4-asset optimization. Max-Sharpe: 3.983. Portfolio: return=10.88%, vol=1.73%. Weights: w_XLP=0.0000, w_AVAX-USD=0.0000, w_XHB=0.0638, w_CSHI=0.9362.

Question:
Assets: XLP, AVAX-USD, XHB, CSHI
Annualized mean returns: XLP:-0.2451, AVAX-USD:0.1327, XHB:0.8134, CSHI:0.0608
Covariance matrix (annualized):
[[0.010473, 0.002711, 0.005969, 9e-06], [0.002711, 0.227481, 0.0352, 0.000473], [0.005969, 0.0352, 0.051302, 9e-05], [9e-06, 0.000473, 9e-05, 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_XLP=0.0000, w_AVAX-USD=0.0000, w_XHB=0.0638, w_CSHI=0.9362

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLP=0.0000, w_AVAX-USD=0.0000, w_XHB=0.0638, w_CSHI=0.9362
Portfolio annualized return: 10.88%, volatility: 1.73%
Sharpe ratio: (0.1088 - 0.0400) / 0.0173 = 3.9833


4-asset optimization. Max-Sharpe: 5.378. Portfolio: return=6.88%, vol=0.54%. Weights: w_QQQ=0.0127, w_XRP-USD=0.0025, w_XHB=0.0003, w_ICSH=0.9845.

Question:
Assets: QQQ, XRP-USD, XHB, ICSH
Annualized mean returns: QQQ:0.4561, XRP-USD:0.3268, XHB:0.8419, ICSH:0.0629
Covariance matrix (annualized):
[[0.028318, -0.001247, 0.02897, 4.9e-05], [-0.001247, 0.235847, -0.013626, -0.000285], [0.02897, -0.013626, 0.065254, 0.000452], [4.9e-05, -0.000285, 0.000452, 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_QQQ=0.0127, w_XRP-USD=0.0025, w_XHB=0.0003, w_ICSH=0.9845

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_QQQ=0.0127, w_XRP-USD=0.0025, w_XHB=0.0003, w_ICSH=0.9845
Portfolio annualized return: 6.88%, volatility: 0.54%
Sharpe ratio: (0.0688 - 0.0400) / 0.0054 = 5.3776


4-asset optimization. Max-Sharpe: 4.664. Portfolio: return=157.06%, vol=32.82%. Weights: w_IVV=0.7069, w_ADA-USD=0.2931, w_INDS=0.0000, w_TLH=0.0000.

Question:
Assets: IVV, ADA-USD, INDS, TLH
Annualized mean returns: IVV:0.2990, ADA-USD:4.6372, INDS:-0.3562, TLH:0.0061
Covariance matrix (annualized):
[[0.012237, 0.032644, 0.000583, -0.001557], [0.032644, 1.024617, 0.014849, 0.006001], [0.000583, 0.014849, 0.031521, 0.01179], [-0.001557, 0.006001, 0.01179, 0.01384]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: bull

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

Answer: w_IVV=0.7069, w_ADA-USD=0.2931, w_INDS=0.0000, w_TLH=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_IVV=0.7069, w_ADA-USD=0.2931, w_INDS=0.0000, w_TLH=0.0000
Portfolio annualized return: 157.06%, volatility: 32.82%
Sharpe ratio: (1.5706 - 0.0400) / 0.3282 = 4.6644


4-asset optimization. Max-Sharpe: 4.554. Portfolio: return=5.24%, vol=0.27%. Weights: w_EFA=0.0000, w_ETH-USD=0.0000, w_STIP=0.0155, w_BIL=0.9845.

Question:
Assets: EFA, ETH-USD, STIP, BIL
Annualized mean returns: EFA:-0.0340, ETH-USD:-0.6485, STIP:0.0552, BIL:0.0524
Covariance matrix (annualized):
[[0.015633, 0.019478, 0.001957, -5.1e-05], [0.019478, 0.105779, 0.00332, -9.7e-05], [0.001957, 0.00332, 0.000702, -2e-06], [-5.1e-05, -9.7e-05, -2e-06, 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_EFA=0.0000, w_ETH-USD=0.0000, w_STIP=0.0155, w_BIL=0.9845

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EFA=0.0000, w_ETH-USD=0.0000, w_STIP=0.0155, w_BIL=0.9845
Portfolio annualized return: 5.24%, volatility: 0.27%
Sharpe ratio: (0.0524 - 0.0400) / 0.0027 = 4.5538


4-asset optimization. Max-Sharpe: 3.631. Portfolio: return=6.10%, vol=0.58%. Weights: w_XLP=0.0000, w_MATIC-USD=0.0000, w_TLH=0.0000, w_CSHI=1.0000.

Question:
Assets: XLP, MATIC-USD, TLH, CSHI
Annualized mean returns: XLP:-0.2022, MATIC-USD:-0.0320, TLH:-0.4241, CSHI:0.0610
Covariance matrix (annualized):
[[0.008873, 0.006707, 0.004946, -1.5e-05], [0.006707, 0.440376, 0.008383, 0.00062], [0.004946, 0.008383, 0.011838, -5.3e-05], [-1.5e-05, 0.00062, -5.3e-05, 3.3e-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_XLP=0.0000, w_MATIC-USD=0.0000, w_TLH=0.0000, w_CSHI=1.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLP=0.0000, w_MATIC-USD=0.0000, w_TLH=0.0000, w_CSHI=1.0000
Portfolio annualized return: 6.10%, volatility: 0.58%
Sharpe ratio: (0.0610 - 0.0400) / 0.0058 = 3.6312


4-asset optimization. Max-Sharpe: 5.521. Portfolio: return=5.24%, vol=0.22%. Weights: w_MTUM=0.0001, w_BTC-USD=0.0000, w_BIL=0.9997, w_BNO=0.0003.

Question:
Assets: MTUM, BTC-USD, BIL, BNO
Annualized mean returns: MTUM:-0.0249, BTC-USD:-0.4063, BIL:0.0523, BNO:0.1050
Covariance matrix (annualized):
[[0.04551, 0.006703, -3.2e-05, 0.009539], [0.006703, 0.116001, 4.1e-05, -0.025773], [-3.2e-05, 4.1e-05, 5e-06, 1.3e-05], [0.009539, -0.025773, 1.3e-05, 0.050601]]
Risk-free rate: 4.00%
Constraints: weights 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=0.0001, w_BTC-USD=0.0000, w_BIL=0.9997, w_BNO=0.0003

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_MTUM=0.0001, w_BTC-USD=0.0000, w_BIL=0.9997, w_BNO=0.0003
Portfolio annualized return: 5.24%, volatility: 0.22%
Sharpe ratio: (0.0524 - 0.0400) / 0.0022 = 5.5212


4-asset optimization. Max-Sharpe: -1.363. Portfolio: return=-17.08%, vol=15.47%. Weights: w_MTUM=0.0000, w_ADA-USD=0.0000, w_HAUZ=1.0000, w_VCIT=0.0000.

Question:
Assets: MTUM, ADA-USD, HAUZ, VCIT
Annualized mean returns: MTUM:-0.1827, ADA-USD:-2.0787, HAUZ:-0.1708, VCIT:-0.0866
Covariance matrix (annualized):
[[0.014525, 0.006512, 0.00843, -0.000355], [0.006512, 0.236054, 0.008172, 0.009573], [0.00843, 0.008172, 0.023926, -0.001086], [-0.000355, 0.009573, -0.001086, 0.004837]]
Risk-free rate: 4.00%
Constraints: weights 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=0.0000, w_HAUZ=1.0000, w_VCIT=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_MTUM=0.0000, w_ADA-USD=0.0000, w_HAUZ=1.0000, w_VCIT=0.0000
Portfolio annualized return: -17.08%, volatility: 15.47%
Sharpe ratio: (-0.1708 - 0.0400) / 0.1547 = -1.3629


4-asset optimization. Max-Sharpe: 5.001. Portfolio: return=68.09%, vol=12.81%. Weights: w_XLI=0.5592, w_DOT-USD=0.1276, w_TLH=0.3133, w_MORT=0.0000.

Question:
Assets: XLI, DOT-USD, TLH, MORT
Annualized mean returns: XLI:0.5071, DOT-USD:2.0685, TLH:0.4261, MORT:0.5771
Covariance matrix (annualized):
[[0.019608, -0.00647, 0.005834, 0.0299], [-0.00647, 0.463214, -0.01118, -0.000952], [0.005834, -0.01118, 0.025717, 0.018833], [0.0299, -0.000952, 0.018833, 0.079745]]
Risk-free rate: 4.00%
Constraints: weights 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=0.5592, w_DOT-USD=0.1276, w_TLH=0.3133, w_MORT=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLI=0.5592, w_DOT-USD=0.1276, w_TLH=0.3133, w_MORT=0.0000
Portfolio annualized return: 68.09%, volatility: 12.81%
Sharpe ratio: (0.6809 - 0.0400) / 0.1281 = 5.0014


4-asset optimization. Max-Sharpe: 2.498. Portfolio: return=214.07%, vol=84.09%. Weights: w_EEM=0.0000, w_MATIC-USD=1.0000, w_VCIT=0.0000, w_IYR=0.0000.

Question:
Assets: EEM, MATIC-USD, VCIT, IYR
Annualized mean returns: EEM:-0.4251, MATIC-USD:2.1407, VCIT:-0.0540, IYR:0.0754
Covariance matrix (annualized):
[[0.023843, 0.010044, 0.002781, 0.004554], [0.010044, 0.707074, 0.007695, 0.022549], [0.002781, 0.007695, 0.003147, 0.006221], [0.004554, 0.022549, 0.006221, 0.026484]]
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_EEM=0.0000, w_MATIC-USD=1.0000, w_VCIT=0.0000, w_IYR=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EEM=0.0000, w_MATIC-USD=1.0000, w_VCIT=0.0000, w_IYR=0.0000
Portfolio annualized return: 214.07%, volatility: 84.09%
Sharpe ratio: (2.1407 - 0.0400) / 0.8409 = 2.4982


4-asset optimization. Max-Sharpe: 2.438. Portfolio: return=36.76%, vol=13.44%. Weights: w_VLUE=0.9856, w_ADA-USD=0.0000, w_DBC=0.0144, w_HAUZ=0.0000.

Question:
Assets: VLUE, ADA-USD, DBC, HAUZ
Annualized mean returns: VLUE:0.3699, ADA-USD:-0.1939, DBC:0.2128, HAUZ:0.2006
Covariance matrix (annualized):
[[0.018317, 0.020543, 0.009244, 0.014746], [0.020543, 0.647003, 0.033739, 0.0288], [0.009244, 0.033739, 0.028859, 0.013781], [0.014746, 0.0288, 0.013781, 0.025484]]
Risk-free rate: 4.00%
Constraints: weights 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=0.9856, w_ADA-USD=0.0000, w_DBC=0.0144, w_HAUZ=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VLUE=0.9856, w_ADA-USD=0.0000, w_DBC=0.0144, w_HAUZ=0.0000
Portfolio annualized return: 36.76%, volatility: 13.44%
Sharpe ratio: (0.3676 - 0.0400) / 0.1344 = 2.4380


4-asset optimization. Max-Sharpe: 3.288. Portfolio: return=57.91%, vol=16.40%. Weights: w_^VIX=0.0000, w_SOL-USD=0.0893, w_IAU=0.0000, w_IYR=0.9107.

Question:
Assets: ^VIX, SOL-USD, IAU, IYR
Annualized mean returns: ^VIX:-1.1287, SOL-USD:1.5554, IAU:-0.0211, IYR:0.4834
Covariance matrix (annualized):
[[0.599195, -0.04023, -0.013129, -0.030296], [-0.04023, 0.66674, 0.009682, 0.017599], [-0.013129, 0.009682, 0.01072, -0.000314], [-0.030296, 0.017599, -0.000314, 0.022558]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_^VIX=0.0000, w_SOL-USD=0.0893, w_IAU=0.0000, w_IYR=0.9107

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_^VIX=0.0000, w_SOL-USD=0.0893, w_IAU=0.0000, w_IYR=0.9107
Portfolio annualized return: 57.91%, volatility: 16.40%
Sharpe ratio: (0.5791 - 0.0400) / 0.1640 = 3.2876


4-asset optimization. Max-Sharpe: 1.799. Portfolio: return=21.99%, vol=10.00%. Weights: w_QUAL=0.2949, w_MATIC-USD=0.0000, w_DBC=0.7051, w_EMB=0.0000.

Question:
Assets: QUAL, MATIC-USD, DBC, EMB
Annualized mean returns: QUAL:0.1494, MATIC-USD:-0.3265, DBC:0.2494, EMB:-0.1053
Covariance matrix (annualized):
[[0.011603, 0.022717, 0.003768, 0.004003], [0.022717, 0.474834, 0.013188, 0.021387], [0.003768, 0.013188, 0.014922, 0.005453], [0.004003, 0.021387, 0.005453, 0.010184]]
Risk-free rate: 4.00%
Constraints: weights 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=0.2949, w_MATIC-USD=0.0000, w_DBC=0.7051, w_EMB=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_QUAL=0.2949, w_MATIC-USD=0.0000, w_DBC=0.7051, w_EMB=0.0000
Portfolio annualized return: 21.99%, volatility: 10.00%
Sharpe ratio: (0.2199 - 0.0400) / 0.1000 = 1.7994


4-asset optimization. Max-Sharpe: 0.951. Portfolio: return=15.39%, vol=11.98%. Weights: w_EEM=0.0000, w_AVAX-USD=0.0000, w_TLH=0.0000, w_GLD=1.0000.

Question:
Assets: EEM, AVAX-USD, TLH, GLD
Annualized mean returns: EEM:-0.3617, AVAX-USD:-0.1254, TLH:-0.5786, GLD:0.1539
Covariance matrix (annualized):
[[0.018877, 0.014666, 0.003938, 0.001438], [0.014666, 0.171176, 0.002415, -0.001323], [0.003938, 0.002415, 0.021474, 0.008089], [0.001438, -0.001323, 0.008089, 0.014344]]
Risk-free rate: 4.00%
Constraints: weights 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_AVAX-USD=0.0000, w_TLH=0.0000, w_GLD=1.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EEM=0.0000, w_AVAX-USD=0.0000, w_TLH=0.0000, w_GLD=1.0000
Portfolio annualized return: 15.39%, volatility: 11.98%
Sharpe ratio: (0.1539 - 0.0400) / 0.1198 = 0.9514


4-asset optimization. Max-Sharpe: 2.397. Portfolio: return=4.87%, vol=0.36%. Weights: w_VEA=0.0000, w_BTC-USD=0.0000, w_LQD=0.0000, w_ICSH=1.0000.

Question:
Assets: VEA, BTC-USD, LQD, ICSH
Annualized mean returns: VEA:0.0128, BTC-USD:-0.3382, LQD:-0.0826, ICSH:0.0487
Covariance matrix (annualized):
[[0.015422, 0.024709, 0.005748, 0.000154], [0.024709, 0.259957, 0.010741, 0.000398], [0.005748, 0.010741, 0.00569, 0.000128], [0.000154, 0.000398, 0.000128, 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_VEA=0.0000, w_BTC-USD=0.0000, w_LQD=0.0000, w_ICSH=1.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VEA=0.0000, w_BTC-USD=0.0000, w_LQD=0.0000, w_ICSH=1.0000
Portfolio annualized return: 4.87%, volatility: 0.36%
Sharpe ratio: (0.0487 - 0.0400) / 0.0036 = 2.3967


4-asset optimization. Max-Sharpe: 3.370. Portfolio: return=35.08%, vol=9.22%. Weights: w_SPY=0.0000, w_BNB-USD=0.1032, w_TLH=0.8783, w_XHB=0.0185.

Question:
Assets: SPY, BNB-USD, TLH, XHB
Annualized mean returns: SPY:-0.1114, BNB-USD:0.3576, TLH:0.3514, XHB:0.2845
Covariance matrix (annualized):
[[0.03259, 0.044102, -0.002736, 0.04148], [0.044102, 0.243076, -0.019854, 0.056732], [-0.002736, -0.019854, 0.012054, -0.001018], [0.04148, 0.056732, -0.001018, 0.093463]]
Risk-free rate: 4.00%
Constraints: weights 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=0.1032, w_TLH=0.8783, w_XHB=0.0185

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_SPY=0.0000, w_BNB-USD=0.1032, w_TLH=0.8783, w_XHB=0.0185
Portfolio annualized return: 35.08%, volatility: 9.22%
Sharpe ratio: (0.3508 - 0.0400) / 0.0922 = 3.3699


4-asset optimization. Max-Sharpe: 5.315. Portfolio: return=11.88%, vol=1.48%. Weights: w_XLU=0.0000, w_AVAX-USD=0.0037, w_CSHI=0.9019, w_IYR=0.0945.

Question:
Assets: XLU, AVAX-USD, CSHI, IYR
Annualized mean returns: XLU:0.3403, AVAX-USD:0.7284, CSHI:0.0556, IYR:0.6986
Covariance matrix (annualized):
[[0.022831, -0.003867, -0.0, 0.01176], [-0.003867, 0.27401, 0.000983, 0.000295], [-0.0, 0.000983, 4.1e-05, 3.4e-05], [0.01176, 0.000295, 3.4e-05, 0.019105]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_XLU=0.0000, w_AVAX-USD=0.0037, w_CSHI=0.9019, w_IYR=0.0945

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLU=0.0000, w_AVAX-USD=0.0037, w_CSHI=0.9019, w_IYR=0.0945
Portfolio annualized return: 11.88%, volatility: 1.48%
Sharpe ratio: (0.1188 - 0.0400) / 0.0148 = 5.3154


4-asset optimization. Max-Sharpe: 4.901. Portfolio: return=5.75%, vol=0.36%. Weights: w_VTI=0.0000, w_XRP-USD=0.0004, w_SGOV=0.9876, w_ITB=0.0120.

Question:
Assets: VTI, XRP-USD, SGOV, ITB
Annualized mean returns: VTI:0.1562, XRP-USD:1.0306, SGOV:0.0496, ITB:0.6743
Covariance matrix (annualized):
[[0.02292, 0.042177, 1.5e-05, 0.018486], [0.042177, 0.737564, 5.9e-05, 0.031342], [1.5e-05, 5.9e-05, 7e-06, 8e-06], [0.018486, 0.031342, 8e-06, 0.036846]]
Risk-free rate: 4.00%
Constraints: weights 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=0.0004, w_SGOV=0.9876, w_ITB=0.0120

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VTI=0.0000, w_XRP-USD=0.0004, w_SGOV=0.9876, w_ITB=0.0120
Portfolio annualized return: 5.75%, volatility: 0.36%
Sharpe ratio: (0.0575 - 0.0400) / 0.0036 = 4.9010


4-asset optimization. Max-Sharpe: 1.297. Portfolio: return=33.18%, vol=22.49%. Weights: w_IWM=0.0000, w_XRP-USD=0.0000, w_XHB=1.0000, w_IAU=0.0000.

Question:
Assets: IWM, XRP-USD, XHB, IAU
Annualized mean returns: IWM:0.2067, XRP-USD:-0.3786, XHB:0.3318, IAU:-0.0528
Covariance matrix (annualized):
[[0.05308, 0.039962, 0.041048, 0.010871], [0.039962, 0.179667, 0.03521, -0.001491], [0.041048, 0.03521, 0.050602, 0.008234], [0.010871, -0.001491, 0.008234, 0.009501]]
Risk-free rate: 4.00%
Constraints: weights 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_XRP-USD=0.0000, w_XHB=1.0000, w_IAU=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_IWM=0.0000, w_XRP-USD=0.0000, w_XHB=1.0000, w_IAU=0.0000
Portfolio annualized return: 33.18%, volatility: 22.49%
Sharpe ratio: (0.3318 - 0.0400) / 0.2249 = 1.2971


4-asset optimization. Max-Sharpe: 4.262. Portfolio: return=12.41%, vol=1.97%. Weights: w_VEA=0.0000, w_SOL-USD=0.0000, w_ITB=0.0843, w_CSHI=0.9157.

Question:
Assets: VEA, SOL-USD, ITB, CSHI
Annualized mean returns: VEA:0.0935, SOL-USD:-0.4047, ITB:0.7865, CSHI:0.0631
Covariance matrix (annualized):
[[0.018698, 0.019019, 0.013112, -0.000132], [0.019019, 0.43031, 0.030734, -0.000139], [0.013112, 0.030734, 0.041185, -1.7e-05], [-0.000132, -0.000139, -1.7e-05, 0.000118]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_VEA=0.0000, w_SOL-USD=0.0000, w_ITB=0.0843, w_CSHI=0.9157

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VEA=0.0000, w_SOL-USD=0.0000, w_ITB=0.0843, w_CSHI=0.9157
Portfolio annualized return: 12.41%, volatility: 1.97%
Sharpe ratio: (0.1241 - 0.0400) / 0.0197 = 4.2620


4-asset optimization. Max-Sharpe: 3.598. Portfolio: return=137.39%, vol=37.07%. Weights: w_XLY=0.0000, w_BTC-USD=1.0000, w_BIL=0.0000, w_PDBC=0.0000.

Question:
Assets: XLY, BTC-USD, BIL, PDBC
Annualized mean returns: XLY:0.2528, BTC-USD:1.3739, BIL:0.0390, PDBC:-0.1058
Covariance matrix (annualized):
[[0.061366, 0.045981, -0.000114, 0.018967], [0.045981, 0.137402, 0.000249, 0.02893], [-0.000114, 0.000249, 1.2e-05, -1.9e-05], [0.018967, 0.02893, -1.9e-05, 0.039522]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_XLY=0.0000, w_BTC-USD=1.0000, w_BIL=0.0000, w_PDBC=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLY=0.0000, w_BTC-USD=1.0000, w_BIL=0.0000, w_PDBC=0.0000
Portfolio annualized return: 137.39%, volatility: 37.07%
Sharpe ratio: (1.3739 - 0.0400) / 0.3707 = 3.5985


4-asset optimization. Max-Sharpe: 6.515. Portfolio: return=151.16%, vol=22.59%. Weights: w_FXI=0.0000, w_BTC-USD=0.4122, w_INDS=0.0000, w_CPER=0.5878.

Question:
Assets: FXI, BTC-USD, INDS, CPER
Annualized mean returns: FXI:0.3136, BTC-USD:2.9564, INDS:-0.2788, CPER:0.4982
Covariance matrix (annualized):
[[0.108208, 0.00024, 0.012329, 0.020093], [0.00024, 0.241286, 0.014394, 0.00281], [0.012329, 0.014394, 0.025089, 0.001242], [0.020093, 0.00281, 0.001242, 0.025061]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_FXI=0.0000, w_BTC-USD=0.4122, w_INDS=0.0000, w_CPER=0.5878

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_FXI=0.0000, w_BTC-USD=0.4122, w_INDS=0.0000, w_CPER=0.5878
Portfolio annualized return: 151.16%, volatility: 22.59%
Sharpe ratio: (1.5116 - 0.0400) / 0.2259 = 6.5148


4-asset optimization. Max-Sharpe: 1.426. Portfolio: return=4.41%, vol=0.29%. Weights: w_VEA=0.0000, w_AVAX-USD=0.0000, w_HAUZ=0.0000, w_SHV=1.0000.

Question:
Assets: VEA, AVAX-USD, HAUZ, SHV
Annualized mean returns: VEA:-0.0790, AVAX-USD:-0.1332, HAUZ:-0.3917, SHV:0.0441
Covariance matrix (annualized):
[[0.016617, 0.024742, 0.015214, 0.000108], [0.024742, 0.756431, 0.027628, -0.000351], [0.015214, 0.027628, 0.020505, 0.000146], [0.000108, -0.000351, 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_VEA=0.0000, w_AVAX-USD=0.0000, w_HAUZ=0.0000, w_SHV=1.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VEA=0.0000, w_AVAX-USD=0.0000, w_HAUZ=0.0000, w_SHV=1.0000
Portfolio annualized return: 4.41%, volatility: 0.29%
Sharpe ratio: (0.0441 - 0.0400) / 0.0029 = 1.4257


4-asset optimization. Max-Sharpe: 2.319. Portfolio: return=37.86%, vol=14.60%. Weights: w_QUAL=0.0000, w_SOL-USD=0.0000, w_SLV=0.0000, w_HAUZ=1.0000.

Question:
Assets: QUAL, SOL-USD, SLV, HAUZ
Annualized mean returns: QUAL:0.1264, SOL-USD:-0.2765, SLV:0.1261, HAUZ:0.3786
Covariance matrix (annualized):
[[0.03375, 0.055386, 0.03742, 0.020649], [0.055386, 0.507119, 0.069917, 0.043682], [0.03742, 0.069917, 0.098869, 0.026961], [0.020649, 0.043682, 0.026961, 0.021314]]
Risk-free rate: 4.00%
Constraints: weights 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=0.0000, w_SLV=0.0000, w_HAUZ=1.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_QUAL=0.0000, w_SOL-USD=0.0000, w_SLV=0.0000, w_HAUZ=1.0000
Portfolio annualized return: 37.86%, volatility: 14.60%
Sharpe ratio: (0.3786 - 0.0400) / 0.1460 = 2.3192


4-asset optimization. Max-Sharpe: 4.588. Portfolio: return=5.24%, vol=0.27%. Weights: w_EFA=0.0000, w_ETH-USD=0.0000, w_WEAT=0.0000, w_BIL=1.0000.

Question:
Assets: EFA, ETH-USD, WEAT, BIL
Annualized mean returns: EFA:-0.3375, ETH-USD:-0.8875, WEAT:-1.1520, BIL:0.0524
Covariance matrix (annualized):
[[0.014011, 0.010849, 0.003742, -8.7e-05], [0.010849, 0.086335, -0.000274, -0.000202], [0.003742, -0.000274, 0.077448, -3.1e-05], [-8.7e-05, -0.000202, -3.1e-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_EFA=0.0000, w_ETH-USD=0.0000, w_WEAT=0.0000, w_BIL=1.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EFA=0.0000, w_ETH-USD=0.0000, w_WEAT=0.0000, w_BIL=1.0000
Portfolio annualized return: 5.24%, volatility: 0.27%
Sharpe ratio: (0.0524 - 0.0400) / 0.0027 = 4.5880


4-asset optimization. Max-Sharpe: 6.771. Portfolio: return=6.21%, vol=0.33%. Weights: w_IWM=0.0000, w_XRP-USD=0.0000, w_BIL=0.9761, w_PDBC=0.0239.

Question:
Assets: IWM, XRP-USD, BIL, PDBC
Annualized mean returns: IWM:-0.2567, XRP-USD:-0.3504, BIL:0.0516, PDBC:0.4893
Covariance matrix (annualized):
[[0.030328, 0.032993, 8.4e-05, -9.7e-05], [0.032993, 0.588697, -5.9e-05, 0.019521], [8.4e-05, -5.9e-05, 6e-06, -1.2e-05], [-9.7e-05, 0.019521, -1.2e-05, 0.009516]]
Risk-free rate: 4.00%
Constraints: weights 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_XRP-USD=0.0000, w_BIL=0.9761, w_PDBC=0.0239

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_IWM=0.0000, w_XRP-USD=0.0000, w_BIL=0.9761, w_PDBC=0.0239
Portfolio annualized return: 6.21%, volatility: 0.33%
Sharpe ratio: (0.0621 - 0.0400) / 0.0033 = 6.7707


4-asset optimization. Max-Sharpe: 6.859. Portfolio: return=5.44%, vol=0.21%. Weights: w_VTI=0.0000, w_ADA-USD=0.0000, w_SGOV=0.9987, w_WEAT=0.0013.

Question:
Assets: VTI, ADA-USD, SGOV, WEAT
Annualized mean returns: VTI:0.1514, ADA-USD:-1.0475, SGOV:0.0546, WEAT:-0.0787
Covariance matrix (annualized):
[[0.013163, 0.031321, 7.1e-05, -0.000978], [0.031321, 0.639251, 0.000265, -0.036198], [7.1e-05, 0.000265, 5e-06, -0.000107], [-0.000978, -0.036198, -0.000107, 0.054184]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_VTI=0.0000, w_ADA-USD=0.0000, w_SGOV=0.9987, w_WEAT=0.0013

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VTI=0.0000, w_ADA-USD=0.0000, w_SGOV=0.9987, w_WEAT=0.0013
Portfolio annualized return: 5.44%, volatility: 0.21%
Sharpe ratio: (0.0544 - 0.0400) / 0.0021 = 6.8586


4-asset optimization. Max-Sharpe: 3.423. Portfolio: return=20.73%, vol=4.89%. Weights: w_EEM=0.1776, w_SOL-USD=0.0000, w_SCHH=0.2662, w_STIP=0.5563.

Question:
Assets: EEM, SOL-USD, SCHH, STIP
Annualized mean returns: EEM:0.5389, SOL-USD:-0.0105, SCHH:0.2621, STIP:0.0753
Covariance matrix (annualized):
[[0.039039, 0.054376, -0.000472, 0.000572], [0.054376, 0.276972, 0.010442, 0.002563], [-0.000472, 0.010442, 0.010696, 0.000734], [0.000572, 0.002563, 0.000734, 0.000372]]
Risk-free rate: 4.00%
Constraints: weights 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=0.1776, w_SOL-USD=0.0000, w_SCHH=0.2662, w_STIP=0.5563

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EEM=0.1776, w_SOL-USD=0.0000, w_SCHH=0.2662, w_STIP=0.5563
Portfolio annualized return: 20.73%, volatility: 4.89%
Sharpe ratio: (0.2073 - 0.0400) / 0.0489 = 3.4231


4-asset optimization. Max-Sharpe: 1.616. Portfolio: return=7.50%, vol=2.17%. Weights: w_VEA=0.1835, w_SOL-USD=0.0014, w_ICSH=0.8151, w_EMB=0.0000.

Question:
Assets: VEA, SOL-USD, ICSH, EMB
Annualized mean returns: VEA:0.2262, SOL-USD:0.3188, ICSH:0.0405, EMB:-0.0381
Covariance matrix (annualized):
[[0.014123, 0.014455, -0.000143, 0.001145], [0.014455, 0.314791, 0.000781, 0.015982], [-0.000143, 0.000781, 4e-05, 0.000239], [0.001145, 0.015982, 0.000239, 0.004418]]
Risk-free rate: 4.00%
Constraints: weights 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=0.1835, w_SOL-USD=0.0014, w_ICSH=0.8151, w_EMB=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VEA=0.1835, w_SOL-USD=0.0014, w_ICSH=0.8151, w_EMB=0.0000
Portfolio annualized return: 7.50%, volatility: 2.17%
Sharpe ratio: (0.0750 - 0.0400) / 0.0217 = 1.6160


4-asset optimization. Max-Sharpe: 4.029. Portfolio: return=52.38%, vol=12.01%. Weights: w_IVV=0.9757, w_MATIC-USD=0.0243, w_WEAT=0.0000, w_SCHH=0.0000.

Question:
Assets: IVV, MATIC-USD, WEAT, SCHH
Annualized mean returns: IVV:0.5078, MATIC-USD:1.1665, WEAT:-0.7744, SCHH:-0.0259
Covariance matrix (annualized):
[[0.013728, 0.022589, 0.001134, 0.011126], [0.022589, 0.475491, -0.002095, 0.019257], [0.001134, -0.002095, 0.046725, -0.006416], [0.011126, 0.019257, -0.006416, 0.029597]]
Risk-free rate: 4.00%
Constraints: weights 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=0.9757, w_MATIC-USD=0.0243, w_WEAT=0.0000, w_SCHH=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_IVV=0.9757, w_MATIC-USD=0.0243, w_WEAT=0.0000, w_SCHH=0.0000
Portfolio annualized return: 52.38%, volatility: 12.01%
Sharpe ratio: (0.5238 - 0.0400) / 0.1201 = 4.0286


4-asset optimization. Max-Sharpe: 6.216. Portfolio: return=41.65%, vol=6.06%. Weights: w_EEM=0.0000, w_ADA-USD=0.1100, w_SLV=0.1252, w_STIP=0.7648.

Question:
Assets: EEM, ADA-USD, SLV, STIP
Annualized mean returns: EEM:0.2055, ADA-USD:2.3103, SLV:0.6100, STIP:0.1124
Covariance matrix (annualized):
[[0.022751, 0.016689, 0.007262, 0.000894], [0.016689, 0.245927, -0.031187, -0.001345], [0.007262, -0.031187, 0.056254, 0.00254], [0.000894, -0.001345, 0.00254, 0.0007]]
Risk-free rate: 4.00%
Constraints: weights 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_ADA-USD=0.1100, w_SLV=0.1252, w_STIP=0.7648

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EEM=0.0000, w_ADA-USD=0.1100, w_SLV=0.1252, w_STIP=0.7648
Portfolio annualized return: 41.65%, volatility: 6.06%
Sharpe ratio: (0.4165 - 0.0400) / 0.0606 = 6.2157


4-asset optimization. Max-Sharpe: 1.693. Portfolio: return=30.75%, vol=15.80%. Weights: w_VLUE=0.0000, w_DOT-USD=0.0000, w_IGOV=0.0000, w_INDS=1.0000.

Question:
Assets: VLUE, DOT-USD, IGOV, INDS
Annualized mean returns: VLUE:0.1432, DOT-USD:-1.1311, IGOV:-0.0237, INDS:0.3075
Covariance matrix (annualized):
[[0.009261, 0.007731, 0.002475, 0.010109], [0.007731, 0.343472, 0.013313, 0.022716], [0.002475, 0.013313, 0.006272, 0.007111], [0.010109, 0.022716, 0.007111, 0.024971]]
Risk-free rate: 4.00%
Constraints: weights 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_DOT-USD=0.0000, w_IGOV=0.0000, w_INDS=1.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VLUE=0.0000, w_DOT-USD=0.0000, w_IGOV=0.0000, w_INDS=1.0000
Portfolio annualized return: 30.75%, volatility: 15.80%
Sharpe ratio: (0.3075 - 0.0400) / 0.1580 = 1.6930


4-asset optimization. Max-Sharpe: 5.359. Portfolio: return=5.18%, vol=0.22%. Weights: w_VEA=0.0000, w_MATIC-USD=0.0000, w_SGOV=1.0000, w_ITB=0.0000.

Question:
Assets: VEA, MATIC-USD, SGOV, ITB
Annualized mean returns: VEA:-0.0637, MATIC-USD:-3.1659, SGOV:0.0518, ITB:-0.2698
Covariance matrix (annualized):
[[0.012278, 0.033701, 7e-06, 0.020511], [0.033701, 0.551484, 0.000213, 0.031907], [7e-06, 0.000213, 5e-06, -3e-06], [0.020511, 0.031907, -3e-06, 0.058629]]
Risk-free rate: 4.00%
Constraints: weights 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_MATIC-USD=0.0000, w_SGOV=1.0000, w_ITB=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VEA=0.0000, w_MATIC-USD=0.0000, w_SGOV=1.0000, w_ITB=0.0000
Portfolio annualized return: 5.18%, volatility: 0.22%
Sharpe ratio: (0.0518 - 0.0400) / 0.0022 = 5.3595


4-asset optimization. Max-Sharpe: 4.959. Portfolio: return=5.36%, vol=0.27%. Weights: w_XLF=0.0000, w_BTC-USD=0.0000, w_IEF=0.0000, w_BIL=1.0000.

Question:
Assets: XLF, BTC-USD, IEF, BIL
Annualized mean returns: XLF:-0.3135, BTC-USD:-0.5282, IEF:-0.2177, BIL:0.0536
Covariance matrix (annualized):
[[0.012793, 0.012192, 0.001968, -8.6e-05], [0.012192, 0.106565, 0.005948, -0.000311], [0.001968, 0.005948, 0.005518, -5.7e-05], [-8.6e-05, -0.000311, -5.7e-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_XLF=0.0000, w_BTC-USD=0.0000, w_IEF=0.0000, w_BIL=1.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLF=0.0000, w_BTC-USD=0.0000, w_IEF=0.0000, w_BIL=1.0000
Portfolio annualized return: 5.36%, volatility: 0.27%
Sharpe ratio: (0.0536 - 0.0400) / 0.0027 = 4.9588


4-asset optimization. Max-Sharpe: 2.214. Portfolio: return=58.81%, vol=24.75%. Weights: w_EWJ=0.0000, w_BNB-USD=0.0000, w_PALL=0.0000, w_ITB=1.0000.

Question:
Assets: EWJ, BNB-USD, PALL, ITB
Annualized mean returns: EWJ:0.1892, BNB-USD:-0.3092, PALL:-0.6637, ITB:0.5881
Covariance matrix (annualized):
[[0.030885, 0.034287, 0.036814, 0.023089], [0.034287, 0.289881, 0.116033, 0.04387], [0.036814, 0.116033, 0.21163, 0.038076], [0.023089, 0.04387, 0.038076, 0.061259]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_EWJ=0.0000, w_BNB-USD=0.0000, w_PALL=0.0000, w_ITB=1.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EWJ=0.0000, w_BNB-USD=0.0000, w_PALL=0.0000, w_ITB=1.0000
Portfolio annualized return: 58.81%, volatility: 24.75%
Sharpe ratio: (0.5881 - 0.0400) / 0.2475 = 2.2144


4-asset optimization. Max-Sharpe: 5.392. Portfolio: return=92.29%, vol=16.38%. Weights: w_VLUE=0.7930, w_BTC-USD=0.2070, w_INDS=0.0000, w_SHY=0.0000.

Question:
Assets: VLUE, BTC-USD, INDS, SHY
Annualized mean returns: VLUE:0.4603, BTC-USD:2.6944, INDS:0.0140, SHY:0.0231
Covariance matrix (annualized):
[[0.012531, 0.01367, 0.013041, 0.001004], [0.01367, 0.337026, 0.016937, 0.000416], [0.013041, 0.016937, 0.025968, 0.001809], [0.001004, 0.000416, 0.001809, 0.000298]]
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_VLUE=0.7930, w_BTC-USD=0.2070, w_INDS=0.0000, w_SHY=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VLUE=0.7930, w_BTC-USD=0.2070, w_INDS=0.0000, w_SHY=0.0000
Portfolio annualized return: 92.29%, volatility: 16.38%
Sharpe ratio: (0.9229 - 0.0400) / 0.1638 = 5.3916


4-asset optimization. Max-Sharpe: 3.877. Portfolio: return=143.38%, vol=35.95%. Weights: w_QQQ=0.2782, w_BTC-USD=0.7218, w_PALL=0.0000, w_IEF=0.0000.

Question:
Assets: QQQ, BTC-USD, PALL, IEF
Annualized mean returns: QQQ:0.6112, BTC-USD:1.7508, PALL:-1.0431, IEF:-0.0809
Covariance matrix (annualized):
[[0.060258, 0.05013, 0.006974, 0.006521], [0.05013, 0.200394, -0.005924, 0.002779], [0.006974, -0.005924, 0.149616, 0.006671], [0.006521, 0.002779, 0.006671, 0.008644]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_QQQ=0.2782, w_BTC-USD=0.7218, w_PALL=0.0000, w_IEF=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_QQQ=0.2782, w_BTC-USD=0.7218, w_PALL=0.0000, w_IEF=0.0000
Portfolio annualized return: 143.38%, volatility: 35.95%
Sharpe ratio: (1.4338 - 0.0400) / 0.3595 = 3.8774


4-asset optimization. Max-Sharpe: 1.800. Portfolio: return=16.79%, vol=7.11%. Weights: w_XLI=0.0000, w_DOT-USD=0.0000, w_PALL=0.0000, w_LQD=1.0000.

Question:
Assets: XLI, DOT-USD, PALL, LQD
Annualized mean returns: XLI:-0.0228, DOT-USD:-1.6231, PALL:-0.1017, LQD:0.1679
Covariance matrix (annualized):
[[0.027047, 0.021126, 0.020819, 0.002437], [0.021126, 0.352853, 0.033638, -0.004741], [0.020819, 0.033638, 0.121114, 0.000745], [0.002437, -0.004741, 0.000745, 0.005049]]
Risk-free rate: 4.00%
Constraints: weights 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_PALL=0.0000, w_LQD=1.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLI=0.0000, w_DOT-USD=0.0000, w_PALL=0.0000, w_LQD=1.0000
Portfolio annualized return: 16.79%, volatility: 7.11%
Sharpe ratio: (0.1679 - 0.0400) / 0.0711 = 1.8002


4-asset optimization. Max-Sharpe: 2.381. Portfolio: return=67.49%, vol=26.67%. Weights: w_XLE=0.2710, w_ETH-USD=0.4210, w_SCHH=0.3080, w_BIL=0.0000.

Question:
Assets: XLE, ETH-USD, SCHH, BIL
Annualized mean returns: XLE:0.4258, ETH-USD:1.0267, SCHH:0.4132, BIL:0.0384
Covariance matrix (annualized):
[[0.071542, 0.044592, 0.016427, -1.4e-05], [0.044592, 0.195818, 0.051948, 4.1e-05], [0.016427, 0.051948, 0.050264, -4.6e-05], [-1.4e-05, 4.1e-05, -4.6e-05, 1.1e-05]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_XLE=0.2710, w_ETH-USD=0.4210, w_SCHH=0.3080, w_BIL=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLE=0.2710, w_ETH-USD=0.4210, w_SCHH=0.3080, w_BIL=0.0000
Portfolio annualized return: 67.49%, volatility: 26.67%
Sharpe ratio: (0.6749 - 0.0400) / 0.2667 = 2.3808


4-asset optimization. Max-Sharpe: 1.912. Portfolio: return=19.86%, vol=8.29%. Weights: w_EFA=0.0000, w_BTC-USD=0.0000, w_HAUZ=0.0000, w_DBC=1.0000.

Question:
Assets: EFA, BTC-USD, HAUZ, DBC
Annualized mean returns: EFA:-0.2824, BTC-USD:-0.3430, HAUZ:-0.3216, DBC:0.1986
Covariance matrix (annualized):
[[0.012892, 0.013137, 0.010487, 0.00316], [0.013137, 0.107946, 0.008545, -0.000756], [0.010487, 0.008545, 0.013386, 0.003316], [0.00316, -0.000756, 0.003316, 0.006878]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_EFA=0.0000, w_BTC-USD=0.0000, w_HAUZ=0.0000, w_DBC=1.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EFA=0.0000, w_BTC-USD=0.0000, w_HAUZ=0.0000, w_DBC=1.0000
Portfolio annualized return: 19.86%, volatility: 8.29%
Sharpe ratio: (0.1986 - 0.0400) / 0.0829 = 1.9120


4-asset optimization. Max-Sharpe: 3.556. Portfolio: return=47.62%, vol=12.27%. Weights: w_VEA=0.9364, w_XRP-USD=0.0000, w_TIP=0.0000, w_REZ=0.0636.

Question:
Assets: VEA, XRP-USD, TIP, REZ
Annualized mean returns: VEA:0.4692, XRP-USD:-0.9896, TIP:0.0714, REZ:0.5783
Covariance matrix (annualized):
[[0.014667, 0.001857, 0.001527, 0.016872], [0.001857, 0.250262, -0.001192, 0.006094], [0.001527, -0.001192, 0.00065, 0.002854], [0.016872, 0.006094, 0.002854, 0.043567]]
Risk-free rate: 4.00%
Constraints: weights 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=0.9364, w_XRP-USD=0.0000, w_TIP=0.0000, w_REZ=0.0636

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VEA=0.9364, w_XRP-USD=0.0000, w_TIP=0.0000, w_REZ=0.0636
Portfolio annualized return: 47.62%, volatility: 12.27%
Sharpe ratio: (0.4762 - 0.0400) / 0.1227 = 3.5556


4-asset optimization. Max-Sharpe: 0.854. Portfolio: return=26.02%, vol=25.79%. Weights: w_VTI=0.0000, w_BNB-USD=1.0000, w_IYR=0.0000, w_TIP=0.0000.

Question:
Assets: VTI, BNB-USD, IYR, TIP
Annualized mean returns: VTI:-0.1208, BNB-USD:0.2602, IYR:-0.3125, TIP:0.0347
Covariance matrix (annualized):
[[0.020045, 0.003081, 0.023605, 0.000645], [0.003081, 0.066528, 0.002229, -0.000434], [0.023605, 0.002229, 0.051191, 0.001828], [0.000645, -0.000434, 0.001828, 0.000623]]
Risk-free rate: 4.00%
Constraints: weights 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_BNB-USD=1.0000, w_IYR=0.0000, w_TIP=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VTI=0.0000, w_BNB-USD=1.0000, w_IYR=0.0000, w_TIP=0.0000
Portfolio annualized return: 26.02%, volatility: 25.79%
Sharpe ratio: (0.2602 - 0.0400) / 0.2579 = 0.8536


4-asset optimization. Max-Sharpe: 2.630. Portfolio: return=4.64%, vol=0.24%. Weights: w_VEA=0.0000, w_AVAX-USD=0.0000, w_BIL=1.0000, w_HYG=0.0000.

Question:
Assets: VEA, AVAX-USD, BIL, HYG
Annualized mean returns: VEA:-0.2275, AVAX-USD:-1.5659, BIL:0.0464, HYG:-0.1459
Covariance matrix (annualized):
[[0.024756, 0.026367, -5.2e-05, 0.010229], [0.026367, 0.616806, -0.000348, 0.019537], [-5.2e-05, -0.000348, 6e-06, 1.2e-05], [0.010229, 0.019537, 1.2e-05, 0.00975]]
Risk-free rate: 4.00%
Constraints: weights 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_BIL=1.0000, w_HYG=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VEA=0.0000, w_AVAX-USD=0.0000, w_BIL=1.0000, w_HYG=0.0000
Portfolio annualized return: 4.64%, volatility: 0.24%
Sharpe ratio: (0.0464 - 0.0400) / 0.0024 = 2.6298


4-asset optimization. Max-Sharpe: 1.412. Portfolio: return=55.52%, vol=36.48%. Weights: w_IVV=0.0000, w_XRP-USD=1.0000, w_PALL=0.0000, w_INDS=0.0000.

Question:
Assets: IVV, XRP-USD, PALL, INDS
Annualized mean returns: IVV:-0.2915, XRP-USD:0.5552, PALL:-0.5135, INDS:-0.9050
Covariance matrix (annualized):
[[0.015752, -0.003456, 0.006842, 0.01829], [-0.003456, 0.13307, 0.00294, -0.001759], [0.006842, 0.00294, 0.057829, 0.012391], [0.01829, -0.001759, 0.012391, 0.037862]]
Risk-free rate: 4.00%
Constraints: weights 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_XRP-USD=1.0000, w_PALL=0.0000, w_INDS=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_IVV=0.0000, w_XRP-USD=1.0000, w_PALL=0.0000, w_INDS=0.0000
Portfolio annualized return: 55.52%, volatility: 36.48%
Sharpe ratio: (0.5552 - 0.0400) / 0.3648 = 1.4123


4-asset optimization. Max-Sharpe: 1.183. Portfolio: return=4.27%, vol=0.23%. Weights: w_XLB=0.0000, w_ETH-USD=0.0000, w_ITB=0.0000, w_BIL=1.0000.

Question:
Assets: XLB, ETH-USD, ITB, BIL
Annualized mean returns: XLB:-0.4629, ETH-USD:-0.0723, ITB:0.0674, BIL:0.0427
Covariance matrix (annualized):
[[0.03366, 0.032292, 0.035082, -4e-06], [0.032292, 0.265575, 0.022808, -9.7e-05], [0.035082, 0.022808, 0.072291, 8.3e-05], [-4e-06, -9.7e-05, 8.3e-05, 5e-06]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_XLB=0.0000, w_ETH-USD=0.0000, w_ITB=0.0000, w_BIL=1.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLB=0.0000, w_ETH-USD=0.0000, w_ITB=0.0000, w_BIL=1.0000
Portfolio annualized return: 4.27%, volatility: 0.23%
Sharpe ratio: (0.0427 - 0.0400) / 0.0023 = 1.1831


4-asset optimization. Max-Sharpe: 5.313. Portfolio: return=90.11%, vol=16.21%. Weights: w_IVV=0.7141, w_ETH-USD=0.2859, w_CPER=0.0000, w_SCHH=0.0000.

Question:
Assets: IVV, ETH-USD, CPER, SCHH
Annualized mean returns: IVV:0.4503, ETH-USD:2.0270, CPER:0.1950, SCHH:0.0110
Covariance matrix (annualized):
[[0.013596, 0.00983, 0.003457, 0.009444], [0.00983, 0.187514, 0.012393, 0.018356], [0.003457, 0.012393, 0.021402, 0.001223], [0.009444, 0.018356, 0.001223, 0.02873]]
Risk-free rate: 4.00%
Constraints: weights 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=0.7141, w_ETH-USD=0.2859, w_CPER=0.0000, w_SCHH=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_IVV=0.7141, w_ETH-USD=0.2859, w_CPER=0.0000, w_SCHH=0.0000
Portfolio annualized return: 90.11%, volatility: 16.21%
Sharpe ratio: (0.9011 - 0.0400) / 0.1621 = 5.3125


4-asset optimization. Max-Sharpe: 2.131. Portfolio: return=7.01%, vol=1.41%. Weights: w_FXI=0.0000, w_ETH-USD=0.0000, w_CSHI=1.0000, w_SCHH=0.0000.

Question:
Assets: FXI, ETH-USD, CSHI, SCHH
Annualized mean returns: FXI:-0.8535, ETH-USD:0.1150, CSHI:0.0701, SCHH:-0.3462
Covariance matrix (annualized):
[[0.074412, 0.053068, 0.000356, 0.016899], [0.053068, 0.286185, 0.0009, 0.013926], [0.000356, 0.0009, 0.000199, 0.000843], [0.016899, 0.013926, 0.000843, 0.041812]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_FXI=0.0000, w_ETH-USD=0.0000, w_CSHI=1.0000, w_SCHH=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_FXI=0.0000, w_ETH-USD=0.0000, w_CSHI=1.0000, w_SCHH=0.0000
Portfolio annualized return: 7.01%, volatility: 1.41%
Sharpe ratio: (0.0701 - 0.0400) / 0.0141 = 2.1305


4-asset optimization. Max-Sharpe: 2.306. Portfolio: return=39.23%, vol=15.28%. Weights: w_IWM=0.8166, w_XRP-USD=0.0000, w_HYG=0.0000, w_DBB=0.1834.

Question:
Assets: IWM, XRP-USD, HYG, DBB
Annualized mean returns: IWM:0.4163, XRP-USD:0.1264, HYG:0.0330, DBB:0.2853
Covariance matrix (annualized):
[[0.027838, 0.050623, 0.006309, 0.012051], [0.050623, 0.912151, 0.022005, 0.036656], [0.006309, 0.022005, 0.00422, 0.005739], [0.012051, 0.036656, 0.005739, 0.035005]]
Risk-free rate: 4.00%
Constraints: weights 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=0.8166, w_XRP-USD=0.0000, w_HYG=0.0000, w_DBB=0.1834

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_IWM=0.8166, w_XRP-USD=0.0000, w_HYG=0.0000, w_DBB=0.1834
Portfolio annualized return: 39.23%, volatility: 15.28%
Sharpe ratio: (0.3923 - 0.0400) / 0.1528 = 2.3056


4-asset optimization. Max-Sharpe: 4.485. Portfolio: return=93.06%, vol=19.86%. Weights: w_VLUE=0.0000, w_LINK-USD=0.0603, w_TIP=0.0000, w_USO=0.9397.

Question:
Assets: VLUE, LINK-USD, TIP, USO
Annualized mean returns: VLUE:-0.0246, LINK-USD:0.9730, TIP:0.0059, USO:0.9278
Covariance matrix (annualized):
[[0.011476, 0.027925, 0.001468, 0.009352], [0.027925, 0.584586, 0.006284, 0.006431], [0.001468, 0.006284, 0.000796, 0.001119], [0.009352, 0.006431, 0.001119, 0.041427]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_VLUE=0.0000, w_LINK-USD=0.0603, w_TIP=0.0000, w_USO=0.9397

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VLUE=0.0000, w_LINK-USD=0.0603, w_TIP=0.0000, w_USO=0.9397
Portfolio annualized return: 93.06%, volatility: 19.86%
Sharpe ratio: (0.9306 - 0.0400) / 0.1986 = 4.4846


4-asset optimization. Max-Sharpe: 3.167. Portfolio: return=30.83%, vol=8.47%. Weights: w_VLUE=0.0000, w_AVAX-USD=0.0280, w_HAUZ=0.3883, w_SHY=0.5836.

Question:
Assets: VLUE, AVAX-USD, HAUZ, SHY
Annualized mean returns: VLUE:-0.1109, AVAX-USD:1.7499, HAUZ:0.5573, SHY:0.0734
Covariance matrix (annualized):
[[0.03377, 0.071994, 0.023074, 0.001149], [0.071994, 0.78071, 0.060735, 0.000449], [0.023074, 0.060735, 0.028882, 0.001569], [0.001149, 0.000449, 0.001569, 0.000464]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_VLUE=0.0000, w_AVAX-USD=0.0280, w_HAUZ=0.3883, w_SHY=0.5836

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VLUE=0.0000, w_AVAX-USD=0.0280, w_HAUZ=0.3883, w_SHY=0.5836
Portfolio annualized return: 30.83%, volatility: 8.47%
Sharpe ratio: (0.3083 - 0.0400) / 0.0847 = 3.1672


4-asset optimization. Max-Sharpe: 1.337. Portfolio: return=75.52%, vol=53.49%. Weights: w_IWM=0.0000, w_MATIC-USD=1.0000, w_MORT=0.0000, w_LQD=0.0000.

Question:
Assets: IWM, MATIC-USD, MORT, LQD
Annualized mean returns: IWM:-0.1357, MATIC-USD:0.7552, MORT:-0.3228, LQD:0.0320
Covariance matrix (annualized):
[[0.047138, 0.002358, 0.057973, 0.011885], [0.002358, 0.286083, 0.009905, -0.003003], [0.057973, 0.009905, 0.102161, 0.023073], [0.011885, -0.003003, 0.023073, 0.013749]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_IWM=0.0000, w_MATIC-USD=1.0000, w_MORT=0.0000, w_LQD=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_IWM=0.0000, w_MATIC-USD=1.0000, w_MORT=0.0000, w_LQD=0.0000
Portfolio annualized return: 75.52%, volatility: 53.49%
Sharpe ratio: (0.7552 - 0.0400) / 0.5349 = 1.3372


4-asset optimization. Max-Sharpe: 2.548. Portfolio: return=68.65%, vol=25.37%. Weights: w_EEM=0.0000, w_AVAX-USD=0.0475, w_ITB=0.9525, w_DBC=0.0000.

Question:
Assets: EEM, AVAX-USD, ITB, DBC
Annualized mean returns: EEM:0.0645, AVAX-USD:0.6683, ITB:0.6874, DBC:0.0147
Covariance matrix (annualized):
[[0.021566, -0.00289, 0.01305, 0.00581], [-0.00289, 0.871819, 0.022214, -0.032274], [0.01305, 0.022214, 0.06655, 0.004295], [0.00581, -0.032274, 0.004295, 0.017454]]
Risk-free rate: 4.00%
Constraints: weights 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_AVAX-USD=0.0475, w_ITB=0.9525, w_DBC=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EEM=0.0000, w_AVAX-USD=0.0475, w_ITB=0.9525, w_DBC=0.0000
Portfolio annualized return: 68.65%, volatility: 25.37%
Sharpe ratio: (0.6865 - 0.0400) / 0.2537 = 2.5485


4-asset optimization. Max-Sharpe: 4.580. Portfolio: return=5.25%, vol=0.27%. Weights: w_XLV=0.0000, w_ADA-USD=0.0000, w_BIL=1.0000, w_SCHP=0.0000.

Question:
Assets: XLV, ADA-USD, BIL, SCHP
Annualized mean returns: XLV:-0.0995, ADA-USD:-2.9342, BIL:0.0525, SCHP:-0.0072
Covariance matrix (annualized):
[[0.010922, 0.010803, -3e-06, 0.001189], [0.010803, 0.398011, 0.000308, 0.001598], [-3e-06, 0.000308, 8e-06, 2e-06], [0.001189, 0.001598, 2e-06, 0.002515]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: bull

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

Answer: w_XLV=0.0000, w_ADA-USD=0.0000, w_BIL=1.0000, w_SCHP=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLV=0.0000, w_ADA-USD=0.0000, w_BIL=1.0000, w_SCHP=0.0000
Portfolio annualized return: 5.25%, volatility: 0.27%
Sharpe ratio: (0.0525 - 0.0400) / 0.0027 = 4.5795


4-asset optimization. Max-Sharpe: 6.233. Portfolio: return=6.99%, vol=0.48%. Weights: w_EWJ=0.0001, w_AVAX-USD=0.0031, w_ICSH=0.9968, w_JNK=0.0000.

Question:
Assets: EWJ, AVAX-USD, ICSH, JNK
Annualized mean returns: EWJ:0.2262, AVAX-USD:2.5058, ICSH:0.0623, JNK:0.2037
Covariance matrix (annualized):
[[0.027236, 0.001256, 0.000138, 0.007519], [0.001256, 0.920855, -0.000953, 0.011351], [0.000138, -0.000953, 2e-05, 0.0001], [0.007519, 0.011351, 0.0001, 0.005942]]
Risk-free rate: 4.00%
Constraints: weights 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=0.0001, w_AVAX-USD=0.0031, w_ICSH=0.9968, w_JNK=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EWJ=0.0001, w_AVAX-USD=0.0031, w_ICSH=0.9968, w_JNK=0.0000
Portfolio annualized return: 6.99%, volatility: 0.48%
Sharpe ratio: (0.0699 - 0.0400) / 0.0048 = 6.2326


4-asset optimization. Max-Sharpe: 5.135. Portfolio: return=7.54%, vol=0.69%. Weights: w_QQQ=0.0000, w_XRP-USD=0.0000, w_WEAT=0.0222, w_ICSH=0.9778.

Question:
Assets: QQQ, XRP-USD, WEAT, ICSH
Annualized mean returns: QQQ:0.1787, XRP-USD:-0.1567, WEAT:1.2007, ICSH:0.0499
Covariance matrix (annualized):
[[0.025808, 0.021617, 0.010016, 0.000105], [0.021617, 0.205891, 0.030223, 0.000599], [0.010016, 0.030223, 0.070417, -4e-06], [0.000105, 0.000599, -4e-06, 1.4e-05]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_QQQ=0.0000, w_XRP-USD=0.0000, w_WEAT=0.0222, w_ICSH=0.9778

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_QQQ=0.0000, w_XRP-USD=0.0000, w_WEAT=0.0222, w_ICSH=0.9778
Portfolio annualized return: 7.54%, volatility: 0.69%
Sharpe ratio: (0.0754 - 0.0400) / 0.0069 = 5.1351


4-asset optimization. Max-Sharpe: 3.480. Portfolio: return=58.58%, vol=15.69%. Weights: w_XLY=0.5882, w_BTC-USD=0.3169, w_PPLT=0.0000, w_MORT=0.0949.

Question:
Assets: XLY, BTC-USD, PPLT, MORT
Annualized mean returns: XLY:0.5015, BTC-USD:0.7841, PPLT:-0.5570, MORT:0.4458
Covariance matrix (annualized):
[[0.030754, 0.002767, 0.011803, 0.019367], [0.002767, 0.098609, -0.00198, 0.007009], [0.011803, -0.00198, 0.045192, 0.020033], [0.019367, 0.007009, 0.020033, 0.049312]]
Risk-free rate: 4.00%
Constraints: weights 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=0.5882, w_BTC-USD=0.3169, w_PPLT=0.0000, w_MORT=0.0949

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLY=0.5882, w_BTC-USD=0.3169, w_PPLT=0.0000, w_MORT=0.0949
Portfolio annualized return: 58.58%, volatility: 15.69%
Sharpe ratio: (0.5858 - 0.0400) / 0.1569 = 3.4796


4-asset optimization. Max-Sharpe: 1.722. Portfolio: return=14.97%, vol=6.37%. Weights: w_XLY=0.0000, w_XRP-USD=0.0000, w_JNK=0.9696, w_UNG=0.0304.

Question:
Assets: XLY, XRP-USD, JNK, UNG
Annualized mean returns: XLY:0.1016, XRP-USD:-1.1788, JNK:0.1430, UNG:0.3634
Covariance matrix (annualized):
[[0.027259, 0.029743, 0.005072, -0.015964], [0.029743, 0.198996, 0.005762, -0.032032], [0.005072, 0.005762, 0.003968, -0.001158], [-0.015964, -0.032032, -0.001158, 0.430794]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_XLY=0.0000, w_XRP-USD=0.0000, w_JNK=0.9696, w_UNG=0.0304

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLY=0.0000, w_XRP-USD=0.0000, w_JNK=0.9696, w_UNG=0.0304
Portfolio annualized return: 14.97%, volatility: 6.37%
Sharpe ratio: (0.1497 - 0.0400) / 0.0637 = 1.7223


4-asset optimization. Max-Sharpe: 3.967. Portfolio: return=9.58%, vol=1.41%. Weights: w_XLK=0.0870, w_XRP-USD=0.0000, w_CSHI=0.9130, w_CPER=0.0000.

Question:
Assets: XLK, XRP-USD, CSHI, CPER
Annualized mean returns: XLK:0.5984, XRP-USD:-1.0702, CSHI:0.0479, CPER:0.0064
Covariance matrix (annualized):
[[0.023086, 0.006635, -3.2e-05, 0.011095], [0.006635, 0.182559, 4.2e-05, 0.023757], [-3.2e-05, 4.2e-05, 3.4e-05, -0.000333], [0.011095, 0.023757, -0.000333, 0.029851]]
Risk-free rate: 4.00%
Constraints: weights 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=0.0870, w_XRP-USD=0.0000, w_CSHI=0.9130, w_CPER=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLK=0.0870, w_XRP-USD=0.0000, w_CSHI=0.9130, w_CPER=0.0000
Portfolio annualized return: 9.58%, volatility: 1.41%
Sharpe ratio: (0.0958 - 0.0400) / 0.0141 = 3.9673


4-asset optimization. Max-Sharpe: -2.510. Portfolio: return=-62.06%, vol=26.32%. Weights: w_QQQ=0.2500, w_MATIC-USD=0.2500, w_BIL=0.2500, w_PALL=0.2500.

Question:
Assets: QQQ, MATIC-USD, BIL, PALL
Annualized mean returns: QQQ:-0.0598, MATIC-USD:-2.8193, BIL:0.0503, PALL:0.3464
Covariance matrix (annualized):
[[0.026898, 0.040782, 0.000173, 0.007377], [0.040782, 0.602578, -5e-06, 0.127976], [0.000173, -5e-06, 6e-06, -1.6e-05], [0.007377, 0.127976, -1.6e-05, 0.126024]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_QQQ=0.2500, w_MATIC-USD=0.2500, w_BIL=0.2500, w_PALL=0.2500

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_QQQ=0.2500, w_MATIC-USD=0.2500, w_BIL=0.2500, w_PALL=0.2500
Portfolio annualized return: -62.06%, volatility: 26.32%
Sharpe ratio: (-0.6206 - 0.0400) / 0.2632 = -2.5101


4-asset optimization. Max-Sharpe: 3.235. Portfolio: return=39.25%, vol=10.90%. Weights: w_^VIX=0.0000, w_SOL-USD=0.0655, w_VNQ=0.4134, w_JNK=0.5210.

Question:
Assets: ^VIX, SOL-USD, VNQ, JNK
Annualized mean returns: ^VIX:-1.5134, SOL-USD:1.6701, VNQ:0.4523, JNK:0.1843
Covariance matrix (annualized):
[[0.617369, -0.042722, -0.033913, -0.026505], [-0.042722, 0.684383, 0.014917, 0.007481], [-0.033913, 0.014917, 0.02524, 0.004751], [-0.026505, 0.007481, 0.004751, 0.004619]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_^VIX=0.0000, w_SOL-USD=0.0655, w_VNQ=0.4134, w_JNK=0.5210

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_^VIX=0.0000, w_SOL-USD=0.0655, w_VNQ=0.4134, w_JNK=0.5210
Portfolio annualized return: 39.25%, volatility: 10.90%
Sharpe ratio: (0.3925 - 0.0400) / 0.1090 = 3.2348


4-asset optimization. Max-Sharpe: 0.926. Portfolio: return=41.96%, vol=40.99%. Weights: w_XLP=0.0000, w_DOT-USD=1.0000, w_WEAT=0.0000, w_HAUZ=0.0000.

Question:
Assets: XLP, DOT-USD, WEAT, HAUZ
Annualized mean returns: XLP:-0.0438, DOT-USD:0.4196, WEAT:-0.8678, HAUZ:-0.2374
Covariance matrix (annualized):
[[0.009013, 0.003254, 0.009039, 0.004208], [0.003254, 0.168055, 0.008192, 0.00155], [0.009039, 0.008192, 0.142396, 0.003986], [0.004208, 0.00155, 0.003986, 0.022163]]
Risk-free rate: 4.00%
Constraints: weights 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=1.0000, w_WEAT=0.0000, w_HAUZ=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLP=0.0000, w_DOT-USD=1.0000, w_WEAT=0.0000, w_HAUZ=0.0000
Portfolio annualized return: 41.96%, volatility: 40.99%
Sharpe ratio: (0.4196 - 0.0400) / 0.4099 = 0.9261


4-asset optimization. Max-Sharpe: 3.531. Portfolio: return=105.09%, vol=28.63%. Weights: w_XLF=0.0000, w_BTC-USD=0.8471, w_IEF=0.1529, w_REZ=0.0000.

Question:
Assets: XLF, BTC-USD, IEF, REZ
Annualized mean returns: XLF:0.1943, BTC-USD:1.2148, IEF:0.1433, REZ:0.1824
Covariance matrix (annualized):
[[0.026491, 0.025131, 0.004808, 0.028182], [0.025131, 0.110993, 0.008166, 0.034419], [0.004808, 0.008166, 0.009552, 0.008978], [0.028182, 0.034419, 0.008978, 0.053339]]
Risk-free rate: 4.00%
Constraints: weights 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=0.8471, w_IEF=0.1529, w_REZ=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLF=0.0000, w_BTC-USD=0.8471, w_IEF=0.1529, w_REZ=0.0000
Portfolio annualized return: 105.09%, volatility: 28.63%
Sharpe ratio: (1.0509 - 0.0400) / 0.2863 = 3.5307


4-asset optimization. Max-Sharpe: 2.397. Portfolio: return=86.35%, vol=34.36%. Weights: w_FXI=0.9251, w_ADA-USD=0.0000, w_UNG=0.0749, w_SCHP=0.0000.

Question:
Assets: FXI, ADA-USD, UNG, SCHP
Annualized mean returns: FXI:0.9325, ADA-USD:-0.3046, UNG:0.0108, SCHP:-0.0249
Covariance matrix (annualized):
[[0.14016, 0.058467, -0.02283, 0.00069], [0.058467, 0.221562, -0.027639, -0.001423], [-0.02283, -0.027639, 0.226196, 0.005429], [0.00069, -0.001423, 0.005429, 0.002049]]
Risk-free rate: 4.00%
Constraints: weights 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=0.9251, w_ADA-USD=0.0000, w_UNG=0.0749, w_SCHP=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_FXI=0.9251, w_ADA-USD=0.0000, w_UNG=0.0749, w_SCHP=0.0000
Portfolio annualized return: 86.35%, volatility: 34.36%
Sharpe ratio: (0.8635 - 0.0400) / 0.3436 = 2.3967


4-asset optimization. Max-Sharpe: -1.717. Portfolio: return=-78.50%, vol=48.06%. Weights: w_XLB=0.0000, w_BNB-USD=1.0000, w_EMB=0.0000, w_VNQ=0.0000.

Question:
Assets: XLB, BNB-USD, EMB, VNQ
Annualized mean returns: XLB:-0.2299, BNB-USD:-0.7850, EMB:-0.0792, VNQ:-0.5743
Covariance matrix (annualized):
[[0.043832, 0.010818, 0.003362, 0.029625], [0.010818, 0.230959, -0.002001, 0.011242], [0.003362, -0.002001, 0.011191, 0.003878], [0.029625, 0.011242, 0.003878, 0.049969]]
Risk-free rate: 4.00%
Constraints: weights 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=1.0000, w_EMB=0.0000, w_VNQ=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLB=0.0000, w_BNB-USD=1.0000, w_EMB=0.0000, w_VNQ=0.0000
Portfolio annualized return: -78.50%, volatility: 48.06%
Sharpe ratio: (-0.7850 - 0.0400) / 0.4806 = -1.7166


4-asset optimization. Max-Sharpe: 2.224. Portfolio: return=4.65%, vol=0.29%. Weights: w_XLK=0.0096, w_MATIC-USD=0.0000, w_IYR=0.0005, w_SGOV=0.9900.

Question:
Assets: XLK, MATIC-USD, IYR, SGOV
Annualized mean returns: XLK:0.2521, MATIC-USD:0.1407, IYR:0.0674, SGOV:0.0445
Covariance matrix (annualized):
[[0.036752, 0.040199, -0.000913, -7.3e-05], [0.040199, 0.638043, 0.024691, 0.000176], [-0.000913, 0.024691, 0.025395, 3.3e-05], [-7.3e-05, 0.000176, 3.3e-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_XLK=0.0096, w_MATIC-USD=0.0000, w_IYR=0.0005, w_SGOV=0.9900

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLK=0.0096, w_MATIC-USD=0.0000, w_IYR=0.0005, w_SGOV=0.9900
Portfolio annualized return: 4.65%, volatility: 0.29%
Sharpe ratio: (0.0465 - 0.0400) / 0.0029 = 2.2240


4-asset optimization. Max-Sharpe: 6.954. Portfolio: return=5.69%, vol=0.24%. Weights: w_XLE=0.0000, w_XRP-USD=0.0000, w_BIL=0.9964, w_ITB=0.0036.

Question:
Assets: XLE, XRP-USD, BIL, ITB
Annualized mean returns: XLE:-0.0542, XRP-USD:0.1049, BIL:0.0553, ITB:0.4996
Covariance matrix (annualized):
[[0.031244, 0.029398, -7.6e-05, 0.012325], [0.029398, 0.294511, -8.6e-05, 0.041968], [-7.6e-05, -8.6e-05, 6e-06, -0.000148], [0.012325, 0.041968, -0.000148, 0.086699]]
Risk-free rate: 4.00%
Constraints: weights 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_XRP-USD=0.0000, w_BIL=0.9964, w_ITB=0.0036

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLE=0.0000, w_XRP-USD=0.0000, w_BIL=0.9964, w_ITB=0.0036
Portfolio annualized return: 5.69%, volatility: 0.24%
Sharpe ratio: (0.0569 - 0.0400) / 0.0024 = 6.9544


4-asset optimization. Max-Sharpe: 2.692. Portfolio: return=57.94%, vol=20.04%. Weights: w_ACWI=0.0000, w_XRP-USD=0.2677, w_CSHI=0.7323, w_PPLT=0.0000.

Question:
Assets: ACWI, XRP-USD, CSHI, PPLT
Annualized mean returns: ACWI:0.0043, XRP-USD:2.0281, CSHI:0.0498, PPLT:-0.7299
Covariance matrix (annualized):
[[0.02915, 0.032447, 0.00125, 0.024739], [0.032447, 0.548253, 0.001661, 0.059958], [0.00125, 0.001661, 0.000385, 0.001764], [0.024739, 0.059958, 0.001764, 0.05993]]
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_ACWI=0.0000, w_XRP-USD=0.2677, w_CSHI=0.7323, w_PPLT=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_ACWI=0.0000, w_XRP-USD=0.2677, w_CSHI=0.7323, w_PPLT=0.0000
Portfolio annualized return: 57.94%, volatility: 20.04%
Sharpe ratio: (0.5794 - 0.0400) / 0.2004 = 2.6918


4-asset optimization. Max-Sharpe: 2.748. Portfolio: return=35.74%, vol=11.55%. Weights: w_ACWI=0.6025, w_ADA-USD=0.0000, w_CSHI=0.1022, w_SCHH=0.2953.

Question:
Assets: ACWI, ADA-USD, CSHI, SCHH
Annualized mean returns: ACWI:0.4283, ADA-USD:0.7777, CSHI:0.0674, SCHH:0.3129
Covariance matrix (annualized):
[[0.021907, 0.050599, 0.001302, 0.01011], [0.050599, 0.347641, 0.005886, 0.028825], [0.001302, 0.005886, 0.000393, 0.001114], [0.01011, 0.028825, 0.001114, 0.017826]]
Risk-free rate: 4.00%
Constraints: weights 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=0.6025, w_ADA-USD=0.0000, w_CSHI=0.1022, w_SCHH=0.2953

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_ACWI=0.6025, w_ADA-USD=0.0000, w_CSHI=0.1022, w_SCHH=0.2953
Portfolio annualized return: 35.74%, volatility: 11.55%
Sharpe ratio: (0.3574 - 0.0400) / 0.1155 = 2.7480


4-asset optimization. Max-Sharpe: 5.349. Portfolio: return=630.46%, vol=117.11%. Weights: w_USMV=0.0000, w_XRP-USD=1.0000, w_LQD=0.0000, w_SOYB=0.0000.

Question:
Assets: USMV, XRP-USD, LQD, SOYB
Annualized mean returns: USMV:-0.0389, XRP-USD:6.3046, LQD:-0.0796, SOYB:-0.1091
Covariance matrix (annualized):
[[0.012378, 0.022212, 0.002388, 0.005885], [0.022212, 1.371565, 0.012999, -0.010209], [0.002388, 0.012999, 0.006828, 0.005468], [0.005885, -0.010209, 0.005468, 0.019884]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_USMV=0.0000, w_XRP-USD=1.0000, w_LQD=0.0000, w_SOYB=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_USMV=0.0000, w_XRP-USD=1.0000, w_LQD=0.0000, w_SOYB=0.0000
Portfolio annualized return: 630.46%, volatility: 117.11%
Sharpe ratio: (6.3046 - 0.0400) / 1.1711 = 5.3492


4-asset optimization. Max-Sharpe: 2.192. Portfolio: return=7.40%, vol=1.55%. Weights: w_USMV=0.0000, w_ADA-USD=0.0000, w_MORT=0.0450, w_CSHI=0.9550.

Question:
Assets: USMV, ADA-USD, MORT, CSHI
Annualized mean returns: USMV:-0.0140, ADA-USD:-1.4030, MORT:0.4886, CSHI:0.0544
Covariance matrix (annualized):
[[0.010032, 0.002643, 0.01766, -0.000259], [0.002643, 0.203739, 0.024538, -0.000954], [0.01766, 0.024538, 0.073603, -0.000147], [-0.000259, -0.000954, -0.000147, 0.000114]]
Risk-free rate: 4.00%
Constraints: weights 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_ADA-USD=0.0000, w_MORT=0.0450, w_CSHI=0.9550

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_USMV=0.0000, w_ADA-USD=0.0000, w_MORT=0.0450, w_CSHI=0.9550
Portfolio annualized return: 7.40%, volatility: 1.55%
Sharpe ratio: (0.0740 - 0.0400) / 0.0155 = 2.1921


4-asset optimization. Max-Sharpe: 5.417. Portfolio: return=53.70%, vol=9.18%. Weights: w_QUAL=0.4649, w_ADA-USD=0.0051, w_INDS=0.2242, w_EMB=0.3058.

Question:
Assets: QUAL, ADA-USD, INDS, EMB
Annualized mean returns: QUAL:0.4195, ADA-USD:2.4749, INDS:0.9114, EMB:0.4089
Covariance matrix (annualized):
[[0.007742, 0.036456, 0.007597, 0.003072], [0.036456, 0.938442, 0.04826, 0.028395], [0.007597, 0.04826, 0.036304, 0.009295], [0.003072, 0.028395, 0.009295, 0.008473]]
Risk-free rate: 4.00%
Constraints: weights 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=0.4649, w_ADA-USD=0.0051, w_INDS=0.2242, w_EMB=0.3058

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_QUAL=0.4649, w_ADA-USD=0.0051, w_INDS=0.2242, w_EMB=0.3058
Portfolio annualized return: 53.70%, volatility: 9.18%
Sharpe ratio: (0.5370 - 0.0400) / 0.0918 = 5.4170


4-asset optimization. Max-Sharpe: 6.113. Portfolio: return=5.32%, vol=0.22%. Weights: w_XLE=0.0000, w_ADA-USD=0.0000, w_SGOV=0.9967, w_BNO=0.0033.

Question:
Assets: XLE, ADA-USD, SGOV, BNO
Annualized mean returns: XLE:0.0905, ADA-USD:-0.2929, SGOV:0.0527, BNO:0.2250
Covariance matrix (annualized):
[[0.028983, 0.000285, -4e-05, 0.018237], [0.000285, 0.207467, -0.0, -0.024401], [-4e-05, -0.0, 5e-06, -9.4e-05], [0.018237, -0.024401, -9.4e-05, 0.048144]]
Risk-free rate: 4.00%
Constraints: weights 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_ADA-USD=0.0000, w_SGOV=0.9967, w_BNO=0.0033

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLE=0.0000, w_ADA-USD=0.0000, w_SGOV=0.9967, w_BNO=0.0033
Portfolio annualized return: 5.32%, volatility: 0.22%
Sharpe ratio: (0.0532 - 0.0400) / 0.0022 = 6.1131


4-asset optimization. Max-Sharpe: 3.202. Portfolio: return=38.32%, vol=10.72%. Weights: w_XLF=0.9887, w_LINK-USD=0.0113, w_CPER=0.0000, w_IYR=0.0000.

Question:
Assets: XLF, LINK-USD, CPER, IYR
Annualized mean returns: XLF:0.3763, LINK-USD:0.9903, CPER:-0.0020, IYR:-0.2692
Covariance matrix (annualized):
[[0.011095, 0.025371, 0.004649, 0.011524], [0.025371, 0.596565, 0.019792, 0.024674], [0.004649, 0.019792, 0.024251, 0.001132], [0.011524, 0.024674, 0.001132, 0.032282]]
Risk-free rate: 4.00%
Constraints: weights 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=0.9887, w_LINK-USD=0.0113, w_CPER=0.0000, w_IYR=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLF=0.9887, w_LINK-USD=0.0113, w_CPER=0.0000, w_IYR=0.0000
Portfolio annualized return: 38.32%, volatility: 10.72%
Sharpe ratio: (0.3832 - 0.0400) / 0.1072 = 3.2022


4-asset optimization. Max-Sharpe: 3.202. Portfolio: return=71.64%, vol=21.12%. Weights: w_EFA=0.5433, w_AVAX-USD=0.1759, w_DBC=0.0000, w_TLT=0.2808.

Question:
Assets: EFA, AVAX-USD, DBC, TLT
Annualized mean returns: EFA:0.3022, AVAX-USD:2.5718, DBC:-0.1395, TLT:0.3554
Covariance matrix (annualized):
[[0.020579, 0.01669, -0.001087, 0.011316], [0.01669, 0.899123, -0.056074, -0.000877], [-0.001087, -0.056074, 0.033334, -0.002417], [0.011316, -0.000877, -0.002417, 0.052743]]
Risk-free rate: 4.00%
Constraints: weights 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=0.5433, w_AVAX-USD=0.1759, w_DBC=0.0000, w_TLT=0.2808

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EFA=0.5433, w_AVAX-USD=0.1759, w_DBC=0.0000, w_TLT=0.2808
Portfolio annualized return: 71.64%, volatility: 21.12%
Sharpe ratio: (0.7164 - 0.0400) / 0.2112 = 3.2023


4-asset optimization. Max-Sharpe: 3.137. Portfolio: return=36.03%, vol=10.21%. Weights: w_SPY=0.7402, w_SOL-USD=0.0000, w_IGOV=0.0000, w_REZ=0.2598.

Question:
Assets: SPY, SOL-USD, IGOV, REZ
Annualized mean returns: SPY:0.4110, SOL-USD:-0.0248, IGOV:-0.0405, REZ:0.2156
Covariance matrix (annualized):
[[0.01542, 0.032548, 0.001709, 0.002533], [0.032548, 0.285962, 0.020217, 0.004841], [0.001709, 0.020217, 0.006619, 0.001624], [0.002533, 0.004841, 0.001624, 0.014771]]
Risk-free rate: 4.00%
Constraints: weights 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=0.7402, w_SOL-USD=0.0000, w_IGOV=0.0000, w_REZ=0.2598

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_SPY=0.7402, w_SOL-USD=0.0000, w_IGOV=0.0000, w_REZ=0.2598
Portfolio annualized return: 36.03%, volatility: 10.21%
Sharpe ratio: (0.3603 - 0.0400) / 0.1021 = 3.1374


4-asset optimization. Max-Sharpe: 0.336. Portfolio: return=13.63%, vol=28.69%. Weights: w_XLP=0.0000, w_XRP-USD=0.0000, w_LQD=0.0000, w_PALL=1.0000.

Question:
Assets: XLP, XRP-USD, LQD, PALL
Annualized mean returns: XLP:-0.0655, XRP-USD:-0.7831, LQD:-0.0823, PALL:0.1363
Covariance matrix (annualized):
[[0.00969, 0.021597, 0.002871, 0.005211], [0.021597, 1.014289, 0.035009, 0.027986], [0.002871, 0.035009, 0.009259, 0.011529], [0.005211, 0.027986, 0.011529, 0.082284]]
Risk-free rate: 4.00%
Constraints: weights 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_XRP-USD=0.0000, w_LQD=0.0000, w_PALL=1.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLP=0.0000, w_XRP-USD=0.0000, w_LQD=0.0000, w_PALL=1.0000
Portfolio annualized return: 13.63%, volatility: 28.69%
Sharpe ratio: (0.1363 - 0.0400) / 0.2869 = 0.3357


4-asset optimization. Max-Sharpe: 1.675. Portfolio: return=28.33%, vol=14.53%. Weights: w_XLI=0.0000, w_ADA-USD=0.1795, w_UNG=0.0000, w_IEF=0.8205.

Question:
Assets: XLI, ADA-USD, UNG, IEF
Annualized mean returns: XLI:-0.1308, ADA-USD:0.9343, UNG:-1.1793, IEF:0.1409
Covariance matrix (annualized):
[[0.032583, 0.026413, 0.039629, -0.008578], [0.026413, 0.429994, 0.06761, 0.000498], [0.039629, 0.06761, 0.544479, -0.006956], [-0.008578, 0.000498, -0.006956, 0.010562]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_XLI=0.0000, w_ADA-USD=0.1795, w_UNG=0.0000, w_IEF=0.8205

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLI=0.0000, w_ADA-USD=0.1795, w_UNG=0.0000, w_IEF=0.8205
Portfolio annualized return: 28.33%, volatility: 14.53%
Sharpe ratio: (0.2833 - 0.0400) / 0.1453 = 1.6746


4-asset optimization. Max-Sharpe: 1.966. Portfolio: return=31.99%, vol=14.24%. Weights: w_VTI=0.0000, w_LINK-USD=0.0000, w_VNQI=1.0000, w_BNO=0.0000.

Question:
Assets: VTI, LINK-USD, VNQI, BNO
Annualized mean returns: VTI:0.1510, LINK-USD:-1.3558, VNQI:0.3199, BNO:0.0685
Covariance matrix (annualized):
[[0.028213, 0.06327, 0.015587, 0.007152], [0.06327, 0.533903, 0.022832, -0.007434], [0.015587, 0.022832, 0.020275, 0.002851], [0.007152, -0.007434, 0.002851, 0.053514]]
Risk-free rate: 4.00%
Constraints: weights 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_LINK-USD=0.0000, w_VNQI=1.0000, w_BNO=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VTI=0.0000, w_LINK-USD=0.0000, w_VNQI=1.0000, w_BNO=0.0000
Portfolio annualized return: 31.99%, volatility: 14.24%
Sharpe ratio: (0.3199 - 0.0400) / 0.1424 = 1.9658


4-asset optimization. Max-Sharpe: 2.176. Portfolio: return=6.37%, vol=1.09%. Weights: w_XLI=0.0473, w_XRP-USD=0.0129, w_ICSH=0.9399, w_VNQI=0.0000.

Question:
Assets: XLI, XRP-USD, ICSH, VNQI
Annualized mean returns: XLI:0.2771, XRP-USD:0.6071, ICSH:0.0456, VNQI:-0.1363
Covariance matrix (annualized):
[[0.029478, 0.016097, -0.000439, 0.01416], [0.016097, 0.160666, 1.5e-05, 0.006913], [-0.000439, 1.5e-05, 5.1e-05, -0.000199], [0.01416, 0.006913, -0.000199, 0.02528]]
Risk-free rate: 4.00%
Constraints: weights 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=0.0473, w_XRP-USD=0.0129, w_ICSH=0.9399, w_VNQI=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLI=0.0473, w_XRP-USD=0.0129, w_ICSH=0.9399, w_VNQI=0.0000
Portfolio annualized return: 6.37%, volatility: 1.09%
Sharpe ratio: (0.0637 - 0.0400) / 0.0109 = 2.1760


4-asset optimization. Max-Sharpe: 2.155. Portfolio: return=20.59%, vol=7.70%. Weights: w_MTUM=0.0000, w_SOL-USD=0.0736, w_PDBC=0.0000, w_LQD=0.9264.

Question:
Assets: MTUM, SOL-USD, PDBC, LQD
Annualized mean returns: MTUM:-0.3571, SOL-USD:1.0635, PDBC:-0.1701, LQD:0.1378
Covariance matrix (annualized):
[[0.062657, 0.068558, 0.010396, 0.001251], [0.068558, 0.673546, -0.011546, -0.014012], [0.010396, -0.011546, 0.016692, 0.000661], [0.001251, -0.014012, 0.000661, 0.004882]]
Risk-free rate: 4.00%
Constraints: weights 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_SOL-USD=0.0736, w_PDBC=0.0000, w_LQD=0.9264

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_MTUM=0.0000, w_SOL-USD=0.0736, w_PDBC=0.0000, w_LQD=0.9264
Portfolio annualized return: 20.59%, volatility: 7.70%
Sharpe ratio: (0.2059 - 0.0400) / 0.0770 = 2.1548


4-asset optimization. Max-Sharpe: 0.121. Portfolio: return=4.08%, vol=0.67%. Weights: w_XLRE=0.0000, w_AVAX-USD=0.0000, w_DBB=0.0000, w_CSHI=1.0000.

Question:
Assets: XLRE, AVAX-USD, DBB, CSHI
Annualized mean returns: XLRE:-0.0464, AVAX-USD:-1.7974, DBB:0.0066, CSHI:0.0408
Covariance matrix (annualized):
[[0.048743, 0.104113, 0.018101, 0.000542], [0.104113, 0.870891, 0.072538, 0.000574], [0.018101, 0.072538, 0.042138, 0.000255], [0.000542, 0.000574, 0.000255, 4.4e-05]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_XLRE=0.0000, w_AVAX-USD=0.0000, w_DBB=0.0000, w_CSHI=1.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLRE=0.0000, w_AVAX-USD=0.0000, w_DBB=0.0000, w_CSHI=1.0000
Portfolio annualized return: 4.08%, volatility: 0.67%
Sharpe ratio: (0.0408 - 0.0400) / 0.0067 = 0.1215


4-asset optimization. Max-Sharpe: 3.709. Portfolio: return=5.89%, vol=0.51%. Weights: w_VTI=0.0117, w_DOT-USD=0.0008, w_CPER=0.0000, w_CSHI=0.9875.

Question:
Assets: VTI, DOT-USD, CPER, CSHI
Annualized mean returns: VTI:0.2724, DOT-USD:1.2428, CPER:-0.2166, CSHI:0.0555
Covariance matrix (annualized):
[[0.01297, 0.044133, -0.003606, 0.000135], [0.044133, 0.816786, -0.032967, 0.000503], [-0.003606, -0.032967, 0.041718, -0.000157], [0.000135, 0.000503, -0.000157, 2e-05]]
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_VTI=0.0117, w_DOT-USD=0.0008, w_CPER=0.0000, w_CSHI=0.9875

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VTI=0.0117, w_DOT-USD=0.0008, w_CPER=0.0000, w_CSHI=0.9875
Portfolio annualized return: 5.89%, volatility: 0.51%
Sharpe ratio: (0.0589 - 0.0400) / 0.0051 = 3.7088


4-asset optimization. Max-Sharpe: 6.307. Portfolio: return=5.24%, vol=0.20%. Weights: w_FXI=0.0000, w_MATIC-USD=0.0000, w_SGOV=0.9993, w_INDS=0.0007.

Question:
Assets: FXI, MATIC-USD, SGOV, INDS
Annualized mean returns: FXI:-0.3388, MATIC-USD:-0.2092, SGOV:0.0526, INDS:-0.2021
Covariance matrix (annualized):
[[0.090251, 0.043787, 4e-06, 0.024003], [0.043787, 0.468166, 0.000139, 0.028807], [4e-06, 0.000139, 4e-06, -9.7e-05], [0.024003, 0.028807, -9.7e-05, 0.029152]]
Risk-free rate: 4.00%
Constraints: weights 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=0.0000, w_SGOV=0.9993, w_INDS=0.0007

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_FXI=0.0000, w_MATIC-USD=0.0000, w_SGOV=0.9993, w_INDS=0.0007
Portfolio annualized return: 5.24%, volatility: 0.20%
Sharpe ratio: (0.0524 - 0.0400) / 0.0020 = 6.3073


4-asset optimization. Max-Sharpe: 2.927. Portfolio: return=7.80%, vol=1.30%. Weights: w_XLB=0.0535, w_BNB-USD=0.0000, w_CSHI=0.9465, w_INDS=0.0000.

Question:
Assets: XLB, BNB-USD, CSHI, INDS
Annualized mean returns: XLB:0.4199, BNB-USD:-0.7838, CSHI:0.0587, INDS:0.0399
Covariance matrix (annualized):
[[0.031989, 0.013612, -2.7e-05, 0.019262], [0.013612, 0.185418, 0.000616, 0.011497], [-2.7e-05, 0.000616, 8.9e-05, -2.2e-05], [0.019262, 0.011497, -2.2e-05, 0.029677]]
Risk-free rate: 4.00%
Constraints: weights 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=0.0535, w_BNB-USD=0.0000, w_CSHI=0.9465, w_INDS=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLB=0.0535, w_BNB-USD=0.0000, w_CSHI=0.9465, w_INDS=0.0000
Portfolio annualized return: 7.80%, volatility: 1.30%
Sharpe ratio: (0.0780 - 0.0400) / 0.0130 = 2.9274


4-asset optimization. Max-Sharpe: 3.205. Portfolio: return=44.43%, vol=12.61%. Weights: w_IVV=0.3338, w_XRP-USD=0.0000, w_DBA=0.3070, w_ITB=0.3592.

Question:
Assets: IVV, XRP-USD, DBA, ITB
Annualized mean returns: IVV:0.3868, XRP-USD:-0.0229, DBA:0.2586, ITB:0.6563
Covariance matrix (annualized):
[[0.016813, 0.013079, 0.00557, 0.0176], [0.013079, 0.185987, 0.007132, 0.026313], [0.00557, 0.007132, 0.015292, 0.005698], [0.0176, 0.026313, 0.005698, 0.04628]]
Risk-free rate: 4.00%
Constraints: weights 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=0.3338, w_XRP-USD=0.0000, w_DBA=0.3070, w_ITB=0.3592

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_IVV=0.3338, w_XRP-USD=0.0000, w_DBA=0.3070, w_ITB=0.3592
Portfolio annualized return: 44.43%, volatility: 12.61%
Sharpe ratio: (0.4443 - 0.0400) / 0.1261 = 3.2054


4-asset optimization. Max-Sharpe: 6.361. Portfolio: return=6.58%, vol=0.41%. Weights: w_QUAL=0.0180, w_LINK-USD=0.0014, w_SGOV=0.9806, w_HAUZ=0.0000.

Question:
Assets: QUAL, LINK-USD, SGOV, HAUZ
Annualized mean returns: QUAL:0.5928, LINK-USD:1.6230, SGOV:0.0539, HAUZ:0.2587
Covariance matrix (annualized):
[[0.013375, 0.021344, 8.4e-05, 0.010806], [0.021344, 0.393812, 7.1e-05, 0.016504], [8.4e-05, 7.1e-05, 7e-06, 7e-06], [0.010806, 0.016504, 7e-06, 0.025695]]
Risk-free rate: 4.00%
Constraints: weights 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=0.0180, w_LINK-USD=0.0014, w_SGOV=0.9806, w_HAUZ=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_QUAL=0.0180, w_LINK-USD=0.0014, w_SGOV=0.9806, w_HAUZ=0.0000
Portfolio annualized return: 6.58%, volatility: 0.41%
Sharpe ratio: (0.0658 - 0.0400) / 0.0041 = 6.3610


4-asset optimization. Max-Sharpe: 6.965. Portfolio: return=14.88%, vol=1.56%. Weights: w_EEM=0.0000, w_DOT-USD=0.0106, w_VNQ=0.0509, w_CSHI=0.9385.

Question:
Assets: EEM, DOT-USD, VNQ, CSHI
Annualized mean returns: EEM:0.5367, DOT-USD:3.2443, VNQ:1.0282, CSHI:0.0662
Covariance matrix (annualized):
[[0.023324, 0.015706, 0.021416, 4e-06], [0.015706, 0.731058, -0.001188, -0.000543], [0.021416, -0.001188, 0.046328, -0.000136], [4e-06, -0.000543, -0.000136, 7.6e-05]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_EEM=0.0000, w_DOT-USD=0.0106, w_VNQ=0.0509, w_CSHI=0.9385

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EEM=0.0000, w_DOT-USD=0.0106, w_VNQ=0.0509, w_CSHI=0.9385
Portfolio annualized return: 14.88%, volatility: 1.56%
Sharpe ratio: (0.1488 - 0.0400) / 0.0156 = 6.9651


4-asset optimization. Max-Sharpe: 4.835. Portfolio: return=97.32%, vol=19.30%. Weights: w_FXI=0.0000, w_BTC-USD=0.3460, w_USO=0.6540, w_VCIT=0.0000.

Question:
Assets: FXI, BTC-USD, USO, VCIT
Annualized mean returns: FXI:-0.3552, BTC-USD:0.9508, USO:0.9851, VCIT:-0.0703
Covariance matrix (annualized):
[[0.096519, -0.004572, 0.019599, 0.007551], [-0.004572, 0.092409, 0.006702, 0.004402], [0.019599, 0.006702, 0.054148, 0.003817], [0.007551, 0.004402, 0.003817, 0.005303]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_FXI=0.0000, w_BTC-USD=0.3460, w_USO=0.6540, w_VCIT=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_FXI=0.0000, w_BTC-USD=0.3460, w_USO=0.6540, w_VCIT=0.0000
Portfolio annualized return: 97.32%, volatility: 19.30%
Sharpe ratio: (0.9732 - 0.0400) / 0.1930 = 4.8350


4-asset optimization. Max-Sharpe: 6.042. Portfolio: return=5.66%, vol=0.27%. Weights: w_USMV=0.0000, w_MATIC-USD=0.0004, w_GLD=0.0123, w_SGOV=0.9873.

Question:
Assets: USMV, MATIC-USD, GLD, SGOV
Annualized mean returns: USMV:0.2168, MATIC-USD:1.3244, GLD:0.4448, SGOV:0.0513
Covariance matrix (annualized):
[[0.00515, 0.011156, 0.003005, 7.6e-05], [0.011156, 0.546992, 0.031347, 1e-06], [0.003005, 0.031347, 0.011371, 3.3e-05], [7.6e-05, 1e-06, 3.3e-05, 5e-06]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: bull

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

Answer: w_USMV=0.0000, w_MATIC-USD=0.0004, w_GLD=0.0123, w_SGOV=0.9873

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_USMV=0.0000, w_MATIC-USD=0.0004, w_GLD=0.0123, w_SGOV=0.9873
Portfolio annualized return: 5.66%, volatility: 0.27%
Sharpe ratio: (0.0566 - 0.0400) / 0.0027 = 6.0421


4-asset optimization. Max-Sharpe: 4.450. Portfolio: return=6.01%, vol=0.45%. Weights: w_EEM=0.0000, w_BTC-USD=0.0073, w_SGOV=0.9927, w_JNK=0.0000.

Question:
Assets: EEM, BTC-USD, SGOV, JNK
Annualized mean returns: EEM:-0.2599, BTC-USD:2.0242, SGOV:0.0457, JNK:0.0562
Covariance matrix (annualized):
[[0.022816, -0.000806, -1.8e-05, 0.002953], [-0.000806, 0.283682, -5e-05, 0.00828], [-1.8e-05, -5e-05, 6e-06, 3e-06], [0.002953, 0.00828, 3e-06, 0.001995]]
Risk-free rate: 4.00%
Constraints: weights 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_BTC-USD=0.0073, w_SGOV=0.9927, w_JNK=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EEM=0.0000, w_BTC-USD=0.0073, w_SGOV=0.9927, w_JNK=0.0000
Portfolio annualized return: 6.01%, volatility: 0.45%
Sharpe ratio: (0.0601 - 0.0400) / 0.0045 = 4.4498


4-asset optimization. Max-Sharpe: 3.686. Portfolio: return=65.82%, vol=16.77%. Weights: w_XLK=0.2493, w_XRP-USD=0.0000, w_PPLT=0.0000, w_XHB=0.7507.

Question:
Assets: XLK, XRP-USD, PPLT, XHB
Annualized mean returns: XLK:0.3238, XRP-USD:-0.5836, PPLT:-0.0852, XHB:0.7692
Covariance matrix (annualized):
[[0.019733, 0.014325, 0.004852, 0.010641], [0.014325, 0.210594, 0.001294, 0.042891], [0.004852, 0.001294, 0.044262, 0.011561], [0.010641, 0.042891, 0.011561, 0.040652]]
Risk-free rate: 4.00%
Constraints: weights 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=0.2493, w_XRP-USD=0.0000, w_PPLT=0.0000, w_XHB=0.7507

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLK=0.2493, w_XRP-USD=0.0000, w_PPLT=0.0000, w_XHB=0.7507
Portfolio annualized return: 65.82%, volatility: 16.77%
Sharpe ratio: (0.6582 - 0.0400) / 0.1677 = 3.6865


4-asset optimization. Max-Sharpe: 1.004. Portfolio: return=32.27%, vol=28.15%. Weights: w_XLB=0.0000, w_LINK-USD=0.0000, w_SOYB=0.0000, w_XHB=1.0000.

Question:
Assets: XLB, LINK-USD, SOYB, XHB
Annualized mean returns: XLB:-0.0725, LINK-USD:-2.4242, SOYB:-0.6479, XHB:0.3227
Covariance matrix (annualized):
[[0.017175, -0.001133, 0.006615, 0.029929], [-0.001133, 0.30837, -0.036727, 0.019624], [0.006615, -0.036727, 0.029085, 0.013162], [0.029929, 0.019624, 0.013162, 0.079268]]
Risk-free rate: 4.00%
Constraints: weights 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_LINK-USD=0.0000, w_SOYB=0.0000, w_XHB=1.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLB=0.0000, w_LINK-USD=0.0000, w_SOYB=0.0000, w_XHB=1.0000
Portfolio annualized return: 32.27%, volatility: 28.15%
Sharpe ratio: (0.3227 - 0.0400) / 0.2815 = 1.0042


4-asset optimization. Max-Sharpe: 3.918. Portfolio: return=5.52%, vol=0.39%. Weights: w_IWM=0.0000, w_AVAX-USD=0.0000, w_XHB=0.0163, w_SGOV=0.9837.

Question:
Assets: IWM, AVAX-USD, XHB, SGOV
Annualized mean returns: IWM:0.1807, AVAX-USD:-0.1463, XHB:0.6007, SGOV:0.0462
Covariance matrix (annualized):
[[0.030876, 0.003771, 0.025795, -0.000104], [0.003771, 0.267007, 0.013363, -0.000116], [0.025795, 0.013363, 0.039412, -8.9e-05], [-0.000104, -0.000116, -8.9e-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_IWM=0.0000, w_AVAX-USD=0.0000, w_XHB=0.0163, w_SGOV=0.9837

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_IWM=0.0000, w_AVAX-USD=0.0000, w_XHB=0.0163, w_SGOV=0.9837
Portfolio annualized return: 5.52%, volatility: 0.39%
Sharpe ratio: (0.0552 - 0.0400) / 0.0039 = 3.9183


4-asset optimization. Max-Sharpe: 9.027. Portfolio: return=6.86%, vol=0.32%. Weights: w_QUAL=0.0276, w_XRP-USD=0.0000, w_TLH=0.0018, w_BIL=0.9706.

Question:
Assets: QUAL, XRP-USD, TLH, BIL
Annualized mean returns: QUAL:0.5672, XRP-USD:-0.1339, TLH:0.3765, BIL:0.0539
Covariance matrix (annualized):
[[0.009203, 0.012048, 0.004553, -8e-05], [0.012048, 0.117511, 0.009486, -1.8e-05], [0.004553, 0.009486, 0.01265, -3.1e-05], [-8e-05, -1.8e-05, -3.1e-05, 7e-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=0.0276, w_XRP-USD=0.0000, w_TLH=0.0018, w_BIL=0.9706

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_QUAL=0.0276, w_XRP-USD=0.0000, w_TLH=0.0018, w_BIL=0.9706
Portfolio annualized return: 6.86%, volatility: 0.32%
Sharpe ratio: (0.0686 - 0.0400) / 0.0032 = 9.0274


4-asset optimization. Max-Sharpe: 8.336. Portfolio: return=65.98%, vol=7.43%. Weights: w_QQQ=0.2308, w_ETH-USD=0.0702, w_PDBC=0.0000, w_VCIT=0.6990.

Question:
Assets: QQQ, ETH-USD, PDBC, VCIT
Annualized mean returns: QQQ:0.8919, ETH-USD:1.3062, PDBC:-0.3596, VCIT:0.5182
Covariance matrix (annualized):
[[0.022499, -0.011894, 0.002139, 0.004636], [-0.011894, 0.275948, 0.003988, -0.00763], [0.002139, 0.003988, 0.031187, -0.000359], [0.004636, -0.00763, -0.000359, 0.005337]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_QQQ=0.2308, w_ETH-USD=0.0702, w_PDBC=0.0000, w_VCIT=0.6990

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_QQQ=0.2308, w_ETH-USD=0.0702, w_PDBC=0.0000, w_VCIT=0.6990
Portfolio annualized return: 65.98%, volatility: 7.43%
Sharpe ratio: (0.6598 - 0.0400) / 0.0743 = 8.3357


4-asset optimization. Max-Sharpe: 3.365. Portfolio: return=28.19%, vol=7.19%. Weights: w_XLV=0.0000, w_AVAX-USD=0.0640, w_ICSH=0.9360, w_TLH=0.0000.

Question:
Assets: XLV, AVAX-USD, ICSH, TLH
Annualized mean returns: XLV:-0.3682, AVAX-USD:3.7771, ICSH:0.0431, TLH:-0.1717
Covariance matrix (annualized):
[[0.016062, 0.029768, 2.4e-05, 0.003645], [0.029768, 1.239514, 0.000577, 0.005896], [2.4e-05, 0.000577, 3.1e-05, 0.000316], [0.003645, 0.005896, 0.000316, 0.013586]]
Risk-free rate: 4.00%
Constraints: weights 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_AVAX-USD=0.0640, w_ICSH=0.9360, w_TLH=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLV=0.0000, w_AVAX-USD=0.0640, w_ICSH=0.9360, w_TLH=0.0000
Portfolio annualized return: 28.19%, volatility: 7.19%
Sharpe ratio: (0.2819 - 0.0400) / 0.0719 = 3.3653


4-asset optimization. Max-Sharpe: 8.009. Portfolio: return=7.75%, vol=0.47%. Weights: w_FXI=0.0000, w_BTC-USD=0.0085, w_ICSH=0.9915, w_BNDX=0.0000.

Question:
Assets: FXI, BTC-USD, ICSH, BNDX
Annualized mean returns: FXI:-0.0116, BTC-USD:1.6954, ICSH:0.0636, BNDX:0.1344
Covariance matrix (annualized):
[[0.063793, 0.022424, 7.5e-05, 0.002945], [0.022424, 0.186928, -0.000632, -0.004583], [7.5e-05, -0.000632, 1.9e-05, 0.000103], [0.002945, -0.004583, 0.000103, 0.003215]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_FXI=0.0000, w_BTC-USD=0.0085, w_ICSH=0.9915, w_BNDX=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_FXI=0.0000, w_BTC-USD=0.0085, w_ICSH=0.9915, w_BNDX=0.0000
Portfolio annualized return: 7.75%, volatility: 0.47%
Sharpe ratio: (0.0775 - 0.0400) / 0.0047 = 8.0089


4-asset optimization. Max-Sharpe: 1.655. Portfolio: return=27.81%, vol=14.38%. Weights: w_ACWI=0.4780, w_BNB-USD=0.0000, w_DBB=0.4688, w_TLT=0.0532.

Question:
Assets: ACWI, BNB-USD, DBB, TLT
Annualized mean returns: ACWI:0.2634, BNB-USD:-0.2833, DBB:0.3088, TLT:0.1385
Covariance matrix (annualized):
[[0.026399, 0.037461, 0.01375, 0.006546], [0.037461, 0.195288, 0.028177, 0.001604], [0.01375, 0.028177, 0.035028, 0.006923], [0.006546, 0.001604, 0.006923, 0.041124]]
Risk-free rate: 4.00%
Constraints: weights 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=0.4780, w_BNB-USD=0.0000, w_DBB=0.4688, w_TLT=0.0532

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_ACWI=0.4780, w_BNB-USD=0.0000, w_DBB=0.4688, w_TLT=0.0532
Portfolio annualized return: 27.81%, volatility: 14.38%
Sharpe ratio: (0.2781 - 0.0400) / 0.1438 = 1.6551


4-asset optimization. Max-Sharpe: 4.359. Portfolio: return=7.47%, vol=0.80%. Weights: w_MTUM=0.0246, w_LINK-USD=0.0065, w_BIL=0.9689, w_INDS=0.0000.

Question:
Assets: MTUM, LINK-USD, BIL, INDS
Annualized mean returns: MTUM:0.3579, LINK-USD:3.5041, BIL:0.0444, INDS:-0.5244
Covariance matrix (annualized):
[[0.015407, 0.0333, -1.6e-05, 0.004612], [0.0333, 0.784846, 0.000396, 0.025762], [-1.6e-05, 0.000396, 6e-06, -5e-06], [0.004612, 0.025762, -5e-06, 0.030015]]
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_MTUM=0.0246, w_LINK-USD=0.0065, w_BIL=0.9689, w_INDS=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_MTUM=0.0246, w_LINK-USD=0.0065, w_BIL=0.9689, w_INDS=0.0000
Portfolio annualized return: 7.47%, volatility: 0.80%
Sharpe ratio: (0.0747 - 0.0400) / 0.0080 = 4.3587


4-asset optimization. Max-Sharpe: 1.503. Portfolio: return=21.72%, vol=11.79%. Weights: w_ACWI=0.8781, w_BTC-USD=0.1219, w_REZ=0.0000, w_TIP=0.0000.

Question:
Assets: ACWI, BTC-USD, REZ, TIP
Annualized mean returns: ACWI:0.2029, BTC-USD:0.3204, REZ:0.0304, TIP:-0.0417
Covariance matrix (annualized):
[[0.013982, 0.004158, 0.010743, -0.000292], [0.004158, 0.150533, 0.003955, 0.001682], [0.010743, 0.003955, 0.03113, -0.000268], [-0.000292, 0.001682, -0.000268, 0.000676]]
Risk-free rate: 4.00%
Constraints: weights 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=0.8781, w_BTC-USD=0.1219, w_REZ=0.0000, w_TIP=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_ACWI=0.8781, w_BTC-USD=0.1219, w_REZ=0.0000, w_TIP=0.0000
Portfolio annualized return: 21.72%, volatility: 11.79%
Sharpe ratio: (0.2172 - 0.0400) / 0.1179 = 1.5026


4-asset optimization. Max-Sharpe: 4.831. Portfolio: return=52.71%, vol=10.08%. Weights: w_XLV=0.0000, w_DOT-USD=0.0000, w_SCHH=0.5750, w_TLT=0.4250.

Question:
Assets: XLV, DOT-USD, SCHH, TLT
Annualized mean returns: XLV:0.2965, DOT-USD:-1.5944, SCHH:0.6055, TLT:0.4211
Covariance matrix (annualized):
[[0.014695, 0.029569, 0.011324, -0.002061], [0.029569, 0.273652, 0.041882, -0.021295], [0.011324, 0.041882, 0.020371, 0.00021], [-0.002061, -0.021295, 0.00021, 0.018434]]
Risk-free rate: 4.00%
Constraints: weights 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_SCHH=0.5750, w_TLT=0.4250

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLV=0.0000, w_DOT-USD=0.0000, w_SCHH=0.5750, w_TLT=0.4250
Portfolio annualized return: 52.71%, volatility: 10.08%
Sharpe ratio: (0.5271 - 0.0400) / 0.1008 = 4.8310


4-asset optimization. Max-Sharpe: 3.397. Portfolio: return=40.29%, vol=10.68%. Weights: w_XLY=0.6761, w_SOL-USD=0.0000, w_REZ=0.3239, w_TLH=0.0000.

Question:
Assets: XLY, SOL-USD, REZ, TLH
Annualized mean returns: XLY:0.4515, SOL-USD:-0.0971, REZ:0.3013, TLH:0.1578
Covariance matrix (annualized):
[[0.017262, 0.012942, 0.003922, 0.001852], [0.012942, 0.459475, 0.00287, 0.003535], [0.003922, 0.00287, 0.017185, 0.009197], [0.001852, 0.003535, 0.009197, 0.015656]]
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=0.6761, w_SOL-USD=0.0000, w_REZ=0.3239, w_TLH=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLY=0.6761, w_SOL-USD=0.0000, w_REZ=0.3239, w_TLH=0.0000
Portfolio annualized return: 40.29%, volatility: 10.68%
Sharpe ratio: (0.4029 - 0.0400) / 0.1068 = 3.3968


4-asset optimization. Max-Sharpe: -3.164. Portfolio: return=-53.13%, vol=18.06%. Weights: w_XLE=0.2500, w_ETH-USD=0.2500, w_IYR=0.2500, w_BIL=0.2500.

Question:
Assets: XLE, ETH-USD, IYR, BIL
Annualized mean returns: XLE:0.2018, ETH-USD:-2.3246, IYR:-0.0534, BIL:0.0512
Covariance matrix (annualized):
[[0.020637, 0.010295, 0.009557, 0.000101], [0.010295, 0.368759, 0.030275, 0.000172], [0.009557, 0.030275, 0.031238, 0.0001], [0.000101, 0.000172, 0.0001, 7e-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_XLE=0.2500, w_ETH-USD=0.2500, w_IYR=0.2500, w_BIL=0.2500

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLE=0.2500, w_ETH-USD=0.2500, w_IYR=0.2500, w_BIL=0.2500
Portfolio annualized return: -53.13%, volatility: 18.06%
Sharpe ratio: (-0.5313 - 0.0400) / 0.1806 = -3.1638


4-asset optimization. Max-Sharpe: 3.460. Portfolio: return=54.82%, vol=14.69%. Weights: w_VTI=0.4097, w_SOL-USD=0.0246, w_CPER=0.5657, w_HYG=0.0000.

Question:
Assets: VTI, SOL-USD, CPER, HYG
Annualized mean returns: VTI:0.4305, SOL-USD:1.4818, CPER:0.5928, HYG:0.0067
Covariance matrix (annualized):
[[0.02891, 0.069648, 0.005329, 0.01368], [0.069648, 1.154582, 0.007495, 0.034603], [0.005329, 0.007495, 0.037288, 0.003395], [0.01368, 0.034603, 0.003395, 0.010654]]
Risk-free rate: 4.00%
Constraints: weights 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=0.4097, w_SOL-USD=0.0246, w_CPER=0.5657, w_HYG=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VTI=0.4097, w_SOL-USD=0.0246, w_CPER=0.5657, w_HYG=0.0000
Portfolio annualized return: 54.82%, volatility: 14.69%
Sharpe ratio: (0.5482 - 0.0400) / 0.1469 = 3.4605