4-asset optimization. Max-Sharpe: 0.695. Portfolio: return=46.25%, vol=60.82%. Weights: w_XLB=0.0000, w_LINK-USD=1.0000, w_MORT=0.0000, w_SHV=0.0000.

Question:
Assets: XLB, LINK-USD, MORT, SHV
Annualized mean returns: XLB:0.0659, LINK-USD:0.4625, MORT:-0.1219, SHV:0.0384
Covariance matrix (annualized):
[[0.034691, 0.025625, 0.037857, -0.000375], [0.025625, 0.369924, -0.011174, 3.5e-05], [0.037857, -0.011174, 0.079101, -0.000505], [-0.000375, 3.5e-05, -0.000505, 1.5e-05]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_XLB=0.0000, w_LINK-USD=1.0000, w_MORT=0.0000, w_SHV=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLB=0.0000, w_LINK-USD=1.0000, w_MORT=0.0000, w_SHV=0.0000
Portfolio annualized return: 46.25%, volatility: 60.82%
Sharpe ratio: (0.4625 - 0.0400) / 0.6082 = 0.6946


4-asset optimization. Max-Sharpe: 4.158. Portfolio: return=6.95%, vol=0.71%. Weights: w_EEM=0.0000, w_SOL-USD=0.0062, w_IGOV=0.0000, w_CSHI=0.9938.

Question:
Assets: EEM, SOL-USD, IGOV, CSHI
Annualized mean returns: EEM:-0.0827, SOL-USD:1.5594, IGOV:-0.3030, CSHI:0.0602
Covariance matrix (annualized):
[[0.042326, 0.034969, 0.007505, 2.1e-05], [0.034969, 0.383817, 0.008906, 0.000203], [0.007505, 0.008906, 0.007396, -5.7e-05], [2.1e-05, 0.000203, -5.7e-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_EEM=0.0000, w_SOL-USD=0.0062, w_IGOV=0.0000, w_CSHI=0.9938

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EEM=0.0000, w_SOL-USD=0.0062, w_IGOV=0.0000, w_CSHI=0.9938
Portfolio annualized return: 6.95%, volatility: 0.71%
Sharpe ratio: (0.0695 - 0.0400) / 0.0071 = 4.1581


4-asset optimization. Max-Sharpe: 0.577. Portfolio: return=33.83%, vol=51.72%. Weights: w_XLB=0.0000, w_LINK-USD=1.0000, w_BNDX=0.0000, w_UNG=0.0000.

Question:
Assets: XLB, LINK-USD, BNDX, UNG
Annualized mean returns: XLB:-0.3980, LINK-USD:0.3383, BNDX:-0.0733, UNG:-0.1303
Covariance matrix (annualized):
[[0.016012, 0.014879, 0.000922, 0.020311], [0.014879, 0.267477, 0.001491, 0.036163], [0.000922, 0.001491, 0.00191, 0.000843], [0.020311, 0.036163, 0.000843, 0.209837]]
Risk-free rate: 4.00%
Constraints: weights 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=1.0000, w_BNDX=0.0000, w_UNG=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLB=0.0000, w_LINK-USD=1.0000, w_BNDX=0.0000, w_UNG=0.0000
Portfolio annualized return: 33.83%, volatility: 51.72%
Sharpe ratio: (0.3383 - 0.0400) / 0.5172 = 0.5769


4-asset optimization. Max-Sharpe: 3.697. Portfolio: return=5.90%, vol=0.51%. Weights: w_QUAL=0.0055, w_ADA-USD=0.0012, w_PDBC=0.0000, w_ICSH=0.9933.

Question:
Assets: QUAL, ADA-USD, PDBC, ICSH
Annualized mean returns: QUAL:0.4629, ADA-USD:0.8731, PDBC:0.1412, ICSH:0.0557
Covariance matrix (annualized):
[[0.038367, 0.056924, 0.017027, 0.000308], [0.056924, 0.391602, 0.041276, 0.000372], [0.017027, 0.041276, 0.041129, 0.000123], [0.000308, 0.000372, 0.000123, 2e-05]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_QUAL=0.0055, w_ADA-USD=0.0012, w_PDBC=0.0000, w_ICSH=0.9933

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_QUAL=0.0055, w_ADA-USD=0.0012, w_PDBC=0.0000, w_ICSH=0.9933
Portfolio annualized return: 5.90%, volatility: 0.51%
Sharpe ratio: (0.0590 - 0.0400) / 0.0051 = 3.6973


4-asset optimization. Max-Sharpe: 3.881. Portfolio: return=7.08%, vol=0.79%. Weights: w_IVV=0.0052, w_ADA-USD=0.0000, w_CSHI=0.9730, w_ITB=0.0218.

Question:
Assets: IVV, ADA-USD, CSHI, ITB
Annualized mean returns: IVV:0.1931, ADA-USD:-0.1286, CSHI:0.0556, ITB:0.7168
Covariance matrix (annualized):
[[0.011639, 0.007937, 2.8e-05, 0.010294], [0.007937, 0.234647, 0.000943, 0.020329], [2.8e-05, 0.000943, 4.5e-05, -0.00055], [0.010294, 0.020329, -0.00055, 0.085429]]
Risk-free rate: 4.00%
Constraints: weights 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=0.0052, w_ADA-USD=0.0000, w_CSHI=0.9730, w_ITB=0.0218

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_IVV=0.0052, w_ADA-USD=0.0000, w_CSHI=0.9730, w_ITB=0.0218
Portfolio annualized return: 7.08%, volatility: 0.79%
Sharpe ratio: (0.0708 - 0.0400) / 0.0079 = 3.8808


4-asset optimization. Max-Sharpe: 4.594. Portfolio: return=5.59%, vol=0.35%. Weights: w_XLB=0.0000, w_MATIC-USD=0.0000, w_ICSH=1.0000, w_VNQ=0.0000.

Question:
Assets: XLB, MATIC-USD, ICSH, VNQ
Annualized mean returns: XLB:-0.0171, MATIC-USD:-1.0041, ICSH:0.0559, VNQ:0.1032
Covariance matrix (annualized):
[[0.014233, 0.010733, 9.1e-05, 0.010523], [0.010733, 0.28085, 0.001281, 0.017412], [9.1e-05, 0.001281, 1.2e-05, 0.000132], [0.010523, 0.017412, 0.000132, 0.023353]]
Risk-free rate: 4.00%
Constraints: weights 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_MATIC-USD=0.0000, w_ICSH=1.0000, w_VNQ=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLB=0.0000, w_MATIC-USD=0.0000, w_ICSH=1.0000, w_VNQ=0.0000
Portfolio annualized return: 5.59%, volatility: 0.35%
Sharpe ratio: (0.0559 - 0.0400) / 0.0035 = 4.5941


4-asset optimization. Max-Sharpe: 0.737. Portfolio: return=16.20%, vol=16.55%. Weights: w_XLU=0.0000, w_AVAX-USD=0.0000, w_IAU=0.0000, w_IYR=1.0000.

Question:
Assets: XLU, AVAX-USD, IAU, IYR
Annualized mean returns: XLU:-0.3291, AVAX-USD:0.0020, IAU:-0.3475, IYR:0.1620
Covariance matrix (annualized):
[[0.020376, 0.002521, 0.002977, 0.015049], [0.002521, 0.23457, 0.005701, 0.011137], [0.002977, 0.005701, 0.011758, 0.001852], [0.015049, 0.011137, 0.001852, 0.027405]]
Risk-free rate: 4.00%
Constraints: weights 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=0.0000, w_IAU=0.0000, w_IYR=1.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLU=0.0000, w_AVAX-USD=0.0000, w_IAU=0.0000, w_IYR=1.0000
Portfolio annualized return: 16.20%, volatility: 16.55%
Sharpe ratio: (0.1620 - 0.0400) / 0.1655 = 0.7368


4-asset optimization. Max-Sharpe: 7.098. Portfolio: return=5.92%, vol=0.27%. Weights: w_XLI=0.0112, w_BNB-USD=0.0002, w_IYR=0.0010, w_BIL=0.9877.

Question:
Assets: XLI, BNB-USD, IYR, BIL
Annualized mean returns: XLI:0.5144, BNB-USD:-0.0008, IYR:0.6741, BIL:0.0535
Covariance matrix (annualized):
[[0.022645, 0.004465, 0.025135, -9.9e-05], [0.004465, 0.178089, 0.004258, -0.000107], [0.025135, 0.004258, 0.046387, -8.6e-05], [-9.9e-05, -0.000107, -8.6e-05, 6e-06]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_XLI=0.0112, w_BNB-USD=0.0002, w_IYR=0.0010, w_BIL=0.9877

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLI=0.0112, w_BNB-USD=0.0002, w_IYR=0.0010, w_BIL=0.9877
Portfolio annualized return: 5.92%, volatility: 0.27%
Sharpe ratio: (0.0592 - 0.0400) / 0.0027 = 7.0977


4-asset optimization. Max-Sharpe: 9.979. Portfolio: return=9.82%, vol=0.58%. Weights: w_XLV=0.0000, w_AVAX-USD=0.0043, w_ICSH=0.9957, w_MORT=0.0000.

Question:
Assets: XLV, AVAX-USD, ICSH, MORT
Annualized mean returns: XLV:0.2007, AVAX-USD:5.6353, ICSH:0.0743, MORT:0.9722
Covariance matrix (annualized):
[[0.015319, 0.003479, 8e-05, 0.01905], [0.003479, 0.992841, -0.001008, 0.018902], [8e-05, -0.001008, 2.4e-05, 0.000564], [0.01905, 0.018902, 0.000564, 0.086796]]
Risk-free rate: 4.00%
Constraints: weights 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=0.0043, w_ICSH=0.9957, w_MORT=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLV=0.0000, w_AVAX-USD=0.0043, w_ICSH=0.9957, w_MORT=0.0000
Portfolio annualized return: 9.82%, volatility: 0.58%
Sharpe ratio: (0.0982 - 0.0400) / 0.0058 = 9.9786


4-asset optimization. Max-Sharpe: 2.041. Portfolio: return=5.64%, vol=0.80%. Weights: w_QQQ=0.0172, w_XRP-USD=0.0033, w_CSHI=0.9795, w_SCHP=0.0000.

Question:
Assets: QQQ, XRP-USD, CSHI, SCHP
Annualized mean returns: QQQ:0.1929, XRP-USD:0.7608, CSHI:0.0516, SCHP:-0.0138
Covariance matrix (annualized):
[[0.022233, 0.025373, 0.000138, 0.00082], [0.025373, 0.516667, 0.000723, -0.002077], [0.000138, 0.000723, 4.2e-05, -0.000108], [0.00082, -0.002077, -0.000108, 0.001927]]
Risk-free rate: 4.00%
Constraints: weights 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=0.0172, w_XRP-USD=0.0033, w_CSHI=0.9795, w_SCHP=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_QQQ=0.0172, w_XRP-USD=0.0033, w_CSHI=0.9795, w_SCHP=0.0000
Portfolio annualized return: 5.64%, volatility: 0.80%
Sharpe ratio: (0.0564 - 0.0400) / 0.0080 = 2.0410


4-asset optimization. Max-Sharpe: 4.055. Portfolio: return=12.45%, vol=2.08%. Weights: w_QQQ=0.0231, w_BNB-USD=0.0000, w_STIP=0.9034, w_SCHH=0.0735.

Question:
Assets: QQQ, BNB-USD, STIP, SCHH
Annualized mean returns: QQQ:0.4386, BNB-USD:0.6691, STIP:0.0940, SCHH:0.4005
Covariance matrix (annualized):
[[0.048001, 0.058686, -3.5e-05, 0.013218], [0.058686, 0.222736, 5.1e-05, 0.027118], [-3.5e-05, 5.1e-05, 0.000288, 0.000247], [0.013218, 0.027118, 0.000247, 0.018017]]
Risk-free rate: 4.00%
Constraints: weights 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=0.0231, w_BNB-USD=0.0000, w_STIP=0.9034, w_SCHH=0.0735

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_QQQ=0.0231, w_BNB-USD=0.0000, w_STIP=0.9034, w_SCHH=0.0735
Portfolio annualized return: 12.45%, volatility: 2.08%
Sharpe ratio: (0.1245 - 0.0400) / 0.0208 = 4.0548


4-asset optimization. Max-Sharpe: -2.805. Portfolio: return=-31.98%, vol=12.83%. Weights: w_VEA=0.0000, w_ADA-USD=0.0000, w_TLH=1.0000, w_REZ=0.0000.

Question:
Assets: VEA, ADA-USD, TLH, REZ
Annualized mean returns: VEA:-0.2525, ADA-USD:-1.6271, TLH:-0.3198, REZ:-0.4684
Covariance matrix (annualized):
[[0.012761, 0.011028, 0.005541, 0.005801], [0.011028, 0.133305, 0.020273, 0.009212], [0.005541, 0.020273, 0.016462, 0.003628], [0.005801, 0.009212, 0.003628, 0.020302]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_VEA=0.0000, w_ADA-USD=0.0000, w_TLH=1.0000, w_REZ=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VEA=0.0000, w_ADA-USD=0.0000, w_TLH=1.0000, w_REZ=0.0000
Portfolio annualized return: -31.98%, volatility: 12.83%
Sharpe ratio: (-0.3198 - 0.0400) / 0.1283 = -2.8046


4-asset optimization. Max-Sharpe: 6.398. Portfolio: return=5.62%, vol=0.25%. Weights: w_QUAL=0.0010, w_MATIC-USD=0.0000, w_REZ=0.0095, w_SGOV=0.9896.

Question:
Assets: QUAL, MATIC-USD, REZ, SGOV
Annualized mean returns: QUAL:0.2326, MATIC-USD:-2.3419, REZ:0.4798, SGOV:0.0519
Covariance matrix (annualized):
[[0.01548, 0.006493, 0.003674, 2.7e-05], [0.006493, 0.268, 0.012628, -0.000151], [0.003674, 0.012628, 0.015608, 2.2e-05], [2.7e-05, -0.000151, 2.2e-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_QUAL=0.0010, w_MATIC-USD=0.0000, w_REZ=0.0095, w_SGOV=0.9896

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_QUAL=0.0010, w_MATIC-USD=0.0000, w_REZ=0.0095, w_SGOV=0.9896
Portfolio annualized return: 5.62%, volatility: 0.25%
Sharpe ratio: (0.0562 - 0.0400) / 0.0025 = 6.3984


4-asset optimization. Max-Sharpe: 1.743. Portfolio: return=38.36%, vol=19.71%. Weights: w_IWM=1.0000, w_SOL-USD=0.0000, w_CPER=0.0000, w_IGOV=0.0000.

Question:
Assets: IWM, SOL-USD, CPER, IGOV
Annualized mean returns: IWM:0.3836, SOL-USD:-0.8538, CPER:-0.2635, IGOV:-0.1514
Covariance matrix (annualized):
[[0.038851, 0.032554, 0.014613, -0.003484], [0.032554, 0.400079, 0.009944, 0.004329], [0.014613, 0.009944, 0.040064, 0.000221], [-0.003484, 0.004329, 0.000221, 0.010236]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_IWM=1.0000, w_SOL-USD=0.0000, w_CPER=0.0000, w_IGOV=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_IWM=1.0000, w_SOL-USD=0.0000, w_CPER=0.0000, w_IGOV=0.0000
Portfolio annualized return: 38.36%, volatility: 19.71%
Sharpe ratio: (0.3836 - 0.0400) / 0.1971 = 1.7431


4-asset optimization. Max-Sharpe: 4.689. Portfolio: return=50.97%, vol=10.02%. Weights: w_XLP=0.4316, w_LINK-USD=0.0822, w_REZ=0.1093, w_EMB=0.3769.

Question:
Assets: XLP, LINK-USD, REZ, EMB
Annualized mean returns: XLP:0.3351, LINK-USD:2.7725, REZ:0.3619, EMB:0.2588
Covariance matrix (annualized):
[[0.008584, 0.01225, 0.006947, 0.002208], [0.01225, 0.613029, 0.000189, 0.00705], [0.006947, 0.000189, 0.030207, 0.001485], [0.002208, 0.00705, 0.001485, 0.007903]]
Risk-free rate: 4.00%
Constraints: weights 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=0.4316, w_LINK-USD=0.0822, w_REZ=0.1093, w_EMB=0.3769

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLP=0.4316, w_LINK-USD=0.0822, w_REZ=0.1093, w_EMB=0.3769
Portfolio annualized return: 50.97%, volatility: 10.02%
Sharpe ratio: (0.5097 - 0.0400) / 0.1002 = 4.6890


4-asset optimization. Max-Sharpe: 4.981. Portfolio: return=6.89%, vol=0.58%. Weights: w_XLU=0.0000, w_SOL-USD=0.0044, w_ICSH=0.9956, w_DBA=0.0000.

Question:
Assets: XLU, SOL-USD, ICSH, DBA
Annualized mean returns: XLU:-0.3329, SOL-USD:2.2126, ICSH:0.0594, DBA:-0.2178
Covariance matrix (annualized):
[[0.024964, 0.012398, 3.7e-05, 0.007867], [0.012398, 0.598598, -0.000117, 0.003308], [3.7e-05, -0.000117, 2.3e-05, 4e-06], [0.007867, 0.003308, 4e-06, 0.014869]]
Risk-free rate: 4.00%
Constraints: weights 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_SOL-USD=0.0044, w_ICSH=0.9956, w_DBA=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLU=0.0000, w_SOL-USD=0.0044, w_ICSH=0.9956, w_DBA=0.0000
Portfolio annualized return: 6.89%, volatility: 0.58%
Sharpe ratio: (0.0689 - 0.0400) / 0.0058 = 4.9805


4-asset optimization. Max-Sharpe: 7.838. Portfolio: return=7.36%, vol=0.43%. Weights: w_MTUM=0.0056, w_ADA-USD=0.0014, w_ICSH=0.9908, w_MORT=0.0022.

Question:
Assets: MTUM, ADA-USD, ICSH, MORT
Annualized mean returns: MTUM:0.4258, ADA-USD:0.7491, ICSH:0.0702, MORT:0.2348
Covariance matrix (annualized):
[[0.059605, 0.066256, -0.000262, 0.018507], [0.066256, 0.339665, -0.00057, 0.04077], [-0.000262, -0.00057, 1.9e-05, -0.000115], [0.018507, 0.04077, -0.000115, 0.026168]]
Risk-free rate: 4.00%
Constraints: weights 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=0.0056, w_ADA-USD=0.0014, w_ICSH=0.9908, w_MORT=0.0022

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_MTUM=0.0056, w_ADA-USD=0.0014, w_ICSH=0.9908, w_MORT=0.0022
Portfolio annualized return: 7.36%, volatility: 0.43%
Sharpe ratio: (0.0736 - 0.0400) / 0.0043 = 7.8377


4-asset optimization. Max-Sharpe: 3.502. Portfolio: return=9.97%, vol=1.70%. Weights: w_XLRE=0.1128, w_XRP-USD=0.0000, w_CSHI=0.6063, w_STIP=0.2809.

Question:
Assets: XLRE, XRP-USD, CSHI, STIP
Annualized mean returns: XLRE:0.3884, XRP-USD:-0.5910, CSHI:0.0570, STIP:0.0759
Covariance matrix (annualized):
[[0.012851, 0.012453, 0.000137, 0.000579], [0.012453, 0.181848, 0.0001, 0.000834], [0.000137, 0.0001, 0.000111, 0.0], [0.000579, 0.000834, 0.0, 0.000388]]
Risk-free rate: 4.00%
Constraints: weights 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=0.1128, w_XRP-USD=0.0000, w_CSHI=0.6063, w_STIP=0.2809

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLRE=0.1128, w_XRP-USD=0.0000, w_CSHI=0.6063, w_STIP=0.2809
Portfolio annualized return: 9.97%, volatility: 1.70%
Sharpe ratio: (0.0997 - 0.0400) / 0.0170 = 3.5022


4-asset optimization. Max-Sharpe: 6.296. Portfolio: return=5.93%, vol=0.31%. Weights: w_XLU=0.0000, w_BNB-USD=0.0038, w_IAU=0.0000, w_SGOV=0.9962.

Question:
Assets: XLU, BNB-USD, IAU, SGOV
Annualized mean returns: XLU:-0.1256, BNB-USD:1.4968, IAU:-0.0852, SGOV:0.0538
Covariance matrix (annualized):
[[0.032014, 0.011915, 0.007729, 4.8e-05], [0.011915, 0.153325, 0.0051, 0.000128], [0.007729, 0.0051, 0.008548, 8.5e-05], [4.8e-05, 0.000128, 8.5e-05, 6e-06]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_XLU=0.0000, w_BNB-USD=0.0038, w_IAU=0.0000, w_SGOV=0.9962

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLU=0.0000, w_BNB-USD=0.0038, w_IAU=0.0000, w_SGOV=0.9962
Portfolio annualized return: 5.93%, volatility: 0.31%
Sharpe ratio: (0.0593 - 0.0400) / 0.0031 = 6.2960


4-asset optimization. Max-Sharpe: -0.102. Portfolio: return=3.16%, vol=8.29%. Weights: w_XLP=1.0000, w_AVAX-USD=0.0000, w_INDS=0.0000, w_LQD=0.0000.

Question:
Assets: XLP, AVAX-USD, INDS, LQD
Annualized mean returns: XLP:0.0316, AVAX-USD:-0.8461, INDS:-0.4238, LQD:-0.1198
Covariance matrix (annualized):
[[0.006865, 0.022901, 0.006524, 0.002358], [0.022901, 0.906873, 0.025855, -0.005048], [0.006524, 0.025855, 0.031153, 0.00826], [0.002358, -0.005048, 0.00826, 0.004741]]
Risk-free rate: 4.00%
Constraints: weights 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=1.0000, w_AVAX-USD=0.0000, w_INDS=0.0000, w_LQD=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLP=1.0000, w_AVAX-USD=0.0000, w_INDS=0.0000, w_LQD=0.0000
Portfolio annualized return: 3.16%, volatility: 8.29%
Sharpe ratio: (0.0316 - 0.0400) / 0.0829 = -0.1016


4-asset optimization. Max-Sharpe: 2.493. Portfolio: return=25.55%, vol=8.65%. Weights: w_IVV=0.4107, w_BNB-USD=0.0919, w_EMB=0.4975, w_MORT=0.0000.

Question:
Assets: IVV, BNB-USD, EMB, MORT
Annualized mean returns: IVV:0.3138, BNB-USD:0.6832, EMB:0.1284, MORT:0.2315
Covariance matrix (annualized):
[[0.014605, 0.020289, 0.003284, 0.008668], [0.020289, 0.139327, 0.00236, 0.018911], [0.003284, 0.00236, 0.003017, 0.004015], [0.008668, 0.018911, 0.004015, 0.020854]]
Risk-free rate: 4.00%
Constraints: weights 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=0.4107, w_BNB-USD=0.0919, w_EMB=0.4975, w_MORT=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_IVV=0.4107, w_BNB-USD=0.0919, w_EMB=0.4975, w_MORT=0.0000
Portfolio annualized return: 25.55%, volatility: 8.65%
Sharpe ratio: (0.2555 - 0.0400) / 0.0865 = 2.4928


4-asset optimization. Max-Sharpe: 3.942. Portfolio: return=6.54%, vol=0.64%. Weights: w_XLI=0.0000, w_SOL-USD=0.0065, w_EMB=0.0000, w_CSHI=0.9935.

Question:
Assets: XLI, SOL-USD, EMB, CSHI
Annualized mean returns: XLI:0.2391, SOL-USD:1.7830, EMB:0.0012, CSHI:0.0542
Covariance matrix (annualized):
[[0.020613, 0.048306, 0.001504, 0.000265], [0.048306, 0.425468, 0.006704, 0.0001], [0.001504, 0.006704, 0.004169, 1.8e-05], [0.000265, 0.0001, 1.8e-05, 2.3e-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_XLI=0.0000, w_SOL-USD=0.0065, w_EMB=0.0000, w_CSHI=0.9935

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLI=0.0000, w_SOL-USD=0.0065, w_EMB=0.0000, w_CSHI=0.9935
Portfolio annualized return: 6.54%, volatility: 0.64%
Sharpe ratio: (0.0654 - 0.0400) / 0.0064 = 3.9422


4-asset optimization. Max-Sharpe: 3.492. Portfolio: return=90.70%, vol=24.83%. Weights: w_FXI=0.0000, w_LINK-USD=0.1384, w_XHB=0.8616, w_PDBC=0.0000.

Question:
Assets: FXI, LINK-USD, XHB, PDBC
Annualized mean returns: FXI:0.3839, LINK-USD:1.0442, XHB:0.8850, PDBC:0.0525
Covariance matrix (annualized):
[[0.108426, 0.046849, 0.03979, -0.000527], [0.046849, 0.273308, 0.038945, 0.015519], [0.03979, 0.038945, 0.06346, 0.004447], [-0.000527, 0.015519, 0.004447, 0.037635]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_FXI=0.0000, w_LINK-USD=0.1384, w_XHB=0.8616, w_PDBC=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_FXI=0.0000, w_LINK-USD=0.1384, w_XHB=0.8616, w_PDBC=0.0000
Portfolio annualized return: 90.70%, volatility: 24.83%
Sharpe ratio: (0.9070 - 0.0400) / 0.2483 = 3.4924


4-asset optimization. Max-Sharpe: 3.115. Portfolio: return=6.30%, vol=0.74%. Weights: w_XLP=0.0199, w_DOT-USD=0.0011, w_SCHH=0.0180, w_CSHI=0.9611.

Question:
Assets: XLP, DOT-USD, SCHH, CSHI
Annualized mean returns: XLP:0.1523, DOT-USD:0.6999, SCHH:0.3928, CSHI:0.0543
Covariance matrix (annualized):
[[0.014375, 0.011273, 0.008245, -0.000187], [0.011273, 0.903531, 0.037173, -0.000306], [0.008245, 0.037173, 0.034912, 6e-06], [-0.000187, -0.000306, 6e-06, 3.9e-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=0.0199, w_DOT-USD=0.0011, w_SCHH=0.0180, w_CSHI=0.9611

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLP=0.0199, w_DOT-USD=0.0011, w_SCHH=0.0180, w_CSHI=0.9611
Portfolio annualized return: 6.30%, volatility: 0.74%
Sharpe ratio: (0.0630 - 0.0400) / 0.0074 = 3.1150


4-asset optimization. Max-Sharpe: 8.238. Portfolio: return=5.74%, vol=0.21%. Weights: w_FXI=0.0031, w_ETH-USD=0.0013, w_SGOV=0.9956, w_JNK=0.0000.

Question:
Assets: FXI, ETH-USD, SGOV, JNK
Annualized mean returns: FXI:0.8251, ETH-USD:1.3933, SGOV:0.0533, JNK:0.0427
Covariance matrix (annualized):
[[0.075817, 0.034289, -7.9e-05, 0.003037], [0.034289, 0.388157, -0.000253, 0.005756], [-7.9e-05, -0.000253, 4e-06, 2.1e-05], [0.003037, 0.005756, 2.1e-05, 0.002122]]
Risk-free rate: 4.00%
Constraints: weights 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=0.0031, w_ETH-USD=0.0013, w_SGOV=0.9956, w_JNK=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_FXI=0.0031, w_ETH-USD=0.0013, w_SGOV=0.9956, w_JNK=0.0000
Portfolio annualized return: 5.74%, volatility: 0.21%
Sharpe ratio: (0.0574 - 0.0400) / 0.0021 = 8.2384


4-asset optimization. Max-Sharpe: 7.150. Portfolio: return=67.01%, vol=8.81%. Weights: w_XLV=0.8068, w_ETH-USD=0.0332, w_VNQI=0.0955, w_WEAT=0.0645.

Question:
Assets: XLV, ETH-USD, VNQI, WEAT
Annualized mean returns: XLV:0.7000, ETH-USD:1.4744, VNQI:0.5401, WEAT:0.0760
Covariance matrix (annualized):
[[0.009719, 0.006561, 0.004137, -0.00495], [0.006561, 0.297476, 0.022222, 0.006237], [0.004137, 0.022222, 0.023218, -0.001996], [-0.00495, 0.006237, -0.001996, 0.068518]]
Risk-free rate: 4.00%
Constraints: weights 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=0.8068, w_ETH-USD=0.0332, w_VNQI=0.0955, w_WEAT=0.0645

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLV=0.8068, w_ETH-USD=0.0332, w_VNQI=0.0955, w_WEAT=0.0645
Portfolio annualized return: 67.01%, volatility: 8.81%
Sharpe ratio: (0.6701 - 0.0400) / 0.0881 = 7.1497


4-asset optimization. Max-Sharpe: 4.531. Portfolio: return=5.30%, vol=0.29%. Weights: w_EEM=0.0000, w_DOT-USD=0.0000, w_IEF=0.0031, w_BIL=0.9969.

Question:
Assets: EEM, DOT-USD, IEF, BIL
Annualized mean returns: EEM:0.2174, DOT-USD:-0.2898, IEF:0.1006, BIL:0.0528
Covariance matrix (annualized):
[[0.02385, 0.036581, 0.003511, 0.000128], [0.036581, 0.818591, 0.001613, 0.000415], [0.003511, 0.001613, 0.006082, 1.9e-05], [0.000128, 0.000415, 1.9e-05, 8e-06]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_EEM=0.0000, w_DOT-USD=0.0000, w_IEF=0.0031, w_BIL=0.9969

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EEM=0.0000, w_DOT-USD=0.0000, w_IEF=0.0031, w_BIL=0.9969
Portfolio annualized return: 5.30%, volatility: 0.29%
Sharpe ratio: (0.0530 - 0.0400) / 0.0029 = 4.5309


4-asset optimization. Max-Sharpe: 4.349. Portfolio: return=10.66%, vol=1.53%. Weights: w_QUAL=0.0000, w_MATIC-USD=0.0000, w_XHB=0.0080, w_SHY=0.9919.

Question:
Assets: QUAL, MATIC-USD, XHB, SHY
Annualized mean returns: QUAL:0.1883, MATIC-USD:-2.2312, XHB:0.6408, SHY:0.1023
Covariance matrix (annualized):
[[0.013926, 0.007936, 0.014134, 0.000412], [0.007936, 0.27452, 0.024268, 0.000886], [0.014134, 0.024268, 0.08287, 0.001461], [0.000412, 0.000886, 0.001461, 0.000209]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_QUAL=0.0000, w_MATIC-USD=0.0000, w_XHB=0.0080, w_SHY=0.9919

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_QUAL=0.0000, w_MATIC-USD=0.0000, w_XHB=0.0080, w_SHY=0.9919
Portfolio annualized return: 10.66%, volatility: 1.53%
Sharpe ratio: (0.1066 - 0.0400) / 0.0153 = 4.3493


4-asset optimization. Max-Sharpe: 5.668. Portfolio: return=6.13%, vol=0.38%. Weights: w_XLU=0.0000, w_SOL-USD=0.0000, w_ICSH=1.0000, w_MORT=0.0000.

Question:
Assets: XLU, SOL-USD, ICSH, MORT
Annualized mean returns: XLU:-0.1741, SOL-USD:0.6522, ICSH:0.0613, MORT:0.0549
Covariance matrix (annualized):
[[0.019245, 0.014822, 5.4e-05, 0.010607], [0.014822, 0.539471, 0.001012, -2.6e-05], [5.4e-05, 0.001012, 1.4e-05, 8.9e-05], [0.010607, -2.6e-05, 8.9e-05, 0.026419]]
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_XLU=0.0000, w_SOL-USD=0.0000, w_ICSH=1.0000, w_MORT=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLU=0.0000, w_SOL-USD=0.0000, w_ICSH=1.0000, w_MORT=0.0000
Portfolio annualized return: 6.13%, volatility: 0.38%
Sharpe ratio: (0.0613 - 0.0400) / 0.0038 = 5.6684


4-asset optimization. Max-Sharpe: 4.417. Portfolio: return=42.73%, vol=8.77%. Weights: w_XLI=0.6328, w_BNB-USD=0.0000, w_WEAT=0.2083, w_HYG=0.1589.

Question:
Assets: XLI, BNB-USD, WEAT, HYG
Annualized mean returns: XLI:0.5169, BNB-USD:0.0395, WEAT:0.4057, HYG:0.0988
Covariance matrix (annualized):
[[0.015676, 0.018596, -0.003747, 0.002061], [0.018596, 0.12499, -0.015343, 0.004447], [-0.003747, -0.015343, 0.047413, -0.001553], [0.002061, 0.004447, -0.001553, 0.001176]]
Risk-free rate: 4.00%
Constraints: weights 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=0.6328, w_BNB-USD=0.0000, w_WEAT=0.2083, w_HYG=0.1589

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLI=0.6328, w_BNB-USD=0.0000, w_WEAT=0.2083, w_HYG=0.1589
Portfolio annualized return: 42.73%, volatility: 8.77%
Sharpe ratio: (0.4273 - 0.0400) / 0.0877 = 4.4173


4-asset optimization. Max-Sharpe: 4.801. Portfolio: return=74.99%, vol=14.79%. Weights: w_MTUM=0.4425, w_DOT-USD=0.0378, w_REZ=0.0000, w_BNO=0.5197.

Question:
Assets: MTUM, DOT-USD, REZ, BNO
Annualized mean returns: MTUM:0.6631, DOT-USD:1.2634, REZ:-0.0754, BNO:0.7865
Covariance matrix (annualized):
[[0.040144, 0.027813, 0.005529, 0.000723], [0.027813, 0.426503, 0.012781, 0.017821], [0.005529, 0.012781, 0.026709, -0.001431], [0.000723, 0.017821, -0.001431, 0.042327]]
Risk-free rate: 4.00%
Constraints: weights 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=0.4425, w_DOT-USD=0.0378, w_REZ=0.0000, w_BNO=0.5197

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_MTUM=0.4425, w_DOT-USD=0.0378, w_REZ=0.0000, w_BNO=0.5197
Portfolio annualized return: 74.99%, volatility: 14.79%
Sharpe ratio: (0.7499 - 0.0400) / 0.1479 = 4.8008


4-asset optimization. Max-Sharpe: 1.441. Portfolio: return=13.33%, vol=6.48%. Weights: w_XLB=0.0000, w_XRP-USD=0.0806, w_HAUZ=0.0000, w_ICSH=0.9194.

Question:
Assets: XLB, XRP-USD, HAUZ, ICSH
Annualized mean returns: XLB:-0.4537, XRP-USD:1.2057, HAUZ:-0.6630, ICSH:0.0394
Covariance matrix (annualized):
[[0.044115, 0.055294, 0.020192, -0.000522], [0.055294, 0.659783, 0.017246, -0.000829], [0.020192, 0.017246, 0.022574, -0.000171], [-0.000522, -0.000829, -0.000171, 4.2e-05]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_XLB=0.0000, w_XRP-USD=0.0806, w_HAUZ=0.0000, w_ICSH=0.9194

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLB=0.0000, w_XRP-USD=0.0806, w_HAUZ=0.0000, w_ICSH=0.9194
Portfolio annualized return: 13.33%, volatility: 6.48%
Sharpe ratio: (0.1333 - 0.0400) / 0.0648 = 1.4411


4-asset optimization. Max-Sharpe: -0.169. Portfolio: return=2.97%, vol=6.06%. Weights: w_FXI=0.0000, w_AVAX-USD=0.0000, w_JNK=1.0000, w_IAU=0.0000.

Question:
Assets: FXI, AVAX-USD, JNK, IAU
Annualized mean returns: FXI:-0.4225, AVAX-USD:-1.0763, JNK:0.0297, IAU:-0.1405
Covariance matrix (annualized):
[[0.086443, 0.016208, 0.006603, 7.8e-05], [0.016208, 0.263606, 0.011583, 0.009916], [0.006603, 0.011583, 0.003671, 0.00161], [7.8e-05, 0.009916, 0.00161, 0.017585]]
Risk-free rate: 4.00%
Constraints: weights 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_AVAX-USD=0.0000, w_JNK=1.0000, w_IAU=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_FXI=0.0000, w_AVAX-USD=0.0000, w_JNK=1.0000, w_IAU=0.0000
Portfolio annualized return: 2.97%, volatility: 6.06%
Sharpe ratio: (0.0297 - 0.0400) / 0.0606 = -0.1694


4-asset optimization. Max-Sharpe: -0.082. Portfolio: return=-2.48%, vol=79.46%. Weights: w_IWM=0.0000, w_AVAX-USD=1.0000, w_SCHH=0.0000, w_IGOV=0.0000.

Question:
Assets: IWM, AVAX-USD, SCHH, IGOV
Annualized mean returns: IWM:-0.0602, AVAX-USD:-0.0248, SCHH:-0.3984, IGOV:-0.2954
Covariance matrix (annualized):
[[0.051595, 0.054787, 0.029609, 0.011282], [0.054787, 0.631407, 0.00743, 0.002715], [0.029609, 0.00743, 0.031179, 0.007931], [0.011282, 0.002715, 0.007931, 0.008145]]
Risk-free rate: 4.00%
Constraints: weights 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=1.0000, w_SCHH=0.0000, w_IGOV=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_IWM=0.0000, w_AVAX-USD=1.0000, w_SCHH=0.0000, w_IGOV=0.0000
Portfolio annualized return: -2.48%, volatility: 79.46%
Sharpe ratio: (-0.0248 - 0.0400) / 0.7946 = -0.0816


4-asset optimization. Max-Sharpe: 7.105. Portfolio: return=6.44%, vol=0.34%. Weights: w_QQQ=0.0000, w_BTC-USD=0.0051, w_STIP=0.0000, w_BIL=0.9949.

Question:
Assets: QQQ, BTC-USD, STIP, BIL
Annualized mean returns: QQQ:0.4174, BTC-USD:2.6869, STIP:0.0327, BIL:0.0510
Covariance matrix (annualized):
[[0.027853, 0.004713, -0.000224, 0.000219], [0.004713, 0.291566, -0.00113, -0.000208], [-0.000224, -0.00113, 0.000507, 1.4e-05], [0.000219, -0.000208, 1.4e-05, 6e-06]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_QQQ=0.0000, w_BTC-USD=0.0051, w_STIP=0.0000, w_BIL=0.9949

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_QQQ=0.0000, w_BTC-USD=0.0051, w_STIP=0.0000, w_BIL=0.9949
Portfolio annualized return: 6.44%, volatility: 0.34%
Sharpe ratio: (0.0644 - 0.0400) / 0.0034 = 7.1048


4-asset optimization. Max-Sharpe: 4.709. Portfolio: return=6.18%, vol=0.46%. Weights: w_XLV=0.0203, w_ETH-USD=0.0016, w_WEAT=0.0072, w_ICSH=0.9709.

Question:
Assets: XLV, ETH-USD, WEAT, ICSH
Annualized mean returns: XLV:0.2554, ETH-USD:0.6031, WEAT:0.3437, ICSH:0.0548
Covariance matrix (annualized):
[[0.009884, 0.024871, -0.002713, -1e-05], [0.024871, 0.397352, -0.03662, -0.000347], [-0.002713, -0.03662, 0.047923, 7.2e-05], [-1e-05, -0.000347, 7.2e-05, 1.5e-05]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_XLV=0.0203, w_ETH-USD=0.0016, w_WEAT=0.0072, w_ICSH=0.9709

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLV=0.0203, w_ETH-USD=0.0016, w_WEAT=0.0072, w_ICSH=0.9709
Portfolio annualized return: 6.18%, volatility: 0.46%
Sharpe ratio: (0.0618 - 0.0400) / 0.0046 = 4.7094


4-asset optimization. Max-Sharpe: 7.212. Portfolio: return=8.78%, vol=0.66%. Weights: w_EEM=0.0000, w_LINK-USD=0.0000, w_XHB=0.0124, w_ICSH=0.9876.

Question:
Assets: EEM, LINK-USD, XHB, ICSH
Annualized mean returns: EEM:0.3658, LINK-USD:-0.4359, XHB:1.2550, ICSH:0.0731
Covariance matrix (annualized):
[[0.019015, 0.023681, 0.019557, 0.000308], [0.023681, 0.650897, 0.063925, -0.000236], [0.019557, 0.063925, 0.051262, 0.000484], [0.000308, -0.000236, 0.000484, 2.5e-05]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_EEM=0.0000, w_LINK-USD=0.0000, w_XHB=0.0124, w_ICSH=0.9876

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EEM=0.0000, w_LINK-USD=0.0000, w_XHB=0.0124, w_ICSH=0.9876
Portfolio annualized return: 8.78%, volatility: 0.66%
Sharpe ratio: (0.0878 - 0.0400) / 0.0066 = 7.2120


4-asset optimization. Max-Sharpe: 3.750. Portfolio: return=5.02%, vol=0.27%. Weights: w_ACWI=0.0000, w_ADA-USD=0.0000, w_BIL=1.0000, w_SCHP=0.0000.

Question:
Assets: ACWI, ADA-USD, BIL, SCHP
Annualized mean returns: ACWI:-0.1633, ADA-USD:-1.0402, BIL:0.0502, SCHP:-0.1240
Covariance matrix (annualized):
[[0.014309, 0.013108, -0.0001, 0.003362], [0.013108, 0.105951, -0.00021, 0.00376], [-0.0001, -0.00021, 7e-06, -8e-06], [0.003362, 0.00376, -8e-06, 0.003647]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

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

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_ACWI=0.0000, w_ADA-USD=0.0000, w_BIL=1.0000, w_SCHP=0.0000
Portfolio annualized return: 5.02%, volatility: 0.27%
Sharpe ratio: (0.0502 - 0.0400) / 0.0027 = 3.7500


4-asset optimization. Max-Sharpe: 2.428. Portfolio: return=19.38%, vol=6.33%. Weights: w_XLP=0.1208, w_ADA-USD=0.0000, w_LQD=0.8791, w_BNO=0.0001.

Question:
Assets: XLP, ADA-USD, LQD, BNO
Annualized mean returns: XLP:0.1498, ADA-USD:-0.6056, LQD:0.1998, BNO:-0.0577
Covariance matrix (annualized):
[[0.01049, -0.0048, 0.001817, 0.001369], [-0.0048, 0.197472, 0.00934, -0.004398], [0.001817, 0.00934, 0.004495, -0.003094], [0.001369, -0.004398, -0.003094, 0.047996]]
Risk-free rate: 4.00%
Constraints: weights 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=0.1208, w_ADA-USD=0.0000, w_LQD=0.8791, w_BNO=0.0001

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLP=0.1208, w_ADA-USD=0.0000, w_LQD=0.8791, w_BNO=0.0001
Portfolio annualized return: 19.38%, volatility: 6.33%
Sharpe ratio: (0.1938 - 0.0400) / 0.0633 = 2.4277


4-asset optimization. Max-Sharpe: 0.072. Portfolio: return=5.94%, vol=26.99%. Weights: w_VEA=0.0000, w_ETH-USD=0.0000, w_ITB=1.0000, w_CORN=0.0000.

Question:
Assets: VEA, ETH-USD, ITB, CORN
Annualized mean returns: VEA:-0.3303, ETH-USD:-0.3024, ITB:0.0594, CORN:-0.4830
Covariance matrix (annualized):
[[0.020197, 0.021951, 0.023428, 0.002904], [0.021951, 0.261094, 0.025019, 0.002379], [0.023428, 0.025019, 0.072854, -0.003992], [0.002904, 0.002379, -0.003992, 0.018094]]
Risk-free rate: 4.00%
Constraints: weights 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_ETH-USD=0.0000, w_ITB=1.0000, w_CORN=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VEA=0.0000, w_ETH-USD=0.0000, w_ITB=1.0000, w_CORN=0.0000
Portfolio annualized return: 5.94%, volatility: 26.99%
Sharpe ratio: (0.0594 - 0.0400) / 0.2699 = 0.0720


4-asset optimization. Max-Sharpe: 6.461. Portfolio: return=5.72%, vol=0.27%. Weights: w_XLF=0.0000, w_ADA-USD=0.0000, w_PPLT=0.0070, w_SGOV=0.9930.

Question:
Assets: XLF, ADA-USD, PPLT, SGOV
Annualized mean returns: XLF:0.0749, ADA-USD:-1.1904, PPLT:0.9136, SGOV:0.0512
Covariance matrix (annualized):
[[0.013866, 0.020427, 0.006968, -1e-06], [0.020427, 0.346293, 0.007864, 0.000238], [0.006968, 0.007864, 0.062345, -7.3e-05], [-1e-06, 0.000238, -7.3e-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_XLF=0.0000, w_ADA-USD=0.0000, w_PPLT=0.0070, w_SGOV=0.9930

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLF=0.0000, w_ADA-USD=0.0000, w_PPLT=0.0070, w_SGOV=0.9930
Portfolio annualized return: 5.72%, volatility: 0.27%
Sharpe ratio: (0.0572 - 0.0400) / 0.0027 = 6.4614


4-asset optimization. Max-Sharpe: 0.808. Portfolio: return=17.67%, vol=16.92%. Weights: w_VLUE=0.2500, w_SOL-USD=0.2500, w_ICSH=0.2500, w_DBC=0.2500.

Question:
Assets: VLUE, SOL-USD, ICSH, DBC
Annualized mean returns: VLUE:0.4688, SOL-USD:-0.2292, ICSH:0.0548, DBC:0.4122
Covariance matrix (annualized):
[[0.015847, 0.034022, 4.5e-05, 0.005496], [0.034022, 0.286596, 0.000217, 0.024575], [4.5e-05, 0.000217, 1.5e-05, -7.9e-05], [0.005496, 0.024575, -7.9e-05, 0.026998]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_VLUE=0.2500, w_SOL-USD=0.2500, w_ICSH=0.2500, w_DBC=0.2500

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VLUE=0.2500, w_SOL-USD=0.2500, w_ICSH=0.2500, w_DBC=0.2500
Portfolio annualized return: 17.67%, volatility: 16.92%
Sharpe ratio: (0.1767 - 0.0400) / 0.1692 = 0.8078


4-asset optimization. Max-Sharpe: 5.874. Portfolio: return=93.18%, vol=15.18%. Weights: w_IWM=0.0630, w_BTC-USD=0.1613, w_IAU=0.7756, w_HYG=0.0000.

Question:
Assets: IWM, BTC-USD, IAU, HYG
Annualized mean returns: IWM:0.5919, BTC-USD:2.8614, IAU:0.5580, HYG:0.0885
Covariance matrix (annualized):
[[0.041574, 0.028937, 0.008991, 0.006694], [0.028937, 0.34763, 0.019349, 0.00116], [0.008991, 0.019349, 0.012505, 0.002767], [0.006694, 0.00116, 0.002767, 0.00233]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: bull

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

Answer: w_IWM=0.0630, w_BTC-USD=0.1613, w_IAU=0.7756, w_HYG=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_IWM=0.0630, w_BTC-USD=0.1613, w_IAU=0.7756, w_HYG=0.0000
Portfolio annualized return: 93.18%, volatility: 15.18%
Sharpe ratio: (0.9318 - 0.0400) / 0.1518 = 5.8741


4-asset optimization. Max-Sharpe: 3.239. Portfolio: return=5.11%, vol=0.34%. Weights: w_XLY=0.0024, w_DOT-USD=0.0000, w_IGOV=0.0269, w_SGOV=0.9707.

Question:
Assets: XLY, DOT-USD, IGOV, SGOV
Annualized mean returns: XLY:0.0112, DOT-USD:-0.8521, IGOV:0.2391, SGOV:0.0460
Covariance matrix (annualized):
[[0.042976, 0.021615, -0.005819, 2.2e-05], [0.021615, 0.342442, 0.010082, 4.3e-05], [-0.005819, 0.010082, 0.008919, -1.5e-05], [2.2e-05, 4.3e-05, -1.5e-05, 7e-06]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_XLY=0.0024, w_DOT-USD=0.0000, w_IGOV=0.0269, w_SGOV=0.9707

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLY=0.0024, w_DOT-USD=0.0000, w_IGOV=0.0269, w_SGOV=0.9707
Portfolio annualized return: 5.11%, volatility: 0.34%
Sharpe ratio: (0.0511 - 0.0400) / 0.0034 = 3.2390


4-asset optimization. Max-Sharpe: 5.833. Portfolio: return=12.01%, vol=1.37%. Weights: w_MTUM=0.0770, w_LINK-USD=0.0000, w_VNQ=0.0000, w_CSHI=0.9230.

Question:
Assets: MTUM, LINK-USD, VNQ, CSHI
Annualized mean returns: MTUM:0.8857, LINK-USD:1.1278, VNQ:0.0642, CSHI:0.0563
Covariance matrix (annualized):
[[0.02559, 0.04311, 0.007355, 2.5e-05], [0.04311, 0.715325, 0.03786, 2.6e-05], [0.007355, 0.03786, 0.039918, -0.00011], [2.5e-05, 2.6e-05, -0.00011, 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_MTUM=0.0770, w_LINK-USD=0.0000, w_VNQ=0.0000, w_CSHI=0.9230

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_MTUM=0.0770, w_LINK-USD=0.0000, w_VNQ=0.0000, w_CSHI=0.9230
Portfolio annualized return: 12.01%, volatility: 1.37%
Sharpe ratio: (0.1201 - 0.0400) / 0.0137 = 5.8326


4-asset optimization. Max-Sharpe: 0.501. Portfolio: return=7.64%, vol=7.27%. Weights: w_USMV=1.0000, w_SOL-USD=0.0000, w_CPER=0.0000, w_TLH=0.0000.

Question:
Assets: USMV, SOL-USD, CPER, TLH
Annualized mean returns: USMV:0.0764, SOL-USD:-0.3928, CPER:0.0265, TLH:-0.1907
Covariance matrix (annualized):
[[0.005288, 0.010537, 0.004686, 0.002911], [0.010537, 0.508936, 0.022075, 0.035362], [0.004686, 0.022075, 0.038561, 0.007408], [0.002911, 0.035362, 0.007408, 0.017881]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_USMV=1.0000, w_SOL-USD=0.0000, w_CPER=0.0000, w_TLH=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_USMV=1.0000, w_SOL-USD=0.0000, w_CPER=0.0000, w_TLH=0.0000
Portfolio annualized return: 7.64%, volatility: 7.27%
Sharpe ratio: (0.0764 - 0.0400) / 0.0727 = 0.5012


4-asset optimization. Max-Sharpe: 0.925. Portfolio: return=87.78%, vol=90.62%. Weights: w_VEA=0.0000, w_DOT-USD=1.0000, w_LQD=0.0000, w_ITB=0.0000.

Question:
Assets: VEA, DOT-USD, LQD, ITB
Annualized mean returns: VEA:-0.2641, DOT-USD:0.8778, LQD:-0.0592, ITB:-0.9397
Covariance matrix (annualized):
[[0.0123, 0.030737, 0.005573, 0.015339], [0.030737, 0.821182, 0.011873, 0.000474], [0.005573, 0.011873, 0.006031, 0.01194], [0.015339, 0.000474, 0.01194, 0.064287]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: bull

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

Answer: w_VEA=0.0000, w_DOT-USD=1.0000, w_LQD=0.0000, w_ITB=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VEA=0.0000, w_DOT-USD=1.0000, w_LQD=0.0000, w_ITB=0.0000
Portfolio annualized return: 87.78%, volatility: 90.62%
Sharpe ratio: (0.8778 - 0.0400) / 0.9062 = 0.9245


4-asset optimization. Max-Sharpe: 5.739. Portfolio: return=15.26%, vol=1.96%. Weights: w_USMV=0.1056, w_BNB-USD=0.0207, w_SOYB=0.0000, w_CSHI=0.8737.

Question:
Assets: USMV, BNB-USD, SOYB, CSHI
Annualized mean returns: USMV:0.2311, BNB-USD:3.9365, SOYB:-0.0735, CSHI:0.0534
Covariance matrix (annualized):
[[0.004704, 0.008384, -0.000722, -2e-05], [0.008384, 0.576441, 0.031847, 0.000576], [-0.000722, 0.031847, 0.018336, 4e-05], [-2e-05, 0.000576, 4e-05, 4.1e-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_USMV=0.1056, w_BNB-USD=0.0207, w_SOYB=0.0000, w_CSHI=0.8737

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_USMV=0.1056, w_BNB-USD=0.0207, w_SOYB=0.0000, w_CSHI=0.8737
Portfolio annualized return: 15.26%, volatility: 1.96%
Sharpe ratio: (0.1526 - 0.0400) / 0.0196 = 5.7386


4-asset optimization. Max-Sharpe: 1.782. Portfolio: return=37.00%, vol=18.52%. Weights: w_QQQ=1.0000, w_SOL-USD=0.0000, w_CPER=0.0000, w_SCHP=0.0000.

Question:
Assets: QQQ, SOL-USD, CPER, SCHP
Annualized mean returns: QQQ:0.3700, SOL-USD:0.3149, CPER:-0.3452, SCHP:-0.0800
Covariance matrix (annualized):
[[0.034284, 0.053376, 0.001525, 0.002424], [0.053376, 0.518609, -0.029157, 0.00603], [0.001525, -0.029157, 0.04015, 0.003651], [0.002424, 0.00603, 0.003651, 0.001683]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_QQQ=1.0000, w_SOL-USD=0.0000, w_CPER=0.0000, w_SCHP=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_QQQ=1.0000, w_SOL-USD=0.0000, w_CPER=0.0000, w_SCHP=0.0000
Portfolio annualized return: 37.00%, volatility: 18.52%
Sharpe ratio: (0.3700 - 0.0400) / 0.1852 = 1.7822


4-asset optimization. Max-Sharpe: 1.256. Portfolio: return=20.31%, vol=12.99%. Weights: w_XLF=0.7697, w_DOT-USD=0.0000, w_XHB=0.2303, w_STIP=0.0000.

Question:
Assets: XLF, DOT-USD, XHB, STIP
Annualized mean returns: XLF:0.1967, DOT-USD:-0.7490, XHB:0.2248, STIP:0.0205
Covariance matrix (annualized):
[[0.017771, 0.017579, 0.010959, -0.000308], [0.017579, 0.212553, 0.034945, 0.001472], [0.010959, 0.034945, 0.046332, 0.001398], [-0.000308, 0.001472, 0.001398, 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_XLF=0.7697, w_DOT-USD=0.0000, w_XHB=0.2303, w_STIP=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLF=0.7697, w_DOT-USD=0.0000, w_XHB=0.2303, w_STIP=0.0000
Portfolio annualized return: 20.31%, volatility: 12.99%
Sharpe ratio: (0.2031 - 0.0400) / 0.1299 = 1.2560


4-asset optimization. Max-Sharpe: 1.558. Portfolio: return=118.16%, vol=73.28%. Weights: w_EFA=0.0000, w_XRP-USD=1.0000, w_PPLT=0.0000, w_MORT=0.0000.

Question:
Assets: EFA, XRP-USD, PPLT, MORT
Annualized mean returns: EFA:-0.0173, XRP-USD:1.1816, PPLT:-0.0823, MORT:0.0770
Covariance matrix (annualized):
[[0.028715, 0.049349, 0.025371, 0.020534], [0.049349, 0.537021, 0.064778, 0.04977], [0.025371, 0.064778, 0.063553, 0.017996], [0.020534, 0.04977, 0.017996, 0.034733]]
Risk-free rate: 4.00%
Constraints: weights 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_XRP-USD=1.0000, w_PPLT=0.0000, w_MORT=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EFA=0.0000, w_XRP-USD=1.0000, w_PPLT=0.0000, w_MORT=0.0000
Portfolio annualized return: 118.16%, volatility: 73.28%
Sharpe ratio: (1.1816 - 0.0400) / 0.7328 = 1.5579


4-asset optimization. Max-Sharpe: 4.180. Portfolio: return=44.73%, vol=9.74%. Weights: w_XLP=0.9780, w_DOT-USD=0.0000, w_XHB=0.0220, w_PPLT=0.0000.

Question:
Assets: XLP, DOT-USD, XHB, PPLT
Annualized mean returns: XLP:0.4470, DOT-USD:-1.3357, XHB:0.4607, PPLT:0.1448
Covariance matrix (annualized):
[[0.009516, 0.022148, 0.008097, 0.007012], [0.022148, 0.293962, 0.077861, 0.071539], [0.008097, 0.077861, 0.085808, 0.034452], [0.007012, 0.071539, 0.034452, 0.065014]]
Risk-free rate: 4.00%
Constraints: weights 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=0.9780, w_DOT-USD=0.0000, w_XHB=0.0220, w_PPLT=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLP=0.9780, w_DOT-USD=0.0000, w_XHB=0.0220, w_PPLT=0.0000
Portfolio annualized return: 44.73%, volatility: 9.74%
Sharpe ratio: (0.4473 - 0.0400) / 0.0974 = 4.1804


4-asset optimization. Max-Sharpe: 0.122. Portfolio: return=4.03%, vol=0.24%. Weights: w_EWJ=0.0000, w_BNB-USD=0.0000, w_INDS=0.0000, w_SHV=1.0000.

Question:
Assets: EWJ, BNB-USD, INDS, SHV
Annualized mean returns: EWJ:-0.3134, BNB-USD:-0.0332, INDS:-0.6285, SHV:0.0403
Covariance matrix (annualized):
[[0.026775, 0.021208, 0.004603, 3.4e-05], [0.021208, 0.138704, 0.011829, 3.1e-05], [0.004603, 0.011829, 0.028436, 0.000126], [3.4e-05, 3.1e-05, 0.000126, 6e-06]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_EWJ=0.0000, w_BNB-USD=0.0000, w_INDS=0.0000, w_SHV=1.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EWJ=0.0000, w_BNB-USD=0.0000, w_INDS=0.0000, w_SHV=1.0000
Portfolio annualized return: 4.03%, volatility: 0.24%
Sharpe ratio: (0.0403 - 0.0400) / 0.0024 = 0.1218


4-asset optimization. Max-Sharpe: -2.363. Portfolio: return=-25.72%, vol=12.58%. Weights: w_QQQ=0.2500, w_XRP-USD=0.2500, w_TIP=0.2500, w_SGOV=0.2500.

Question:
Assets: QQQ, XRP-USD, TIP, SGOV
Annualized mean returns: QQQ:0.0552, XRP-USD:-1.1818, TIP:0.0451, SGOV:0.0528
Covariance matrix (annualized):
[[0.028359, 0.004214, 0.001371, -6.1e-05], [0.004214, 0.215498, -0.000932, -0.000239], [0.001371, -0.000932, 0.000559, 7e-06], [-6.1e-05, -0.000239, 7e-06, 6e-06]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_QQQ=0.2500, w_XRP-USD=0.2500, w_TIP=0.2500, w_SGOV=0.2500

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_QQQ=0.2500, w_XRP-USD=0.2500, w_TIP=0.2500, w_SGOV=0.2500
Portfolio annualized return: -25.72%, volatility: 12.58%
Sharpe ratio: (-0.2572 - 0.0400) / 0.1258 = -2.3627


4-asset optimization. Max-Sharpe: 3.847. Portfolio: return=5.74%, vol=0.45%. Weights: w_XLE=0.0046, w_ETH-USD=0.0057, w_SCHP=0.0000, w_BIL=0.9897.

Question:
Assets: XLE, ETH-USD, SCHP, BIL
Annualized mean returns: XLE:0.3175, ETH-USD:2.0172, SCHP:-0.0961, BIL:0.0449
Covariance matrix (annualized):
[[0.03403, 0.028108, -0.001692, 1.1e-05], [0.028108, 0.399004, 0.006352, -8.4e-05], [-0.001692, 0.006352, 0.001921, 4e-06], [1.1e-05, -8.4e-05, 4e-06, 6e-06]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: bull

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

Answer: w_XLE=0.0046, w_ETH-USD=0.0057, w_SCHP=0.0000, w_BIL=0.9897

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLE=0.0046, w_ETH-USD=0.0057, w_SCHP=0.0000, w_BIL=0.9897
Portfolio annualized return: 5.74%, volatility: 0.45%
Sharpe ratio: (0.0574 - 0.0400) / 0.0045 = 3.8469


4-asset optimization. Max-Sharpe: 3.934. Portfolio: return=157.90%, vol=39.12%. Weights: w_XLY=0.7462, w_AVAX-USD=0.2538, w_SCHH=0.0000, w_UNG=0.0000.

Question:
Assets: XLY, AVAX-USD, SCHH, UNG
Annualized mean returns: XLY:0.8534, AVAX-USD:3.7117, SCHH:0.4849, UNG:-4.5348
Covariance matrix (annualized):
[[0.063563, 0.131767, 0.040037, 0.042837], [0.131767, 1.050797, 0.106784, 0.169231], [0.040037, 0.106784, 0.044005, 0.04922], [0.042837, 0.169231, 0.04922, 0.576004]]
Risk-free rate: 4.00%
Constraints: weights 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=0.7462, w_AVAX-USD=0.2538, w_SCHH=0.0000, w_UNG=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLY=0.7462, w_AVAX-USD=0.2538, w_SCHH=0.0000, w_UNG=0.0000
Portfolio annualized return: 157.90%, volatility: 39.12%
Sharpe ratio: (1.5790 - 0.0400) / 0.3912 = 3.9343


4-asset optimization. Max-Sharpe: 3.677. Portfolio: return=45.10%, vol=11.18%. Weights: w_SPY=0.8160, w_LINK-USD=0.0000, w_VNQI=0.0000, w_SLV=0.1840.

Question:
Assets: SPY, LINK-USD, VNQI, SLV
Annualized mean returns: SPY:0.4320, LINK-USD:0.3755, VNQI:0.2318, SLV:0.5354
Covariance matrix (annualized):
[[0.013221, 0.021252, 0.006382, 0.006123], [0.021252, 0.393433, 0.005618, 0.025609], [0.006382, 0.005618, 0.014228, 0.014567], [0.006123, 0.025609, 0.014567, 0.054701]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: bull

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

Answer: w_SPY=0.8160, w_LINK-USD=0.0000, w_VNQI=0.0000, w_SLV=0.1840

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_SPY=0.8160, w_LINK-USD=0.0000, w_VNQI=0.0000, w_SLV=0.1840
Portfolio annualized return: 45.10%, volatility: 11.18%
Sharpe ratio: (0.4510 - 0.0400) / 0.1118 = 3.6772


4-asset optimization. Max-Sharpe: 4.884. Portfolio: return=5.19%, vol=0.24%. Weights: w_XLU=0.0027, w_DOT-USD=0.0000, w_SGOV=0.9973, w_XHB=0.0000.

Question:
Assets: XLU, DOT-USD, SGOV, XHB
Annualized mean returns: XLU:0.0146, DOT-USD:-0.7286, SGOV:0.0520, XHB:-0.3839
Covariance matrix (annualized):
[[0.021733, 0.018348, -7.1e-05, 0.016298], [0.018348, 0.325242, -0.000204, 0.030207], [-7.1e-05, -0.000204, 6e-06, -8.4e-05], [0.016298, 0.030207, -8.4e-05, 0.05549]]
Risk-free rate: 4.00%
Constraints: weights 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=0.0027, w_DOT-USD=0.0000, w_SGOV=0.9973, w_XHB=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLU=0.0027, w_DOT-USD=0.0000, w_SGOV=0.9973, w_XHB=0.0000
Portfolio annualized return: 5.19%, volatility: 0.24%
Sharpe ratio: (0.0519 - 0.0400) / 0.0024 = 4.8837


4-asset optimization. Max-Sharpe: 2.927. Portfolio: return=7.70%, vol=1.26%. Weights: w_MTUM=0.0000, w_DOT-USD=0.0000, w_DBC=0.0925, w_CSHI=0.9075.

Question:
Assets: MTUM, DOT-USD, DBC, CSHI
Annualized mean returns: MTUM:0.0166, DOT-USD:-1.1155, DBC:0.2988, CSHI:0.0544
Covariance matrix (annualized):
[[0.032414, 0.031673, 0.005531, 9.5e-05], [0.031673, 0.419527, 0.002453, 0.001287], [0.005531, 0.002453, 0.010829, 0.000128], [9.5e-05, 0.001287, 0.000128, 5.5e-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_MTUM=0.0000, w_DOT-USD=0.0000, w_DBC=0.0925, w_CSHI=0.9075

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_MTUM=0.0000, w_DOT-USD=0.0000, w_DBC=0.0925, w_CSHI=0.9075
Portfolio annualized return: 7.70%, volatility: 1.26%
Sharpe ratio: (0.0770 - 0.0400) / 0.0126 = 2.9268


4-asset optimization. Max-Sharpe: 2.382. Portfolio: return=39.11%, vol=14.74%. Weights: w_XLE=1.0000, w_MATIC-USD=0.0000, w_VNQ=0.0000, w_PALL=0.0000.

Question:
Assets: XLE, MATIC-USD, VNQ, PALL
Annualized mean returns: XLE:0.3911, MATIC-USD:-3.5076, VNQ:-0.2891, PALL:-0.2566
Covariance matrix (annualized):
[[0.021734, 0.013123, 0.006433, 0.008837], [0.013123, 0.444898, 0.024843, 0.055752], [0.006433, 0.024843, 0.030494, 0.021956], [0.008837, 0.055752, 0.021956, 0.107508]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_XLE=1.0000, w_MATIC-USD=0.0000, w_VNQ=0.0000, w_PALL=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLE=1.0000, w_MATIC-USD=0.0000, w_VNQ=0.0000, w_PALL=0.0000
Portfolio annualized return: 39.11%, volatility: 14.74%
Sharpe ratio: (0.3911 - 0.0400) / 0.1474 = 2.3818


4-asset optimization. Max-Sharpe: -1.047. Portfolio: return=-12.16%, vol=15.43%. Weights: w_USMV=0.0000, w_SOL-USD=0.0000, w_VNQI=1.0000, w_DBB=0.0000.

Question:
Assets: USMV, SOL-USD, VNQI, DBB
Annualized mean returns: USMV:-0.0381, SOL-USD:-2.3299, VNQI:-0.1216, DBB:-0.5554
Covariance matrix (annualized):
[[0.008467, 0.014071, 0.007858, 0.008369], [0.014071, 0.328225, 0.030913, 0.018597], [0.007858, 0.030913, 0.023814, 0.014794], [0.008369, 0.018597, 0.014794, 0.034637]]
Risk-free rate: 4.00%
Constraints: weights 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_SOL-USD=0.0000, w_VNQI=1.0000, w_DBB=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_USMV=0.0000, w_SOL-USD=0.0000, w_VNQI=1.0000, w_DBB=0.0000
Portfolio annualized return: -12.16%, volatility: 15.43%
Sharpe ratio: (-0.1216 - 0.0400) / 0.1543 = -1.0473


4-asset optimization. Max-Sharpe: 0.718. Portfolio: return=10.40%, vol=8.92%. Weights: w_XLI=0.7067, w_DOT-USD=0.0000, w_IAU=0.2933, w_IYR=0.0000.

Question:
Assets: XLI, DOT-USD, IAU, IYR
Annualized mean returns: XLI:0.1136, DOT-USD:-0.8624, IAU:0.0811, IYR:-0.1439
Covariance matrix (annualized):
[[0.0113, 0.017965, 0.003942, 0.00936], [0.017965, 0.150792, 0.002727, 0.019824], [0.003942, 0.002727, 0.007904, 0.00528], [0.00936, 0.019824, 0.00528, 0.016345]]
Risk-free rate: 4.00%
Constraints: weights 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=0.7067, w_DOT-USD=0.0000, w_IAU=0.2933, w_IYR=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLI=0.7067, w_DOT-USD=0.0000, w_IAU=0.2933, w_IYR=0.0000
Portfolio annualized return: 10.40%, volatility: 8.92%
Sharpe ratio: (0.1040 - 0.0400) / 0.0892 = 0.7179


4-asset optimization. Max-Sharpe: 0.575. Portfolio: return=11.78%, vol=13.52%. Weights: w_IVV=0.3449, w_MATIC-USD=0.0000, w_DBC=0.6551, w_MORT=0.0000.

Question:
Assets: IVV, MATIC-USD, DBC, MORT
Annualized mean returns: IVV:0.0690, MATIC-USD:-1.6559, DBC:0.1434, MORT:-0.2140
Covariance matrix (annualized):
[[0.0152, 0.022581, 0.002412, 0.008984], [0.022581, 0.17358, -0.001248, 0.030177], [0.002412, -0.001248, 0.035853, -0.001851], [0.008984, 0.030177, -0.001851, 0.02366]]
Risk-free rate: 4.00%
Constraints: weights 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=0.3449, w_MATIC-USD=0.0000, w_DBC=0.6551, w_MORT=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_IVV=0.3449, w_MATIC-USD=0.0000, w_DBC=0.6551, w_MORT=0.0000
Portfolio annualized return: 11.78%, volatility: 13.52%
Sharpe ratio: (0.1178 - 0.0400) / 0.1352 = 0.5752


4-asset optimization. Max-Sharpe: 5.299. Portfolio: return=43.22%, vol=7.40%. Weights: w_EEM=0.0000, w_SOL-USD=0.0760, w_CSHI=0.0000, w_IGOV=0.9240.

Question:
Assets: EEM, SOL-USD, CSHI, IGOV
Annualized mean returns: EEM:0.1433, SOL-USD:1.6498, CSHI:0.0557, IGOV:0.3321
Covariance matrix (annualized):
[[0.027721, 0.024683, 0.001127, 0.000382], [0.024683, 0.623504, 0.008132, -0.02694], [0.001127, 0.008132, 0.000355, -0.000313], [0.000382, -0.02694, -0.000313, 0.006632]]
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_SOL-USD=0.0760, w_CSHI=0.0000, w_IGOV=0.9240

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EEM=0.0000, w_SOL-USD=0.0760, w_CSHI=0.0000, w_IGOV=0.9240
Portfolio annualized return: 43.22%, volatility: 7.40%
Sharpe ratio: (0.4322 - 0.0400) / 0.0740 = 5.2986


4-asset optimization. Max-Sharpe: 1.783. Portfolio: return=17.69%, vol=7.68%. Weights: w_VLUE=0.0000, w_DOT-USD=0.0000, w_PDBC=0.0000, w_JNK=1.0000.

Question:
Assets: VLUE, DOT-USD, PDBC, JNK
Annualized mean returns: VLUE:0.1702, DOT-USD:-0.2135, PDBC:-0.3264, JNK:0.1769
Covariance matrix (annualized):
[[0.023339, 0.000755, 0.001024, 0.008496], [0.000755, 0.321627, -0.016529, 0.001254], [0.001024, -0.016529, 0.032868, -0.000333], [0.008496, 0.001254, -0.000333, 0.0059]]
Risk-free rate: 4.00%
Constraints: weights 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_PDBC=0.0000, w_JNK=1.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VLUE=0.0000, w_DOT-USD=0.0000, w_PDBC=0.0000, w_JNK=1.0000
Portfolio annualized return: 17.69%, volatility: 7.68%
Sharpe ratio: (0.1769 - 0.0400) / 0.0768 = 1.7827


4-asset optimization. Max-Sharpe: 5.966. Portfolio: return=6.09%, vol=0.35%. Weights: w_XLI=0.0134, w_MATIC-USD=0.0015, w_WEAT=0.0000, w_SGOV=0.9851.

Question:
Assets: XLI, MATIC-USD, WEAT, SGOV
Annualized mean returns: XLI:0.5614, MATIC-USD:1.4879, WEAT:-0.0025, SGOV:0.0519
Covariance matrix (annualized):
[[0.019622, 0.003086, -0.00601, 3.8e-05], [0.003086, 0.423984, 0.040953, 0.000193], [-0.00601, 0.040953, 0.058596, 0.000148], [3.8e-05, 0.000193, 0.000148, 6e-06]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_XLI=0.0134, w_MATIC-USD=0.0015, w_WEAT=0.0000, w_SGOV=0.9851

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLI=0.0134, w_MATIC-USD=0.0015, w_WEAT=0.0000, w_SGOV=0.9851
Portfolio annualized return: 6.09%, volatility: 0.35%
Sharpe ratio: (0.0609 - 0.0400) / 0.0035 = 5.9663


4-asset optimization. Max-Sharpe: 4.368. Portfolio: return=8.18%, vol=0.96%. Weights: w_XLV=0.0238, w_ETH-USD=0.0000, w_SGOV=0.9452, w_SLV=0.0310.

Question:
Assets: XLV, ETH-USD, SGOV, SLV
Annualized mean returns: XLV:0.3281, ETH-USD:0.1818, SGOV:0.0443, SLV:1.0362
Covariance matrix (annualized):
[[0.018977, -0.002431, 8.1e-05, 0.003342], [-0.002431, 0.274025, 0.000309, 0.033739], [8.1e-05, 0.000309, 7e-06, 4e-05], [0.003342, 0.033739, 4e-05, 0.066681]]
Risk-free rate: 4.00%
Constraints: weights 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=0.0238, w_ETH-USD=0.0000, w_SGOV=0.9452, w_SLV=0.0310

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLV=0.0238, w_ETH-USD=0.0000, w_SGOV=0.9452, w_SLV=0.0310
Portfolio annualized return: 8.18%, volatility: 0.96%
Sharpe ratio: (0.0818 - 0.0400) / 0.0096 = 4.3675


4-asset optimization. Max-Sharpe: 6.150. Portfolio: return=6.69%, vol=0.44%. Weights: w_QUAL=0.0230, w_XRP-USD=0.0000, w_TLT=0.0000, w_SGOV=0.9770.

Question:
Assets: QUAL, XRP-USD, TLT, SGOV
Annualized mean returns: QUAL:0.6174, XRP-USD:0.3678, TLT:-0.1499, SGOV:0.0539
Covariance matrix (annualized):
[[0.015015, 0.011717, -0.000302, 6.6e-05], [0.011717, 0.171094, -0.000109, -2.4e-05], [-0.000302, -0.000109, 0.017038, 8.8e-05], [6.6e-05, -2.4e-05, 8.8e-05, 9e-06]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_QUAL=0.0230, w_XRP-USD=0.0000, w_TLT=0.0000, w_SGOV=0.9770

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_QUAL=0.0230, w_XRP-USD=0.0000, w_TLT=0.0000, w_SGOV=0.9770
Portfolio annualized return: 6.69%, volatility: 0.44%
Sharpe ratio: (0.0669 - 0.0400) / 0.0044 = 6.1504


4-asset optimization. Max-Sharpe: 1.310. Portfolio: return=31.97%, vol=21.35%. Weights: w_ACWI=0.1636, w_XRP-USD=0.0000, w_BIL=0.0000, w_REZ=0.8364.

Question:
Assets: ACWI, XRP-USD, BIL, REZ
Annualized mean returns: ACWI:0.2090, XRP-USD:0.1722, BIL:0.0393, REZ:0.3413
Covariance matrix (annualized):
[[0.026155, 0.037826, -6.6e-05, 0.027808], [0.037826, 0.223794, -0.000263, 0.051923], [-6.6e-05, -0.000263, 1.1e-05, -4.5e-05], [0.027808, 0.051923, -4.5e-05, 0.053259]]
Risk-free rate: 4.00%
Constraints: weights 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=0.1636, w_XRP-USD=0.0000, w_BIL=0.0000, w_REZ=0.8364

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_ACWI=0.1636, w_XRP-USD=0.0000, w_BIL=0.0000, w_REZ=0.8364
Portfolio annualized return: 31.97%, volatility: 21.35%
Sharpe ratio: (0.3197 - 0.0400) / 0.2135 = 1.3101


4-asset optimization. Max-Sharpe: 1.789. Portfolio: return=6.35%, vol=1.31%. Weights: w_^VIX=0.0000, w_ADA-USD=0.0240, w_SOYB=0.0000, w_CSHI=0.9760.

Question:
Assets: ^VIX, ADA-USD, SOYB, CSHI
Annualized mean returns: ^VIX:-1.6773, ADA-USD:0.5102, SOYB:-0.2124, CSHI:0.0525
Covariance matrix (annualized):
[[0.662705, -0.03796, -0.029677, 0.000156], [-0.03796, 0.203098, 0.007473, -0.001451], [-0.029677, 0.007473, 0.01904, -0.000243], [0.000156, -0.001451, -0.000243, 0.00013]]
Risk-free rate: 4.00%
Constraints: weights 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_ADA-USD=0.0240, w_SOYB=0.0000, w_CSHI=0.9760

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_^VIX=0.0000, w_ADA-USD=0.0240, w_SOYB=0.0000, w_CSHI=0.9760
Portfolio annualized return: 6.35%, volatility: 1.31%
Sharpe ratio: (0.0635 - 0.0400) / 0.0131 = 1.7893


4-asset optimization. Max-Sharpe: -0.050. Portfolio: return=3.11%, vol=17.93%. Weights: w_XLE=0.0000, w_LINK-USD=0.0000, w_IYR=1.0000, w_PALL=0.0000.

Question:
Assets: XLE, LINK-USD, IYR, PALL
Annualized mean returns: XLE:-0.4112, LINK-USD:-0.4471, IYR:0.0311, PALL:-0.5576
Covariance matrix (annualized):
[[0.030438, 0.044206, 0.016362, 0.008759], [0.044206, 0.439928, 0.028919, 0.02105], [0.016362, 0.028919, 0.032138, 0.025398], [0.008759, 0.02105, 0.025398, 0.111076]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_XLE=0.0000, w_LINK-USD=0.0000, w_IYR=1.0000, w_PALL=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLE=0.0000, w_LINK-USD=0.0000, w_IYR=1.0000, w_PALL=0.0000
Portfolio annualized return: 3.11%, volatility: 17.93%
Sharpe ratio: (0.0311 - 0.0400) / 0.1793 = -0.0497


4-asset optimization. Max-Sharpe: -0.217. Portfolio: return=-2.15%, vol=28.34%. Weights: w_FXI=1.0000, w_ETH-USD=0.0000, w_IAU=0.0000, w_VCIT=0.0000.

Question:
Assets: FXI, ETH-USD, IAU, VCIT
Annualized mean returns: FXI:-0.0215, ETH-USD:-0.8470, IAU:-0.1768, VCIT:-0.0863
Covariance matrix (annualized):
[[0.08034, 0.015111, -0.000828, -0.003248], [0.015111, 0.156035, 0.006003, 0.004853], [-0.000828, 0.006003, 0.015285, 0.005401], [-0.003248, 0.004853, 0.005401, 0.004795]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_FXI=1.0000, w_ETH-USD=0.0000, w_IAU=0.0000, w_VCIT=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_FXI=1.0000, w_ETH-USD=0.0000, w_IAU=0.0000, w_VCIT=0.0000
Portfolio annualized return: -2.15%, volatility: 28.34%
Sharpe ratio: (-0.0215 - 0.0400) / 0.2834 = -0.2169


4-asset optimization. Max-Sharpe: 2.855. Portfolio: return=6.61%, vol=0.91%. Weights: w_EEM=0.0000, w_MATIC-USD=0.0108, w_BIL=0.9881, w_SCHH=0.0011.

Question:
Assets: EEM, MATIC-USD, BIL, SCHH
Annualized mean returns: EEM:0.0271, MATIC-USD:2.1391, BIL:0.0434, SCHH:0.1727
Covariance matrix (annualized):
[[0.026107, 0.037556, 2.7e-05, 0.014626], [0.037556, 0.601585, 0.000217, 0.034329], [2.7e-05, 0.000217, 9e-06, 8e-06], [0.014626, 0.034329, 8e-06, 0.042653]]
Risk-free rate: 4.00%
Constraints: weights 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_MATIC-USD=0.0108, w_BIL=0.9881, w_SCHH=0.0011

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EEM=0.0000, w_MATIC-USD=0.0108, w_BIL=0.9881, w_SCHH=0.0011
Portfolio annualized return: 6.61%, volatility: 0.91%
Sharpe ratio: (0.0661 - 0.0400) / 0.0091 = 2.8548


4-asset optimization. Max-Sharpe: 4.570. Portfolio: return=221.75%, vol=47.65%. Weights: w_XLRE=0.0000, w_SOL-USD=0.6072, w_UNG=0.0000, w_SCHP=0.3928.

Question:
Assets: XLRE, SOL-USD, UNG, SCHP
Annualized mean returns: XLRE:0.0129, SOL-USD:3.6375, UNG:-1.9026, SCHP:0.0222
Covariance matrix (annualized):
[[0.024382, 0.009185, -0.006362, 0.003733], [0.009185, 0.620737, -0.100687, -0.004638], [-0.006362, -0.100687, 0.272348, -0.004569], [0.003733, -0.004638, -0.004569, 0.002431]]
Risk-free rate: 4.00%
Constraints: weights 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_SOL-USD=0.6072, w_UNG=0.0000, w_SCHP=0.3928

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLRE=0.0000, w_SOL-USD=0.6072, w_UNG=0.0000, w_SCHP=0.3928
Portfolio annualized return: 221.75%, volatility: 47.65%
Sharpe ratio: (2.2175 - 0.0400) / 0.4765 = 4.5699


4-asset optimization. Max-Sharpe: -1.061. Portfolio: return=-15.09%, vol=17.99%. Weights: w_IWM=0.2500, w_ETH-USD=0.2500, w_SOYB=0.2500, w_BIL=0.2500.

Question:
Assets: IWM, ETH-USD, SOYB, BIL
Annualized mean returns: IWM:0.4339, ETH-USD:-0.4788, SOYB:-0.6102, BIL:0.0514
Covariance matrix (annualized):
[[0.066878, 0.069228, -0.003397, -0.000132], [0.069228, 0.404884, -0.062143, 3e-06], [-0.003397, -0.062143, 0.039076, -6.2e-05], [-0.000132, 3e-06, -6.2e-05, 6e-06]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: bull

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

Answer: w_IWM=0.2500, w_ETH-USD=0.2500, w_SOYB=0.2500, w_BIL=0.2500

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_IWM=0.2500, w_ETH-USD=0.2500, w_SOYB=0.2500, w_BIL=0.2500
Portfolio annualized return: -15.09%, volatility: 17.99%
Sharpe ratio: (-0.1509 - 0.0400) / 0.1799 = -1.0612


4-asset optimization. Max-Sharpe: 5.436. Portfolio: return=5.21%, vol=0.22%. Weights: w_ACWI=0.0102, w_ETH-USD=0.0000, w_BIL=0.9898, w_PPLT=0.0000.

Question:
Assets: ACWI, ETH-USD, BIL, PPLT
Annualized mean returns: ACWI:0.2010, ETH-USD:-0.7454, BIL:0.0506, PPLT:-0.5019
Covariance matrix (annualized):
[[0.008069, 0.00056, -1.6e-05, 0.007906], [0.00056, 0.125866, -2.4e-05, -0.011632], [-1.6e-05, -2.4e-05, 5e-06, -9.2e-05], [0.007906, -0.011632, -9.2e-05, 0.067483]]
Risk-free rate: 4.00%
Constraints: weights 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=0.0102, w_ETH-USD=0.0000, w_BIL=0.9898, w_PPLT=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_ACWI=0.0102, w_ETH-USD=0.0000, w_BIL=0.9898, w_PPLT=0.0000
Portfolio annualized return: 5.21%, volatility: 0.22%
Sharpe ratio: (0.0521 - 0.0400) / 0.0022 = 5.4363


4-asset optimization. Max-Sharpe: 1.410. Portfolio: return=33.37%, vol=20.83%. Weights: w_VEA=0.0000, w_ETH-USD=0.4302, w_DBA=0.0526, w_XHB=0.5171.

Question:
Assets: VEA, ETH-USD, DBA, XHB
Annualized mean returns: VEA:0.0199, ETH-USD:0.5205, DBA:0.1024, XHB:0.2018
Covariance matrix (annualized):
[[0.015054, 0.012051, 0.007127, 0.01338], [0.012051, 0.157373, 0.014143, 0.004958], [0.007127, 0.014143, 0.012727, 0.00476], [0.01338, 0.004958, 0.00476, 0.041622]]
Risk-free rate: 4.00%
Constraints: weights 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_ETH-USD=0.4302, w_DBA=0.0526, w_XHB=0.5171

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VEA=0.0000, w_ETH-USD=0.4302, w_DBA=0.0526, w_XHB=0.5171
Portfolio annualized return: 33.37%, volatility: 20.83%
Sharpe ratio: (0.3337 - 0.0400) / 0.2083 = 1.4096


4-asset optimization. Max-Sharpe: 5.886. Portfolio: return=43.65%, vol=6.74%. Weights: w_XLRE=0.3481, w_ETH-USD=0.0000, w_SCHP=0.5863, w_IAU=0.0657.

Question:
Assets: XLRE, ETH-USD, SCHP, IAU
Annualized mean returns: XLRE:0.8514, ETH-USD:-0.0916, SCHP:0.1775, IAU:0.5500
Covariance matrix (annualized):
[[0.024164, 0.041292, 0.000726, 0.006871], [0.041292, 0.430325, -0.003267, 0.032691], [0.000726, -0.003267, 0.001909, 0.003081], [0.006871, 0.032691, 0.003081, 0.024969]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: bull

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

Answer: w_XLRE=0.3481, w_ETH-USD=0.0000, w_SCHP=0.5863, w_IAU=0.0657

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLRE=0.3481, w_ETH-USD=0.0000, w_SCHP=0.5863, w_IAU=0.0657
Portfolio annualized return: 43.65%, volatility: 6.74%
Sharpe ratio: (0.4365 - 0.0400) / 0.0674 = 5.8857


4-asset optimization. Max-Sharpe: 4.785. Portfolio: return=59.80%, vol=11.66%. Weights: w_XLV=0.7207, w_DOT-USD=0.0000, w_WEAT=0.0101, w_IYR=0.2691.

Question:
Assets: XLV, DOT-USD, WEAT, IYR
Annualized mean returns: XLV:0.5586, DOT-USD:0.5544, WEAT:0.0003, IYR:0.7261
Covariance matrix (annualized):
[[0.013533, 0.01962, -0.002569, 0.010823], [0.01962, 0.834146, 0.012611, 0.037856], [-0.002569, 0.012611, 0.068047, 0.00072], [0.010823, 0.037856, 0.00072, 0.033127]]
Risk-free rate: 4.00%
Constraints: weights 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=0.7207, w_DOT-USD=0.0000, w_WEAT=0.0101, w_IYR=0.2691

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLV=0.7207, w_DOT-USD=0.0000, w_WEAT=0.0101, w_IYR=0.2691
Portfolio annualized return: 59.80%, volatility: 11.66%
Sharpe ratio: (0.5980 - 0.0400) / 0.1166 = 4.7845


4-asset optimization. Max-Sharpe: 3.739. Portfolio: return=60.90%, vol=15.22%. Weights: w_EEM=0.0000, w_BNB-USD=0.0000, w_GLD=0.0486, w_VNQ=0.9514.

Question:
Assets: EEM, BNB-USD, GLD, VNQ
Annualized mean returns: EEM:-0.0329, BNB-USD:-0.4660, GLD:0.2943, VNQ:0.6251
Covariance matrix (annualized):
[[0.026074, 0.018012, 0.014061, 0.010507], [0.018012, 0.236495, 0.002749, 0.02808], [0.014061, 0.002749, 0.024349, 0.009636], [0.010507, 0.02808, 0.009636, 0.02454]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_EEM=0.0000, w_BNB-USD=0.0000, w_GLD=0.0486, w_VNQ=0.9514

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EEM=0.0000, w_BNB-USD=0.0000, w_GLD=0.0486, w_VNQ=0.9514
Portfolio annualized return: 60.90%, volatility: 15.22%
Sharpe ratio: (0.6090 - 0.0400) / 0.1522 = 3.7388


4-asset optimization. Max-Sharpe: 6.068. Portfolio: return=7.38%, vol=0.56%. Weights: w_XLV=0.0000, w_LINK-USD=0.0088, w_HYG=0.0000, w_ICSH=0.9912.

Question:
Assets: XLV, LINK-USD, HYG, ICSH
Annualized mean returns: XLV:-0.2818, LINK-USD:2.2107, HYG:-0.0442, ICSH:0.0548
Covariance matrix (annualized):
[[0.012038, -0.00744, 0.004681, -2.6e-05], [-0.00744, 0.254682, -0.000287, -0.000252], [0.004681, -0.000287, 0.004944, 5.3e-05], [-2.6e-05, -0.000252, 5.3e-05, 1.6e-05]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_XLV=0.0000, w_LINK-USD=0.0088, w_HYG=0.0000, w_ICSH=0.9912

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLV=0.0000, w_LINK-USD=0.0088, w_HYG=0.0000, w_ICSH=0.9912
Portfolio annualized return: 7.38%, volatility: 0.56%
Sharpe ratio: (0.0738 - 0.0400) / 0.0056 = 6.0685


4-asset optimization. Max-Sharpe: -1.120. Portfolio: return=-17.03%, vol=18.79%. Weights: w_USMV=0.2500, w_MATIC-USD=0.2500, w_UNG=0.2500, w_BIL=0.2500.

Question:
Assets: USMV, MATIC-USD, UNG, BIL
Annualized mean returns: USMV:0.3810, MATIC-USD:1.4298, UNG:-2.5438, BIL:0.0516
Covariance matrix (annualized):
[[0.010729, -0.003141, 0.000386, -6.6e-05], [-0.003141, 0.414464, -0.03719, 6.1e-05], [0.000386, -0.03719, 0.219316, 3.8e-05], [-6.6e-05, 6.1e-05, 3.8e-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_USMV=0.2500, w_MATIC-USD=0.2500, w_UNG=0.2500, w_BIL=0.2500

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_USMV=0.2500, w_MATIC-USD=0.2500, w_UNG=0.2500, w_BIL=0.2500
Portfolio annualized return: -17.03%, volatility: 18.79%
Sharpe ratio: (-0.1703 - 0.0400) / 0.1879 = -1.1195


4-asset optimization. Max-Sharpe: 6.292. Portfolio: return=6.38%, vol=0.38%. Weights: w_XLU=0.0000, w_LINK-USD=0.0000, w_ICSH=1.0000, w_DBA=0.0000.

Question:
Assets: XLU, LINK-USD, ICSH, DBA
Annualized mean returns: XLU:-0.1190, LINK-USD:-1.3494, ICSH:0.0638, DBA:-0.1155
Covariance matrix (annualized):
[[0.023766, -0.004103, 0.000146, -0.006403], [-0.004103, 0.313748, 0.00026, -0.016266], [0.000146, 0.00026, 1.4e-05, 0.000105], [-0.006403, -0.016266, 0.000105, 0.033202]]
Risk-free rate: 4.00%
Constraints: weights 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_LINK-USD=0.0000, w_ICSH=1.0000, w_DBA=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLU=0.0000, w_LINK-USD=0.0000, w_ICSH=1.0000, w_DBA=0.0000
Portfolio annualized return: 6.38%, volatility: 0.38%
Sharpe ratio: (0.0638 - 0.0400) / 0.0038 = 6.2920


4-asset optimization. Max-Sharpe: 2.915. Portfolio: return=40.34%, vol=12.47%. Weights: w_VEA=0.6732, w_AVAX-USD=0.0782, w_EMB=0.1843, w_DBA=0.0642.

Question:
Assets: VEA, AVAX-USD, EMB, DBA
Annualized mean returns: VEA:0.3257, AVAX-USD:1.8441, EMB:0.2097, DBA:0.0199
Covariance matrix (annualized):
[[0.014816, 0.01163, 0.007184, 0.000122], [0.01163, 0.870497, 0.012759, -0.017622], [0.007184, 0.012759, 0.008512, -0.002325], [0.000122, -0.017622, -0.002325, 0.013494]]
Risk-free rate: 4.00%
Constraints: weights 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=0.6732, w_AVAX-USD=0.0782, w_EMB=0.1843, w_DBA=0.0642

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VEA=0.6732, w_AVAX-USD=0.0782, w_EMB=0.1843, w_DBA=0.0642
Portfolio annualized return: 40.34%, volatility: 12.47%
Sharpe ratio: (0.4034 - 0.0400) / 0.1247 = 2.9154


4-asset optimization. Max-Sharpe: 4.970. Portfolio: return=5.40%, vol=0.28%. Weights: w_EEM=0.0000, w_XRP-USD=0.0000, w_SGOV=1.0000, w_LQD=0.0000.

Question:
Assets: EEM, XRP-USD, SGOV, LQD
Annualized mean returns: EEM:0.0678, XRP-USD:-0.8762, SGOV:0.0540, LQD:-0.1132
Covariance matrix (annualized):
[[0.023111, 0.006182, 0.000147, 0.003785], [0.006182, 0.166122, 0.000131, 0.000897], [0.000147, 0.000131, 8e-06, 4e-05], [0.003785, 0.000897, 4e-05, 0.0057]]
Risk-free rate: 4.00%
Constraints: weights 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_XRP-USD=0.0000, w_SGOV=1.0000, w_LQD=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EEM=0.0000, w_XRP-USD=0.0000, w_SGOV=1.0000, w_LQD=0.0000
Portfolio annualized return: 5.40%, volatility: 0.28%
Sharpe ratio: (0.0540 - 0.0400) / 0.0028 = 4.9704


4-asset optimization. Max-Sharpe: 6.833. Portfolio: return=7.20%, vol=0.47%. Weights: w_IVV=0.0237, w_BTC-USD=0.0000, w_IYR=0.0054, w_ICSH=0.9708.

Question:
Assets: IVV, BTC-USD, IYR, ICSH
Annualized mean returns: IVV:0.3408, BTC-USD:-0.3375, IYR:0.4276, ICSH:0.0635
Covariance matrix (annualized):
[[0.007227, 0.005794, 0.000698, 3.2e-05], [0.005794, 0.140071, -0.000267, 0.000164], [0.000698, -0.000267, 0.019885, 0.000146], [3.2e-05, 0.000164, 0.000146, 1.5e-05]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_IVV=0.0237, w_BTC-USD=0.0000, w_IYR=0.0054, w_ICSH=0.9708

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_IVV=0.0237, w_BTC-USD=0.0000, w_IYR=0.0054, w_ICSH=0.9708
Portfolio annualized return: 7.20%, volatility: 0.47%
Sharpe ratio: (0.0720 - 0.0400) / 0.0047 = 6.8328


4-asset optimization. Max-Sharpe: 2.561. Portfolio: return=6.86%, vol=1.11%. Weights: w_XLI=0.0000, w_ETH-USD=0.0161, w_CSHI=0.9839, w_EMB=0.0000.

Question:
Assets: XLI, ETH-USD, CSHI, EMB
Annualized mean returns: XLI:0.0072, ETH-USD:0.7454, CSHI:0.0574, EMB:0.0056
Covariance matrix (annualized):
[[0.025325, -0.004715, 0.000458, 0.010272], [-0.004715, 0.184393, 9.5e-05, -0.00261], [0.000458, 9.5e-05, 7.6e-05, 3.1e-05], [0.010272, -0.00261, 3.1e-05, 0.0117]]
Risk-free rate: 4.00%
Constraints: weights 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_ETH-USD=0.0161, w_CSHI=0.9839, w_EMB=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLI=0.0000, w_ETH-USD=0.0161, w_CSHI=0.9839, w_EMB=0.0000
Portfolio annualized return: 6.86%, volatility: 1.11%
Sharpe ratio: (0.0686 - 0.0400) / 0.0111 = 2.5611


4-asset optimization. Max-Sharpe: 3.895. Portfolio: return=100.55%, vol=24.79%. Weights: w_^VIX=0.0000, w_ETH-USD=0.0000, w_SOYB=1.0000, w_CSHI=0.0000.

Question:
Assets: ^VIX, ETH-USD, SOYB, CSHI
Annualized mean returns: ^VIX:-2.0623, ETH-USD:0.4144, SOYB:1.0055, CSHI:0.0459
Covariance matrix (annualized):
[[0.533768, -0.05933, 0.005293, -0.000245], [-0.05933, 0.167293, 0.037695, 0.001137], [0.005293, 0.037695, 0.061456, 0.000524], [-0.000245, 0.001137, 0.000524, 5.3e-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_^VIX=0.0000, w_ETH-USD=0.0000, w_SOYB=1.0000, w_CSHI=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_^VIX=0.0000, w_ETH-USD=0.0000, w_SOYB=1.0000, w_CSHI=0.0000
Portfolio annualized return: 100.55%, volatility: 24.79%
Sharpe ratio: (1.0055 - 0.0400) / 0.2479 = 3.8948


4-asset optimization. Max-Sharpe: 2.942. Portfolio: return=7.53%, vol=1.20%. Weights: w_USMV=0.0370, w_XRP-USD=0.0126, w_ICSH=0.9504, w_ITB=0.0000.

Question:
Assets: USMV, XRP-USD, ICSH, ITB
Annualized mean returns: USMV:0.1588, XRP-USD:1.9499, ICSH:0.0471, ITB:0.1496
Covariance matrix (annualized):
[[0.013614, 0.009476, -0.000147, 0.014801], [0.009476, 0.67743, -0.001165, 0.0337], [-0.000147, -0.001165, 5.2e-05, -0.000393], [0.014801, 0.0337, -0.000393, 0.046823]]
Risk-free rate: 4.00%
Constraints: weights 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=0.0370, w_XRP-USD=0.0126, w_ICSH=0.9504, w_ITB=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_USMV=0.0370, w_XRP-USD=0.0126, w_ICSH=0.9504, w_ITB=0.0000
Portfolio annualized return: 7.53%, volatility: 1.20%
Sharpe ratio: (0.0753 - 0.0400) / 0.0120 = 2.9421


4-asset optimization. Max-Sharpe: 7.418. Portfolio: return=8.09%, vol=0.55%. Weights: w_XLB=0.0000, w_AVAX-USD=0.0034, w_ICSH=0.9935, w_TLT=0.0031.

Question:
Assets: XLB, AVAX-USD, ICSH, TLT
Annualized mean returns: XLB:0.2331, AVAX-USD:3.3185, ICSH:0.0674, TLT:0.8315
Covariance matrix (annualized):
[[0.029549, 0.013031, 0.00027, 0.01091], [0.013031, 0.901974, -0.000678, 0.00338], [0.00027, -0.000678, 2.2e-05, 0.000425], [0.01091, 0.00338, 0.000425, 0.050626]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_XLB=0.0000, w_AVAX-USD=0.0034, w_ICSH=0.9935, w_TLT=0.0031

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLB=0.0000, w_AVAX-USD=0.0034, w_ICSH=0.9935, w_TLT=0.0031
Portfolio annualized return: 8.09%, volatility: 0.55%
Sharpe ratio: (0.0809 - 0.0400) / 0.0055 = 7.4182


4-asset optimization. Max-Sharpe: 3.026. Portfolio: return=60.69%, vol=18.73%. Weights: w_XLK=0.8743, w_DOT-USD=0.0000, w_XHB=0.1257, w_IAU=0.0000.

Question:
Assets: XLK, DOT-USD, XHB, IAU
Annualized mean returns: XLK:0.6368, DOT-USD:-0.5159, XHB:0.3985, IAU:-0.1009
Covariance matrix (annualized):
[[0.039493, 0.015246, 0.019164, -0.008573], [0.015246, 0.173943, 0.020844, 0.011986], [0.019164, 0.020844, 0.043259, -0.006998], [-0.008573, 0.011986, -0.006998, 0.018469]]
Risk-free rate: 4.00%
Constraints: weights 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=0.8743, w_DOT-USD=0.0000, w_XHB=0.1257, w_IAU=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLK=0.8743, w_DOT-USD=0.0000, w_XHB=0.1257, w_IAU=0.0000
Portfolio annualized return: 60.69%, volatility: 18.73%
Sharpe ratio: (0.6069 - 0.0400) / 0.1873 = 3.0263


4-asset optimization. Max-Sharpe: -0.416. Portfolio: return=-21.32%, vol=60.80%. Weights: w_IWM=0.0000, w_ADA-USD=0.9631, w_SGOV=0.0369, w_PDBC=0.0000.

Question:
Assets: IWM, ADA-USD, SGOV, PDBC
Annualized mean returns: IWM:-0.0223, ADA-USD:-0.2229, SGOV:0.0400, PDBC:-0.4194
Covariance matrix (annualized):
[[0.05313, 0.081838, -9.3e-05, 0.027433], [0.081838, 0.398579, -4.6e-05, 0.026354], [-9.3e-05, -4.6e-05, 8e-06, -0.000139], [0.027433, 0.026354, -0.000139, 0.04113]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_IWM=0.0000, w_ADA-USD=0.9631, w_SGOV=0.0369, w_PDBC=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_IWM=0.0000, w_ADA-USD=0.9631, w_SGOV=0.0369, w_PDBC=0.0000
Portfolio annualized return: -21.32%, volatility: 60.80%
Sharpe ratio: (-0.2132 - 0.0400) / 0.6080 = -0.4164


4-asset optimization. Max-Sharpe: 1.735. Portfolio: return=7.02%, vol=1.74%. Weights: w_QUAL=0.1347, w_AVAX-USD=0.0000, w_USO=0.0000, w_ICSH=0.8653.

Question:
Assets: QUAL, AVAX-USD, USO, ICSH
Annualized mean returns: QUAL:0.2720, AVAX-USD:-0.9738, USO:-0.5393, ICSH:0.0388
Covariance matrix (annualized):
[[0.019918, 0.018594, 0.019058, -0.000413], [0.018594, 0.27246, 0.014333, -0.0001], [0.019058, 0.014333, 0.115151, -0.000907], [-0.000413, -0.0001, -0.000907, 5e-05]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_QUAL=0.1347, w_AVAX-USD=0.0000, w_USO=0.0000, w_ICSH=0.8653

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_QUAL=0.1347, w_AVAX-USD=0.0000, w_USO=0.0000, w_ICSH=0.8653
Portfolio annualized return: 7.02%, volatility: 1.74%
Sharpe ratio: (0.0702 - 0.0400) / 0.0174 = 1.7351


4-asset optimization. Max-Sharpe: 7.837. Portfolio: return=7.52%, vol=0.45%. Weights: w_SPY=0.0000, w_BNB-USD=0.0037, w_VNQI=0.0079, w_ICSH=0.9885.

Question:
Assets: SPY, BNB-USD, VNQI, ICSH
Annualized mean returns: SPY:-0.0526, BNB-USD:0.7412, VNQI:0.5045, ICSH:0.0694
Covariance matrix (annualized):
[[0.029648, 0.038063, 0.017556, -0.000106], [0.038063, 0.230775, 0.015909, -0.000577], [0.017556, 0.015909, 0.022085, 3.5e-05], [-0.000106, -0.000577, 3.5e-05, 1.9e-05]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_SPY=0.0000, w_BNB-USD=0.0037, w_VNQI=0.0079, w_ICSH=0.9885

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_SPY=0.0000, w_BNB-USD=0.0037, w_VNQI=0.0079, w_ICSH=0.9885
Portfolio annualized return: 7.52%, volatility: 0.45%
Sharpe ratio: (0.0752 - 0.0400) / 0.0045 = 7.8375


4-asset optimization. Max-Sharpe: 0.654. Portfolio: return=14.50%, vol=16.06%. Weights: w_EFA=1.0000, w_MATIC-USD=0.0000, w_DBC=0.0000, w_IYR=0.0000.

Question:
Assets: EFA, MATIC-USD, DBC, IYR
Annualized mean returns: EFA:0.1450, MATIC-USD:-0.2348, DBC:-0.0099, IYR:-0.3852
Covariance matrix (annualized):
[[0.025783, 0.006016, 0.011962, 0.019064], [0.006016, 0.502232, -0.003288, -0.02386], [0.011962, -0.003288, 0.022275, 0.00295], [0.019064, -0.02386, 0.00295, 0.05173]]
Risk-free rate: 4.00%
Constraints: weights 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=1.0000, w_MATIC-USD=0.0000, w_DBC=0.0000, w_IYR=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EFA=1.0000, w_MATIC-USD=0.0000, w_DBC=0.0000, w_IYR=0.0000
Portfolio annualized return: 14.50%, volatility: 16.06%
Sharpe ratio: (0.1450 - 0.0400) / 0.1606 = 0.6537


4-asset optimization. Max-Sharpe: 4.908. Portfolio: return=5.18%, vol=0.24%. Weights: w_XLV=0.0084, w_LINK-USD=0.0000, w_SLV=0.0056, w_BIL=0.9860.

Question:
Assets: XLV, LINK-USD, SLV, BIL
Annualized mean returns: XLV:0.0937, LINK-USD:0.3767, SLV:0.4955, BIL:0.0489
Covariance matrix (annualized):
[[0.011246, 0.024383, -0.000821, -6.5e-05], [0.024383, 0.561699, 0.011991, 0.000424], [-0.000821, 0.011991, 0.063808, -0.000129], [-6.5e-05, 0.000424, -0.000129, 6e-06]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_XLV=0.0084, w_LINK-USD=0.0000, w_SLV=0.0056, w_BIL=0.9860

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLV=0.0084, w_LINK-USD=0.0000, w_SLV=0.0056, w_BIL=0.9860
Portfolio annualized return: 5.18%, volatility: 0.24%
Sharpe ratio: (0.0518 - 0.0400) / 0.0024 = 4.9079


4-asset optimization. Max-Sharpe: 5.985. Portfolio: return=5.97%, vol=0.33%. Weights: w_XLI=0.0084, w_DOT-USD=0.0027, w_DBC=0.0000, w_SGOV=0.9889.

Question:
Assets: XLI, DOT-USD, DBC, SGOV
Annualized mean returns: XLI:0.4245, DOT-USD:1.7659, DBC:-0.3208, SGOV:0.0520
Covariance matrix (annualized):
[[0.020291, -0.007756, -0.005196, 6.1e-05], [-0.007756, 0.444626, -0.022227, -0.000168], [-0.005196, -0.022227, 0.031753, -7.1e-05], [6.1e-05, -0.000168, -7.1e-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_XLI=0.0084, w_DOT-USD=0.0027, w_DBC=0.0000, w_SGOV=0.9889

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLI=0.0084, w_DOT-USD=0.0027, w_DBC=0.0000, w_SGOV=0.9889
Portfolio annualized return: 5.97%, volatility: 0.33%
Sharpe ratio: (0.0597 - 0.0400) / 0.0033 = 5.9853


4-asset optimization. Max-Sharpe: 2.802. Portfolio: return=8.07%, vol=1.45%. Weights: w_IVV=0.0000, w_BNB-USD=0.0211, w_CSHI=0.9672, w_HAUZ=0.0117.

Question:
Assets: IVV, BNB-USD, CSHI, HAUZ
Annualized mean returns: IVV:0.2776, BNB-USD:0.9819, CSHI:0.0594, HAUZ:0.2169
Covariance matrix (annualized):
[[0.028698, 0.033037, 0.000573, 0.018735], [0.033037, 0.194289, 0.000583, 0.018192], [0.000573, 0.000583, 8.8e-05, 0.000247], [0.018735, 0.018192, 0.000247, 0.025172]]
Risk-free rate: 4.00%
Constraints: weights 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_BNB-USD=0.0211, w_CSHI=0.9672, w_HAUZ=0.0117

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_IVV=0.0000, w_BNB-USD=0.0211, w_CSHI=0.9672, w_HAUZ=0.0117
Portfolio annualized return: 8.07%, volatility: 1.45%
Sharpe ratio: (0.0807 - 0.0400) / 0.0145 = 2.8023


4-asset optimization. Max-Sharpe: 4.076. Portfolio: return=47.66%, vol=10.71%. Weights: w_VLUE=0.7265, w_SOL-USD=0.0149, w_ICSH=0.0908, w_DBB=0.1678.

Question:
Assets: VLUE, SOL-USD, ICSH, DBB
Annualized mean returns: VLUE:0.5161, SOL-USD:1.7428, ICSH:0.0386, DBB:0.4303
Covariance matrix (annualized):
[[0.015485, 0.049897, -9.1e-05, 0.00313], [0.049897, 0.353029, -0.000506, 0.019533], [-9.1e-05, -0.000506, 1.6e-05, 0.000207], [0.00313, 0.019533, 0.000207, 0.04574]]
Risk-free rate: 4.00%
Constraints: weights 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=0.7265, w_SOL-USD=0.0149, w_ICSH=0.0908, w_DBB=0.1678

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VLUE=0.7265, w_SOL-USD=0.0149, w_ICSH=0.0908, w_DBB=0.1678
Portfolio annualized return: 47.66%, volatility: 10.71%
Sharpe ratio: (0.4766 - 0.0400) / 0.1071 = 4.0759


4-asset optimization. Max-Sharpe: 5.537. Portfolio: return=103.52%, vol=17.97%. Weights: w_XLY=1.0000, w_SOL-USD=0.0000, w_HAUZ=0.0000, w_SLV=0.0000.

Question:
Assets: XLY, SOL-USD, HAUZ, SLV
Annualized mean returns: XLY:1.0352, SOL-USD:1.5963, HAUZ:-0.5202, SLV:-0.1429
Covariance matrix (annualized):
[[0.032303, 0.051533, 0.002294, -0.003026], [0.051533, 0.459901, 0.003805, -0.019762], [0.002294, 0.003805, 0.018993, 0.012622], [-0.003026, -0.019762, 0.012622, 0.089601]]
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=1.0000, w_SOL-USD=0.0000, w_HAUZ=0.0000, w_SLV=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLY=1.0000, w_SOL-USD=0.0000, w_HAUZ=0.0000, w_SLV=0.0000
Portfolio annualized return: 103.52%, volatility: 17.97%
Sharpe ratio: (1.0352 - 0.0400) / 0.1797 = 5.5372


4-asset optimization. Max-Sharpe: 2.862. Portfolio: return=8.09%, vol=1.43%. Weights: w_EWJ=0.0826, w_ADA-USD=0.0062, w_JNK=0.0000, w_BIL=0.9112.

Question:
Assets: EWJ, ADA-USD, JNK, BIL
Annualized mean returns: EWJ:0.4493, ADA-USD:0.8832, JNK:0.1190, BIL:0.0420
Covariance matrix (annualized):
[[0.022686, 0.021158, 0.009438, 4.2e-05], [0.021158, 0.424099, 0.020686, -0.000179], [0.009438, 0.020686, 0.009774, 1.2e-05], [4.2e-05, -0.000179, 1.2e-05, 9e-06]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_EWJ=0.0826, w_ADA-USD=0.0062, w_JNK=0.0000, w_BIL=0.9112

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EWJ=0.0826, w_ADA-USD=0.0062, w_JNK=0.0000, w_BIL=0.9112
Portfolio annualized return: 8.09%, volatility: 1.43%
Sharpe ratio: (0.0809 - 0.0400) / 0.0143 = 2.8621


4-asset optimization. Max-Sharpe: 1.311. Portfolio: return=5.60%, vol=1.22%. Weights: w_VTI=0.0000, w_ETH-USD=0.0263, w_BNO=0.0000, w_SGOV=0.9737.

Question:
Assets: VTI, ETH-USD, BNO, SGOV
Annualized mean returns: VTI:0.0450, ETH-USD:0.5867, BNO:0.0351, SGOV:0.0417
Covariance matrix (annualized):
[[0.035111, 0.049325, 0.027856, -0.000117], [0.049325, 0.205341, 0.056093, -1.2e-05], [0.027856, 0.056093, 0.127589, -0.00022], [-0.000117, -1.2e-05, -0.00022, 9e-06]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_VTI=0.0000, w_ETH-USD=0.0263, w_BNO=0.0000, w_SGOV=0.9737

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VTI=0.0000, w_ETH-USD=0.0263, w_BNO=0.0000, w_SGOV=0.9737
Portfolio annualized return: 5.60%, volatility: 1.22%
Sharpe ratio: (0.0560 - 0.0400) / 0.0122 = 1.3113


4-asset optimization. Max-Sharpe: 5.692. Portfolio: return=13.65%, vol=1.70%. Weights: w_QQQ=0.1028, w_DOT-USD=0.0000, w_WEAT=0.0000, w_ICSH=0.8972.

Question:
Assets: QQQ, DOT-USD, WEAT, ICSH
Annualized mean returns: QQQ:0.9530, DOT-USD:-1.3503, WEAT:0.0795, ICSH:0.0429
Covariance matrix (annualized):
[[0.029525, 0.009447, 0.004995, -0.000352], [0.009447, 0.122631, 0.019194, -6.7e-05], [0.004995, 0.019194, 0.108386, -0.00032], [-0.000352, -6.7e-05, -0.00032, 5e-05]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_QQQ=0.1028, w_DOT-USD=0.0000, w_WEAT=0.0000, w_ICSH=0.8972

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_QQQ=0.1028, w_DOT-USD=0.0000, w_WEAT=0.0000, w_ICSH=0.8972
Portfolio annualized return: 13.65%, volatility: 1.70%
Sharpe ratio: (0.1365 - 0.0400) / 0.0170 = 5.6915