4-asset optimization. Max-Sharpe: 2.834. Portfolio: return=32.99%, vol=10.23%. Weights: w_VTI=0.8945, w_DOT-USD=0.1055, w_HAUZ=0.0000, w_CORN=0.0000.

Question:
Assets: VTI, DOT-USD, HAUZ, CORN
Annualized mean returns: VTI:0.3017, DOT-USD:0.5697, HAUZ:-0.0123, CORN:-0.1167
Covariance matrix (annualized):
[[0.010458, 0.00084, 0.008761, 0.000182], [0.00084, 0.174045, -0.004778, -0.016409], [0.008761, -0.004778, 0.021607, -0.000357], [0.000182, -0.016409, -0.000357, 0.122788]]
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=0.8945, w_DOT-USD=0.1055, w_HAUZ=0.0000, w_CORN=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VTI=0.8945, w_DOT-USD=0.1055, w_HAUZ=0.0000, w_CORN=0.0000
Portfolio annualized return: 32.99%, volatility: 10.23%
Sharpe ratio: (0.3299 - 0.0400) / 0.1023 = 2.8344


4-asset optimization. Max-Sharpe: 5.953. Portfolio: return=5.94%, vol=0.33%. Weights: w_USMV=0.0043, w_BTC-USD=0.0033, w_HAUZ=0.0000, w_SGOV=0.9924.

Question:
Assets: USMV, BTC-USD, HAUZ, SGOV
Annualized mean returns: USMV:0.2525, BTC-USD:1.2706, HAUZ:-0.1671, SGOV:0.0545
Covariance matrix (annualized):
[[0.006172, 0.001737, 0.007079, 8.5e-05], [0.001737, 0.198158, 0.007884, 6e-06], [0.007079, 0.007884, 0.029123, 9.4e-05], [8.5e-05, 6e-06, 9.4e-05, 8e-06]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_USMV=0.0043, w_BTC-USD=0.0033, w_HAUZ=0.0000, w_SGOV=0.9924

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_USMV=0.0043, w_BTC-USD=0.0033, w_HAUZ=0.0000, w_SGOV=0.9924
Portfolio annualized return: 5.94%, volatility: 0.33%
Sharpe ratio: (0.0594 - 0.0400) / 0.0033 = 5.9526


4-asset optimization. Max-Sharpe: 1.253. Portfolio: return=47.85%, vol=35.00%. Weights: w_^VIX=0.2453, w_AVAX-USD=0.4844, w_ICSH=0.0000, w_BNO=0.2704.

Question:
Assets: ^VIX, AVAX-USD, ICSH, BNO
Annualized mean returns: ^VIX:0.5255, AVAX-USD:0.6412, ICSH:0.0343, BNO:0.1445
Covariance matrix (annualized):
[[1.065536, -0.331477, 0.000977, 0.128766], [-0.331477, 0.554511, -0.000441, -0.07172], [0.000977, -0.000441, 1.7e-05, 8.5e-05], [0.128766, -0.07172, 8.5e-05, 0.119641]]
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=0.2453, w_AVAX-USD=0.4844, w_ICSH=0.0000, w_BNO=0.2704

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_^VIX=0.2453, w_AVAX-USD=0.4844, w_ICSH=0.0000, w_BNO=0.2704
Portfolio annualized return: 47.85%, volatility: 35.00%
Sharpe ratio: (0.4785 - 0.0400) / 0.3500 = 1.2531


4-asset optimization. Max-Sharpe: -1.820. Portfolio: return=-26.42%, vol=16.71%. Weights: w_XLB=0.2500, w_DOT-USD=0.2500, w_SHY=0.2500, w_ICSH=0.2500.

Question:
Assets: XLB, DOT-USD, SHY, ICSH
Annualized mean returns: XLB:-0.1322, DOT-USD:-1.0310, SHY:0.0532, ICSH:0.0533
Covariance matrix (annualized):
[[0.016302, 0.023521, 0.000762, 0.000148], [0.023521, 0.374523, 0.002218, 0.00122], [0.000762, 0.002218, 0.000221, 2.8e-05], [0.000148, 0.00122, 2.8e-05, 1.3e-05]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_XLB=0.2500, w_DOT-USD=0.2500, w_SHY=0.2500, w_ICSH=0.2500

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLB=0.2500, w_DOT-USD=0.2500, w_SHY=0.2500, w_ICSH=0.2500
Portfolio annualized return: -26.42%, volatility: 16.71%
Sharpe ratio: (-0.2642 - 0.0400) / 0.1671 = -1.8202


4-asset optimization. Max-Sharpe: 3.885. Portfolio: return=42.09%, vol=9.80%. Weights: w_XLP=0.7354, w_ADA-USD=0.0000, w_VNQI=0.2646, w_DBC=0.0000.

Question:
Assets: XLP, ADA-USD, VNQI, DBC
Annualized mean returns: XLP:0.4088, ADA-USD:-0.5750, VNQI:0.4546, DBC:-0.1552
Covariance matrix (annualized):
[[0.010152, 0.014991, 0.00696, -0.003091], [0.014991, 0.346804, 0.032935, 0.016997], [0.00696, 0.032935, 0.020201, 0.006769], [-0.003091, 0.016997, 0.006769, 0.026892]]
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=0.7354, w_ADA-USD=0.0000, w_VNQI=0.2646, w_DBC=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLP=0.7354, w_ADA-USD=0.0000, w_VNQI=0.2646, w_DBC=0.0000
Portfolio annualized return: 42.09%, volatility: 9.80%
Sharpe ratio: (0.4209 - 0.0400) / 0.0980 = 3.8847


4-asset optimization. Max-Sharpe: 2.205. Portfolio: return=147.69%, vol=65.18%. Weights: w_MTUM=0.0000, w_ADA-USD=1.0000, w_DBA=0.0000, w_VNQI=0.0000.

Question:
Assets: MTUM, ADA-USD, DBA, VNQI
Annualized mean returns: MTUM:-0.2278, ADA-USD:1.4769, DBA:0.0210, VNQI:0.0403
Covariance matrix (annualized):
[[0.018688, 0.020829, 0.003988, 0.003329], [0.020829, 0.424781, 0.006645, 0.031109], [0.003988, 0.006645, 0.011798, -0.000239], [0.003329, 0.031109, -0.000239, 0.021869]]
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=0.0000, w_ADA-USD=1.0000, w_DBA=0.0000, w_VNQI=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_MTUM=0.0000, w_ADA-USD=1.0000, w_DBA=0.0000, w_VNQI=0.0000
Portfolio annualized return: 147.69%, volatility: 65.18%
Sharpe ratio: (1.4769 - 0.0400) / 0.6518 = 2.2046


4-asset optimization. Max-Sharpe: 2.458. Portfolio: return=19.66%, vol=6.37%. Weights: w_FXI=0.1385, w_DOT-USD=0.0000, w_CORN=0.0541, w_EMB=0.8074.

Question:
Assets: FXI, DOT-USD, CORN, EMB
Annualized mean returns: FXI:0.4228, DOT-USD:0.4348, CORN:-0.0615, EMB:0.1751
Covariance matrix (annualized):
[[0.05755, 0.05107, -0.009828, 0.003072], [0.05107, 0.493864, 0.011756, 0.004721], [-0.009828, 0.011756, 0.028698, -0.003497], [0.003072, 0.004721, -0.003497, 0.004043]]
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=0.1385, w_DOT-USD=0.0000, w_CORN=0.0541, w_EMB=0.8074

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_FXI=0.1385, w_DOT-USD=0.0000, w_CORN=0.0541, w_EMB=0.8074
Portfolio annualized return: 19.66%, volatility: 6.37%
Sharpe ratio: (0.1966 - 0.0400) / 0.0637 = 2.4584


4-asset optimization. Max-Sharpe: 2.227. Portfolio: return=159.66%, vol=69.91%. Weights: w_XLRE=0.0000, w_LINK-USD=1.0000, w_ICSH=0.0000, w_CORN=0.0000.

Question:
Assets: XLRE, LINK-USD, ICSH, CORN
Annualized mean returns: XLRE:-0.2093, LINK-USD:1.5966, ICSH:0.0363, CORN:-0.0004
Covariance matrix (annualized):
[[0.024626, 0.008116, 0.000162, -0.000278], [0.008116, 0.488779, -0.000779, -0.002196], [0.000162, -0.000779, 1.8e-05, -4.7e-05], [-0.000278, -0.002196, -4.7e-05, 0.018974]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_XLRE=0.0000, w_LINK-USD=1.0000, w_ICSH=0.0000, w_CORN=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLRE=0.0000, w_LINK-USD=1.0000, w_ICSH=0.0000, w_CORN=0.0000
Portfolio annualized return: 159.66%, volatility: 69.91%
Sharpe ratio: (1.5966 - 0.0400) / 0.6991 = 2.2265


4-asset optimization. Max-Sharpe: 3.762. Portfolio: return=5.65%, vol=0.44%. Weights: w_USMV=0.0021, w_XRP-USD=0.0000, w_ICSH=0.9979, w_XHB=0.0000.

Question:
Assets: USMV, XRP-USD, ICSH, XHB
Annualized mean returns: USMV:0.0426, XRP-USD:-2.3557, ICSH:0.0565, XHB:-0.2563
Covariance matrix (annualized):
[[0.005205, 0.014144, -8e-06, 0.007276], [0.014144, 0.254386, -4e-06, 0.042163], [-8e-06, -4e-06, 1.9e-05, 7.2e-05], [0.007276, 0.042163, 7.2e-05, 0.040512]]
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=0.0021, w_XRP-USD=0.0000, w_ICSH=0.9979, w_XHB=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_USMV=0.0021, w_XRP-USD=0.0000, w_ICSH=0.9979, w_XHB=0.0000
Portfolio annualized return: 5.65%, volatility: 0.44%
Sharpe ratio: (0.0565 - 0.0400) / 0.0044 = 3.7621


4-asset optimization. Max-Sharpe: 3.102. Portfolio: return=88.08%, vol=27.11%. Weights: w_XLY=0.8236, w_LINK-USD=0.1764, w_TIP=0.0000, w_SCHH=0.0000.

Question:
Assets: XLY, LINK-USD, TIP, SCHH
Annualized mean returns: XLY:0.7715, LINK-USD:1.3910, TIP:0.0312, SCHH:0.2261
Covariance matrix (annualized):
[[0.06323, 0.067186, 0.001507, 0.040815], [0.067186, 0.355597, 0.002017, 0.043699], [0.001507, 0.002017, 0.000805, 0.002107], [0.040815, 0.043699, 0.002107, 0.043225]]
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=0.8236, w_LINK-USD=0.1764, w_TIP=0.0000, w_SCHH=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLY=0.8236, w_LINK-USD=0.1764, w_TIP=0.0000, w_SCHH=0.0000
Portfolio annualized return: 88.08%, volatility: 27.11%
Sharpe ratio: (0.8808 - 0.0400) / 0.2711 = 3.1018


4-asset optimization. Max-Sharpe: 5.894. Portfolio: return=5.46%, vol=0.25%. Weights: w_XLB=0.0000, w_ADA-USD=0.0000, w_SGOV=1.0000, w_VNQI=0.0000.

Question:
Assets: XLB, ADA-USD, SGOV, VNQI
Annualized mean returns: XLB:-0.2258, ADA-USD:-0.4944, SGOV:0.0546, VNQI:-0.1609
Covariance matrix (annualized):
[[0.011696, 0.000822, -6.3e-05, 0.006651], [0.000822, 0.239598, -0.000235, 0.018095], [-6.3e-05, -0.000235, 6e-06, -1.3e-05], [0.006651, 0.018095, -1.3e-05, 0.01617]]
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_ADA-USD=0.0000, w_SGOV=1.0000, w_VNQI=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLB=0.0000, w_ADA-USD=0.0000, w_SGOV=1.0000, w_VNQI=0.0000
Portfolio annualized return: 5.46%, volatility: 0.25%
Sharpe ratio: (0.0546 - 0.0400) / 0.0025 = 5.8944


4-asset optimization. Max-Sharpe: 4.928. Portfolio: return=7.41%, vol=0.69%. Weights: w_FXI=0.0000, w_ADA-USD=0.0078, w_ICSH=0.9922, w_TLT=0.0000.

Question:
Assets: FXI, ADA-USD, ICSH, TLT
Annualized mean returns: FXI:0.0302, ADA-USD:2.6046, ICSH:0.0543, TLT:0.0310
Covariance matrix (annualized):
[[0.106528, 0.023232, 0.000125, 0.004033], [0.023232, 0.520106, -0.000435, 0.009892], [0.000125, -0.000435, 2.4e-05, 0.000389], [0.004033, 0.009892, 0.000389, 0.022729]]
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_ADA-USD=0.0078, w_ICSH=0.9922, w_TLT=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_FXI=0.0000, w_ADA-USD=0.0078, w_ICSH=0.9922, w_TLT=0.0000
Portfolio annualized return: 7.41%, volatility: 0.69%
Sharpe ratio: (0.0741 - 0.0400) / 0.0069 = 4.9280


4-asset optimization. Max-Sharpe: 5.858. Portfolio: return=5.39%, vol=0.24%. Weights: w_VTI=0.0000, w_XRP-USD=0.0017, w_SGOV=0.9949, w_DBA=0.0034.

Question:
Assets: VTI, XRP-USD, SGOV, DBA
Annualized mean returns: VTI:-0.2395, XRP-USD:0.6042, SGOV:0.0528, DBA:0.0864
Covariance matrix (annualized):
[[0.015924, -0.004672, -2.4e-05, 0.002954], [-0.004672, 0.135986, 6e-06, -0.004539], [-2.4e-05, 6e-06, 5e-06, -4e-06], [0.002954, -0.004539, -4e-06, 0.009189]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_VTI=0.0000, w_XRP-USD=0.0017, w_SGOV=0.9949, w_DBA=0.0034

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VTI=0.0000, w_XRP-USD=0.0017, w_SGOV=0.9949, w_DBA=0.0034
Portfolio annualized return: 5.39%, volatility: 0.24%
Sharpe ratio: (0.0539 - 0.0400) / 0.0024 = 5.8579


4-asset optimization. Max-Sharpe: 6.926. Portfolio: return=6.12%, vol=0.31%. Weights: w_EFA=0.0078, w_ETH-USD=0.0036, w_SHV=0.9837, w_SOYB=0.0049.

Question:
Assets: EFA, ETH-USD, SHV, SOYB
Annualized mean returns: EFA:0.3343, ETH-USD:1.3896, SHV:0.0537, SOYB:0.1753
Covariance matrix (annualized):
[[0.018539, -0.006165, 5e-06, 0.000578], [-0.006165, 0.229839, -7.6e-05, -0.020336], [5e-06, -7.6e-05, 6e-06, -3e-06], [0.000578, -0.020336, -3e-06, 0.026726]]
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=0.0078, w_ETH-USD=0.0036, w_SHV=0.9837, w_SOYB=0.0049

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EFA=0.0078, w_ETH-USD=0.0036, w_SHV=0.9837, w_SOYB=0.0049
Portfolio annualized return: 6.12%, volatility: 0.31%
Sharpe ratio: (0.0612 - 0.0400) / 0.0031 = 6.9260


4-asset optimization. Max-Sharpe: 0.676. Portfolio: return=18.52%, vol=21.47%. Weights: w_XLI=0.0000, w_DOT-USD=0.0000, w_VNQ=1.0000, w_PALL=0.0000.

Question:
Assets: XLI, DOT-USD, VNQ, PALL
Annualized mean returns: XLI:-0.0716, DOT-USD:0.2196, VNQ:0.1852, PALL:-1.0241
Covariance matrix (annualized):
[[0.032533, 0.031248, 0.02927, 0.024824], [0.031248, 0.336313, 0.064884, 0.034659], [0.02927, 0.064884, 0.046111, 0.042098], [0.024824, 0.034659, 0.042098, 0.196758]]
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_DOT-USD=0.0000, w_VNQ=1.0000, w_PALL=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLI=0.0000, w_DOT-USD=0.0000, w_VNQ=1.0000, w_PALL=0.0000
Portfolio annualized return: 18.52%, volatility: 21.47%
Sharpe ratio: (0.1852 - 0.0400) / 0.2147 = 0.6762


4-asset optimization. Max-Sharpe: 4.342. Portfolio: return=5.83%, vol=0.42%. Weights: w_QUAL=0.0126, w_DOT-USD=0.0028, w_DBA=0.0206, w_SGOV=0.9640.

Question:
Assets: QUAL, DOT-USD, DBA, SGOV
Annualized mean returns: QUAL:0.2505, DOT-USD:2.0137, DBA:0.2697, SGOV:0.0456
Covariance matrix (annualized):
[[0.012805, 0.023186, -0.00039, -1.5e-05], [0.023186, 0.573066, -0.008672, 0.000188], [-0.00039, -0.008672, 0.013849, -3.3e-05], [-1.5e-05, 0.000188, -3.3e-05, 6e-06]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: bull

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

Answer: w_QUAL=0.0126, w_DOT-USD=0.0028, w_DBA=0.0206, w_SGOV=0.9640

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_QUAL=0.0126, w_DOT-USD=0.0028, w_DBA=0.0206, w_SGOV=0.9640
Portfolio annualized return: 5.83%, volatility: 0.42%
Sharpe ratio: (0.0583 - 0.0400) / 0.0042 = 4.3424


4-asset optimization. Max-Sharpe: -2.970. Portfolio: return=-66.25%, vol=23.66%. Weights: w_IVV=0.2500, w_AVAX-USD=0.2500, w_IYR=0.2500, w_BIL=0.2500.

Question:
Assets: IVV, AVAX-USD, IYR, BIL
Annualized mean returns: IVV:0.0765, AVAX-USD:-2.4911, IYR:-0.2877, BIL:0.0525
Covariance matrix (annualized):
[[0.014363, 0.042805, 0.01479, -5.6e-05], [0.042805, 0.640491, 0.046923, 0.00031], [0.01479, 0.046923, 0.030996, -5.2e-05], [-5.6e-05, 0.00031, -5.2e-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_IVV=0.2500, w_AVAX-USD=0.2500, w_IYR=0.2500, w_BIL=0.2500

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_IVV=0.2500, w_AVAX-USD=0.2500, w_IYR=0.2500, w_BIL=0.2500
Portfolio annualized return: -66.25%, volatility: 23.66%
Sharpe ratio: (-0.6625 - 0.0400) / 0.2366 = -2.9696


4-asset optimization. Max-Sharpe: 9.131. Portfolio: return=6.45%, vol=0.27%. Weights: w_VLUE=0.0000, w_ETH-USD=0.0000, w_USO=0.0101, w_SGOV=0.9899.

Question:
Assets: VLUE, ETH-USD, USO, SGOV
Annualized mean returns: VLUE:-0.1389, ETH-USD:-0.7754, USO:1.1436, SGOV:0.0534
Covariance matrix (annualized):
[[0.010081, 0.00925, 0.00748, -3.1e-05], [0.00925, 0.086429, -0.001466, -7.2e-05], [0.00748, -0.001466, 0.03243, -4e-06], [-3.1e-05, -7.2e-05, -4e-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_VLUE=0.0000, w_ETH-USD=0.0000, w_USO=0.0101, w_SGOV=0.9899

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VLUE=0.0000, w_ETH-USD=0.0000, w_USO=0.0101, w_SGOV=0.9899
Portfolio annualized return: 6.45%, volatility: 0.27%
Sharpe ratio: (0.0645 - 0.0400) / 0.0027 = 9.1313


4-asset optimization. Max-Sharpe: 2.715. Portfolio: return=6.07%, vol=0.76%. Weights: w_XLB=0.0000, w_XRP-USD=0.0000, w_CSHI=0.9853, w_PPLT=0.0147.

Question:
Assets: XLB, XRP-USD, CSHI, PPLT
Annualized mean returns: XLB:-0.1420, XRP-USD:0.0832, CSHI:0.0548, PPLT:0.4563
Covariance matrix (annualized):
[[0.016683, 0.020925, 0.00021, 0.018195], [0.020925, 0.176619, 0.000959, 0.003074], [0.00021, 0.000959, 4.1e-05, 4.9e-05], [0.018195, 0.003074, 4.9e-05, 0.076072]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: bull

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

Answer: w_XLB=0.0000, w_XRP-USD=0.0000, w_CSHI=0.9853, w_PPLT=0.0147

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLB=0.0000, w_XRP-USD=0.0000, w_CSHI=0.9853, w_PPLT=0.0147
Portfolio annualized return: 6.07%, volatility: 0.76%
Sharpe ratio: (0.0607 - 0.0400) / 0.0076 = 2.7151


4-asset optimization. Max-Sharpe: 8.493. Portfolio: return=6.80%, vol=0.33%. Weights: w_SPY=0.0332, w_AVAX-USD=0.0000, w_STIP=0.0262, w_SGOV=0.9406.

Question:
Assets: SPY, AVAX-USD, STIP, SGOV
Annualized mean returns: SPY:0.4918, AVAX-USD:-0.3498, STIP:0.0837, SGOV:0.0526
Covariance matrix (annualized):
[[0.005622, 0.010007, 0.000459, -2.5e-05], [0.010007, 0.483684, 0.002279, -0.000359], [0.000459, 0.002279, 0.000249, -5e-06], [-2.5e-05, -0.000359, -5e-06, 6e-06]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: bull

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

Answer: w_SPY=0.0332, w_AVAX-USD=0.0000, w_STIP=0.0262, w_SGOV=0.9406

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_SPY=0.0332, w_AVAX-USD=0.0000, w_STIP=0.0262, w_SGOV=0.9406
Portfolio annualized return: 6.80%, volatility: 0.33%
Sharpe ratio: (0.0680 - 0.0400) / 0.0033 = 8.4927


4-asset optimization. Max-Sharpe: 3.378. Portfolio: return=5.39%, vol=0.41%. Weights: w_VEA=0.0000, w_SOL-USD=0.0053, w_JNK=0.0000, w_SGOV=0.9947.

Question:
Assets: VEA, SOL-USD, JNK, SGOV
Annualized mean returns: VEA:-0.2606, SOL-USD:1.6786, JNK:0.0254, SGOV:0.0453
Covariance matrix (annualized):
[[0.017681, 0.032005, 0.002186, 1e-05], [0.032005, 0.380466, 0.010985, -6e-06], [0.002186, 0.010985, 0.001224, 2.3e-05], [1e-05, -6e-06, 2.3e-05, 7e-06]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_VEA=0.0000, w_SOL-USD=0.0053, w_JNK=0.0000, w_SGOV=0.9947

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VEA=0.0000, w_SOL-USD=0.0053, w_JNK=0.0000, w_SGOV=0.9947
Portfolio annualized return: 5.39%, volatility: 0.41%
Sharpe ratio: (0.0539 - 0.0400) / 0.0041 = 3.3785


4-asset optimization. Max-Sharpe: 5.343. Portfolio: return=77.49%, vol=13.75%. Weights: w_VLUE=0.8774, w_LINK-USD=0.1226, w_JNK=0.0000, w_PPLT=0.0000.

Question:
Assets: VLUE, LINK-USD, JNK, PPLT
Annualized mean returns: VLUE:0.4844, LINK-USD:2.8533, JNK:0.0941, PPLT:-0.4414
Covariance matrix (annualized):
[[0.013367, -0.002362, 0.003646, 0.005278], [-0.002362, 0.607295, 0.00315, -0.011528], [0.003646, 0.00315, 0.004257, 0.008384], [0.005278, -0.011528, 0.008384, 0.049939]]
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=0.8774, w_LINK-USD=0.1226, w_JNK=0.0000, w_PPLT=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VLUE=0.8774, w_LINK-USD=0.1226, w_JNK=0.0000, w_PPLT=0.0000
Portfolio annualized return: 77.49%, volatility: 13.75%
Sharpe ratio: (0.7749 - 0.0400) / 0.1375 = 5.3435


4-asset optimization. Max-Sharpe: 1.707. Portfolio: return=6.38%, vol=1.40%. Weights: w_IWM=0.0000, w_ADA-USD=0.0000, w_PDBC=0.0000, w_CSHI=1.0000.

Question:
Assets: IWM, ADA-USD, PDBC, CSHI
Annualized mean returns: IWM:-0.4510, ADA-USD:-0.2406, PDBC:-0.5461, CSHI:0.0638
Covariance matrix (annualized):
[[0.05521, 0.048243, 0.00764, 0.000904], [0.048243, 0.461579, 0.019159, 0.000503], [0.00764, 0.019159, 0.031792, -6.2e-05], [0.000904, 0.000503, -6.2e-05, 0.000195]]
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_ADA-USD=0.0000, w_PDBC=0.0000, w_CSHI=1.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_IWM=0.0000, w_ADA-USD=0.0000, w_PDBC=0.0000, w_CSHI=1.0000
Portfolio annualized return: 6.38%, volatility: 1.40%
Sharpe ratio: (0.0638 - 0.0400) / 0.0140 = 1.7075


4-asset optimization. Max-Sharpe: 1.613. Portfolio: return=5.10%, vol=0.68%. Weights: w_VLUE=0.0000, w_XRP-USD=0.0000, w_CSHI=1.0000, w_SCHH=0.0000.

Question:
Assets: VLUE, XRP-USD, CSHI, SCHH
Annualized mean returns: VLUE:-0.0049, XRP-USD:-0.2934, CSHI:0.0510, SCHH:-0.2980
Covariance matrix (annualized):
[[0.013613, 0.030444, 0.000135, 0.015705], [0.030444, 0.561787, 0.001439, 0.023324], [0.000135, 0.001439, 4.7e-05, -2.7e-05], [0.015705, 0.023324, -2.7e-05, 0.028691]]
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_XRP-USD=0.0000, w_CSHI=1.0000, w_SCHH=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VLUE=0.0000, w_XRP-USD=0.0000, w_CSHI=1.0000, w_SCHH=0.0000
Portfolio annualized return: 5.10%, volatility: 0.68%
Sharpe ratio: (0.0510 - 0.0400) / 0.0068 = 1.6128


4-asset optimization. Max-Sharpe: 5.504. Portfolio: return=67.04%, vol=11.45%. Weights: w_XLF=0.9447, w_SOL-USD=0.0553, w_HYG=0.0000, w_MORT=0.0000.

Question:
Assets: XLF, SOL-USD, HYG, MORT
Annualized mean returns: XLF:0.5583, SOL-USD:2.5850, HYG:0.1698, MORT:0.2102
Covariance matrix (annualized):
[[0.011248, 0.002881, 0.002885, 0.015978], [0.002881, 0.908697, 0.003374, 0.040433], [0.002885, 0.003374, 0.003428, 0.009811], [0.015978, 0.040433, 0.009811, 0.053869]]
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=0.9447, w_SOL-USD=0.0553, w_HYG=0.0000, w_MORT=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLF=0.9447, w_SOL-USD=0.0553, w_HYG=0.0000, w_MORT=0.0000
Portfolio annualized return: 67.04%, volatility: 11.45%
Sharpe ratio: (0.6704 - 0.0400) / 0.1145 = 5.5039


4-asset optimization. Max-Sharpe: 3.652. Portfolio: return=8.21%, vol=1.15%. Weights: w_MTUM=0.0000, w_LINK-USD=0.0088, w_CSHI=0.9912, w_SCHP=0.0000.

Question:
Assets: MTUM, LINK-USD, CSHI, SCHP
Annualized mean returns: MTUM:-0.1227, LINK-USD:1.4289, CSHI:0.0701, SCHP:0.0253
Covariance matrix (annualized):
[[0.020462, 0.018168, 0.000422, -0.000263], [0.018168, 0.331499, 0.00147, 0.001615], [0.000422, 0.00147, 8.3e-05, 4.3e-05], [-0.000263, 0.001615, 4.3e-05, 0.004978]]
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=0.0000, w_LINK-USD=0.0088, w_CSHI=0.9912, w_SCHP=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_MTUM=0.0000, w_LINK-USD=0.0088, w_CSHI=0.9912, w_SCHP=0.0000
Portfolio annualized return: 8.21%, volatility: 1.15%
Sharpe ratio: (0.0821 - 0.0400) / 0.0115 = 3.6525


4-asset optimization. Max-Sharpe: 6.150. Portfolio: return=9.50%, vol=0.89%. Weights: w_SPY=0.0395, w_BNB-USD=0.0091, w_GLD=0.0000, w_ICSH=0.9513.

Question:
Assets: SPY, BNB-USD, GLD, ICSH
Annualized mean returns: SPY:0.5730, BNB-USD:2.1421, GLD:0.3325, ICSH:0.0554
Covariance matrix (annualized):
[[0.013636, 0.018803, 0.003104, 6.7e-05], [0.018803, 0.280285, 0.010088, -0.000265], [0.003104, 0.010088, 0.011889, 0.000305], [6.7e-05, -0.000265, 0.000305, 2.3e-05]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_SPY=0.0395, w_BNB-USD=0.0091, w_GLD=0.0000, w_ICSH=0.9513

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_SPY=0.0395, w_BNB-USD=0.0091, w_GLD=0.0000, w_ICSH=0.9513
Portfolio annualized return: 9.50%, volatility: 0.89%
Sharpe ratio: (0.0950 - 0.0400) / 0.0089 = 6.1497


4-asset optimization. Max-Sharpe: 4.090. Portfolio: return=11.21%, vol=1.76%. Weights: w_IVV=0.0000, w_SOL-USD=0.0013, w_SLV=0.0557, w_CSHI=0.9430.

Question:
Assets: IVV, SOL-USD, SLV, CSHI
Annualized mean returns: IVV:-0.0335, SOL-USD:0.7750, SLV:1.0997, CSHI:0.0529
Covariance matrix (annualized):
[[0.012124, 0.024711, 0.000787, 0.000222], [0.024711, 0.799869, 0.022523, 0.00094], [0.000787, 0.022523, 0.079815, 9.9e-05], [0.000222, 0.00094, 9.9e-05, 5.2e-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_IVV=0.0000, w_SOL-USD=0.0013, w_SLV=0.0557, w_CSHI=0.9430

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_IVV=0.0000, w_SOL-USD=0.0013, w_SLV=0.0557, w_CSHI=0.9430
Portfolio annualized return: 11.21%, volatility: 1.76%
Sharpe ratio: (0.1121 - 0.0400) / 0.0176 = 4.0904


4-asset optimization. Max-Sharpe: 1.682. Portfolio: return=65.91%, vol=36.80%. Weights: w_XLV=0.0000, w_BTC-USD=1.0000, w_TLT=0.0000, w_USO=0.0000.

Question:
Assets: XLV, BTC-USD, TLT, USO
Annualized mean returns: XLV:-0.2680, BTC-USD:0.6591, TLT:-0.3224, USO:-0.0387
Covariance matrix (annualized):
[[0.009289, 0.009565, 0.001115, -0.006499], [0.009565, 0.135402, 0.001984, -0.011426], [0.001115, 0.001984, 0.014657, -0.014581], [-0.006499, -0.011426, -0.014581, 0.130596]]
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_BTC-USD=1.0000, w_TLT=0.0000, w_USO=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLV=0.0000, w_BTC-USD=1.0000, w_TLT=0.0000, w_USO=0.0000
Portfolio annualized return: 65.91%, volatility: 36.80%
Sharpe ratio: (0.6591 - 0.0400) / 0.3680 = 1.6825


4-asset optimization. Max-Sharpe: 3.304. Portfolio: return=46.13%, vol=12.75%. Weights: w_ACWI=0.0000, w_DOT-USD=0.0000, w_DBB=0.5399, w_REZ=0.4601.

Question:
Assets: ACWI, DOT-USD, DBB, REZ
Annualized mean returns: ACWI:0.1071, DOT-USD:-1.0432, DBB:0.5069, REZ:0.4077
Covariance matrix (annualized):
[[0.012563, 0.030825, 0.000851, 0.013771], [0.030825, 0.391532, 0.014444, 0.037791], [0.000851, 0.014444, 0.034217, -0.000996], [0.013771, 0.037791, -0.000996, 0.032001]]
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_DOT-USD=0.0000, w_DBB=0.5399, w_REZ=0.4601

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_ACWI=0.0000, w_DOT-USD=0.0000, w_DBB=0.5399, w_REZ=0.4601
Portfolio annualized return: 46.13%, volatility: 12.75%
Sharpe ratio: (0.4613 - 0.0400) / 0.1275 = 3.3043


4-asset optimization. Max-Sharpe: 3.910. Portfolio: return=5.65%, vol=0.42%. Weights: w_USMV=0.0000, w_LINK-USD=0.0000, w_ICSH=1.0000, w_SHY=0.0000.

Question:
Assets: USMV, LINK-USD, ICSH, SHY
Annualized mean returns: USMV:-0.0605, LINK-USD:-0.0411, ICSH:0.0565, SHY:0.0044
Covariance matrix (annualized):
[[0.005317, 0.008094, -7e-06, 0.000221], [0.008094, 0.247085, 7.6e-05, -7.4e-05], [-7e-06, 7.6e-05, 1.8e-05, 3.6e-05], [0.000221, -7.4e-05, 3.6e-05, 0.000228]]
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_LINK-USD=0.0000, w_ICSH=1.0000, w_SHY=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_USMV=0.0000, w_LINK-USD=0.0000, w_ICSH=1.0000, w_SHY=0.0000
Portfolio annualized return: 5.65%, volatility: 0.42%
Sharpe ratio: (0.0565 - 0.0400) / 0.0042 = 3.9105


4-asset optimization. Max-Sharpe: 3.877. Portfolio: return=5.14%, vol=0.29%. Weights: w_XLRE=0.0044, w_ADA-USD=0.0000, w_PALL=0.0000, w_BIL=0.9956.

Question:
Assets: XLRE, ADA-USD, PALL, BIL
Annualized mean returns: XLRE:0.2777, ADA-USD:-0.9384, PALL:-1.1713, BIL:0.0504
Covariance matrix (annualized):
[[0.028035, -0.003213, 0.019938, 5.6e-05], [-0.003213, 0.278112, 0.00094, 9.5e-05], [0.019938, 0.00094, 0.078011, -1.9e-05], [5.6e-05, 9.5e-05, -1.9e-05, 8e-06]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_XLRE=0.0044, w_ADA-USD=0.0000, w_PALL=0.0000, w_BIL=0.9956

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLRE=0.0044, w_ADA-USD=0.0000, w_PALL=0.0000, w_BIL=0.9956
Portfolio annualized return: 5.14%, volatility: 0.29%
Sharpe ratio: (0.0514 - 0.0400) / 0.0029 = 3.8768


4-asset optimization. Max-Sharpe: 6.603. Portfolio: return=6.43%, vol=0.37%. Weights: w_MTUM=0.0078, w_BNB-USD=0.0031, w_SGOV=0.9892, w_REZ=0.0000.

Question:
Assets: MTUM, BNB-USD, SGOV, REZ
Annualized mean returns: MTUM:0.8647, BNB-USD:1.1953, SGOV:0.0545, REZ:-0.3952
Covariance matrix (annualized):
[[0.0351, 0.005381, 0.000173, 0.006051], [0.005381, 0.142553, 0.000167, 0.018085], [0.000173, 0.000167, 6e-06, 0.000105], [0.006051, 0.018085, 0.000105, 0.031431]]
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=0.0078, w_BNB-USD=0.0031, w_SGOV=0.9892, w_REZ=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_MTUM=0.0078, w_BNB-USD=0.0031, w_SGOV=0.9892, w_REZ=0.0000
Portfolio annualized return: 6.43%, volatility: 0.37%
Sharpe ratio: (0.0643 - 0.0400) / 0.0037 = 6.6034


4-asset optimization. Max-Sharpe: 3.378. Portfolio: return=4.86%, vol=0.25%. Weights: w_VEA=0.0000, w_AVAX-USD=0.0000, w_CORN=0.0000, w_SGOV=1.0000.

Question:
Assets: VEA, AVAX-USD, CORN, SGOV
Annualized mean returns: VEA:-0.2088, AVAX-USD:0.2661, CORN:0.0608, SGOV:0.0486
Covariance matrix (annualized):
[[0.01794, 0.046117, -0.002549, -4.7e-05], [0.046117, 0.350146, -0.015052, 0.000322], [-0.002549, -0.015052, 0.020795, 1.5e-05], [-4.7e-05, 0.000322, 1.5e-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_VEA=0.0000, w_AVAX-USD=0.0000, w_CORN=0.0000, w_SGOV=1.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VEA=0.0000, w_AVAX-USD=0.0000, w_CORN=0.0000, w_SGOV=1.0000
Portfolio annualized return: 4.86%, volatility: 0.25%
Sharpe ratio: (0.0486 - 0.0400) / 0.0025 = 3.3778


4-asset optimization. Max-Sharpe: 1.651. Portfolio: return=5.49%, vol=0.90%. Weights: w_XLU=0.0000, w_ADA-USD=0.0021, w_CSHI=0.9979, w_JNK=0.0000.

Question:
Assets: XLU, ADA-USD, CSHI, JNK
Annualized mean returns: XLU:-0.3274, ADA-USD:0.6599, CSHI:0.0537, JNK:0.0240
Covariance matrix (annualized):
[[0.025583, 0.018734, 0.000354, 0.003112], [0.018734, 0.518898, 0.002315, 0.012858], [0.000354, 0.002315, 7e-05, 8.6e-05], [0.003112, 0.012858, 8.6e-05, 0.004066]]
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_ADA-USD=0.0021, w_CSHI=0.9979, w_JNK=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLU=0.0000, w_ADA-USD=0.0021, w_CSHI=0.9979, w_JNK=0.0000
Portfolio annualized return: 5.49%, volatility: 0.90%
Sharpe ratio: (0.0549 - 0.0400) / 0.0090 = 1.6507


4-asset optimization. Max-Sharpe: 4.783. Portfolio: return=38.96%, vol=7.31%. Weights: w_QUAL=0.7292, w_ETH-USD=0.0000, w_UNG=0.0000, w_SCHH=0.2708.

Question:
Assets: QUAL, ETH-USD, UNG, SCHH
Annualized mean returns: QUAL:0.3826, ETH-USD:0.2476, UNG:-0.3338, SCHH:0.4086
Covariance matrix (annualized):
[[0.006979, 0.007898, 0.005892, 0.000544], [0.007898, 0.280033, 0.043483, 0.001556], [0.005892, 0.043483, 0.349623, -0.006192], [0.000544, 0.001556, -0.006192, 0.019342]]
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=0.7292, w_ETH-USD=0.0000, w_UNG=0.0000, w_SCHH=0.2708

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_QUAL=0.7292, w_ETH-USD=0.0000, w_UNG=0.0000, w_SCHH=0.2708
Portfolio annualized return: 38.96%, volatility: 7.31%
Sharpe ratio: (0.3896 - 0.0400) / 0.0731 = 4.7828


4-asset optimization. Max-Sharpe: 3.368. Portfolio: return=261.12%, vol=76.33%. Weights: w_XLU=0.0000, w_MATIC-USD=1.0000, w_SOYB=0.0000, w_EMB=0.0000.

Question:
Assets: XLU, MATIC-USD, SOYB, EMB
Annualized mean returns: XLU:-0.4726, MATIC-USD:2.6112, SOYB:-0.0803, EMB:0.0533
Covariance matrix (annualized):
[[0.02795, 0.037088, 0.002469, 0.00603], [0.037088, 0.582641, 0.003459, 0.018321], [0.002469, 0.003459, 0.013849, -0.002126], [0.00603, 0.018321, -0.002126, 0.017504]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_XLU=0.0000, w_MATIC-USD=1.0000, w_SOYB=0.0000, w_EMB=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLU=0.0000, w_MATIC-USD=1.0000, w_SOYB=0.0000, w_EMB=0.0000
Portfolio annualized return: 261.12%, volatility: 76.33%
Sharpe ratio: (2.6112 - 0.0400) / 0.7633 = 3.3685


4-asset optimization. Max-Sharpe: 5.593. Portfolio: return=5.75%, vol=0.31%. Weights: w_XLK=0.0000, w_ADA-USD=0.0008, w_SGOV=0.9702, w_VCIT=0.0290.

Question:
Assets: XLK, ADA-USD, SGOV, VCIT
Annualized mean returns: XLK:-0.2570, ADA-USD:0.9003, SGOV:0.0509, VCIT:0.2566
Covariance matrix (annualized):
[[0.098053, 0.056794, 0.0001, 0.002563], [0.056794, 0.385869, 0.000218, -0.00183], [0.0001, 0.000218, 5e-06, 5e-05], [0.002563, -0.00183, 5e-05, 0.002572]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: bull

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

Answer: w_XLK=0.0000, w_ADA-USD=0.0008, w_SGOV=0.9702, w_VCIT=0.0290

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLK=0.0000, w_ADA-USD=0.0008, w_SGOV=0.9702, w_VCIT=0.0290
Portfolio annualized return: 5.75%, volatility: 0.31%
Sharpe ratio: (0.0575 - 0.0400) / 0.0031 = 5.5933


4-asset optimization. Max-Sharpe: 3.722. Portfolio: return=5.03%, vol=0.28%. Weights: w_XLU=0.0000, w_XRP-USD=0.0028, w_BIL=0.9972, w_SHV=0.0000.

Question:
Assets: XLU, XRP-USD, BIL, SHV
Annualized mean returns: XLU:-0.1242, XRP-USD:1.7633, BIL:0.0455, SHV:0.0410
Covariance matrix (annualized):
[[0.040396, -0.018107, 7.1e-05, -1.1e-05], [-0.018107, 0.673293, -0.000606, -0.001086], [7.1e-05, -0.000606, 6e-06, 5e-06], [-1.1e-05, -0.001086, 5e-06, 1.3e-05]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_XLU=0.0000, w_XRP-USD=0.0028, w_BIL=0.9972, w_SHV=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLU=0.0000, w_XRP-USD=0.0028, w_BIL=0.9972, w_SHV=0.0000
Portfolio annualized return: 5.03%, volatility: 0.28%
Sharpe ratio: (0.0503 - 0.0400) / 0.0028 = 3.7216


4-asset optimization. Max-Sharpe: 3.887. Portfolio: return=5.52%, vol=0.39%. Weights: w_VEA=0.0179, w_SOL-USD=0.0000, w_SGOV=0.9150, w_TIP=0.0671.

Question:
Assets: VEA, SOL-USD, SGOV, TIP
Annualized mean returns: VEA:0.2981, SOL-USD:-0.1497, SGOV:0.0467, TIP:0.1070
Covariance matrix (annualized):
[[0.023364, 0.020174, -3.3e-05, -0.001915], [0.020174, 0.499613, -0.000137, 0.002893], [-3.3e-05, -0.000137, 7e-06, 9e-06], [-0.001915, 0.002893, 9e-06, 0.001392]]
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=0.0179, w_SOL-USD=0.0000, w_SGOV=0.9150, w_TIP=0.0671

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VEA=0.0179, w_SOL-USD=0.0000, w_SGOV=0.9150, w_TIP=0.0671
Portfolio annualized return: 5.52%, volatility: 0.39%
Sharpe ratio: (0.0552 - 0.0400) / 0.0039 = 3.8873


4-asset optimization. Max-Sharpe: 5.894. Portfolio: return=382.39%, vol=64.20%. Weights: w_QUAL=0.0000, w_SOL-USD=1.0000, w_MORT=0.0000, w_SLV=0.0000.

Question:
Assets: QUAL, SOL-USD, MORT, SLV
Annualized mean returns: QUAL:-0.0548, SOL-USD:3.8239, MORT:-0.5078, SLV:-0.0633
Covariance matrix (annualized):
[[0.021005, 0.00063, 0.028147, -0.002602], [0.00063, 0.412143, 0.006943, -0.004366], [0.028147, 0.006943, 0.085614, 0.005005], [-0.002602, -0.004366, 0.005005, 0.05018]]
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_SOL-USD=1.0000, w_MORT=0.0000, w_SLV=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_QUAL=0.0000, w_SOL-USD=1.0000, w_MORT=0.0000, w_SLV=0.0000
Portfolio annualized return: 382.39%, volatility: 64.20%
Sharpe ratio: (3.8239 - 0.0400) / 0.6420 = 5.8941


4-asset optimization. Max-Sharpe: 4.153. Portfolio: return=85.53%, vol=19.63%. Weights: w_FXI=0.8061, w_ADA-USD=0.0000, w_REZ=0.1939, w_IEF=0.0000.

Question:
Assets: FXI, ADA-USD, REZ, IEF
Annualized mean returns: FXI:0.9495, ADA-USD:-2.3439, REZ:0.4636, IEF:0.0509
Covariance matrix (annualized):
[[0.049268, 0.060815, 0.016962, 0.000709], [0.060815, 0.414922, 0.034774, 0.002929], [0.016962, 0.034774, 0.032787, 0.006447], [0.000709, 0.002929, 0.006447, 0.004327]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: bull

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

Answer: w_FXI=0.8061, w_ADA-USD=0.0000, w_REZ=0.1939, w_IEF=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_FXI=0.8061, w_ADA-USD=0.0000, w_REZ=0.1939, w_IEF=0.0000
Portfolio annualized return: 85.53%, volatility: 19.63%
Sharpe ratio: (0.8553 - 0.0400) / 0.1963 = 4.1526


4-asset optimization. Max-Sharpe: 5.056. Portfolio: return=5.30%, vol=0.26%. Weights: w_EFA=0.0000, w_AVAX-USD=0.0000, w_BIL=1.0000, w_ITB=0.0000.

Question:
Assets: EFA, AVAX-USD, BIL, ITB
Annualized mean returns: EFA:-0.0258, AVAX-USD:-0.5338, BIL:0.0530, ITB:-0.0024
Covariance matrix (annualized):
[[0.010442, 0.028429, 5.9e-05, 0.01796], [0.028429, 0.896193, 0.000143, 0.026794], [5.9e-05, 0.000143, 7e-06, 9e-05], [0.01796, 0.026794, 9e-05, 0.056015]]
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_AVAX-USD=0.0000, w_BIL=1.0000, w_ITB=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EFA=0.0000, w_AVAX-USD=0.0000, w_BIL=1.0000, w_ITB=0.0000
Portfolio annualized return: 5.30%, volatility: 0.26%
Sharpe ratio: (0.0530 - 0.0400) / 0.0026 = 5.0563


4-asset optimization. Max-Sharpe: 8.779. Portfolio: return=8.15%, vol=0.47%. Weights: w_QUAL=0.0115, w_BTC-USD=0.0019, w_VNQ=0.0000, w_ICSH=0.9866.

Question:
Assets: QUAL, BTC-USD, VNQ, ICSH
Annualized mean returns: QUAL:0.4051, BTC-USD:0.5546, VNQ:0.6559, ICSH:0.0769
Covariance matrix (annualized):
[[0.007571, 0.004671, 0.007132, 0.000102], [0.004671, 0.2395, 0.026073, -0.000224], [0.007132, 0.026073, 0.029391, 0.000365], [0.000102, -0.000224, 0.000365, 1.9e-05]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_QUAL=0.0115, w_BTC-USD=0.0019, w_VNQ=0.0000, w_ICSH=0.9866

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_QUAL=0.0115, w_BTC-USD=0.0019, w_VNQ=0.0000, w_ICSH=0.9866
Portfolio annualized return: 8.15%, volatility: 0.47%
Sharpe ratio: (0.0815 - 0.0400) / 0.0047 = 8.7789


4-asset optimization. Max-Sharpe: 0.030. Portfolio: return=4.63%, vol=21.26%. Weights: w_EEM=0.2500, w_DOT-USD=0.2500, w_SHV=0.2500, w_XHB=0.2500.

Question:
Assets: EEM, DOT-USD, SHV, XHB
Annualized mean returns: EEM:0.2279, DOT-USD:-0.7218, SHV:0.0570, XHB:0.6224
Covariance matrix (annualized):
[[0.032206, 0.053862, -3.2e-05, 0.034937], [0.053862, 0.267854, 0.000155, 0.079399], [-3.2e-05, 0.000155, 7e-06, 5.5e-05], [0.034937, 0.079399, 5.5e-05, 0.086384]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_EEM=0.2500, w_DOT-USD=0.2500, w_SHV=0.2500, w_XHB=0.2500

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EEM=0.2500, w_DOT-USD=0.2500, w_SHV=0.2500, w_XHB=0.2500
Portfolio annualized return: 4.63%, volatility: 21.26%
Sharpe ratio: (0.0463 - 0.0400) / 0.2126 = 0.0299


4-asset optimization. Max-Sharpe: 0.853. Portfolio: return=13.30%, vol=10.89%. Weights: w_XLI=1.0000, w_ETH-USD=0.0000, w_DBA=0.0000, w_TLH=0.0000.

Question:
Assets: XLI, ETH-USD, DBA, TLH
Annualized mean returns: XLI:0.1330, ETH-USD:-0.6292, DBA:0.0145, TLH:-0.3520
Covariance matrix (annualized):
[[0.011868, 0.015918, 0.002265, 0.003808], [0.015918, 0.114933, 0.003519, 0.013499], [0.002265, 0.003519, 0.013078, 0.00306], [0.003808, 0.013499, 0.00306, 0.018424]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_XLI=1.0000, w_ETH-USD=0.0000, w_DBA=0.0000, w_TLH=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLI=1.0000, w_ETH-USD=0.0000, w_DBA=0.0000, w_TLH=0.0000
Portfolio annualized return: 13.30%, volatility: 10.89%
Sharpe ratio: (0.1330 - 0.0400) / 0.1089 = 0.8533


4-asset optimization. Max-Sharpe: 0.219. Portfolio: return=7.10%, vol=14.18%. Weights: w_EEM=1.0000, w_ETH-USD=0.0000, w_USO=0.0000, w_VNQI=0.0000.

Question:
Assets: EEM, ETH-USD, USO, VNQI
Annualized mean returns: EEM:0.0710, ETH-USD:-0.0716, USO:-0.4883, VNQI:0.0016
Covariance matrix (annualized):
[[0.020117, 0.02136, 0.002989, 0.017923], [0.02136, 0.373749, 0.024463, 0.021095], [0.002989, 0.024463, 0.036679, 0.000248], [0.017923, 0.021095, 0.000248, 0.024767]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_EEM=1.0000, w_ETH-USD=0.0000, w_USO=0.0000, w_VNQI=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EEM=1.0000, w_ETH-USD=0.0000, w_USO=0.0000, w_VNQI=0.0000
Portfolio annualized return: 7.10%, volatility: 14.18%
Sharpe ratio: (0.0710 - 0.0400) / 0.1418 = 0.2186


4-asset optimization. Max-Sharpe: 2.481. Portfolio: return=61.65%, vol=23.23%. Weights: w_XLV=0.0000, w_DOT-USD=0.0000, w_PALL=0.3456, w_ITB=0.6544.

Question:
Assets: XLV, DOT-USD, PALL, ITB
Annualized mean returns: XLV:-0.0370, DOT-USD:0.6115, PALL:0.7881, ITB:0.5259
Covariance matrix (annualized):
[[0.01095, 0.011167, 0.006986, 0.015517], [0.011167, 0.502095, 0.149597, 0.016587], [0.006986, 0.149597, 0.148741, 0.028483], [0.015517, 0.016587, 0.028483, 0.054462]]
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_DOT-USD=0.0000, w_PALL=0.3456, w_ITB=0.6544

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLV=0.0000, w_DOT-USD=0.0000, w_PALL=0.3456, w_ITB=0.6544
Portfolio annualized return: 61.65%, volatility: 23.23%
Sharpe ratio: (0.6165 - 0.0400) / 0.2323 = 2.4815


4-asset optimization. Max-Sharpe: 4.307. Portfolio: return=51.88%, vol=11.12%. Weights: w_XLY=0.6512, w_MATIC-USD=0.0000, w_SCHH=0.3488, w_DBC=0.0000.

Question:
Assets: XLY, MATIC-USD, SCHH, DBC
Annualized mean returns: XLY:0.5680, MATIC-USD:-1.8355, SCHH:0.4270, DBC:-0.1705
Covariance matrix (annualized):
[[0.018429, -0.003577, 0.004656, 0.003486], [-0.003577, 0.325978, 0.000701, -0.002055], [0.004656, 0.000701, 0.019939, 0.000755], [0.003486, -0.002055, 0.000755, 0.018493]]
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=0.6512, w_MATIC-USD=0.0000, w_SCHH=0.3488, w_DBC=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLY=0.6512, w_MATIC-USD=0.0000, w_SCHH=0.3488, w_DBC=0.0000
Portfolio annualized return: 51.88%, volatility: 11.12%
Sharpe ratio: (0.5188 - 0.0400) / 0.1112 = 4.3074


4-asset optimization. Max-Sharpe: 3.734. Portfolio: return=98.36%, vol=25.27%. Weights: w_EFA=0.4203, w_BTC-USD=0.5797, w_IYR=0.0000, w_PALL=0.0000.

Question:
Assets: EFA, BTC-USD, IYR, PALL
Annualized mean returns: EFA:0.1743, BTC-USD:1.5703, IYR:0.0987, PALL:-0.9337
Covariance matrix (annualized):
[[0.021487, 9.9e-05, 0.024081, 0.021642], [9.9e-05, 0.178575, -0.010027, 0.004453], [0.024081, -0.010027, 0.049612, 0.028195], [0.021642, 0.004453, 0.028195, 0.097307]]
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=0.4203, w_BTC-USD=0.5797, w_IYR=0.0000, w_PALL=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EFA=0.4203, w_BTC-USD=0.5797, w_IYR=0.0000, w_PALL=0.0000
Portfolio annualized return: 98.36%, volatility: 25.27%
Sharpe ratio: (0.9836 - 0.0400) / 0.2527 = 3.7340


4-asset optimization. Max-Sharpe: 3.485. Portfolio: return=68.54%, vol=18.52%. Weights: w_XLY=0.3610, w_DOT-USD=0.1057, w_SLV=0.5333, w_MORT=0.0000.

Question:
Assets: XLY, DOT-USD, SLV, MORT
Annualized mean returns: XLY:0.2935, DOT-USD:1.7314, SLV:0.7434, MORT:-0.0556
Covariance matrix (annualized):
[[0.025376, 0.019281, 0.004265, 0.017146], [0.019281, 0.452598, 0.065793, 0.030158], [0.004265, 0.065793, 0.054168, 0.029963], [0.017146, 0.030158, 0.029963, 0.057039]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: bull

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

Answer: w_XLY=0.3610, w_DOT-USD=0.1057, w_SLV=0.5333, w_MORT=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLY=0.3610, w_DOT-USD=0.1057, w_SLV=0.5333, w_MORT=0.0000
Portfolio annualized return: 68.54%, volatility: 18.52%
Sharpe ratio: (0.6854 - 0.0400) / 0.1852 = 3.4850


4-asset optimization. Max-Sharpe: 4.279. Portfolio: return=13.73%, vol=2.27%. Weights: w_XLV=0.0833, w_BTC-USD=0.0000, w_STIP=0.8790, w_GLD=0.0377.

Question:
Assets: XLV, BTC-USD, STIP, GLD
Annualized mean returns: XLV:0.4023, BTC-USD:0.3352, STIP:0.0959, GLD:0.5166
Covariance matrix (annualized):
[[0.018778, 0.035458, 0.000137, 0.006404], [0.035458, 0.296769, -0.000325, 0.014817], [0.000137, -0.000325, 0.000273, 0.001218], [0.006404, 0.014817, 0.001218, 0.024629]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: bull

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

Answer: w_XLV=0.0833, w_BTC-USD=0.0000, w_STIP=0.8790, w_GLD=0.0377

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLV=0.0833, w_BTC-USD=0.0000, w_STIP=0.8790, w_GLD=0.0377
Portfolio annualized return: 13.73%, volatility: 2.27%
Sharpe ratio: (0.1373 - 0.0400) / 0.0227 = 4.2793


4-asset optimization. Max-Sharpe: 1.122. Portfolio: return=86.99%, vol=73.99%. Weights: w_XLRE=0.0000, w_DOT-USD=1.0000, w_HAUZ=0.0000, w_UNG=0.0000.

Question:
Assets: XLRE, DOT-USD, HAUZ, UNG
Annualized mean returns: XLRE:0.0187, DOT-USD:0.8699, HAUZ:-0.1245, UNG:-1.3948
Covariance matrix (annualized):
[[0.039157, 0.021031, 0.020562, 0.017607], [0.021031, 0.547407, 0.020596, -0.016749], [0.020562, 0.020596, 0.019206, 0.014366], [0.017607, -0.016749, 0.014366, 0.656941]]
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_DOT-USD=1.0000, w_HAUZ=0.0000, w_UNG=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLRE=0.0000, w_DOT-USD=1.0000, w_HAUZ=0.0000, w_UNG=0.0000
Portfolio annualized return: 86.99%, volatility: 73.99%
Sharpe ratio: (0.8699 - 0.0400) / 0.7399 = 1.1217


4-asset optimization. Max-Sharpe: 3.892. Portfolio: return=4.98%, vol=0.25%. Weights: w_XLP=0.0000, w_DOT-USD=0.0000, w_SGOV=1.0000, w_BNDX=0.0000.

Question:
Assets: XLP, DOT-USD, SGOV, BNDX
Annualized mean returns: XLP:0.0239, DOT-USD:-1.0138, SGOV:0.0498, BNDX:0.0307
Covariance matrix (annualized):
[[0.007892, 0.010015, 9.1e-05, 0.000971], [0.010015, 0.211001, 0.000186, 0.002033], [9.1e-05, 0.000186, 6e-06, 2.1e-05], [0.000971, 0.002033, 2.1e-05, 0.000997]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_XLP=0.0000, w_DOT-USD=0.0000, w_SGOV=1.0000, w_BNDX=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLP=0.0000, w_DOT-USD=0.0000, w_SGOV=1.0000, w_BNDX=0.0000
Portfolio annualized return: 4.98%, volatility: 0.25%
Sharpe ratio: (0.0498 - 0.0400) / 0.0025 = 3.8924


4-asset optimization. Max-Sharpe: -0.054. Portfolio: return=3.38%, vol=11.64%. Weights: w_XLF=1.0000, w_LINK-USD=0.0000, w_ITB=0.0000, w_PALL=0.0000.

Question:
Assets: XLF, LINK-USD, ITB, PALL
Annualized mean returns: XLF:0.0338, LINK-USD:-2.8300, ITB:-0.2894, PALL:-0.1255
Covariance matrix (annualized):
[[0.013557, 0.02329, 0.017946, 0.009399], [0.02329, 0.415176, 0.018503, 0.077377], [0.017946, 0.018503, 0.06003, 0.023811], [0.009399, 0.077377, 0.023811, 0.12399]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_XLF=1.0000, w_LINK-USD=0.0000, w_ITB=0.0000, w_PALL=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLF=1.0000, w_LINK-USD=0.0000, w_ITB=0.0000, w_PALL=0.0000
Portfolio annualized return: 3.38%, volatility: 11.64%
Sharpe ratio: (0.0338 - 0.0400) / 0.1164 = -0.0535


4-asset optimization. Max-Sharpe: 2.875. Portfolio: return=6.29%, vol=0.80%. Weights: w_SPY=0.0437, w_MATIC-USD=0.0000, w_SOYB=0.0012, w_CSHI=0.9551.

Question:
Assets: SPY, MATIC-USD, SOYB, CSHI
Annualized mean returns: SPY:0.2433, MATIC-USD:-0.6941, SOYB:0.0407, CSHI:0.0547
Covariance matrix (annualized):
[[0.012029, 0.015785, 0.000481, 4e-05], [0.015785, 0.596982, 0.032121, 0.000307], [0.000481, 0.032121, 0.016067, -4e-05], [4e-05, 0.000307, -4e-05, 4.1e-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_SPY=0.0437, w_MATIC-USD=0.0000, w_SOYB=0.0012, w_CSHI=0.9551

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_SPY=0.0437, w_MATIC-USD=0.0000, w_SOYB=0.0012, w_CSHI=0.9551
Portfolio annualized return: 6.29%, volatility: 0.80%
Sharpe ratio: (0.0629 - 0.0400) / 0.0080 = 2.8752


4-asset optimization. Max-Sharpe: 6.706. Portfolio: return=5.48%, vol=0.22%. Weights: w_XLF=0.0055, w_ADA-USD=0.0000, w_SGOV=0.9945, w_SCHH=0.0000.

Question:
Assets: XLF, ADA-USD, SGOV, SCHH
Annualized mean returns: XLF:0.2515, ADA-USD:0.2490, SGOV:0.0537, SCHH:-0.0280
Covariance matrix (annualized):
[[0.013226, 0.019096, -3e-06, 0.014118], [0.019096, 0.523275, 0.000102, 0.038306], [-3e-06, 0.000102, 5e-06, 5.4e-05], [0.014118, 0.038306, 5.4e-05, 0.030974]]
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=0.0055, w_ADA-USD=0.0000, w_SGOV=0.9945, w_SCHH=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLF=0.0055, w_ADA-USD=0.0000, w_SGOV=0.9945, w_SCHH=0.0000
Portfolio annualized return: 5.48%, volatility: 0.22%
Sharpe ratio: (0.0548 - 0.0400) / 0.0022 = 6.7056


4-asset optimization. Max-Sharpe: 5.854. Portfolio: return=5.66%, vol=0.28%. Weights: w_VLUE=0.0000, w_BTC-USD=0.0019, w_SGOV=0.9981, w_MORT=0.0000.

Question:
Assets: VLUE, BTC-USD, SGOV, MORT
Annualized mean returns: VLUE:0.1064, BTC-USD:0.8587, SGOV:0.0551, MORT:-0.5246
Covariance matrix (annualized):
[[0.014035, 0.011106, 9.9e-05, 0.021551], [0.011106, 0.190101, 4e-05, 0.031582], [9.9e-05, 4e-05, 7e-06, 0.00017], [0.021551, 0.031582, 0.00017, 0.061586]]
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=0.0019, w_SGOV=0.9981, w_MORT=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VLUE=0.0000, w_BTC-USD=0.0019, w_SGOV=0.9981, w_MORT=0.0000
Portfolio annualized return: 5.66%, volatility: 0.28%
Sharpe ratio: (0.0566 - 0.0400) / 0.0028 = 5.8536


4-asset optimization. Max-Sharpe: 2.003. Portfolio: return=18.54%, vol=7.26%. Weights: w_XLF=0.0000, w_XRP-USD=0.0000, w_LQD=1.0000, w_SOYB=0.0000.

Question:
Assets: XLF, XRP-USD, LQD, SOYB
Annualized mean returns: XLF:-0.0441, XRP-USD:-0.2540, LQD:0.1854, SOYB:-0.5761
Covariance matrix (annualized):
[[0.024633, 0.051191, 0.000164, -0.006431], [0.051191, 0.321048, 0.000222, -0.030024], [0.000164, 0.000222, 0.005268, 0.003819], [-0.006431, -0.030024, 0.003819, 0.03409]]
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_XRP-USD=0.0000, w_LQD=1.0000, w_SOYB=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLF=0.0000, w_XRP-USD=0.0000, w_LQD=1.0000, w_SOYB=0.0000
Portfolio annualized return: 18.54%, volatility: 7.26%
Sharpe ratio: (0.1854 - 0.0400) / 0.0726 = 2.0026


4-asset optimization. Max-Sharpe: 2.514. Portfolio: return=7.40%, vol=1.35%. Weights: w_SPY=0.0000, w_BTC-USD=0.0041, w_CSHI=0.1677, w_STIP=0.8283.

Question:
Assets: SPY, BTC-USD, CSHI, STIP
Annualized mean returns: SPY:-0.0393, BTC-USD:0.4490, CSHI:0.0546, STIP:0.0761
Covariance matrix (annualized):
[[0.03034, 0.047399, 0.001382, 0.000124], [0.047399, 0.288637, 0.005823, 5.6e-05], [0.001382, 0.005823, 0.000379, -1.1e-05], [0.000124, 5.6e-05, -1.1e-05, 0.000236]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: bull

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

Answer: w_SPY=0.0000, w_BTC-USD=0.0041, w_CSHI=0.1677, w_STIP=0.8283

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_SPY=0.0000, w_BTC-USD=0.0041, w_CSHI=0.1677, w_STIP=0.8283
Portfolio annualized return: 7.40%, volatility: 1.35%
Sharpe ratio: (0.0740 - 0.0400) / 0.0135 = 2.5137


4-asset optimization. Max-Sharpe: 1.766. Portfolio: return=6.04%, vol=1.15%. Weights: w_FXI=0.0000, w_MATIC-USD=0.0124, w_ICSH=0.9876, w_PALL=0.0000.

Question:
Assets: FXI, MATIC-USD, ICSH, PALL
Annualized mean returns: FXI:-0.9223, MATIC-USD:1.3591, ICSH:0.0441, PALL:-1.1400
Covariance matrix (annualized):
[[0.079809, 0.069956, -2.2e-05, 0.038184], [0.069956, 0.664538, 0.000403, -0.017054], [-2.2e-05, 0.000403, 2.2e-05, 0.000417], [0.038184, -0.017054, 0.000417, 0.129475]]
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=0.0124, w_ICSH=0.9876, w_PALL=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_FXI=0.0000, w_MATIC-USD=0.0124, w_ICSH=0.9876, w_PALL=0.0000
Portfolio annualized return: 6.04%, volatility: 1.15%
Sharpe ratio: (0.0604 - 0.0400) / 0.0115 = 1.7658


4-asset optimization. Max-Sharpe: 3.520. Portfolio: return=12.46%, vol=2.40%. Weights: w_IWM=0.0000, w_BTC-USD=0.0460, w_ICSH=0.9245, w_USO=0.0295.

Question:
Assets: IWM, BTC-USD, ICSH, USO
Annualized mean returns: IWM:-0.2122, BTC-USD:1.7486, ICSH:0.0434, USO:0.1390
Covariance matrix (annualized):
[[0.039649, 0.061006, 0.000225, -0.009586], [0.061006, 0.274029, 2.4e-05, -0.032432], [0.000225, 2.4e-05, 3e-05, -0.000186], [-0.009586, -0.032432, -0.000186, 0.079347]]
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_BTC-USD=0.0460, w_ICSH=0.9245, w_USO=0.0295

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_IWM=0.0000, w_BTC-USD=0.0460, w_ICSH=0.9245, w_USO=0.0295
Portfolio annualized return: 12.46%, volatility: 2.40%
Sharpe ratio: (0.1246 - 0.0400) / 0.0240 = 3.5199


4-asset optimization. Max-Sharpe: -0.102. Portfolio: return=1.63%, vol=23.29%. Weights: w_EEM=0.2500, w_LINK-USD=0.2500, w_IYR=0.2500, w_BIL=0.2500.

Question:
Assets: EEM, LINK-USD, IYR, BIL
Annualized mean returns: EEM:0.2280, LINK-USD:-1.0275, IYR:0.8119, BIL:0.0530
Covariance matrix (annualized):
[[0.020365, 0.024202, 0.016533, 5.7e-05], [0.024202, 0.630469, 0.051565, 0.000143], [0.016533, 0.051565, 0.031976, -1e-06], [5.7e-05, 0.000143, -1e-06, 7e-06]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_EEM=0.2500, w_LINK-USD=0.2500, w_IYR=0.2500, w_BIL=0.2500

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EEM=0.2500, w_LINK-USD=0.2500, w_IYR=0.2500, w_BIL=0.2500
Portfolio annualized return: 1.63%, volatility: 23.29%
Sharpe ratio: (0.0163 - 0.0400) / 0.2329 = -0.1017


4-asset optimization. Max-Sharpe: 5.458. Portfolio: return=25.84%, vol=4.00%. Weights: w_EWJ=0.0000, w_XRP-USD=0.0333, w_STIP=0.0000, w_ICSH=0.9667.

Question:
Assets: EWJ, XRP-USD, STIP, ICSH
Annualized mean returns: EWJ:0.0129, XRP-USD:6.3630, STIP:0.0183, ICSH:0.0479
Covariance matrix (annualized):
[[0.023403, 0.056304, 0.001037, 0.000135], [0.056304, 1.365971, 0.002305, 0.000852], [0.001037, 0.002305, 0.000241, 3.2e-05], [0.000135, 0.000852, 3.2e-05, 3.1e-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_EWJ=0.0000, w_XRP-USD=0.0333, w_STIP=0.0000, w_ICSH=0.9667

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EWJ=0.0000, w_XRP-USD=0.0333, w_STIP=0.0000, w_ICSH=0.9667
Portfolio annualized return: 25.84%, volatility: 4.00%
Sharpe ratio: (0.2584 - 0.0400) / 0.0400 = 5.4581


4-asset optimization. Max-Sharpe: 4.035. Portfolio: return=27.30%, vol=5.77%. Weights: w_IWM=0.0000, w_SOL-USD=0.0355, w_LQD=0.9645, w_ITB=0.0000.

Question:
Assets: IWM, SOL-USD, LQD, ITB
Annualized mean returns: IWM:-0.0768, SOL-USD:0.8895, LQD:0.2503, ITB:0.3461
Covariance matrix (annualized):
[[0.063275, 0.112217, -0.000419, 0.056096], [0.112217, 0.486237, -0.005291, 0.090344], [-0.000419, -0.005291, 0.003316, 0.003001], [0.056096, 0.090344, 0.003001, 0.067707]]
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_SOL-USD=0.0355, w_LQD=0.9645, w_ITB=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_IWM=0.0000, w_SOL-USD=0.0355, w_LQD=0.9645, w_ITB=0.0000
Portfolio annualized return: 27.30%, volatility: 5.77%
Sharpe ratio: (0.2730 - 0.0400) / 0.0577 = 4.0352


4-asset optimization. Max-Sharpe: 2.937. Portfolio: return=52.55%, vol=16.53%. Weights: w_IWM=0.8332, w_AVAX-USD=0.0000, w_WEAT=0.1668, w_TLT=0.0000.

Question:
Assets: IWM, AVAX-USD, WEAT, TLT
Annualized mean returns: IWM:0.5554, AVAX-USD:0.5848, WEAT:0.3762, TLT:-0.0386
Covariance matrix (annualized):
[[0.035325, 0.023978, -0.002529, -0.001501], [0.023978, 0.278945, 0.071154, 0.01277], [-0.002529, 0.071154, 0.126077, 0.002661], [-0.001501, 0.01277, 0.002661, 0.017593]]
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=0.8332, w_AVAX-USD=0.0000, w_WEAT=0.1668, w_TLT=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_IWM=0.8332, w_AVAX-USD=0.0000, w_WEAT=0.1668, w_TLT=0.0000
Portfolio annualized return: 52.55%, volatility: 16.53%
Sharpe ratio: (0.5255 - 0.0400) / 0.1653 = 2.9368


4-asset optimization. Max-Sharpe: 3.769. Portfolio: return=64.30%, vol=16.00%. Weights: w_IWM=0.2500, w_ETH-USD=0.2500, w_XHB=0.2500, w_BIL=0.2500.

Question:
Assets: IWM, ETH-USD, XHB, BIL
Annualized mean returns: IWM:0.7902, ETH-USD:0.4933, XHB:1.2387, BIL:0.0497
Covariance matrix (annualized):
[[0.033949, 0.025006, 0.030843, -7e-05], [0.025006, 0.161203, 0.030723, 0.000177], [0.030843, 0.030723, 0.04111, -8.7e-05], [-7e-05, 0.000177, -8.7e-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_IWM=0.2500, w_ETH-USD=0.2500, w_XHB=0.2500, w_BIL=0.2500

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_IWM=0.2500, w_ETH-USD=0.2500, w_XHB=0.2500, w_BIL=0.2500
Portfolio annualized return: 64.30%, volatility: 16.00%
Sharpe ratio: (0.6430 - 0.0400) / 0.1600 = 3.7692


4-asset optimization. Max-Sharpe: 0.970. Portfolio: return=62.22%, vol=60.05%. Weights: w_XLB=0.0000, w_ADA-USD=1.0000, w_CPER=0.0000, w_VNQI=0.0000.

Question:
Assets: XLB, ADA-USD, CPER, VNQI
Annualized mean returns: XLB:-0.0890, ADA-USD:0.6222, CPER:-0.0363, VNQI:0.0390
Covariance matrix (annualized):
[[0.041917, 0.016141, 0.01795, 0.017811], [0.016141, 0.360547, 0.024603, 0.00123], [0.01795, 0.024603, 0.040631, 0.00959], [0.017811, 0.00123, 0.00959, 0.016531]]
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_ADA-USD=1.0000, w_CPER=0.0000, w_VNQI=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLB=0.0000, w_ADA-USD=1.0000, w_CPER=0.0000, w_VNQI=0.0000
Portfolio annualized return: 62.22%, volatility: 60.05%
Sharpe ratio: (0.6222 - 0.0400) / 0.6005 = 0.9696


4-asset optimization. Max-Sharpe: 3.002. Portfolio: return=41.37%, vol=12.45%. Weights: w_XLV=0.3014, w_MATIC-USD=0.0000, w_PALL=0.0000, w_VNQI=0.6986.

Question:
Assets: XLV, MATIC-USD, PALL, VNQI
Annualized mean returns: XLV:0.3327, MATIC-USD:0.5518, PALL:-0.1107, VNQI:0.4486
Covariance matrix (annualized):
[[0.018291, 0.037457, 0.017192, 0.009479], [0.037457, 0.498536, 0.068905, 0.016629], [0.017192, 0.068905, 0.11952, 0.024861], [0.009479, 0.016629, 0.024861, 0.020154]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: bull

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

Answer: w_XLV=0.3014, w_MATIC-USD=0.0000, w_PALL=0.0000, w_VNQI=0.6986

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLV=0.3014, w_MATIC-USD=0.0000, w_PALL=0.0000, w_VNQI=0.6986
Portfolio annualized return: 41.37%, volatility: 12.45%
Sharpe ratio: (0.4137 - 0.0400) / 0.1245 = 3.0024


4-asset optimization. Max-Sharpe: 2.176. Portfolio: return=45.70%, vol=19.16%. Weights: w_XLRE=0.5673, w_BTC-USD=0.4327, w_VNQ=0.0000, w_SCHP=0.0000.

Question:
Assets: XLRE, BTC-USD, VNQ, SCHP
Annualized mean returns: XLRE:0.1949, BTC-USD:0.8006, VNQ:0.1764, SCHP:-0.0529
Covariance matrix (annualized):
[[0.015275, 0.011503, 0.014735, 0.002394], [0.011503, 0.139671, 0.015312, 0.000519], [0.014735, 0.015312, 0.014733, 0.00217], [0.002394, 0.000519, 0.00217, 0.00215]]
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=0.5673, w_BTC-USD=0.4327, w_VNQ=0.0000, w_SCHP=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLRE=0.5673, w_BTC-USD=0.4327, w_VNQ=0.0000, w_SCHP=0.0000
Portfolio annualized return: 45.70%, volatility: 19.16%
Sharpe ratio: (0.4570 - 0.0400) / 0.1916 = 2.1763


4-asset optimization. Max-Sharpe: 3.363. Portfolio: return=9.78%, vol=1.72%. Weights: w_XLB=0.0224, w_ADA-USD=0.0223, w_CSHI=0.9517, w_PALL=0.0036.

Question:
Assets: XLB, ADA-USD, CSHI, PALL
Annualized mean returns: XLB:0.2080, ADA-USD:1.4040, CSHI:0.0641, PALL:0.2253
Covariance matrix (annualized):
[[0.02664, 0.011504, -2.2e-05, 0.007208], [0.011504, 0.332588, -0.000695, -0.009289], [-2.2e-05, -0.000695, 0.000144, 0.000559], [0.007208, -0.009289, 0.000559, 0.127869]]
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=0.0224, w_ADA-USD=0.0223, w_CSHI=0.9517, w_PALL=0.0036

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLB=0.0224, w_ADA-USD=0.0223, w_CSHI=0.9517, w_PALL=0.0036
Portfolio annualized return: 9.78%, volatility: 1.72%
Sharpe ratio: (0.0978 - 0.0400) / 0.0172 = 3.3634


4-asset optimization. Max-Sharpe: 2.621. Portfolio: return=6.41%, vol=0.92%. Weights: w_XLB=0.0000, w_DOT-USD=0.0000, w_CSHI=1.0000, w_UNG=0.0000.

Question:
Assets: XLB, DOT-USD, CSHI, UNG
Annualized mean returns: XLB:0.2774, DOT-USD:0.5710, CSHI:0.0641, UNG:-5.3234
Covariance matrix (annualized):
[[0.034423, 0.04945, 0.000856, 0.041264], [0.04945, 0.423489, 0.001894, 0.132237], [0.000856, 0.001894, 8.4e-05, -0.000143], [0.041264, 0.132237, -0.000143, 0.576055]]
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_DOT-USD=0.0000, w_CSHI=1.0000, w_UNG=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLB=0.0000, w_DOT-USD=0.0000, w_CSHI=1.0000, w_UNG=0.0000
Portfolio annualized return: 6.41%, volatility: 0.92%
Sharpe ratio: (0.0641 - 0.0400) / 0.0092 = 2.6210


4-asset optimization. Max-Sharpe: 4.772. Portfolio: return=84.20%, vol=16.81%. Weights: w_MTUM=1.0000, w_AVAX-USD=0.0000, w_IGOV=0.0000, w_HAUZ=0.0000.

Question:
Assets: MTUM, AVAX-USD, IGOV, HAUZ
Annualized mean returns: MTUM:0.8420, AVAX-USD:-1.0457, IGOV:-0.2978, HAUZ:-0.2067
Covariance matrix (annualized):
[[0.028245, 0.060992, 0.005392, 0.010449], [0.060992, 0.695295, 0.002262, 0.014148], [0.005392, 0.002262, 0.008908, 0.010591], [0.010449, 0.014148, 0.010591, 0.027718]]
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=1.0000, w_AVAX-USD=0.0000, w_IGOV=0.0000, w_HAUZ=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_MTUM=1.0000, w_AVAX-USD=0.0000, w_IGOV=0.0000, w_HAUZ=0.0000
Portfolio annualized return: 84.20%, volatility: 16.81%
Sharpe ratio: (0.8420 - 0.0400) / 0.1681 = 4.7719


4-asset optimization. Max-Sharpe: 3.015. Portfolio: return=52.00%, vol=15.92%. Weights: w_VEA=0.9526, w_MATIC-USD=0.0474, w_SOYB=0.0000, w_LQD=0.0000.

Question:
Assets: VEA, MATIC-USD, SOYB, LQD
Annualized mean returns: VEA:0.4858, MATIC-USD:1.2074, SOYB:0.0935, LQD:0.0513
Covariance matrix (annualized):
[[0.022594, 0.0424, 0.003254, 0.007722], [0.0424, 0.44776, 0.003353, 0.006165], [0.003254, 0.003353, 0.016674, 0.00011], [0.007722, 0.006165, 0.00011, 0.011618]]
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=0.9526, w_MATIC-USD=0.0474, w_SOYB=0.0000, w_LQD=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VEA=0.9526, w_MATIC-USD=0.0474, w_SOYB=0.0000, w_LQD=0.0000
Portfolio annualized return: 52.00%, volatility: 15.92%
Sharpe ratio: (0.5200 - 0.0400) / 0.1592 = 3.0153


4-asset optimization. Max-Sharpe: 3.384. Portfolio: return=82.29%, vol=23.14%. Weights: w_XLK=0.4162, w_BNB-USD=0.0235, w_XHB=0.5603, w_VCIT=0.0000.

Question:
Assets: XLK, BNB-USD, XHB, VCIT
Annualized mean returns: XLK:0.7798, BNB-USD:0.5315, XHB:0.8671, VCIT:-0.0184
Covariance matrix (annualized):
[[0.056989, 0.031654, 0.046622, 0.007656], [0.031654, 0.170953, 0.029304, 0.000223], [0.046622, 0.029304, 0.065078, 0.011987], [0.007656, 0.000223, 0.011987, 0.007158]]
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=0.4162, w_BNB-USD=0.0235, w_XHB=0.5603, w_VCIT=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLK=0.4162, w_BNB-USD=0.0235, w_XHB=0.5603, w_VCIT=0.0000
Portfolio annualized return: 82.29%, volatility: 23.14%
Sharpe ratio: (0.8229 - 0.0400) / 0.2314 = 3.3838


4-asset optimization. Max-Sharpe: 1.166. Portfolio: return=96.18%, vol=79.09%. Weights: w_XLU=0.0000, w_MATIC-USD=1.0000, w_MORT=0.0000, w_CORN=0.0000.

Question:
Assets: XLU, MATIC-USD, MORT, CORN
Annualized mean returns: XLU:0.0943, MATIC-USD:0.9618, MORT:-0.1360, CORN:-0.0446
Covariance matrix (annualized):
[[0.029449, 0.039075, 0.009422, -0.000295], [0.039075, 0.625502, 0.049979, 0.018333], [0.009422, 0.049979, 0.021299, -0.004844], [-0.000295, 0.018333, -0.004844, 0.017021]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_XLU=0.0000, w_MATIC-USD=1.0000, w_MORT=0.0000, w_CORN=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLU=0.0000, w_MATIC-USD=1.0000, w_MORT=0.0000, w_CORN=0.0000
Portfolio annualized return: 96.18%, volatility: 79.09%
Sharpe ratio: (0.9618 - 0.0400) / 0.7909 = 1.1655


4-asset optimization. Max-Sharpe: 4.487. Portfolio: return=10.93%, vol=1.54%. Weights: w_XLF=0.0000, w_BTC-USD=0.0263, w_CSHI=0.9684, w_MORT=0.0053.

Question:
Assets: XLF, BTC-USD, CSHI, MORT
Annualized mean returns: XLF:-0.1088, BTC-USD:1.3977, CSHI:0.0754, MORT:-0.1017
Covariance matrix (annualized):
[[0.052932, -0.023076, -3.6e-05, 0.048293], [-0.023076, 0.239478, -0.001542, -0.025167], [-3.6e-05, -0.001542, 0.000169, -0.000242], [0.048293, -0.025167, -0.000242, 0.07724]]
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_BTC-USD=0.0263, w_CSHI=0.9684, w_MORT=0.0053

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLF=0.0000, w_BTC-USD=0.0263, w_CSHI=0.9684, w_MORT=0.0053
Portfolio annualized return: 10.93%, volatility: 1.54%
Sharpe ratio: (0.1093 - 0.0400) / 0.0154 = 4.4874


4-asset optimization. Max-Sharpe: 6.323. Portfolio: return=5.74%, vol=0.27%. Weights: w_^VIX=0.0015, w_DOT-USD=0.0000, w_SGOV=0.9985, w_SCHH=0.0000.

Question:
Assets: ^VIX, DOT-USD, SGOV, SCHH
Annualized mean returns: ^VIX:0.8101, DOT-USD:0.7745, SGOV:0.0562, SCHH:-0.1400
Covariance matrix (annualized):
[[0.567485, -0.018828, -0.000541, -0.057825], [-0.018828, 0.683104, 0.000763, 0.027605], [-0.000541, 0.000763, 8e-06, 0.000187], [-0.057825, 0.027605, 0.000187, 0.031111]]
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=0.0015, w_DOT-USD=0.0000, w_SGOV=0.9985, w_SCHH=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_^VIX=0.0015, w_DOT-USD=0.0000, w_SGOV=0.9985, w_SCHH=0.0000
Portfolio annualized return: 5.74%, volatility: 0.27%
Sharpe ratio: (0.0574 - 0.0400) / 0.0027 = 6.3229


4-asset optimization. Max-Sharpe: 4.667. Portfolio: return=60.80%, vol=12.17%. Weights: w_QUAL=1.0000, w_ADA-USD=0.0000, w_REZ=0.0000, w_SHY=0.0000.

Question:
Assets: QUAL, ADA-USD, REZ, SHY
Annualized mean returns: QUAL:0.6080, ADA-USD:0.3818, REZ:0.2927, SHY:-0.0265
Covariance matrix (annualized):
[[0.014808, 0.025351, 0.006598, -0.000127], [0.025351, 0.576514, 0.005853, 0.003585], [0.006598, 0.005853, 0.0295, -8.4e-05], [-0.000127, 0.003585, -8.4e-05, 0.000487]]
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_ADA-USD=0.0000, w_REZ=0.0000, w_SHY=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_QUAL=1.0000, w_ADA-USD=0.0000, w_REZ=0.0000, w_SHY=0.0000
Portfolio annualized return: 60.80%, volatility: 12.17%
Sharpe ratio: (0.6080 - 0.0400) / 0.1217 = 4.6674


4-asset optimization. Max-Sharpe: 8.655. Portfolio: return=85.12%, vol=9.37%. Weights: w_XLP=0.3824, w_BNB-USD=0.0827, w_HAUZ=0.0496, w_TLH=0.4854.

Question:
Assets: XLP, BNB-USD, HAUZ, TLH
Annualized mean returns: XLP:0.5049, BNB-USD:2.2814, HAUZ:0.9945, TLH:0.8659
Covariance matrix (annualized):
[[0.014648, 0.008334, 0.006273, -0.003227], [0.008334, 0.307934, 0.017431, -0.010779], [0.006273, 0.017431, 0.028365, 0.010488], [-0.003227, -0.010779, 0.010488, 0.021731]]
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=0.3824, w_BNB-USD=0.0827, w_HAUZ=0.0496, w_TLH=0.4854

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLP=0.3824, w_BNB-USD=0.0827, w_HAUZ=0.0496, w_TLH=0.4854
Portfolio annualized return: 85.12%, volatility: 9.37%
Sharpe ratio: (0.8512 - 0.0400) / 0.0937 = 8.6553


4-asset optimization. Max-Sharpe: 1.785. Portfolio: return=35.32%, vol=17.54%. Weights: w_VLUE=0.2500, w_DOT-USD=0.2500, w_IYR=0.2500, w_SGOV=0.2500.

Question:
Assets: VLUE, DOT-USD, IYR, SGOV
Annualized mean returns: VLUE:0.2222, DOT-USD:1.1533, IYR:-0.0185, SGOV:0.0557
Covariance matrix (annualized):
[[0.013692, 0.009352, 0.014942, 0.000109], [0.009352, 0.369427, 0.0157, 0.000285], [0.014942, 0.0157, 0.028263, 0.000147], [0.000109, 0.000285, 0.000147, 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_VLUE=0.2500, w_DOT-USD=0.2500, w_IYR=0.2500, w_SGOV=0.2500

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VLUE=0.2500, w_DOT-USD=0.2500, w_IYR=0.2500, w_SGOV=0.2500
Portfolio annualized return: 35.32%, volatility: 17.54%
Sharpe ratio: (0.3532 - 0.0400) / 0.1754 = 1.7851


4-asset optimization. Max-Sharpe: 3.116. Portfolio: return=5.34%, vol=0.43%. Weights: w_EEM=0.0000, w_ETH-USD=0.0000, w_PPLT=0.0000, w_ICSH=1.0000.

Question:
Assets: EEM, ETH-USD, PPLT, ICSH
Annualized mean returns: EEM:-0.5240, ETH-USD:-0.6957, PPLT:-0.3328, ICSH:0.0534
Covariance matrix (annualized):
[[0.016704, 0.007808, 0.011899, -4.8e-05], [0.007808, 0.102214, 0.012029, 0.000131], [0.011899, 0.012029, 0.047529, 9e-06], [-4.8e-05, 0.000131, 9e-06, 1.8e-05]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_EEM=0.0000, w_ETH-USD=0.0000, w_PPLT=0.0000, w_ICSH=1.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EEM=0.0000, w_ETH-USD=0.0000, w_PPLT=0.0000, w_ICSH=1.0000
Portfolio annualized return: 5.34%, volatility: 0.43%
Sharpe ratio: (0.0534 - 0.0400) / 0.0043 = 3.1155


4-asset optimization. Max-Sharpe: 2.818. Portfolio: return=50.27%, vol=16.42%. Weights: w_XLB=0.0000, w_DOT-USD=0.0000, w_SCHH=0.6805, w_SLV=0.3195.

Question:
Assets: XLB, DOT-USD, SCHH, SLV
Annualized mean returns: XLB:-0.1733, DOT-USD:-0.7820, SCHH:0.2956, SLV:0.9439
Covariance matrix (annualized):
[[0.012536, 0.003755, 0.008904, 0.014192], [0.003755, 0.360684, 0.021775, 0.046102], [0.008904, 0.021775, 0.0179, 0.008498], [0.014192, 0.046102, 0.008498, 0.146801]]
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_DOT-USD=0.0000, w_SCHH=0.6805, w_SLV=0.3195

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLB=0.0000, w_DOT-USD=0.0000, w_SCHH=0.6805, w_SLV=0.3195
Portfolio annualized return: 50.27%, volatility: 16.42%
Sharpe ratio: (0.5027 - 0.0400) / 0.1642 = 2.8176


4-asset optimization. Max-Sharpe: -0.250. Portfolio: return=-2.01%, vol=23.98%. Weights: w_XLB=0.0000, w_BNB-USD=0.0000, w_PALL=0.0000, w_ITB=1.0000.

Question:
Assets: XLB, BNB-USD, PALL, ITB
Annualized mean returns: XLB:-0.3106, BNB-USD:-0.4450, PALL:-0.8781, ITB:-0.0201
Covariance matrix (annualized):
[[0.044221, 0.00886, 0.005522, 0.033538], [0.00886, 0.23738, -0.017577, 0.014339], [0.005522, -0.017577, 0.114024, 0.001135], [0.033538, 0.014339, 0.001135, 0.057497]]
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_BNB-USD=0.0000, w_PALL=0.0000, w_ITB=1.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLB=0.0000, w_BNB-USD=0.0000, w_PALL=0.0000, w_ITB=1.0000
Portfolio annualized return: -2.01%, volatility: 23.98%
Sharpe ratio: (-0.0201 - 0.0400) / 0.2398 = -0.2505


4-asset optimization. Max-Sharpe: 8.107. Portfolio: return=7.08%, vol=0.38%. Weights: w_XLU=0.0018, w_AVAX-USD=0.0034, w_SOYB=0.0102, w_SGOV=0.9846.

Question:
Assets: XLU, AVAX-USD, SOYB, SGOV
Annualized mean returns: XLU:0.3497, AVAX-USD:5.7177, SOYB:-0.0137, SGOV:0.0517
Covariance matrix (annualized):
[[0.03225, 0.015825, -0.001734, 5.2e-05], [0.015825, 1.014753, -0.06117, -0.00019], [-0.001734, -0.06117, 0.025804, -8e-05], [5.2e-05, -0.00019, -8e-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_XLU=0.0018, w_AVAX-USD=0.0034, w_SOYB=0.0102, w_SGOV=0.9846

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLU=0.0018, w_AVAX-USD=0.0034, w_SOYB=0.0102, w_SGOV=0.9846
Portfolio annualized return: 7.08%, volatility: 0.38%
Sharpe ratio: (0.0708 - 0.0400) / 0.0038 = 8.1066


4-asset optimization. Max-Sharpe: 1.111. Portfolio: return=37.82%, vol=30.46%. Weights: w_QUAL=0.0000, w_MATIC-USD=0.0000, w_XHB=1.0000, w_UNG=0.0000.

Question:
Assets: QUAL, MATIC-USD, XHB, UNG
Annualized mean returns: QUAL:0.1350, MATIC-USD:-0.3406, XHB:0.3782, UNG:-1.4717
Covariance matrix (annualized):
[[0.030055, 0.045636, 0.029712, 0.017373], [0.045636, 0.404917, 0.042705, 0.055729], [0.029712, 0.042705, 0.092759, 0.045144], [0.017373, 0.055729, 0.045144, 0.220733]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: bull

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

Answer: w_QUAL=0.0000, w_MATIC-USD=0.0000, w_XHB=1.0000, w_UNG=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_QUAL=0.0000, w_MATIC-USD=0.0000, w_XHB=1.0000, w_UNG=0.0000
Portfolio annualized return: 37.82%, volatility: 30.46%
Sharpe ratio: (0.3782 - 0.0400) / 0.3046 = 1.1105


4-asset optimization. Max-Sharpe: 6.187. Portfolio: return=46.80%, vol=6.92%. Weights: w_XLP=0.3700, w_XRP-USD=0.0000, w_REZ=0.0000, w_LQD=0.6300.

Question:
Assets: XLP, XRP-USD, REZ, LQD
Annualized mean returns: XLP:0.4222, XRP-USD:-0.6609, REZ:0.7818, LQD:0.4949
Covariance matrix (annualized):
[[0.014259, -0.001489, 0.007718, -0.001592], [-0.001489, 0.234187, -0.005212, -0.008231], [0.007718, -0.005212, 0.040597, 0.00915], [-0.001592, -0.008231, 0.00915, 0.009006]]
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=0.3700, w_XRP-USD=0.0000, w_REZ=0.0000, w_LQD=0.6300

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLP=0.3700, w_XRP-USD=0.0000, w_REZ=0.0000, w_LQD=0.6300
Portfolio annualized return: 46.80%, volatility: 6.92%
Sharpe ratio: (0.4680 - 0.0400) / 0.0692 = 6.1874


4-asset optimization. Max-Sharpe: 2.957. Portfolio: return=25.11%, vol=7.14%. Weights: w_VTI=0.0943, w_ADA-USD=0.0000, w_LQD=0.9057, w_BNO=0.0000.

Question:
Assets: VTI, ADA-USD, LQD, BNO
Annualized mean returns: VTI:0.0915, ADA-USD:0.4224, LQD:0.2677, BNO:-0.0901
Covariance matrix (annualized):
[[0.023797, 0.012488, -0.001104, 0.012076], [0.012488, 0.37503, 0.010874, 0.018134], [-0.001104, 0.010874, 0.006186, -0.00013], [0.012076, 0.018134, -0.00013, 0.105863]]
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=0.0943, w_ADA-USD=0.0000, w_LQD=0.9057, w_BNO=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VTI=0.0943, w_ADA-USD=0.0000, w_LQD=0.9057, w_BNO=0.0000
Portfolio annualized return: 25.11%, volatility: 7.14%
Sharpe ratio: (0.2511 - 0.0400) / 0.0714 = 2.9567


4-asset optimization. Max-Sharpe: 1.411. Portfolio: return=152.02%, vol=104.93%. Weights: w_MTUM=0.0000, w_AVAX-USD=1.0000, w_UNG=0.0000, w_BNDX=0.0000.

Question:
Assets: MTUM, AVAX-USD, UNG, BNDX
Annualized mean returns: MTUM:-0.3531, AVAX-USD:1.5202, UNG:-1.5994, BNDX:-0.0493
Covariance matrix (annualized):
[[0.017876, 0.024665, 0.026828, -0.00096], [0.024665, 1.100962, 0.001278, 0.001429], [0.026828, 0.001278, 0.647891, -0.002412], [-0.00096, 0.001429, -0.002412, 0.002829]]
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=0.0000, w_AVAX-USD=1.0000, w_UNG=0.0000, w_BNDX=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_MTUM=0.0000, w_AVAX-USD=1.0000, w_UNG=0.0000, w_BNDX=0.0000
Portfolio annualized return: 152.02%, volatility: 104.93%
Sharpe ratio: (1.5202 - 0.0400) / 1.0493 = 1.4107


4-asset optimization. Max-Sharpe: 0.399. Portfolio: return=4.20%, vol=0.51%. Weights: w_VTI=0.0103, w_MATIC-USD=0.0000, w_SHV=0.9649, w_PDBC=0.0248.

Question:
Assets: VTI, MATIC-USD, SHV, PDBC
Annualized mean returns: VTI:0.0552, MATIC-USD:-1.8242, SHV:0.0408, PDBC:0.0841
Covariance matrix (annualized):
[[0.025525, 0.013366, -0.000234, 0.006344], [0.013366, 0.383478, 0.000185, 0.012444], [-0.000234, 0.000185, 1.5e-05, -8.3e-05], [0.006344, 0.012444, -8.3e-05, 0.02319]]
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=0.0103, w_MATIC-USD=0.0000, w_SHV=0.9649, w_PDBC=0.0248

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VTI=0.0103, w_MATIC-USD=0.0000, w_SHV=0.9649, w_PDBC=0.0248
Portfolio annualized return: 4.20%, volatility: 0.51%
Sharpe ratio: (0.0420 - 0.0400) / 0.0051 = 0.3990


4-asset optimization. Max-Sharpe: 4.168. Portfolio: return=5.09%, vol=0.26%. Weights: w_XLRE=0.0000, w_MATIC-USD=0.0000, w_BIL=1.0000, w_VCIT=0.0000.

Question:
Assets: XLRE, MATIC-USD, BIL, VCIT
Annualized mean returns: XLRE:-0.6351, MATIC-USD:-1.6468, BIL:0.0509, VCIT:-0.1751
Covariance matrix (annualized):
[[0.022853, 0.024523, -0.000107, 0.004181], [0.024523, 0.167628, -0.000362, 0.008329], [-0.000107, -0.000362, 7e-06, -2.9e-05], [0.004181, 0.008329, -2.9e-05, 0.00387]]
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=0.0000, w_BIL=1.0000, w_VCIT=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLRE=0.0000, w_MATIC-USD=0.0000, w_BIL=1.0000, w_VCIT=0.0000
Portfolio annualized return: 5.09%, volatility: 0.26%
Sharpe ratio: (0.0509 - 0.0400) / 0.0026 = 4.1681


4-asset optimization. Max-Sharpe: -1.746. Portfolio: return=-132.50%, vol=78.19%. Weights: w_XLE=0.0000, w_AVAX-USD=1.0000, w_HAUZ=0.0000, w_IEF=0.0000.

Question:
Assets: XLE, AVAX-USD, HAUZ, IEF
Annualized mean returns: XLE:-0.5425, AVAX-USD:-1.3250, HAUZ:-0.6380, IEF:-0.0642
Covariance matrix (annualized):
[[0.085861, 0.035231, 0.016149, -0.01593], [0.035231, 0.611435, 0.017985, -0.000278], [0.016149, 0.017985, 0.022948, -0.001337], [-0.01593, -0.000278, -0.001337, 0.011055]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_XLE=0.0000, w_AVAX-USD=1.0000, w_HAUZ=0.0000, w_IEF=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLE=0.0000, w_AVAX-USD=1.0000, w_HAUZ=0.0000, w_IEF=0.0000
Portfolio annualized return: -132.50%, volatility: 78.19%
Sharpe ratio: (-1.3250 - 0.0400) / 0.7819 = -1.7457


4-asset optimization. Max-Sharpe: 6.420. Portfolio: return=52.14%, vol=7.50%. Weights: w_^VIX=0.0541, w_DOT-USD=0.0000, w_VNQ=0.5123, w_CSHI=0.4335.

Question:
Assets: ^VIX, DOT-USD, VNQ, CSHI
Annualized mean returns: ^VIX:3.3903, DOT-USD:-1.1772, VNQ:0.6197, CSHI:0.0471
Covariance matrix (annualized):
[[1.874518, -0.435513, -0.110685, -0.012912], [-0.435513, 0.377382, 0.035495, 0.005153], [-0.110685, 0.035495, 0.023802, 0.001305], [-0.012912, 0.005153, 0.001305, 0.000259]]
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=0.0541, w_DOT-USD=0.0000, w_VNQ=0.5123, w_CSHI=0.4335

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_^VIX=0.0541, w_DOT-USD=0.0000, w_VNQ=0.5123, w_CSHI=0.4335
Portfolio annualized return: 52.14%, volatility: 7.50%
Sharpe ratio: (0.5214 - 0.0400) / 0.0750 = 6.4196


4-asset optimization. Max-Sharpe: 0.605. Portfolio: return=10.28%, vol=10.37%. Weights: w_VEA=0.0000, w_AVAX-USD=0.0000, w_SHY=0.0000, w_DBA=1.0000.

Question:
Assets: VEA, AVAX-USD, SHY, DBA
Annualized mean returns: VEA:-0.2301, AVAX-USD:-0.2583, SHY:-0.0098, DBA:0.1028
Covariance matrix (annualized):
[[0.021378, 0.044828, -0.000271, 0.00592], [0.044828, 0.774716, -0.002231, 0.023057], [-0.000271, -0.002231, 0.000601, -0.000384], [0.00592, 0.023057, -0.000384, 0.010762]]
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_AVAX-USD=0.0000, w_SHY=0.0000, w_DBA=1.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VEA=0.0000, w_AVAX-USD=0.0000, w_SHY=0.0000, w_DBA=1.0000
Portfolio annualized return: 10.28%, volatility: 10.37%
Sharpe ratio: (0.1028 - 0.0400) / 0.1037 = 0.6052


4-asset optimization. Max-Sharpe: -0.657. Portfolio: return=-7.00%, vol=16.74%. Weights: w_EFA=0.2500, w_DOT-USD=0.2500, w_BIL=0.2500, w_GLD=0.2500.

Question:
Assets: EFA, DOT-USD, BIL, GLD
Annualized mean returns: EFA:0.2587, DOT-USD:-0.9662, BIL:0.0511, GLD:0.3765
Covariance matrix (annualized):
[[0.026997, 0.032954, 4.8e-05, 0.012599], [0.032954, 0.288816, 0.000361, 0.007713], [4.8e-05, 0.000361, 7e-06, 7.2e-05], [0.012599, 0.007713, 7.2e-05, 0.025095]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: bull

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

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

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EFA=0.2500, w_DOT-USD=0.2500, w_BIL=0.2500, w_GLD=0.2500
Portfolio annualized return: -7.00%, volatility: 16.74%
Sharpe ratio: (-0.0700 - 0.0400) / 0.1674 = -0.6569


4-asset optimization. Max-Sharpe: 2.536. Portfolio: return=66.14%, vol=24.50%. Weights: w_XLU=0.0000, w_BTC-USD=0.5863, w_BIL=0.0000, w_WEAT=0.4137.

Question:
Assets: XLU, BTC-USD, BIL, WEAT
Annualized mean returns: XLU:-0.3478, BTC-USD:0.9633, BIL:0.0394, WEAT:0.2336
Covariance matrix (annualized):
[[0.029406, 0.019509, -0.000126, 0.004352], [0.019509, 0.15263, 7.3e-05, -0.000704], [-0.000126, 7.3e-05, 1.1e-05, 3.7e-05], [0.004352, -0.000704, 3.7e-05, 0.046197]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_XLU=0.0000, w_BTC-USD=0.5863, w_BIL=0.0000, w_WEAT=0.4137

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLU=0.0000, w_BTC-USD=0.5863, w_BIL=0.0000, w_WEAT=0.4137
Portfolio annualized return: 66.14%, volatility: 24.50%
Sharpe ratio: (0.6614 - 0.0400) / 0.2450 = 2.5362


4-asset optimization. Max-Sharpe: 4.224. Portfolio: return=6.06%, vol=0.49%. Weights: w_USMV=0.0177, w_AVAX-USD=0.0016, w_SGOV=0.9685, w_PPLT=0.0122.

Question:
Assets: USMV, AVAX-USD, SGOV, PPLT
Annualized mean returns: USMV:0.2744, AVAX-USD:0.6657, SGOV:0.0468, PPLT:0.7714
Covariance matrix (annualized):
[[0.01347, 0.003698, 4.7e-05, -0.001517], [0.003698, 0.432011, -7.8e-05, 0.002038], [4.7e-05, -7.8e-05, 7e-06, 3.7e-05], [-0.001517, 0.002038, 3.7e-05, 0.068526]]
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=0.0177, w_AVAX-USD=0.0016, w_SGOV=0.9685, w_PPLT=0.0122

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_USMV=0.0177, w_AVAX-USD=0.0016, w_SGOV=0.9685, w_PPLT=0.0122
Portfolio annualized return: 6.06%, volatility: 0.49%
Sharpe ratio: (0.0606 - 0.0400) / 0.0049 = 4.2239


4-asset optimization. Max-Sharpe: 3.396. Portfolio: return=5.46%, vol=0.43%. Weights: w_XLK=0.0035, w_AVAX-USD=0.0000, w_PALL=0.0000, w_ICSH=0.9965.

Question:
Assets: XLK, AVAX-USD, PALL, ICSH
Annualized mean returns: XLK:0.0477, AVAX-USD:-0.9993, PALL:-0.7232, ICSH:0.0547
Covariance matrix (annualized):
[[0.03435, 0.022157, 0.008177, -0.000112], [0.022157, 0.215821, 0.042446, -0.00012], [0.008177, 0.042446, 0.06703, 9.1e-05], [-0.000112, -0.00012, 9.1e-05, 1.9e-05]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_XLK=0.0035, w_AVAX-USD=0.0000, w_PALL=0.0000, w_ICSH=0.9965

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLK=0.0035, w_AVAX-USD=0.0000, w_PALL=0.0000, w_ICSH=0.9965
Portfolio annualized return: 5.46%, volatility: 0.43%
Sharpe ratio: (0.0546 - 0.0400) / 0.0043 = 3.3961


4-asset optimization. Max-Sharpe: 3.516. Portfolio: return=5.37%, vol=0.39%. Weights: w_XLP=0.0000, w_BNB-USD=0.0059, w_TLH=0.0000, w_ICSH=0.9941.

Question:
Assets: XLP, BNB-USD, TLH, ICSH
Annualized mean returns: XLP:-0.1872, BNB-USD:0.2486, TLH:-0.2240, ICSH:0.0525
Covariance matrix (annualized):
[[0.015699, 0.001419, 0.00451, -4.5e-05], [0.001419, 0.068127, 0.001369, -0.00017], [0.00451, 0.001369, 0.028419, 0.000211], [-4.5e-05, -0.00017, 0.000211, 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_XLP=0.0000, w_BNB-USD=0.0059, w_TLH=0.0000, w_ICSH=0.9941

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLP=0.0000, w_BNB-USD=0.0059, w_TLH=0.0000, w_ICSH=0.9941
Portfolio annualized return: 5.37%, volatility: 0.39%
Sharpe ratio: (0.0537 - 0.0400) / 0.0039 = 3.5163


4-asset optimization. Max-Sharpe: 3.842. Portfolio: return=83.10%, vol=20.59%. Weights: w_IVV=0.7799, w_SOL-USD=0.2201, w_PALL=0.0000, w_EMB=0.0000.

Question:
Assets: IVV, SOL-USD, PALL, EMB
Annualized mean returns: IVV:0.4299, SOL-USD:2.2523, PALL:-0.4764, EMB:-0.0146
Covariance matrix (annualized):
[[0.013679, 0.046458, 0.006273, 0.002263], [0.046458, 0.373956, -0.001353, 0.008775], [0.006273, -0.001353, 0.170788, 0.00498], [0.002263, 0.008775, 0.00498, 0.003782]]
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=0.7799, w_SOL-USD=0.2201, w_PALL=0.0000, w_EMB=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_IVV=0.7799, w_SOL-USD=0.2201, w_PALL=0.0000, w_EMB=0.0000
Portfolio annualized return: 83.10%, volatility: 20.59%
Sharpe ratio: (0.8310 - 0.0400) / 0.2059 = 3.8423


4-asset optimization. Max-Sharpe: 7.570. Portfolio: return=6.39%, vol=0.32%. Weights: w_IVV=0.0272, w_BTC-USD=0.0000, w_USO=0.0000, w_BIL=0.9728.

Question:
Assets: IVV, BTC-USD, USO, BIL
Annualized mean returns: IVV:0.4959, BTC-USD:-0.4496, USO:-0.0311, BIL:0.0518
Covariance matrix (annualized):
[[0.008984, 0.020623, 0.006349, -5.6e-05], [0.020623, 0.211638, 0.009015, 6.4e-05], [0.006349, 0.009015, 0.055515, -5.7e-05], [-5.6e-05, 6.4e-05, -5.7e-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_IVV=0.0272, w_BTC-USD=0.0000, w_USO=0.0000, w_BIL=0.9728

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_IVV=0.0272, w_BTC-USD=0.0000, w_USO=0.0000, w_BIL=0.9728
Portfolio annualized return: 6.39%, volatility: 0.32%
Sharpe ratio: (0.0639 - 0.0400) / 0.0032 = 7.5701


4-asset optimization. Max-Sharpe: 4.200. Portfolio: return=55.96%, vol=12.37%. Weights: w_SPY=0.0000, w_BNB-USD=0.0000, w_DBB=0.2364, w_IYR=0.7636.

Question:
Assets: SPY, BNB-USD, DBB, IYR
Annualized mean returns: SPY:0.2949, BNB-USD:0.5170, DBB:0.5237, IYR:0.5707
Covariance matrix (annualized):
[[0.027621, 0.044772, 0.02292, 0.010344], [0.044772, 0.218887, 0.031013, 0.030167], [0.02292, 0.031013, 0.039478, 0.006432], [0.010344, 0.030167, 0.006432, 0.018477]]
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_SPY=0.0000, w_BNB-USD=0.0000, w_DBB=0.2364, w_IYR=0.7636

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_SPY=0.0000, w_BNB-USD=0.0000, w_DBB=0.2364, w_IYR=0.7636
Portfolio annualized return: 55.96%, volatility: 12.37%
Sharpe ratio: (0.5596 - 0.0400) / 0.1237 = 4.2004


4-asset optimization. Max-Sharpe: 6.163. Portfolio: return=5.94%, vol=0.31%. Weights: w_^VIX=0.0010, w_ADA-USD=0.0012, w_INDS=0.0018, w_SGOV=0.9961.

Question:
Assets: ^VIX, ADA-USD, INDS, SGOV
Annualized mean returns: ^VIX:0.1379, ADA-USD:2.1320, INDS:0.5440, SGOV:0.0559
Covariance matrix (annualized):
[[0.373638, -0.103624, -0.024501, -0.000143], [-0.103624, 0.910746, 0.050705, -2.6e-05], [-0.024501, 0.050705, 0.041766, 0.000146], [-0.000143, -2.6e-05, 0.000146, 8e-06]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_^VIX=0.0010, w_ADA-USD=0.0012, w_INDS=0.0018, w_SGOV=0.9961

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_^VIX=0.0010, w_ADA-USD=0.0012, w_INDS=0.0018, w_SGOV=0.9961
Portfolio annualized return: 5.94%, volatility: 0.31%
Sharpe ratio: (0.0594 - 0.0400) / 0.0031 = 6.1631