=0.0467, w_VNQI=0.9533.

Question:
Assets: IVV, BTC-USD, WEAT, VNQI
Annualized mean returns: IVV:-0.0443, BTC-USD:-1.7966, WEAT:0.0618, VNQI:0.1113
Covariance matrix (annualized):
[[0.037365, -0.008237, -0.002211, 0.019979], [-0.008237, 0.563323, 0.004293, -0.017589], [-0.002211, 0.004293, 0.068398, 0.001591], [0.019979, -0.017589, 0.001591, 0.016105]]
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_BTC-USD=0.0000, w_WEAT=0.0467, w_VNQI=0.9533

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_IVV=0.0000, w_BTC-USD=0.0000, w_WEAT=0.0467, w_VNQI=0.9533
Portfolio annualized return: 10.90%, volatility: 12.22%
Sharpe ratio: (0.1090 - 0.0400) / 0.1222 = 0.5647