4-asset optimization. Max-Sharpe: 0.415. Portfolio: return=14.19%, vol=24.53%. Weights: w_^VIX=0.0000, w_DOT-USD=0.0000, w_TIP=0.0000, w_WEAT=1.0000.

Question:
Assets: ^VIX, DOT-USD, TIP, WEAT
Annualized mean returns: ^VIX:-2.3460, DOT-USD:-0.7037, TIP:0.0341, WEAT:0.1419
Covariance matrix (annualized):
[[1.189431, -0.228039, 0.006811, 0.102528], [-0.228039, 0.488856, -0.003366, -0.033328], [0.006811, -0.003366, 0.000337, 0.000319], [0.102528, -0.033328, 0.000319, 0.060184]]
Risk-free rate: 4.00%
Constraints: weights 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_DOT-USD=0.0000, w_TIP=0.0000, w_WEAT=1.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_^VIX=0.0000, w_DOT-USD=0.0000, w_TIP=0.0000, w_WEAT=1.0000
Portfolio annualized return: 14.19%, volatility: 24.53%
Sharpe ratio: (0.1419 - 0.0400) / 0.2453 = 0.4152


4-asset optimization. Max-Sharpe: 4.488. Portfolio: return=70.16%, vol=14.74%. Weights: w_IVV=0.9058, w_ETH-USD=0.0942, w_BNDX=0.0000, w_VNQ=0.0000.

Question:
Assets: IVV, ETH-USD, BNDX, VNQ
Annualized mean returns: IVV:0.5662, ETH-USD:2.0042, BNDX:0.0288, VNQ:0.2929
Covariance matrix (annualized):
[[0.016442, 0.025407, 0.000195, 0.010777], [0.025407, 0.440779, -0.003834, 0.003749], [0.000195, -0.003834, 0.001234, 0.002391], [0.010777, 0.003749, 0.002391, 0.017776]]
Risk-free rate: 4.00%
Constraints: weights 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=0.9058, w_ETH-USD=0.0942, w_BNDX=0.0000, w_VNQ=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_IVV=0.9058, w_ETH-USD=0.0942, w_BNDX=0.0000, w_VNQ=0.0000
Portfolio annualized return: 70.16%, volatility: 14.74%
Sharpe ratio: (0.7016 - 0.0400) / 0.1474 = 4.4879


4-asset optimization. Max-Sharpe: 10.055. Portfolio: return=98.14%, vol=9.36%. Weights: w_VLUE=0.2310, w_AVAX-USD=0.0000, w_TLT=0.4161, w_SLV=0.3529.

Question:
Assets: VLUE, AVAX-USD, TLT, SLV
Annualized mean returns: VLUE:0.4974, AVAX-USD:-0.2367, TLT:0.3374, SLV:2.0574
Covariance matrix (annualized):
[[0.019289, 0.073299, -0.00183, 0.001601], [0.073299, 0.890962, -0.014402, 0.027775], [-0.00183, -0.014402, 0.009826, -0.00254], [0.001601, 0.027775, -0.00254, 0.055171]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: bull

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

Answer: w_VLUE=0.2310, w_AVAX-USD=0.0000, w_TLT=0.4161, w_SLV=0.3529

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VLUE=0.2310, w_AVAX-USD=0.0000, w_TLT=0.4161, w_SLV=0.3529
Portfolio annualized return: 98.14%, volatility: 9.36%
Sharpe ratio: (0.9814 - 0.0400) / 0.0936 = 10.0550


4-asset optimization. Max-Sharpe: 4.273. Portfolio: return=73.69%, vol=16.31%. Weights: w_VLUE=1.0000, w_SOL-USD=0.0000, w_REZ=0.0000, w_ICSH=0.0000.

Question:
Assets: VLUE, SOL-USD, REZ, ICSH
Annualized mean returns: VLUE:0.7369, SOL-USD:-2.1882, REZ:0.1299, ICSH:0.0398
Covariance matrix (annualized):
[[0.026594, 0.048689, 0.00567, 3.7e-05], [0.048689, 0.504831, -0.001165, -9.2e-05], [0.00567, -0.001165, 0.020904, 8.7e-05], [3.7e-05, -9.2e-05, 8.7e-05, 1.4e-05]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_VLUE=1.0000, w_SOL-USD=0.0000, w_REZ=0.0000, w_ICSH=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VLUE=1.0000, w_SOL-USD=0.0000, w_REZ=0.0000, w_ICSH=0.0000
Portfolio annualized return: 73.69%, volatility: 16.31%
Sharpe ratio: (0.7369 - 0.0400) / 0.1631 = 4.2733


4-asset optimization. Max-Sharpe: 4.865. Portfolio: return=15.37%, vol=2.34%. Weights: w_IWM=0.1227, w_DOT-USD=0.0000, w_STIP=0.8513, w_IYR=0.0260.

Question:
Assets: IWM, DOT-USD, STIP, IYR
Annualized mean returns: IWM:0.7262, DOT-USD:-0.4323, STIP:0.0630, IYR:0.4242
Covariance matrix (annualized):
[[0.028915, 0.025348, -0.000663, 0.012055], [0.025348, 0.377563, -0.000122, 0.011429], [-0.000663, -0.000122, 0.000225, 1.4e-05], [0.012055, 0.011429, 1.4e-05, 0.013651]]
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=0.1227, w_DOT-USD=0.0000, w_STIP=0.8513, w_IYR=0.0260

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_IWM=0.1227, w_DOT-USD=0.0000, w_STIP=0.8513, w_IYR=0.0260
Portfolio annualized return: 15.37%, volatility: 2.34%
Sharpe ratio: (0.1537 - 0.0400) / 0.0234 = 4.8653


4-asset optimization. Max-Sharpe: 2.505. Portfolio: return=5.02%, vol=0.41%. Weights: w_XLU=0.0000, w_BTC-USD=0.0000, w_SGOV=0.9725, w_TLT=0.0275.

Question:
Assets: XLU, BTC-USD, SGOV, TLT
Annualized mean returns: XLU:0.1192, BTC-USD:-0.8630, SGOV:0.0421, TLT:0.3359
Covariance matrix (annualized):
[[0.022015, -0.006076, -2.4e-05, 0.005647], [-0.006076, 0.206787, 4.7e-05, -0.019346], [-2.4e-05, 4.7e-05, 3e-06, 5e-06], [0.005647, -0.019346, 5e-06, 0.017302]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: bear

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

Answer: w_XLU=0.0000, w_BTC-USD=0.0000, w_SGOV=0.9725, w_TLT=0.0275

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLU=0.0000, w_BTC-USD=0.0000, w_SGOV=0.9725, w_TLT=0.0275
Portfolio annualized return: 5.02%, volatility: 0.41%
Sharpe ratio: (0.0502 - 0.0400) / 0.0041 = 2.5046


4-asset optimization. Max-Sharpe: 3.926. Portfolio: return=15.38%, vol=2.90%. Weights: w_XLE=0.1106, w_LINK-USD=0.0000, w_BIL=0.6741, w_DBB=0.2154.

Question:
Assets: XLE, LINK-USD, BIL, DBB
Annualized mean returns: XLE:0.3158, LINK-USD:0.9767, BIL:0.0404, DBB:0.4254
Covariance matrix (annualized):
[[0.024907, 0.016678, -2e-05, -0.003269], [0.016678, 0.738044, 6.8e-05, 0.030268], [-2e-05, 6.8e-05, 4e-06, 1.1e-05], [-0.003269, 0.030268, 1.1e-05, 0.014856]]
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=0.1106, w_LINK-USD=0.0000, w_BIL=0.6741, w_DBB=0.2154

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLE=0.1106, w_LINK-USD=0.0000, w_BIL=0.6741, w_DBB=0.2154
Portfolio annualized return: 15.38%, volatility: 2.90%
Sharpe ratio: (0.1538 - 0.0400) / 0.0290 = 3.9256


4-asset optimization. Max-Sharpe: 1.672. Portfolio: return=21.62%, vol=10.54%. Weights: w_XLU=0.5560, w_SOL-USD=0.0000, w_PPLT=0.0423, w_REZ=0.4017.

Question:
Assets: XLU, SOL-USD, PPLT, REZ
Annualized mean returns: XLU:0.2108, SOL-USD:-2.6537, PPLT:0.2439, REZ:0.2208
Covariance matrix (annualized):
[[0.014159, 0.029526, 0.01336, 0.005796], [0.029526, 0.580596, 0.076046, -7.8e-05], [0.01336, 0.076046, 0.100595, 0.002897], [0.005796, -7.8e-05, 0.002897, 0.020036]]
Risk-free rate: 4.00%
Constraints: weights 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=0.5560, w_SOL-USD=0.0000, w_PPLT=0.0423, w_REZ=0.4017

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLU=0.5560, w_SOL-USD=0.0000, w_PPLT=0.0423, w_REZ=0.4017
Portfolio annualized return: 21.62%, volatility: 10.54%
Sharpe ratio: (0.2162 - 0.0400) / 0.1054 = 1.6722


4-asset optimization. Max-Sharpe: 3.508. Portfolio: return=22.48%, vol=5.27%. Weights: w_FXI=0.1225, w_SOL-USD=0.0000, w_LQD=0.8775, w_SCHH=0.0000.

Question:
Assets: FXI, SOL-USD, LQD, SCHH
Annualized mean returns: FXI:0.2845, SOL-USD:0.4235, LQD:0.2165, SCHH:-0.0441
Covariance matrix (annualized):
[[0.02992, 0.037712, 7e-06, 0.006923], [0.037712, 0.38002, 0.004775, 0.037425], [7e-06, 0.004775, 0.00302, 0.003477], [0.006923, 0.037425, 0.003477, 0.019264]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: bull

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

Answer: w_FXI=0.1225, w_SOL-USD=0.0000, w_LQD=0.8775, w_SCHH=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_FXI=0.1225, w_SOL-USD=0.0000, w_LQD=0.8775, w_SCHH=0.0000
Portfolio annualized return: 22.48%, volatility: 5.27%
Sharpe ratio: (0.2248 - 0.0400) / 0.0527 = 3.5077


4-asset optimization. Max-Sharpe: 5.710. Portfolio: return=6.80%, vol=0.49%. Weights: w_EFA=0.0078, w_ADA-USD=0.0000, w_ICSH=0.9728, w_IAU=0.0194.

Question:
Assets: EFA, ADA-USD, ICSH, IAU
Annualized mean returns: EFA:0.4942, ADA-USD:-2.0732, ICSH:0.0558, IAU:0.5076
Covariance matrix (annualized):
[[0.023419, 0.009831, 5.9e-05, 0.007762], [0.009831, 0.790047, -0.000299, -0.000917], [5.9e-05, -0.000299, 1.4e-05, -8e-06], [0.007762, -0.000917, -8e-06, 0.017969]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_EFA=0.0078, w_ADA-USD=0.0000, w_ICSH=0.9728, w_IAU=0.0194

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EFA=0.0078, w_ADA-USD=0.0000, w_ICSH=0.9728, w_IAU=0.0194
Portfolio annualized return: 6.80%, volatility: 0.49%
Sharpe ratio: (0.0680 - 0.0400) / 0.0049 = 5.7096


4-asset optimization. Max-Sharpe: 2.178. Portfolio: return=55.96%, vol=23.85%. Weights: w_EWJ=0.0000, w_LINK-USD=0.0000, w_TLT=0.0000, w_CPER=1.0000.

Question:
Assets: EWJ, LINK-USD, TLT, CPER
Annualized mean returns: EWJ:0.1405, LINK-USD:-1.1746, TLT:-0.0025, CPER:0.5596
Covariance matrix (annualized):
[[0.028807, 0.016041, 0.005516, 0.01361], [0.016041, 0.433304, -0.017175, 0.005751], [0.005516, -0.017175, 0.015754, 0.000576], [0.01361, 0.005751, 0.000576, 0.056901]]
Risk-free rate: 4.00%
Constraints: weights 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_LINK-USD=0.0000, w_TLT=0.0000, w_CPER=1.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EWJ=0.0000, w_LINK-USD=0.0000, w_TLT=0.0000, w_CPER=1.0000
Portfolio annualized return: 55.96%, volatility: 23.85%
Sharpe ratio: (0.5596 - 0.0400) / 0.2385 = 2.1785


4-asset optimization. Max-Sharpe: 4.119. Portfolio: return=8.90%, vol=1.19%. Weights: w_EFA=0.0000, w_BNB-USD=0.0178, w_DBB=0.0562, w_CSHI=0.9259.

Question:
Assets: EFA, BNB-USD, DBB, CSHI
Annualized mean returns: EFA:0.1514, BNB-USD:0.6786, DBB:0.3520, CSHI:0.0617
Covariance matrix (annualized):
[[0.016581, 0.006909, 0.006428, 7.3e-05], [0.006909, 0.067522, 0.013788, -0.000147], [0.006428, 0.013788, 0.015077, -0.000209], [7.3e-05, -0.000147, -0.000209, 8.3e-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_EFA=0.0000, w_BNB-USD=0.0178, w_DBB=0.0562, w_CSHI=0.9259

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EFA=0.0000, w_BNB-USD=0.0178, w_DBB=0.0562, w_CSHI=0.9259
Portfolio annualized return: 8.90%, volatility: 1.19%
Sharpe ratio: (0.0890 - 0.0400) / 0.0119 = 4.1195


4-asset optimization. Max-Sharpe: 4.033. Portfolio: return=7.27%, vol=0.81%. Weights: w_^VIX=0.0060, w_AVAX-USD=0.0024, w_IYR=0.0000, w_BIL=0.9916.

Question:
Assets: ^VIX, AVAX-USD, IYR, BIL
Annualized mean returns: ^VIX:5.5834, AVAX-USD:-0.8652, IYR:-0.6715, BIL:0.0416
Covariance matrix (annualized):
[[2.057724, -0.581109, -0.177145, 0.000201], [-0.581109, 0.799489, -0.001234, -0.000269], [-0.177145, -0.001234, 0.042329, -3e-05], [0.000201, -0.000269, -3e-05, 3e-06]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: bear

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

Answer: w_^VIX=0.0060, w_AVAX-USD=0.0024, w_IYR=0.0000, w_BIL=0.9916

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_^VIX=0.0060, w_AVAX-USD=0.0024, w_IYR=0.0000, w_BIL=0.9916
Portfolio annualized return: 7.27%, volatility: 0.81%
Sharpe ratio: (0.0727 - 0.0400) / 0.0081 = 4.0326


4-asset optimization. Max-Sharpe: 4.098. Portfolio: return=5.68%, vol=0.41%. Weights: w_MTUM=0.0252, w_DOT-USD=0.0001, w_WEAT=0.0000, w_ICSH=0.9747.

Question:
Assets: MTUM, DOT-USD, WEAT, ICSH
Annualized mean returns: MTUM:0.2698, DOT-USD:0.8790, WEAT:-0.2654, ICSH:0.0512
Covariance matrix (annualized):
[[0.011271, 0.023741, -0.003895, -5.8e-05], [0.023741, 0.44468, -0.004158, 0.000204], [-0.003895, -0.004158, 0.020937, -2e-06], [-5.8e-05, 0.000204, -2e-06, 1.3e-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_MTUM=0.0252, w_DOT-USD=0.0001, w_WEAT=0.0000, w_ICSH=0.9747

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_MTUM=0.0252, w_DOT-USD=0.0001, w_WEAT=0.0000, w_ICSH=0.9747
Portfolio annualized return: 5.68%, volatility: 0.41%
Sharpe ratio: (0.0568 - 0.0400) / 0.0041 = 4.0978


4-asset optimization. Max-Sharpe: 1.061. Portfolio: return=18.10%, vol=13.29%. Weights: w_EEM=0.3997, w_XRP-USD=0.0000, w_INDS=0.6003, w_DBC=0.0000.

Question:
Assets: EEM, XRP-USD, INDS, DBC
Annualized mean returns: EEM:0.1881, XRP-USD:-2.4519, INDS:0.1763, DBC:-0.0043
Covariance matrix (annualized):
[[0.030018, 0.079529, 0.010906, 0.013514], [0.079529, 0.499386, 0.027544, 0.040061], [0.010906, 0.027544, 0.021171, 0.005018], [0.013514, 0.040061, 0.005018, 0.017545]]
Risk-free rate: 4.00%
Constraints: weights 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=0.3997, w_XRP-USD=0.0000, w_INDS=0.6003, w_DBC=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EEM=0.3997, w_XRP-USD=0.0000, w_INDS=0.6003, w_DBC=0.0000
Portfolio annualized return: 18.10%, volatility: 13.29%
Sharpe ratio: (0.1810 - 0.0400) / 0.1329 = 1.0613


4-asset optimization. Max-Sharpe: 3.643. Portfolio: return=4.81%, vol=0.22%. Weights: w_VEA=0.0034, w_SOL-USD=0.0005, w_SGOV=0.9781, w_STIP=0.0180.

Question:
Assets: VEA, SOL-USD, SGOV, STIP
Annualized mean returns: VEA:0.1292, SOL-USD:0.6946, SGOV:0.0476, STIP:0.0468
Covariance matrix (annualized):
[[0.014933, 0.042416, -3.5e-05, 0.001006], [0.042416, 0.441212, -1.9e-05, 0.004088], [-3.5e-05, -1.9e-05, 5e-06, -6e-06], [0.001006, 0.004088, -6e-06, 0.000251]]
Risk-free rate: 4.00%
Constraints: weights 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=0.0034, w_SOL-USD=0.0005, w_SGOV=0.9781, w_STIP=0.0180

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VEA=0.0034, w_SOL-USD=0.0005, w_SGOV=0.9781, w_STIP=0.0180
Portfolio annualized return: 4.81%, volatility: 0.22%
Sharpe ratio: (0.0481 - 0.0400) / 0.0022 = 3.6426


4-asset optimization. Max-Sharpe: -0.483. Portfolio: return=-7.43%, vol=23.65%. Weights: w_XLP=0.0000, w_DOT-USD=0.0000, w_IYR=0.0000, w_BNO=1.0000.

Question:
Assets: XLP, DOT-USD, IYR, BNO
Annualized mean returns: XLP:-0.3468, DOT-USD:-2.3441, IYR:-0.1648, BNO:-0.0743
Covariance matrix (annualized):
[[0.012919, -0.005734, 0.008477, -0.005286], [-0.005734, 0.601593, 0.00779, 0.055127], [0.008477, 0.00779, 0.015905, 3.3e-05], [-0.005286, 0.055127, 3.3e-05, 0.055947]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_XLP=0.0000, w_DOT-USD=0.0000, w_IYR=0.0000, w_BNO=1.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLP=0.0000, w_DOT-USD=0.0000, w_IYR=0.0000, w_BNO=1.0000
Portfolio annualized return: -7.43%, volatility: 23.65%
Sharpe ratio: (-0.0743 - 0.0400) / 0.2365 = -0.4832


4-asset optimization. Max-Sharpe: 2.405. Portfolio: return=5.40%, vol=0.58%. Weights: w_EEM=0.0000, w_MATIC-USD=0.0000, w_VCIT=0.0000, w_CSHI=1.0000.

Question:
Assets: EEM, MATIC-USD, VCIT, CSHI
Annualized mean returns: EEM:0.0013, MATIC-USD:0.4558, VCIT:-0.0036, CSHI:0.0540
Covariance matrix (annualized):
[[0.017485, 0.028276, 0.003518, 0.000269], [0.028276, 0.872039, 0.01614, 0.00197], [0.003518, 0.01614, 0.003314, 0.000124], [0.000269, 0.00197, 0.000124, 3.4e-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_EEM=0.0000, w_MATIC-USD=0.0000, w_VCIT=0.0000, w_CSHI=1.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EEM=0.0000, w_MATIC-USD=0.0000, w_VCIT=0.0000, w_CSHI=1.0000
Portfolio annualized return: 5.40%, volatility: 0.58%
Sharpe ratio: (0.0540 - 0.0400) / 0.0058 = 2.4052


4-asset optimization. Max-Sharpe: -1.234. Portfolio: return=-117.32%, vol=98.30%. Weights: w_VEA=0.0000, w_SOL-USD=1.0000, w_JNK=0.0000, w_CSHI=0.0000.

Question:
Assets: VEA, SOL-USD, JNK, CSHI
Annualized mean returns: VEA:-0.1694, SOL-USD:-1.1732, JNK:-0.2098, CSHI:0.0086
Covariance matrix (annualized):
[[0.041064, 0.056666, 0.013786, 0.005916], [0.056666, 0.966239, 0.026013, 0.010063], [0.013786, 0.026013, 0.007304, 0.002916], [0.005916, 0.010063, 0.002916, 0.002046]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: bear

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

Answer: w_VEA=0.0000, w_SOL-USD=1.0000, w_JNK=0.0000, w_CSHI=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VEA=0.0000, w_SOL-USD=1.0000, w_JNK=0.0000, w_CSHI=0.0000
Portfolio annualized return: -117.32%, volatility: 98.30%
Sharpe ratio: (-1.1732 - 0.0400) / 0.9830 = -1.2342


4-asset optimization. Max-Sharpe: 3.173. Portfolio: return=5.71%, vol=0.54%. Weights: w_XLF=0.0000, w_SOL-USD=0.0021, w_PPLT=0.0000, w_CSHI=0.9979.

Question:
Assets: XLF, SOL-USD, PPLT, CSHI
Annualized mean returns: XLF:0.1073, SOL-USD:1.0227, PPLT:-0.5290, CSHI:0.0551
Covariance matrix (annualized):
[[0.027967, 0.068315, 0.003029, 0.000345], [0.068315, 0.519338, 0.035483, 0.000571], [0.003029, 0.035483, 0.039478, 1.9e-05], [0.000345, 0.000571, 1.9e-05, 2.4e-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_XLF=0.0000, w_SOL-USD=0.0021, w_PPLT=0.0000, w_CSHI=0.9979

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLF=0.0000, w_SOL-USD=0.0021, w_PPLT=0.0000, w_CSHI=0.9979
Portfolio annualized return: 5.71%, volatility: 0.54%
Sharpe ratio: (0.0571 - 0.0400) / 0.0054 = 3.1730


4-asset optimization. Max-Sharpe: 1.012. Portfolio: return=15.63%, vol=11.49%. Weights: w_XLY=0.0000, w_SOL-USD=0.0000, w_VNQI=1.0000, w_CSHI=0.0000.

Question:
Assets: XLY, SOL-USD, VNQI, CSHI
Annualized mean returns: XLY:-0.5254, SOL-USD:-1.8356, VNQI:0.1563, CSHI:0.0331
Covariance matrix (annualized):
[[0.031397, 0.058128, 0.008866, 0.000365], [0.058128, 0.789324, 0.010544, 0.001495], [0.008866, 0.010544, 0.013209, -5.2e-05], [0.000365, 0.001495, -5.2e-05, 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_XLY=0.0000, w_SOL-USD=0.0000, w_VNQI=1.0000, w_CSHI=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLY=0.0000, w_SOL-USD=0.0000, w_VNQI=1.0000, w_CSHI=0.0000
Portfolio annualized return: 15.63%, volatility: 11.49%
Sharpe ratio: (0.1563 - 0.0400) / 0.1149 = 1.0121


4-asset optimization. Max-Sharpe: 1.278. Portfolio: return=24.66%, vol=16.17%. Weights: w_XLP=0.8526, w_LINK-USD=0.1474, w_ITB=0.0000, w_BNDX=0.0000.

Question:
Assets: XLP, LINK-USD, ITB, BNDX
Annualized mean returns: XLP:0.1451, LINK-USD:0.8333, ITB:-0.2296, BNDX:-0.0048
Covariance matrix (annualized):
[[0.015017, 0.003349, 0.011926, 0.001202], [0.003349, 0.661315, 0.022394, 0.005788], [0.011926, 0.022394, 0.058317, 0.003016], [0.001202, 0.005788, 0.003016, 0.001415]]
Risk-free rate: 4.00%
Constraints: weights 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=0.8526, w_LINK-USD=0.1474, w_ITB=0.0000, w_BNDX=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLP=0.8526, w_LINK-USD=0.1474, w_ITB=0.0000, w_BNDX=0.0000
Portfolio annualized return: 24.66%, volatility: 16.17%
Sharpe ratio: (0.2466 - 0.0400) / 0.1617 = 1.2779


4-asset optimization. Max-Sharpe: 0.964. Portfolio: return=5.61%, vol=1.67%. Weights: w_IWM=0.0000, w_ETH-USD=0.0000, w_HAUZ=0.0000, w_TIP=1.0000.

Question:
Assets: IWM, ETH-USD, HAUZ, TIP
Annualized mean returns: IWM:-0.1952, ETH-USD:-0.3550, HAUZ:0.0413, TIP:0.0561
Covariance matrix (annualized):
[[0.032296, 0.041568, 0.019536, 0.001506], [0.041568, 0.324314, 0.036971, 0.002593], [0.019536, 0.036971, 0.018607, 0.001202], [0.001506, 0.002593, 0.001202, 0.000277]]
Risk-free rate: 4.00%
Constraints: weights 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_ETH-USD=0.0000, w_HAUZ=0.0000, w_TIP=1.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_IWM=0.0000, w_ETH-USD=0.0000, w_HAUZ=0.0000, w_TIP=1.0000
Portfolio annualized return: 5.61%, volatility: 1.67%
Sharpe ratio: (0.0561 - 0.0400) / 0.0167 = 0.9644


4-asset optimization. Max-Sharpe: -0.198. Portfolio: return=1.41%, vol=13.05%. Weights: w_XLI=1.0000, w_BTC-USD=0.0000, w_USO=0.0000, w_ITB=0.0000.

Question:
Assets: XLI, BTC-USD, USO, ITB
Annualized mean returns: XLI:0.0141, BTC-USD:-0.6957, USO:-0.2969, ITB:-0.4689
Covariance matrix (annualized):
[[0.017023, 0.019933, -0.000665, 0.016535], [0.019933, 0.103729, 0.014957, 0.01885], [-0.000665, 0.014957, 0.069694, -0.01663], [0.016535, 0.01885, -0.01663, 0.056425]]
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=1.0000, w_BTC-USD=0.0000, w_USO=0.0000, w_ITB=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLI=1.0000, w_BTC-USD=0.0000, w_USO=0.0000, w_ITB=0.0000
Portfolio annualized return: 1.41%, volatility: 13.05%
Sharpe ratio: (0.0141 - 0.0400) / 0.1305 = -0.1981


4-asset optimization. Max-Sharpe: 2.553. Portfolio: return=4.99%, vol=0.39%. Weights: w_QQQ=0.0125, w_ADA-USD=0.0000, w_TLT=0.0284, w_SGOV=0.9592.

Question:
Assets: QQQ, ADA-USD, TLT, SGOV
Annualized mean returns: QQQ:0.1034, ADA-USD:-1.0290, TLT:0.2535, SGOV:0.0432
Covariance matrix (annualized):
[[0.018102, 0.064319, -0.001419, -9.2e-05], [0.064319, 0.573957, -0.012693, -0.000221], [-0.001419, -0.012693, 0.010854, 3.7e-05], [-9.2e-05, -0.000221, 3.7e-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_QQQ=0.0125, w_ADA-USD=0.0000, w_TLT=0.0284, w_SGOV=0.9592

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_QQQ=0.0125, w_ADA-USD=0.0000, w_TLT=0.0284, w_SGOV=0.9592
Portfolio annualized return: 4.99%, volatility: 0.39%
Sharpe ratio: (0.0499 - 0.0400) / 0.0039 = 2.5526


4-asset optimization. Max-Sharpe: 2.735. Portfolio: return=7.58%, vol=1.31%. Weights: w_SPY=0.0560, w_ADA-USD=0.0047, w_TLH=0.0000, w_SGOV=0.9393.

Question:
Assets: SPY, ADA-USD, TLH, SGOV
Annualized mean returns: SPY:0.5488, ADA-USD:1.1632, TLH:-0.3298, SGOV:0.0422
Covariance matrix (annualized):
[[0.03755, 0.052668, 0.011637, 9.1e-05], [0.052668, 0.479531, -0.003843, 0.000194], [0.011637, -0.003843, 0.015822, 2e-05], [9.1e-05, 0.000194, 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_SPY=0.0560, w_ADA-USD=0.0047, w_TLH=0.0000, w_SGOV=0.9393

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_SPY=0.0560, w_ADA-USD=0.0047, w_TLH=0.0000, w_SGOV=0.9393
Portfolio annualized return: 7.58%, volatility: 1.31%
Sharpe ratio: (0.0758 - 0.0400) / 0.0131 = 2.7352


4-asset optimization. Max-Sharpe: 1.872. Portfolio: return=5.13%, vol=0.60%. Weights: w_QQQ=0.0000, w_SOL-USD=0.0012, w_CSHI=0.9988, w_XHB=0.0000.

Question:
Assets: QQQ, SOL-USD, CSHI, XHB
Annualized mean returns: QQQ:0.2623, SOL-USD:0.5304, CSHI:0.0507, XHB:-0.4314
Covariance matrix (annualized):
[[0.036564, 0.066348, 0.000637, 0.021252], [0.066348, 0.499258, 0.000976, 0.037483], [0.000637, 0.000976, 3.3e-05, 0.000566], [0.021252, 0.037483, 0.000566, 0.0619]]
Risk-free rate: 4.00%
Constraints: weights 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_SOL-USD=0.0012, w_CSHI=0.9988, w_XHB=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_QQQ=0.0000, w_SOL-USD=0.0012, w_CSHI=0.9988, w_XHB=0.0000
Portfolio annualized return: 5.13%, volatility: 0.60%
Sharpe ratio: (0.0513 - 0.0400) / 0.0060 = 1.8721


4-asset optimization. Max-Sharpe: 3.676. Portfolio: return=17.96%, vol=3.80%. Weights: w_IVV=0.0583, w_XRP-USD=0.0234, w_SCHH=0.0000, w_JNK=0.9183.

Question:
Assets: IVV, XRP-USD, SCHH, JNK
Annualized mean returns: IVV:0.3172, XRP-USD:1.4899, SCHH:-0.0005, JNK:0.1375
Covariance matrix (annualized):
[[0.009831, 0.020636, 0.005118, 0.00197], [0.020636, 0.438646, 0.024876, 0.00384], [0.005118, 0.024876, 0.019441, 0.00206], [0.00197, 0.00384, 0.00206, 0.000875]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: bull

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

Answer: w_IVV=0.0583, w_XRP-USD=0.0234, w_SCHH=0.0000, w_JNK=0.9183

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_IVV=0.0583, w_XRP-USD=0.0234, w_SCHH=0.0000, w_JNK=0.9183
Portfolio annualized return: 17.96%, volatility: 3.80%
Sharpe ratio: (0.1796 - 0.0400) / 0.0380 = 3.6757


4-asset optimization. Max-Sharpe: 3.773. Portfolio: return=9.43%, vol=1.44%. Weights: w_XLY=0.0221, w_ADA-USD=0.0043, w_STIP=0.6311, w_CSHI=0.3425.

Question:
Assets: XLY, ADA-USD, STIP, CSHI
Annualized mean returns: XLY:0.3193, ADA-USD:1.7239, STIP:0.1021, CSHI:0.0450
Covariance matrix (annualized):
[[0.024919, 0.050951, 0.000289, 0.000329], [0.050951, 0.552672, 0.004617, 4e-06], [0.000289, 0.004617, 0.000346, -2.3e-05], [0.000329, 4e-06, -2.3e-05, 7.7e-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_XLY=0.0221, w_ADA-USD=0.0043, w_STIP=0.6311, w_CSHI=0.3425

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLY=0.0221, w_ADA-USD=0.0043, w_STIP=0.6311, w_CSHI=0.3425
Portfolio annualized return: 9.43%, volatility: 1.44%
Sharpe ratio: (0.0943 - 0.0400) / 0.0144 = 3.7727


4-asset optimization. Max-Sharpe: 3.847. Portfolio: return=23.58%, vol=5.09%. Weights: w_XLY=0.0942, w_SOL-USD=0.0000, w_DBA=0.0847, w_EMB=0.8211.

Question:
Assets: XLY, SOL-USD, DBA, EMB
Annualized mean returns: XLY:0.4494, SOL-USD:0.9362, DBA:0.2445, EMB:0.2103
Covariance matrix (annualized):
[[0.026864, 0.059464, 0.006317, 0.002865], [0.059464, 0.619816, 0.007323, 0.009786], [0.006317, 0.007323, 0.015468, 0.000975], [0.002865, 0.009786, 0.000975, 0.002315]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: bull

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

Answer: w_XLY=0.0942, w_SOL-USD=0.0000, w_DBA=0.0847, w_EMB=0.8211

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLY=0.0942, w_SOL-USD=0.0000, w_DBA=0.0847, w_EMB=0.8211
Portfolio annualized return: 23.58%, volatility: 5.09%
Sharpe ratio: (0.2358 - 0.0400) / 0.0509 = 3.8466


4-asset optimization. Max-Sharpe: 1.207. Portfolio: return=4.73%, vol=0.60%. Weights: w_XLE=0.0000, w_SOL-USD=0.0067, w_IEF=0.0510, w_BIL=0.9423.

Question:
Assets: XLE, SOL-USD, IEF, BIL
Annualized mean returns: XLE:-0.2352, SOL-USD:0.8418, IEF:0.0678, BIL:0.0405
Covariance matrix (annualized):
[[0.101812, 0.130743, -0.001767, -2e-05], [0.130743, 0.747908, -0.016839, -0.000205], [-0.001767, -0.016839, 0.005071, -7e-06], [-2e-05, -0.000205, -7e-06, 4e-06]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: bear

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

Answer: w_XLE=0.0000, w_SOL-USD=0.0067, w_IEF=0.0510, w_BIL=0.9423

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLE=0.0000, w_SOL-USD=0.0067, w_IEF=0.0510, w_BIL=0.9423
Portfolio annualized return: 4.73%, volatility: 0.60%
Sharpe ratio: (0.0473 - 0.0400) / 0.0060 = 1.2068


4-asset optimization. Max-Sharpe: 2.455. Portfolio: return=147.93%, vol=58.62%. Weights: w_XLRE=0.0000, w_DOT-USD=1.0000, w_CPER=0.0000, w_SHV=0.0000.

Question:
Assets: XLRE, DOT-USD, CPER, SHV
Annualized mean returns: XLRE:-0.2079, DOT-USD:1.4793, CPER:0.0439, SHV:0.0386
Covariance matrix (annualized):
[[0.054184, 0.050318, 0.036752, -8e-06], [0.050318, 0.343648, 0.069159, 3.5e-05], [0.036752, 0.069159, 0.100683, -0.000133], [-8e-06, 3.5e-05, -0.000133, 4e-06]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_XLRE=0.0000, w_DOT-USD=1.0000, w_CPER=0.0000, w_SHV=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLRE=0.0000, w_DOT-USD=1.0000, w_CPER=0.0000, w_SHV=0.0000
Portfolio annualized return: 147.93%, volatility: 58.62%
Sharpe ratio: (1.4793 - 0.0400) / 0.5862 = 2.4552


4-asset optimization. Max-Sharpe: 0.831. Portfolio: return=14.35%, vol=12.45%. Weights: w_IVV=1.0000, w_ETH-USD=0.0000, w_HAUZ=0.0000, w_LQD=0.0000.

Question:
Assets: IVV, ETH-USD, HAUZ, LQD
Annualized mean returns: IVV:0.1435, ETH-USD:-3.2970, HAUZ:-0.1376, LQD:-0.0326
Covariance matrix (annualized):
[[0.015499, 0.042392, 0.005936, 0.000374], [0.042392, 0.335135, 0.024789, -0.000538], [0.005936, 0.024789, 0.010728, 0.002519], [0.000374, -0.000538, 0.002519, 0.00192]]
Risk-free rate: 4.00%
Constraints: weights 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=1.0000, w_ETH-USD=0.0000, w_HAUZ=0.0000, w_LQD=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_IVV=1.0000, w_ETH-USD=0.0000, w_HAUZ=0.0000, w_LQD=0.0000
Portfolio annualized return: 14.35%, volatility: 12.45%
Sharpe ratio: (0.1435 - 0.0400) / 0.1245 = 0.8314


4-asset optimization. Max-Sharpe: 2.218. Portfolio: return=102.46%, vol=44.39%. Weights: w_EEM=0.0000, w_SOL-USD=0.0000, w_PALL=1.0000, w_SCHP=0.0000.

Question:
Assets: EEM, SOL-USD, PALL, SCHP
Annualized mean returns: EEM:0.0452, SOL-USD:-3.9389, PALL:1.0246, SCHP:0.0038
Covariance matrix (annualized):
[[0.030542, 0.075074, 0.034166, -0.000953], [0.075074, 0.547157, 0.097027, -0.003316], [0.034166, 0.097027, 0.197041, 0.001702], [-0.000953, -0.003316, 0.001702, 0.001047]]
Risk-free rate: 4.00%
Constraints: weights 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=0.0000, w_PALL=1.0000, w_SCHP=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EEM=0.0000, w_SOL-USD=0.0000, w_PALL=1.0000, w_SCHP=0.0000
Portfolio annualized return: 102.46%, volatility: 44.39%
Sharpe ratio: (1.0246 - 0.0400) / 0.4439 = 2.2180


4-asset optimization. Max-Sharpe: 1.184. Portfolio: return=4.24%, vol=0.20%. Weights: w_QUAL=0.0000, w_SOL-USD=0.0000, w_SGOV=1.0000, w_USO=0.0000.

Question:
Assets: QUAL, SOL-USD, SGOV, USO
Annualized mean returns: QUAL:-0.2033, SOL-USD:-1.6968, SGOV:0.0424, USO:-0.7338
Covariance matrix (annualized):
[[0.020234, 0.045414, -3e-05, 0.008209], [0.045414, 0.78307, 0.000169, 0.04698], [-3e-05, 0.000169, 4e-06, 0.000102], [0.008209, 0.04698, 0.000102, 0.056003]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_QUAL=0.0000, w_SOL-USD=0.0000, w_SGOV=1.0000, w_USO=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_QUAL=0.0000, w_SOL-USD=0.0000, w_SGOV=1.0000, w_USO=0.0000
Portfolio annualized return: 4.24%, volatility: 0.20%
Sharpe ratio: (0.0424 - 0.0400) / 0.0020 = 1.1841


4-asset optimization. Max-Sharpe: 4.123. Portfolio: return=35.84%, vol=7.72%. Weights: w_XLRE=0.0000, w_LINK-USD=0.0321, w_VNQ=0.5508, w_DBC=0.4171.

Question:
Assets: XLRE, LINK-USD, VNQ, DBC
Annualized mean returns: XLRE:0.2725, LINK-USD:0.7385, VNQ:0.3112, DBC:0.3915
Covariance matrix (annualized):
[[0.013283, 0.022902, 0.013119, -0.007879], [0.022902, 0.478054, 0.024751, -0.038094], [0.013119, 0.024751, 0.013396, -0.007417], [-0.007879, -0.038094, -0.007417, 0.028514]]
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=0.0000, w_LINK-USD=0.0321, w_VNQ=0.5508, w_DBC=0.4171

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLRE=0.0000, w_LINK-USD=0.0321, w_VNQ=0.5508, w_DBC=0.4171
Portfolio annualized return: 35.84%, volatility: 7.72%
Sharpe ratio: (0.3584 - 0.0400) / 0.0772 = 4.1228


4-asset optimization. Max-Sharpe: 1.897. Portfolio: return=70.16%, vol=34.87%. Weights: w_SPY=0.2411, w_XRP-USD=0.0000, w_UNG=0.7589, w_VNQ=0.0000.

Question:
Assets: SPY, XRP-USD, UNG, VNQ
Annualized mean returns: SPY:0.0966, XRP-USD:-2.4117, UNG:0.8938, VNQ:-0.0118
Covariance matrix (annualized):
[[0.01997, 0.069092, 0.00736, 0.007165], [0.069092, 0.512719, -0.001449, 0.024977], [0.00736, -0.001449, 0.204394, 0.016059], [0.007165, 0.024977, 0.016059, 0.019384]]
Risk-free rate: 4.00%
Constraints: weights 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=0.2411, w_XRP-USD=0.0000, w_UNG=0.7589, w_VNQ=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_SPY=0.2411, w_XRP-USD=0.0000, w_UNG=0.7589, w_VNQ=0.0000
Portfolio annualized return: 70.16%, volatility: 34.87%
Sharpe ratio: (0.7016 - 0.0400) / 0.3487 = 1.8974


4-asset optimization. Max-Sharpe: 1.767. Portfolio: return=12.51%, vol=4.82%. Weights: w_VLUE=0.0917, w_AVAX-USD=0.0000, w_EMB=0.8847, w_REZ=0.0235.

Question:
Assets: VLUE, AVAX-USD, EMB, REZ
Annualized mean returns: VLUE:0.2356, AVAX-USD:-5.1973, EMB:0.1133, REZ:0.1375
Covariance matrix (annualized):
[[0.022696, 0.073074, 0.003528, 0.005386], [0.073074, 0.655008, 0.013468, 0.011786], [0.003528, 0.013468, 0.001842, 0.001901], [0.005386, 0.011786, 0.001901, 0.020489]]
Risk-free rate: 4.00%
Constraints: weights 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=0.0917, w_AVAX-USD=0.0000, w_EMB=0.8847, w_REZ=0.0235

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VLUE=0.0917, w_AVAX-USD=0.0000, w_EMB=0.8847, w_REZ=0.0235
Portfolio annualized return: 12.51%, volatility: 4.82%
Sharpe ratio: (0.1251 - 0.0400) / 0.0482 = 1.7675


4-asset optimization. Max-Sharpe: 2.016. Portfolio: return=23.95%, vol=9.90%. Weights: w_XLU=0.5101, w_DOT-USD=0.0000, w_PDBC=0.4899, w_REZ=0.0000.

Question:
Assets: XLU, DOT-USD, PDBC, REZ
Annualized mean returns: XLU:0.1860, DOT-USD:-0.6866, PDBC:0.2953, REZ:0.0885
Covariance matrix (annualized):
[[0.01906, -0.012397, -0.00522, 0.012621], [-0.012397, 0.380887, -0.02032, -0.000983], [-0.00522, -0.02032, 0.031024, -0.005816], [0.012621, -0.000983, -0.005816, 0.018366]]
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=0.5101, w_DOT-USD=0.0000, w_PDBC=0.4899, w_REZ=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLU=0.5101, w_DOT-USD=0.0000, w_PDBC=0.4899, w_REZ=0.0000
Portfolio annualized return: 23.95%, volatility: 9.90%
Sharpe ratio: (0.2395 - 0.0400) / 0.0990 = 2.0159


4-asset optimization. Max-Sharpe: 4.841. Portfolio: return=5.75%, vol=0.36%. Weights: w_XLRE=0.0000, w_BNB-USD=0.0020, w_ICSH=0.9898, w_HAUZ=0.0083.

Question:
Assets: XLRE, BNB-USD, ICSH, HAUZ
Annualized mean returns: XLRE:0.0128, BNB-USD:0.5725, ICSH:0.0543, HAUZ:0.3192
Covariance matrix (annualized):
[[0.017584, 0.001012, 0.000121, 0.008116], [0.001012, 0.079542, 0.000252, -0.000964], [0.000121, 0.000252, 9e-06, 0.000124], [0.008116, -0.000964, 0.000124, 0.010679]]
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=0.0000, w_BNB-USD=0.0020, w_ICSH=0.9898, w_HAUZ=0.0083

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLRE=0.0000, w_BNB-USD=0.0020, w_ICSH=0.9898, w_HAUZ=0.0083
Portfolio annualized return: 5.75%, volatility: 0.36%
Sharpe ratio: (0.0575 - 0.0400) / 0.0036 = 4.8413


4-asset optimization. Max-Sharpe: 4.653. Portfolio: return=58.55%, vol=11.72%. Weights: w_XLK=0.2689, w_ETH-USD=0.1447, w_REZ=0.0000, w_IEF=0.5864.

Question:
Assets: XLK, ETH-USD, REZ, IEF
Annualized mean returns: XLK:0.5265, ETH-USD:2.6999, REZ:0.0687, IEF:0.0907
Covariance matrix (annualized):
[[0.020623, 0.052016, -0.004195, -0.001386], [0.052016, 0.365945, 0.011605, 0.000139], [-0.004195, 0.011605, 0.022994, 0.003768], [-0.001386, 0.000139, 0.003768, 0.00278]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: bull

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

Answer: w_XLK=0.2689, w_ETH-USD=0.1447, w_REZ=0.0000, w_IEF=0.5864

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLK=0.2689, w_ETH-USD=0.1447, w_REZ=0.0000, w_IEF=0.5864
Portfolio annualized return: 58.55%, volatility: 11.72%
Sharpe ratio: (0.5855 - 0.0400) / 0.1172 = 4.6525


4-asset optimization. Max-Sharpe: 3.780. Portfolio: return=16.78%, vol=3.38%. Weights: w_XLF=0.0000, w_BTC-USD=0.0581, w_HYG=0.9419, w_SCHH=0.0000.

Question:
Assets: XLF, BTC-USD, HYG, SCHH
Annualized mean returns: XLF:0.1764, BTC-USD:0.6820, HYG:0.1361, SCHH:0.0053
Covariance matrix (annualized):
[[0.019162, 0.012966, 0.002543, 0.009551], [0.012966, 0.077836, 0.001296, 0.014061], [0.002543, 0.001296, 0.000833, 0.002128], [0.009551, 0.014061, 0.002128, 0.019491]]
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_BTC-USD=0.0581, w_HYG=0.9419, w_SCHH=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLF=0.0000, w_BTC-USD=0.0581, w_HYG=0.9419, w_SCHH=0.0000
Portfolio annualized return: 16.78%, volatility: 3.38%
Sharpe ratio: (0.1678 - 0.0400) / 0.0338 = 3.7796


4-asset optimization. Max-Sharpe: 2.526. Portfolio: return=168.80%, vol=65.24%. Weights: w_ACWI=0.0000, w_ETH-USD=1.0000, w_MORT=0.0000, w_TLH=0.0000.

Question:
Assets: ACWI, ETH-USD, MORT, TLH
Annualized mean returns: ACWI:-0.0398, ETH-USD:1.6880, MORT:0.0816, TLH:-0.0992
Covariance matrix (annualized):
[[0.013074, 0.037277, 0.013097, 0.004594], [0.037277, 0.425582, 0.054132, 0.025241], [0.013097, 0.054132, 0.027895, 0.008701], [0.004594, 0.025241, 0.008701, 0.010589]]
Risk-free rate: 4.00%
Constraints: weights 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_ETH-USD=1.0000, w_MORT=0.0000, w_TLH=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_ACWI=0.0000, w_ETH-USD=1.0000, w_MORT=0.0000, w_TLH=0.0000
Portfolio annualized return: 168.80%, volatility: 65.24%
Sharpe ratio: (1.6880 - 0.0400) / 0.6524 = 2.5262


4-asset optimization. Max-Sharpe: -0.589. Portfolio: return=-27.84%, vol=54.11%. Weights: w_FXI=0.0000, w_AVAX-USD=0.0000, w_BIL=0.0000, w_UNG=1.0000.

Question:
Assets: FXI, AVAX-USD, BIL, UNG
Annualized mean returns: FXI:-0.1125, AVAX-USD:-2.6256, BIL:0.0395, UNG:-0.2784
Covariance matrix (annualized):
[[0.024724, 0.006806, 2e-06, 0.008516], [0.006806, 0.605837, 0.000456, -0.101239], [2e-06, 0.000456, 4e-06, -0.00014], [0.008516, -0.101239, -0.00014, 0.292762]]
Risk-free rate: 4.00%
Constraints: weights 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_BIL=0.0000, w_UNG=1.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_FXI=0.0000, w_AVAX-USD=0.0000, w_BIL=0.0000, w_UNG=1.0000
Portfolio annualized return: -27.84%, volatility: 54.11%
Sharpe ratio: (-0.2784 - 0.0400) / 0.5411 = -0.5885


4-asset optimization. Max-Sharpe: 1.804. Portfolio: return=42.17%, vol=21.15%. Weights: w_VEA=0.0000, w_ETH-USD=0.0000, w_CPER=1.0000, w_SGOV=0.0000.

Question:
Assets: VEA, ETH-USD, CPER, SGOV
Annualized mean returns: VEA:0.1747, ETH-USD:-2.3013, CPER:0.4217, SGOV:0.0386
Covariance matrix (annualized):
[[0.013604, 0.027685, 0.016896, 7e-06], [0.027685, 0.366734, 0.038822, -0.000113], [0.016896, 0.038822, 0.04475, -2.8e-05], [7e-06, -0.000113, -2.8e-05, 2e-06]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_VEA=0.0000, w_ETH-USD=0.0000, w_CPER=1.0000, w_SGOV=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VEA=0.0000, w_ETH-USD=0.0000, w_CPER=1.0000, w_SGOV=0.0000
Portfolio annualized return: 42.17%, volatility: 21.15%
Sharpe ratio: (0.4217 - 0.0400) / 0.2115 = 1.8042


4-asset optimization. Max-Sharpe: 2.584. Portfolio: return=37.65%, vol=13.02%. Weights: w_EFA=0.0706, w_LINK-USD=0.0000, w_DBB=0.9294, w_ITB=0.0000.

Question:
Assets: EFA, LINK-USD, DBB, ITB
Annualized mean returns: EFA:0.1441, LINK-USD:-3.8668, DBB:0.3941, ITB:-0.7489
Covariance matrix (annualized):
[[0.010617, 0.050996, 0.004835, 0.010172], [0.050996, 0.722378, 0.052415, 0.048994], [0.004835, 0.052415, 0.018829, -0.003208], [0.010172, 0.048994, -0.003208, 0.040914]]
Risk-free rate: 4.00%
Constraints: weights 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=0.0706, w_LINK-USD=0.0000, w_DBB=0.9294, w_ITB=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EFA=0.0706, w_LINK-USD=0.0000, w_DBB=0.9294, w_ITB=0.0000
Portfolio annualized return: 37.65%, volatility: 13.02%
Sharpe ratio: (0.3765 - 0.0400) / 0.1302 = 2.5842


4-asset optimization. Max-Sharpe: 0.638. Portfolio: return=4.13%, vol=0.20%. Weights: w_FXI=0.0016, w_LINK-USD=0.0000, w_HYG=0.0000, w_SGOV=0.9984.

Question:
Assets: FXI, LINK-USD, HYG, SGOV
Annualized mean returns: FXI:0.1105, LINK-USD:-0.6974, HYG:-0.1313, SGOV:0.0411
Covariance matrix (annualized):
[[0.117531, 0.197528, 0.013139, 3.2e-05], [0.197528, 0.901705, 0.023827, -3.7e-05], [0.013139, 0.023827, 0.005412, -8e-06], [3.2e-05, -3.7e-05, -8e-06, 3e-06]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: bear

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

Answer: w_FXI=0.0016, w_LINK-USD=0.0000, w_HYG=0.0000, w_SGOV=0.9984

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_FXI=0.0016, w_LINK-USD=0.0000, w_HYG=0.0000, w_SGOV=0.9984
Portfolio annualized return: 4.13%, volatility: 0.20%
Sharpe ratio: (0.0413 - 0.0400) / 0.0020 = 0.6381


4-asset optimization. Max-Sharpe: 5.503. Portfolio: return=85.84%, vol=14.87%. Weights: w_IWM=0.4998, w_ADA-USD=0.0000, w_INDS=0.0558, w_PPLT=0.4445.

Question:
Assets: IWM, ADA-USD, INDS, PPLT
Annualized mean returns: IWM:0.6213, ADA-USD:0.8041, INDS:0.2819, PPLT:1.1975
Covariance matrix (annualized):
[[0.028658, 0.059755, 0.013973, 0.001366], [0.059755, 0.450247, 0.019735, 0.023182], [0.013973, 0.019735, 0.023908, -0.004005], [0.001366, 0.023182, -0.004005, 0.069351]]
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=0.4998, w_ADA-USD=0.0000, w_INDS=0.0558, w_PPLT=0.4445

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_IWM=0.4998, w_ADA-USD=0.0000, w_INDS=0.0558, w_PPLT=0.4445
Portfolio annualized return: 85.84%, volatility: 14.87%
Sharpe ratio: (0.8584 - 0.0400) / 0.1487 = 5.5030


4-asset optimization. Max-Sharpe: 1.949. Portfolio: return=4.81%, vol=0.41%. Weights: w_XLV=0.0000, w_SOL-USD=0.0030, w_PALL=0.0074, w_SGOV=0.9896.

Question:
Assets: XLV, SOL-USD, PALL, SGOV
Annualized mean returns: XLV:-0.2161, SOL-USD:0.6742, PALL:0.6430, SGOV:0.0417
Covariance matrix (annualized):
[[0.026051, 0.004345, -0.002155, 3.3e-05], [0.004345, 0.381227, 0.055145, -0.000197], [-0.002155, 0.055145, 0.153451, -2.3e-05], [3.3e-05, -0.000197, -2.3e-05, 4e-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_XLV=0.0000, w_SOL-USD=0.0030, w_PALL=0.0074, w_SGOV=0.9896

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLV=0.0000, w_SOL-USD=0.0030, w_PALL=0.0074, w_SGOV=0.9896
Portfolio annualized return: 4.81%, volatility: 0.41%
Sharpe ratio: (0.0481 - 0.0400) / 0.0041 = 1.9494


4-asset optimization. Max-Sharpe: 5.128. Portfolio: return=72.09%, vol=13.28%. Weights: w_XLV=0.8299, w_XRP-USD=0.0000, w_SGOV=0.0000, w_PALL=0.1701.

Question:
Assets: XLV, XRP-USD, SGOV, PALL
Annualized mean returns: XLV:0.6007, XRP-USD:-2.8786, SGOV:0.0370, PALL:1.3073
Covariance matrix (annualized):
[[0.017781, 0.029424, -2.8e-05, -0.001377], [0.029424, 0.466098, -0.000276, 0.041542], [-2.8e-05, -0.000276, 3e-06, -0.000214], [-0.001377, 0.041542, -0.000214, 0.199692]]
Risk-free rate: 4.00%
Constraints: weights 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=0.8299, w_XRP-USD=0.0000, w_SGOV=0.0000, w_PALL=0.1701

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLV=0.8299, w_XRP-USD=0.0000, w_SGOV=0.0000, w_PALL=0.1701
Portfolio annualized return: 72.09%, volatility: 13.28%
Sharpe ratio: (0.7209 - 0.0400) / 0.1328 = 5.1276


4-asset optimization. Max-Sharpe: 3.893. Portfolio: return=60.48%, vol=14.51%. Weights: w_EWJ=0.6942, w_AVAX-USD=0.0008, w_IYR=0.0000, w_SLV=0.3051.

Question:
Assets: EWJ, AVAX-USD, IYR, SLV
Annualized mean returns: EWJ:0.6200, AVAX-USD:1.4042, IYR:0.1009, SLV:0.5681
Covariance matrix (annualized):
[[0.027117, 0.042423, 0.006473, 0.009051], [0.042423, 0.676975, 0.022185, 0.068466], [0.006473, 0.022185, 0.021201, 0.007152], [0.009051, 0.068466, 0.007152, 0.043754]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: bull

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

Answer: w_EWJ=0.6942, w_AVAX-USD=0.0008, w_IYR=0.0000, w_SLV=0.3051

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EWJ=0.6942, w_AVAX-USD=0.0008, w_IYR=0.0000, w_SLV=0.3051
Portfolio annualized return: 60.48%, volatility: 14.51%
Sharpe ratio: (0.6048 - 0.0400) / 0.1451 = 3.8928


4-asset optimization. Max-Sharpe: -1.364. Portfolio: return=-36.98%, vol=30.04%. Weights: w_^VIX=0.2500, w_BNB-USD=0.2500, w_GLD=0.2500, w_BIL=0.2500.

Question:
Assets: ^VIX, BNB-USD, GLD, BIL
Annualized mean returns: ^VIX:-2.0279, BNB-USD:0.3941, GLD:0.1126, BIL:0.0418
Covariance matrix (annualized):
[[1.188792, -0.067481, 0.125126, 0.000412], [-0.067481, 0.098024, -0.003555, -2.3e-05], [0.125126, -0.003555, 0.047914, 2.9e-05], [0.000412, -2.3e-05, 2.9e-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_^VIX=0.2500, w_BNB-USD=0.2500, w_GLD=0.2500, w_BIL=0.2500

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_^VIX=0.2500, w_BNB-USD=0.2500, w_GLD=0.2500, w_BIL=0.2500
Portfolio annualized return: -36.98%, volatility: 30.04%
Sharpe ratio: (-0.3698 - 0.0400) / 0.3004 = -1.3643


4-asset optimization. Max-Sharpe: 3.584. Portfolio: return=6.21%, vol=0.62%. Weights: w_^VIX=0.0010, w_XRP-USD=0.0000, w_SGOV=0.9585, w_IAU=0.0405.

Question:
Assets: ^VIX, XRP-USD, SGOV, IAU
Annualized mean returns: ^VIX:-1.1004, XRP-USD:-1.7897, SGOV:0.0410, IAU:0.5894
Covariance matrix (annualized):
[[1.221515, -0.273426, -0.000395, -0.068345], [-0.273426, 0.398763, 6.3e-05, 0.031864], [-0.000395, 6.3e-05, 3e-06, -2.4e-05], [-0.068345, 0.031864, -2.4e-05, 0.025557]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_^VIX=0.0010, w_XRP-USD=0.0000, w_SGOV=0.9585, w_IAU=0.0405

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_^VIX=0.0010, w_XRP-USD=0.0000, w_SGOV=0.9585, w_IAU=0.0405
Portfolio annualized return: 6.21%, volatility: 0.62%
Sharpe ratio: (0.0621 - 0.0400) / 0.0062 = 3.5844


4-asset optimization. Max-Sharpe: 3.946. Portfolio: return=8.43%, vol=1.12%. Weights: w_EFA=0.0795, w_BNB-USD=0.0069, w_SHY=0.1672, w_CSHI=0.7464.

Question:
Assets: EFA, BNB-USD, SHY, CSHI
Annualized mean returns: EFA:0.4788, BNB-USD:0.2027, SHY:0.0601, CSHI:0.0466
Covariance matrix (annualized):
[[0.014671, -0.00338, 0.000525, 2.3e-05], [-0.00338, 0.165061, -0.001374, -0.00023], [0.000525, -0.001374, 0.000181, -7e-06], [2.3e-05, -0.00023, -7e-06, 2.6e-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_EFA=0.0795, w_BNB-USD=0.0069, w_SHY=0.1672, w_CSHI=0.7464

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EFA=0.0795, w_BNB-USD=0.0069, w_SHY=0.1672, w_CSHI=0.7464
Portfolio annualized return: 8.43%, volatility: 1.12%
Sharpe ratio: (0.0843 - 0.0400) / 0.0112 = 3.9464


4-asset optimization. Max-Sharpe: 3.868. Portfolio: return=36.57%, vol=8.42%. Weights: w_XLK=0.5461, w_DOT-USD=0.0000, w_SCHP=0.4539, w_ITB=0.0000.

Question:
Assets: XLK, DOT-USD, SCHP, ITB
Annualized mean returns: XLK:0.5839, DOT-USD:-0.9085, SCHP:0.1031, ITB:0.4565
Covariance matrix (annualized):
[[0.020757, 0.026063, 0.001112, 0.015928], [0.026063, 0.391441, -0.00869, 0.039955], [0.001112, -0.00869, 0.00169, 0.004356], [0.015928, 0.039955, 0.004356, 0.081841]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: bull

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

Answer: w_XLK=0.5461, w_DOT-USD=0.0000, w_SCHP=0.4539, w_ITB=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLK=0.5461, w_DOT-USD=0.0000, w_SCHP=0.4539, w_ITB=0.0000
Portfolio annualized return: 36.57%, volatility: 8.42%
Sharpe ratio: (0.3657 - 0.0400) / 0.0842 = 3.8681


4-asset optimization. Max-Sharpe: 0.563. Portfolio: return=12.67%, vol=15.41%. Weights: w_XLP=0.0000, w_ETH-USD=0.0000, w_BNDX=0.0000, w_MORT=1.0000.

Question:
Assets: XLP, ETH-USD, BNDX, MORT
Annualized mean returns: XLP:0.0580, ETH-USD:-3.6730, BNDX:0.0267, MORT:0.1267
Covariance matrix (annualized):
[[0.01725, -0.008268, 0.000911, 0.012027], [-0.008268, 0.390734, -0.001366, 0.015601], [0.000911, -0.001366, 0.000645, 0.001086], [0.012027, 0.015601, 0.001086, 0.023739]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_XLP=0.0000, w_ETH-USD=0.0000, w_BNDX=0.0000, w_MORT=1.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLP=0.0000, w_ETH-USD=0.0000, w_BNDX=0.0000, w_MORT=1.0000
Portfolio annualized return: 12.67%, volatility: 15.41%
Sharpe ratio: (0.1267 - 0.0400) / 0.1541 = 0.5626


4-asset optimization. Max-Sharpe: 3.739. Portfolio: return=41.93%, vol=10.14%. Weights: w_XLF=0.4642, w_BNB-USD=0.1811, w_CORN=0.0000, w_SCHP=0.3547.

Question:
Assets: XLF, BNB-USD, CORN, SCHP
Annualized mean returns: XLF:0.5453, BNB-USD:0.7613, CORN:-0.4195, SCHP:0.0795
Covariance matrix (annualized):
[[0.027041, 0.003733, -0.005284, 0.001353], [0.003733, 0.104262, -0.004236, -0.002948], [-0.005284, -0.004236, 0.018737, -0.002169], [0.001353, -0.002948, -0.002169, 0.002758]]
Risk-free rate: 4.00%
Constraints: weights 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=0.4642, w_BNB-USD=0.1811, w_CORN=0.0000, w_SCHP=0.3547

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLF=0.4642, w_BNB-USD=0.1811, w_CORN=0.0000, w_SCHP=0.3547
Portfolio annualized return: 41.93%, volatility: 10.14%
Sharpe ratio: (0.4193 - 0.0400) / 0.1014 = 3.7389


4-asset optimization. Max-Sharpe: 4.649. Portfolio: return=19.25%, vol=3.28%. Weights: w_USMV=0.0000, w_BTC-USD=0.0496, w_JNK=0.9504, w_INDS=0.0000.

Question:
Assets: USMV, BTC-USD, JNK, INDS
Annualized mean returns: USMV:0.0584, BTC-USD:0.7646, JNK:0.1626, INDS:-0.0831
Covariance matrix (annualized):
[[0.009115, 0.006067, 0.001676, 0.008524], [0.006067, 0.063226, 0.002077, 0.013764], [0.001676, 0.002077, 0.000802, 0.00176], [0.008524, 0.013764, 0.00176, 0.025834]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: bull

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

Answer: w_USMV=0.0000, w_BTC-USD=0.0496, w_JNK=0.9504, w_INDS=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_USMV=0.0000, w_BTC-USD=0.0496, w_JNK=0.9504, w_INDS=0.0000
Portfolio annualized return: 19.25%, volatility: 3.28%
Sharpe ratio: (0.1925 - 0.0400) / 0.0328 = 4.6493


4-asset optimization. Max-Sharpe: 1.198. Portfolio: return=5.32%, vol=1.10%. Weights: w_XLRE=0.0586, w_AVAX-USD=0.0000, w_ICSH=0.9318, w_GLD=0.0096.

Question:
Assets: XLRE, AVAX-USD, ICSH, GLD
Annualized mean returns: XLRE:0.1959, AVAX-USD:-0.3034, ICSH:0.0441, GLD:0.0603
Covariance matrix (annualized):
[[0.021079, -0.009172, 0.000284, -0.007202], [-0.009172, 0.559047, -0.001001, -0.048071], [0.000284, -0.001001, 2.2e-05, 8.2e-05], [-0.007202, -0.048071, 8.2e-05, 0.05518]]
Risk-free rate: 4.00%
Constraints: weights 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=0.0586, w_AVAX-USD=0.0000, w_ICSH=0.9318, w_GLD=0.0096

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLRE=0.0586, w_AVAX-USD=0.0000, w_ICSH=0.9318, w_GLD=0.0096
Portfolio annualized return: 5.32%, volatility: 1.10%
Sharpe ratio: (0.0532 - 0.0400) / 0.0110 = 1.1981


4-asset optimization. Max-Sharpe: 4.027. Portfolio: return=8.94%, vol=1.23%. Weights: w_EWJ=0.0000, w_AVAX-USD=0.0159, w_BIL=0.9841, w_REZ=0.0000.

Question:
Assets: EWJ, AVAX-USD, BIL, REZ
Annualized mean returns: EWJ:0.2542, AVAX-USD:3.1118, BIL:0.0405, REZ:0.0558
Covariance matrix (annualized):
[[0.048641, 0.059861, 1e-06, 0.028012], [0.059861, 0.599099, -0.000189, 0.032472], [1e-06, -0.000189, 5e-06, -5.4e-05], [0.028012, 0.032472, -5.4e-05, 0.049746]]
Risk-free rate: 4.00%
Constraints: weights 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_AVAX-USD=0.0159, w_BIL=0.9841, w_REZ=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EWJ=0.0000, w_AVAX-USD=0.0159, w_BIL=0.9841, w_REZ=0.0000
Portfolio annualized return: 8.94%, volatility: 1.23%
Sharpe ratio: (0.0894 - 0.0400) / 0.0123 = 4.0273


4-asset optimization. Max-Sharpe: 2.421. Portfolio: return=10.63%, vol=2.74%. Weights: w_VLUE=0.0000, w_XRP-USD=0.0000, w_TIP=1.0000, w_DBB=0.0000.

Question:
Assets: VLUE, XRP-USD, TIP, DBB
Annualized mean returns: VLUE:-0.4430, XRP-USD:-0.3046, TIP:0.1063, DBB:-0.2176
Covariance matrix (annualized):
[[0.060948, 0.059692, 0.000453, 0.029235], [0.059692, 0.723742, -0.002714, 0.063], [0.000453, -0.002714, 0.00075, -0.000829], [0.029235, 0.063, -0.000829, 0.037902]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: bear

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

Answer: w_VLUE=0.0000, w_XRP-USD=0.0000, w_TIP=1.0000, w_DBB=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VLUE=0.0000, w_XRP-USD=0.0000, w_TIP=1.0000, w_DBB=0.0000
Portfolio annualized return: 10.63%, volatility: 2.74%
Sharpe ratio: (0.1063 - 0.0400) / 0.0274 = 2.4215


4-asset optimization. Max-Sharpe: 3.020. Portfolio: return=16.23%, vol=4.05%. Weights: w_QUAL=0.0000, w_BNB-USD=0.0406, w_HAUZ=0.0000, w_JNK=0.9594.

Question:
Assets: QUAL, BNB-USD, HAUZ, JNK
Annualized mean returns: QUAL:0.2246, BNB-USD:0.8816, HAUZ:0.1637, JNK:0.1319
Covariance matrix (annualized):
[[0.009815, 0.018676, 0.005419, 0.002339], [0.018676, 0.149661, 0.016561, 0.005429], [0.005419, 0.016561, 0.012193, 0.002171], [0.002339, 0.005429, 0.002171, 0.001055]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: bull

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

Answer: w_QUAL=0.0000, w_BNB-USD=0.0406, w_HAUZ=0.0000, w_JNK=0.9594

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_QUAL=0.0000, w_BNB-USD=0.0406, w_HAUZ=0.0000, w_JNK=0.9594
Portfolio annualized return: 16.23%, volatility: 4.05%
Sharpe ratio: (0.1623 - 0.0400) / 0.0405 = 3.0201


4-asset optimization. Max-Sharpe: 2.590. Portfolio: return=41.24%, vol=14.38%. Weights: w_XLY=0.0000, w_LINK-USD=0.0000, w_TIP=0.0000, w_DBB=1.0000.

Question:
Assets: XLY, LINK-USD, TIP, DBB
Annualized mean returns: XLY:0.0790, LINK-USD:-3.7997, TIP:0.0127, DBB:0.4124
Covariance matrix (annualized):
[[0.044684, 0.068814, 0.000185, 0.016274], [0.068814, 0.828191, -0.00123, 0.061282], [0.000185, -0.00123, 0.000173, 5.9e-05], [0.016274, 0.061282, 5.9e-05, 0.020668]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_XLY=0.0000, w_LINK-USD=0.0000, w_TIP=0.0000, w_DBB=1.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLY=0.0000, w_LINK-USD=0.0000, w_TIP=0.0000, w_DBB=1.0000
Portfolio annualized return: 41.24%, volatility: 14.38%
Sharpe ratio: (0.4124 - 0.0400) / 0.1438 = 2.5902


4-asset optimization. Max-Sharpe: 6.090. Portfolio: return=9.98%, vol=0.98%. Weights: w_EWJ=0.0089, w_ADA-USD=0.0000, w_ICSH=0.8157, w_EMB=0.1754.

Question:
Assets: EWJ, ADA-USD, ICSH, EMB
Annualized mean returns: EWJ:0.5631, ADA-USD:0.9649, ICSH:0.0542, EMB:0.2882
Covariance matrix (annualized):
[[0.027938, 0.038926, 7.2e-05, 0.00305], [0.038926, 0.481285, 5.3e-05, 0.010831], [7.2e-05, 5.3e-05, 2.1e-05, 2.8e-05], [0.00305, 0.010831, 2.8e-05, 0.001994]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: bull

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

Answer: w_EWJ=0.0089, w_ADA-USD=0.0000, w_ICSH=0.8157, w_EMB=0.1754

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EWJ=0.0089, w_ADA-USD=0.0000, w_ICSH=0.8157, w_EMB=0.1754
Portfolio annualized return: 9.98%, volatility: 0.98%
Sharpe ratio: (0.0998 - 0.0400) / 0.0098 = 6.0900


4-asset optimization. Max-Sharpe: 2.142. Portfolio: return=8.02%, vol=1.88%. Weights: w_^VIX=0.0034, w_ADA-USD=0.0048, w_IYR=0.0000, w_TIP=0.9918.

Question:
Assets: ^VIX, ADA-USD, IYR, TIP
Annualized mean returns: ^VIX:0.2772, ADA-USD:0.4963, IYR:-0.0527, TIP:0.0775
Covariance matrix (annualized):
[[1.056234, -0.336201, -0.041999, 0.000109], [-0.336201, 0.454111, 0.020114, 0.002993], [-0.041999, 0.020114, 0.020355, 0.001241], [0.000109, 0.002993, 0.001241, 0.000317]]
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_^VIX=0.0034, w_ADA-USD=0.0048, w_IYR=0.0000, w_TIP=0.9918

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_^VIX=0.0034, w_ADA-USD=0.0048, w_IYR=0.0000, w_TIP=0.9918
Portfolio annualized return: 8.02%, volatility: 1.88%
Sharpe ratio: (0.0802 - 0.0400) / 0.0188 = 2.1421


4-asset optimization. Max-Sharpe: 6.147. Portfolio: return=5.80%, vol=0.29%. Weights: w_EWJ=0.0000, w_LINK-USD=0.0004, w_SGOV=0.9916, w_USO=0.0080.

Question:
Assets: EWJ, LINK-USD, SGOV, USO
Annualized mean returns: EWJ:-0.1361, LINK-USD:2.3912, SGOV:0.0495, USO:0.9770
Covariance matrix (annualized):
[[0.025023, 0.040564, -4.6e-05, -0.0021], [0.040564, 1.371363, 0.000388, 0.015531], [-4.6e-05, 0.000388, 5e-06, -3.2e-05], [-0.0021, 0.015531, -3.2e-05, 0.058919]]
Risk-free rate: 4.00%
Constraints: weights 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_LINK-USD=0.0004, w_SGOV=0.9916, w_USO=0.0080

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EWJ=0.0000, w_LINK-USD=0.0004, w_SGOV=0.9916, w_USO=0.0080
Portfolio annualized return: 5.80%, volatility: 0.29%
Sharpe ratio: (0.0580 - 0.0400) / 0.0029 = 6.1471


4-asset optimization. Max-Sharpe: 2.462. Portfolio: return=78.87%, vol=30.41%. Weights: w_XLF=0.0000, w_ETH-USD=0.3464, w_MORT=0.6536, w_PDBC=0.0000.

Question:
Assets: XLF, ETH-USD, MORT, PDBC
Annualized mean returns: XLF:0.1139, ETH-USD:1.6483, MORT:0.3332, PDBC:-0.0300
Covariance matrix (annualized):
[[0.016687, 0.035444, 0.008875, 0.000722], [0.035444, 0.476199, 0.051545, 0.006912], [0.008875, 0.051545, 0.028082, -0.005058], [0.000722, 0.006912, -0.005058, 0.011913]]
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_ETH-USD=0.3464, w_MORT=0.6536, w_PDBC=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLF=0.0000, w_ETH-USD=0.3464, w_MORT=0.6536, w_PDBC=0.0000
Portfolio annualized return: 78.87%, volatility: 30.41%
Sharpe ratio: (0.7887 - 0.0400) / 0.3041 = 2.4622


4-asset optimization. Max-Sharpe: 4.342. Portfolio: return=31.26%, vol=6.28%. Weights: w_IVV=0.0769, w_ADA-USD=0.0133, w_BIL=0.5628, w_VNQI=0.3470.

Question:
Assets: IVV, ADA-USD, BIL, VNQI
Annualized mean returns: IVV:0.5952, ADA-USD:0.9667, BIL:0.0408, VNQI:0.6657
Covariance matrix (annualized):
[[0.042324, 0.058883, -4e-05, 0.011563], [0.058883, 0.473823, -0.000172, 0.007731], [-4e-05, -0.000172, 5e-06, 4.1e-05], [0.011563, 0.007731, 4.1e-05, 0.023142]]
Risk-free rate: 4.00%
Constraints: weights 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=0.0769, w_ADA-USD=0.0133, w_BIL=0.5628, w_VNQI=0.3470

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_IVV=0.0769, w_ADA-USD=0.0133, w_BIL=0.5628, w_VNQI=0.3470
Portfolio annualized return: 31.26%, volatility: 6.28%
Sharpe ratio: (0.3126 - 0.0400) / 0.0628 = 4.3422


4-asset optimization. Max-Sharpe: 1.462. Portfolio: return=4.39%, vol=0.26%. Weights: w_EFA=0.0120, w_BTC-USD=0.0000, w_SGOV=0.9880, w_UNG=0.0000.

Question:
Assets: EFA, BTC-USD, SGOV, UNG
Annualized mean returns: EFA:0.1364, BTC-USD:-0.1546, SGOV:0.0427, UNG:-0.9904
Covariance matrix (annualized):
[[0.017383, 0.017745, -3.5e-05, -0.026398], [0.017745, 0.086729, -8.4e-05, -0.011287], [-3.5e-05, -8.4e-05, 5e-06, 9.1e-05], [-0.026398, -0.011287, 9.1e-05, 0.19279]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: bull

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

Answer: w_EFA=0.0120, w_BTC-USD=0.0000, w_SGOV=0.9880, w_UNG=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EFA=0.0120, w_BTC-USD=0.0000, w_SGOV=0.9880, w_UNG=0.0000
Portfolio annualized return: 4.39%, volatility: 0.26%
Sharpe ratio: (0.0439 - 0.0400) / 0.0026 = 1.4615


4-asset optimization. Max-Sharpe: 1.947. Portfolio: return=8.34%, vol=2.23%. Weights: w_USMV=0.0000, w_AVAX-USD=0.0015, w_CSHI=0.8300, w_IAU=0.1685.

Question:
Assets: USMV, AVAX-USD, CSHI, IAU
Annualized mean returns: USMV:0.0639, AVAX-USD:0.6435, CSHI:0.0441, IAU:0.2720
Covariance matrix (annualized):
[[0.008256, 0.012028, 7.2e-05, 0.00148], [0.012028, 0.578016, 0.001296, 0.029402], [7.2e-05, 0.001296, 8.1e-05, -0.000135], [0.00148, 0.029402, -0.000135, 0.016141]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: bull

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

Answer: w_USMV=0.0000, w_AVAX-USD=0.0015, w_CSHI=0.8300, w_IAU=0.1685

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_USMV=0.0000, w_AVAX-USD=0.0015, w_CSHI=0.8300, w_IAU=0.1685
Portfolio annualized return: 8.34%, volatility: 2.23%
Sharpe ratio: (0.0834 - 0.0400) / 0.0223 = 1.9474


4-asset optimization. Max-Sharpe: 2.854. Portfolio: return=5.99%, vol=0.70%. Weights: w_QUAL=0.0000, w_BTC-USD=0.0073, w_CSHI=0.9927, w_HAUZ=0.0000.

Question:
Assets: QUAL, BTC-USD, CSHI, HAUZ
Annualized mean returns: QUAL:0.0153, BTC-USD:0.9463, CSHI:0.0534, HAUZ:-0.2852
Covariance matrix (annualized):
[[0.014088, 0.024822, 0.000338, 0.011797], [0.024822, 0.196221, 0.000791, 0.021821], [0.000338, 0.000791, 2.7e-05, 0.000386], [0.011797, 0.021821, 0.000386, 0.018407]]
Risk-free rate: 4.00%
Constraints: weights 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_BTC-USD=0.0073, w_CSHI=0.9927, w_HAUZ=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_QUAL=0.0000, w_BTC-USD=0.0073, w_CSHI=0.9927, w_HAUZ=0.0000
Portfolio annualized return: 5.99%, volatility: 0.70%
Sharpe ratio: (0.0599 - 0.0400) / 0.0070 = 2.8543


4-asset optimization. Max-Sharpe: 2.115. Portfolio: return=237.67%, vol=110.49%. Weights: w_XLV=0.0000, w_AVAX-USD=1.0000, w_PALL=0.0000, w_MORT=0.0000.

Question:
Assets: XLV, AVAX-USD, PALL, MORT
Annualized mean returns: XLV:-0.0032, AVAX-USD:2.3767, PALL:-0.0562, MORT:0.0694
Covariance matrix (annualized):
[[0.013865, 0.011232, 0.004871, 0.008003], [0.011232, 1.220728, 0.040897, 0.065833], [0.004871, 0.040897, 0.080083, 0.013387], [0.008003, 0.065833, 0.013387, 0.030765]]
Risk-free rate: 4.00%
Constraints: weights 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=1.0000, w_PALL=0.0000, w_MORT=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLV=0.0000, w_AVAX-USD=1.0000, w_PALL=0.0000, w_MORT=0.0000
Portfolio annualized return: 237.67%, volatility: 110.49%
Sharpe ratio: (2.3767 - 0.0400) / 1.1049 = 2.1149


4-asset optimization. Max-Sharpe: 2.655. Portfolio: return=43.19%, vol=14.76%. Weights: w_EWJ=0.8653, w_AVAX-USD=0.0000, w_PPLT=0.1347, w_ITB=0.0000.

Question:
Assets: EWJ, AVAX-USD, PPLT, ITB
Annualized mean returns: EWJ:0.4226, AVAX-USD:-3.2457, PPLT:0.4911, ITB:0.1900
Covariance matrix (annualized):
[[0.022676, 0.01029, 0.012258, 0.016177], [0.01029, 0.577993, 0.080996, 0.022109], [0.012258, 0.080996, 0.107418, -0.005011], [0.016177, 0.022109, -0.005011, 0.070736]]
Risk-free rate: 4.00%
Constraints: weights 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=0.8653, w_AVAX-USD=0.0000, w_PPLT=0.1347, w_ITB=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EWJ=0.8653, w_AVAX-USD=0.0000, w_PPLT=0.1347, w_ITB=0.0000
Portfolio annualized return: 43.19%, volatility: 14.76%
Sharpe ratio: (0.4319 - 0.0400) / 0.1476 = 2.6550


4-asset optimization. Max-Sharpe: 2.510. Portfolio: return=34.53%, vol=12.16%. Weights: w_FXI=0.3025, w_DOT-USD=0.0000, w_CSHI=0.0000, w_IGOV=0.6975.

Question:
Assets: FXI, DOT-USD, CSHI, IGOV
Annualized mean returns: FXI:0.7225, DOT-USD:-0.2844, CSHI:0.0373, IGOV:0.1817
Covariance matrix (annualized):
[[0.091732, 0.109663, 0.000672, 0.007625], [0.109663, 0.514999, 0.001292, -0.004159], [0.000672, 0.001292, 0.000118, -4.4e-05], [0.007625, -0.004159, -4.4e-05, 0.006535]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: bear

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

Answer: w_FXI=0.3025, w_DOT-USD=0.0000, w_CSHI=0.0000, w_IGOV=0.6975

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_FXI=0.3025, w_DOT-USD=0.0000, w_CSHI=0.0000, w_IGOV=0.6975
Portfolio annualized return: 34.53%, volatility: 12.16%
Sharpe ratio: (0.3453 - 0.0400) / 0.1216 = 2.5103


4-asset optimization. Max-Sharpe: 1.643. Portfolio: return=4.61%, vol=0.37%. Weights: w_XLV=0.0000, w_SOL-USD=0.0019, w_ITB=0.0077, w_BIL=0.9904.

Question:
Assets: XLV, SOL-USD, ITB, BIL
Annualized mean returns: XLV:0.0234, SOL-USD:0.7013, ITB:0.4039, BIL:0.0420
Covariance matrix (annualized):
[[0.020804, 0.021319, 0.018295, 6.7e-05], [0.021319, 0.536137, 0.057655, 4e-06], [0.018295, 0.057655, 0.08264, 6.8e-05], [6.7e-05, 4e-06, 6.8e-05, 4e-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_XLV=0.0000, w_SOL-USD=0.0019, w_ITB=0.0077, w_BIL=0.9904

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLV=0.0000, w_SOL-USD=0.0019, w_ITB=0.0077, w_BIL=0.9904
Portfolio annualized return: 4.61%, volatility: 0.37%
Sharpe ratio: (0.0461 - 0.0400) / 0.0037 = 1.6433


4-asset optimization. Max-Sharpe: 2.796. Portfolio: return=22.23%, vol=6.52%. Weights: w_VEA=0.1567, w_ADA-USD=0.0000, w_DBB=0.2205, w_TLH=0.6228.

Question:
Assets: VEA, ADA-USD, DBB, TLH
Annualized mean returns: VEA:0.1713, ADA-USD:-2.4204, DBB:0.1035, TLH:0.2772
Covariance matrix (annualized):
[[0.021746, 0.017894, 0.004184, -0.002037], [0.017894, 0.789529, 0.024895, -0.028574], [0.004184, 0.024895, 0.016233, -0.004422], [-0.002037, -0.028574, -0.004422, 0.010958]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: bear

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

Answer: w_VEA=0.1567, w_ADA-USD=0.0000, w_DBB=0.2205, w_TLH=0.6228

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VEA=0.1567, w_ADA-USD=0.0000, w_DBB=0.2205, w_TLH=0.6228
Portfolio annualized return: 22.23%, volatility: 6.52%
Sharpe ratio: (0.2223 - 0.0400) / 0.0652 = 2.7960


4-asset optimization. Max-Sharpe: 0.556. Portfolio: return=26.61%, vol=40.64%. Weights: w_^VIX=0.2500, w_XRP-USD=0.2500, w_SGOV=0.2500, w_UNG=0.2500.

Question:
Assets: ^VIX, XRP-USD, SGOV, UNG
Annualized mean returns: ^VIX:-3.5598, XRP-USD:2.7476, SGOV:0.0464, UNG:1.8302
Covariance matrix (annualized):
[[1.643037, -0.171785, -0.000326, 0.037817], [-0.171785, 0.463459, 0.000178, 0.116968], [-0.000326, 0.000178, 4e-06, -0.000415], [0.037817, 0.116968, -0.000415, 0.570607]]
Risk-free rate: 4.00%
Constraints: weights 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=0.2500, w_XRP-USD=0.2500, w_SGOV=0.2500, w_UNG=0.2500

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_^VIX=0.2500, w_XRP-USD=0.2500, w_SGOV=0.2500, w_UNG=0.2500
Portfolio annualized return: 26.61%, volatility: 40.64%
Sharpe ratio: (0.2661 - 0.0400) / 0.4064 = 0.5565


4-asset optimization. Max-Sharpe: 4.444. Portfolio: return=15.29%, vol=2.54%. Weights: w_VLUE=0.1265, w_BNB-USD=0.0000, w_EMB=0.2559, w_BIL=0.6175.

Question:
Assets: VLUE, BNB-USD, EMB, BIL
Annualized mean returns: VLUE:0.5961, BNB-USD:-0.3674, EMB:0.2094, BIL:0.0387
Covariance matrix (annualized):
[[0.01889, 0.017471, 0.003202, -4.7e-05], [0.017471, 0.412013, 0.003347, 5e-06], [0.003202, 0.003347, 0.002236, -1.4e-05], [-4.7e-05, 5e-06, -1.4e-05, 4e-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_VLUE=0.1265, w_BNB-USD=0.0000, w_EMB=0.2559, w_BIL=0.6175

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VLUE=0.1265, w_BNB-USD=0.0000, w_EMB=0.2559, w_BIL=0.6175
Portfolio annualized return: 15.29%, volatility: 2.54%
Sharpe ratio: (0.1529 - 0.0400) / 0.0254 = 4.4436


4-asset optimization. Max-Sharpe: 0.694. Portfolio: return=13.87%, vol=14.22%. Weights: w_VLUE=1.0000, w_DOT-USD=0.0000, w_ITB=0.0000, w_USO=0.0000.

Question:
Assets: VLUE, DOT-USD, ITB, USO
Annualized mean returns: VLUE:0.1387, DOT-USD:-0.0387, ITB:-0.1458, USO:-0.4169
Covariance matrix (annualized):
[[0.020224, 0.028253, 0.021374, 0.002092], [0.028253, 0.568492, 0.024811, 0.012778], [0.021374, 0.024811, 0.07235, -0.009117], [0.002092, 0.012778, -0.009117, 0.069147]]
Risk-free rate: 4.00%
Constraints: weights 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=1.0000, w_DOT-USD=0.0000, w_ITB=0.0000, w_USO=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VLUE=1.0000, w_DOT-USD=0.0000, w_ITB=0.0000, w_USO=0.0000
Portfolio annualized return: 13.87%, volatility: 14.22%
Sharpe ratio: (0.1387 - 0.0400) / 0.1422 = 0.6942


4-asset optimization. Max-Sharpe: 4.136. Portfolio: return=10.98%, vol=1.69%. Weights: w_EWJ=0.0586, w_DOT-USD=0.0000, w_IEF=0.0000, w_CSHI=0.9414.

Question:
Assets: EWJ, DOT-USD, IEF, CSHI
Annualized mean returns: EWJ:0.4720, DOT-USD:-0.1363, IEF:0.0325, CSHI:0.0873
Covariance matrix (annualized):
[[0.020983, 0.010802, 0.002272, 0.000567], [0.010802, 0.398786, -0.011061, 0.002048], [0.002272, -0.011061, 0.004267, 6e-06], [0.000567, 0.002048, 6e-06, 0.00017]]
Risk-free rate: 4.00%
Constraints: weights 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=0.0586, w_DOT-USD=0.0000, w_IEF=0.0000, w_CSHI=0.9414

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EWJ=0.0586, w_DOT-USD=0.0000, w_IEF=0.0000, w_CSHI=0.9414
Portfolio annualized return: 10.98%, volatility: 1.69%
Sharpe ratio: (0.1098 - 0.0400) / 0.0169 = 4.1356


4-asset optimization. Max-Sharpe: 0.924. Portfolio: return=17.31%, vol=14.41%. Weights: w_XLE=0.0000, w_AVAX-USD=0.0000, w_INDS=1.0000, w_IGOV=0.0000.

Question:
Assets: XLE, AVAX-USD, INDS, IGOV
Annualized mean returns: XLE:0.0799, AVAX-USD:-3.2558, INDS:0.1731, IGOV:-0.0717
Covariance matrix (annualized):
[[0.027476, 0.046644, 0.007198, -0.001656], [0.046644, 0.75111, 0.044135, -0.004828], [0.007198, 0.044135, 0.020754, 0.003276], [-0.001656, -0.004828, 0.003276, 0.003778]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_XLE=0.0000, w_AVAX-USD=0.0000, w_INDS=1.0000, w_IGOV=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLE=0.0000, w_AVAX-USD=0.0000, w_INDS=1.0000, w_IGOV=0.0000
Portfolio annualized return: 17.31%, volatility: 14.41%
Sharpe ratio: (0.1731 - 0.0400) / 0.1441 = 0.9237


4-asset optimization. Max-Sharpe: 2.366. Portfolio: return=181.10%, vol=74.86%. Weights: w_FXI=0.0000, w_ETH-USD=1.0000, w_CSHI=0.0000, w_LQD=0.0000.

Question:
Assets: FXI, ETH-USD, CSHI, LQD
Annualized mean returns: FXI:-0.1268, ETH-USD:1.8110, CSHI:0.0456, LQD:-0.0230
Covariance matrix (annualized):
[[0.100131, 0.110207, 0.008562, 0.006638], [0.110207, 0.560451, 0.016224, 0.018043], [0.008562, 0.016224, 0.00207, 0.001649], [0.006638, 0.018043, 0.001649, 0.008225]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

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

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_FXI=0.0000, w_ETH-USD=1.0000, w_CSHI=0.0000, w_LQD=0.0000
Portfolio annualized return: 181.10%, volatility: 74.86%
Sharpe ratio: (1.8110 - 0.0400) / 0.7486 = 2.3656


4-asset optimization. Max-Sharpe: 1.661. Portfolio: return=4.35%, vol=0.21%. Weights: w_XLY=0.0000, w_ETH-USD=0.0001, w_DBC=0.0000, w_SGOV=0.9999.

Question:
Assets: XLY, ETH-USD, DBC, SGOV
Annualized mean returns: XLY:-0.5434, ETH-USD:0.3238, DBC:-0.2451, SGOV:0.0435
Covariance matrix (annualized):
[[0.107393, 0.137591, 0.036824, 9.7e-05], [0.137591, 0.4397, 0.050622, 0.000335], [0.036824, 0.050622, 0.032795, 4.5e-05], [9.7e-05, 0.000335, 4.5e-05, 4e-06]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_XLY=0.0000, w_ETH-USD=0.0001, w_DBC=0.0000, w_SGOV=0.9999

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLY=0.0000, w_ETH-USD=0.0001, w_DBC=0.0000, w_SGOV=0.9999
Portfolio annualized return: 4.35%, volatility: 0.21%
Sharpe ratio: (0.0435 - 0.0400) / 0.0021 = 1.6606


4-asset optimization. Max-Sharpe: 3.345. Portfolio: return=53.20%, vol=14.71%. Weights: w_IWM=0.0000, w_LINK-USD=0.0711, w_PDBC=0.9289, w_VCIT=0.0000.

Question:
Assets: IWM, LINK-USD, PDBC, VCIT
Annualized mean returns: IWM:-0.4626, LINK-USD:2.3020, PDBC:0.3965, VCIT:-0.0747
Covariance matrix (annualized):
[[0.031422, 0.056442, -0.001573, 0.005855], [0.056442, 1.3787, 0.001603, 0.011103], [-0.001573, 0.001603, 0.016756, -0.001206], [0.005855, 0.011103, -0.001206, 0.002499]]
Risk-free rate: 4.00%
Constraints: weights 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_LINK-USD=0.0711, w_PDBC=0.9289, w_VCIT=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_IWM=0.0000, w_LINK-USD=0.0711, w_PDBC=0.9289, w_VCIT=0.0000
Portfolio annualized return: 53.20%, volatility: 14.71%
Sharpe ratio: (0.5320 - 0.0400) / 0.1471 = 3.3446


4-asset optimization. Max-Sharpe: -1.431. Portfolio: return=-26.53%, vol=21.34%. Weights: w_VLUE=0.2500, w_DOT-USD=0.2500, w_REZ=0.2500, w_SGOV=0.2500.

Question:
Assets: VLUE, DOT-USD, REZ, SGOV
Annualized mean returns: VLUE:0.4809, DOT-USD:-1.6591, REZ:0.0762, SGOV:0.0408
Covariance matrix (annualized):
[[0.017952, 0.059577, 0.007668, -8.8e-05], [0.059577, 0.568477, -0.002754, -0.000732], [0.007668, -0.002754, 0.014861, 3.6e-05], [-8.8e-05, -0.000732, 3.6e-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_VLUE=0.2500, w_DOT-USD=0.2500, w_REZ=0.2500, w_SGOV=0.2500

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VLUE=0.2500, w_DOT-USD=0.2500, w_REZ=0.2500, w_SGOV=0.2500
Portfolio annualized return: -26.53%, volatility: 21.34%
Sharpe ratio: (-0.2653 - 0.0400) / 0.2134 = -1.4305


4-asset optimization. Max-Sharpe: 5.657. Portfolio: return=148.26%, vol=25.50%. Weights: w_ACWI=0.6172, w_ETH-USD=0.3828, w_CSHI=0.0000, w_VNQ=0.0000.

Question:
Assets: ACWI, ETH-USD, CSHI, VNQ
Annualized mean returns: ACWI:0.4173, ETH-USD:3.2004, CSHI:0.0541, VNQ:0.0105
Covariance matrix (annualized):
[[0.00971, 0.028784, 0.000268, 0.005429], [0.028784, 0.325847, 0.001317, 0.024796], [0.000268, 0.001317, 0.0001, 9e-06], [0.005429, 0.024796, 9e-06, 0.01938]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: bull

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

Answer: w_ACWI=0.6172, w_ETH-USD=0.3828, w_CSHI=0.0000, w_VNQ=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_ACWI=0.6172, w_ETH-USD=0.3828, w_CSHI=0.0000, w_VNQ=0.0000
Portfolio annualized return: 148.26%, volatility: 25.50%
Sharpe ratio: (1.4826 - 0.0400) / 0.2550 = 5.6566


4-asset optimization. Max-Sharpe: 2.003. Portfolio: return=4.49%, vol=0.25%. Weights: w_VTI=0.0000, w_XRP-USD=0.0009, w_BIL=0.9695, w_STIP=0.0296.

Question:
Assets: VTI, XRP-USD, BIL, STIP
Annualized mean returns: VTI:-0.0165, XRP-USD:0.8526, BIL:0.0440, STIP:0.0515
Covariance matrix (annualized):
[[0.021587, 0.052892, -1.5e-05, 0.001059], [0.052892, 0.677405, 0.000224, 0.006288], [-1.5e-05, 0.000224, 5e-06, 1e-06], [0.001059, 0.006288, 1e-06, 0.000254]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_VTI=0.0000, w_XRP-USD=0.0009, w_BIL=0.9695, w_STIP=0.0296

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VTI=0.0000, w_XRP-USD=0.0009, w_BIL=0.9695, w_STIP=0.0296
Portfolio annualized return: 4.49%, volatility: 0.25%
Sharpe ratio: (0.0449 - 0.0400) / 0.0025 = 2.0032


4-asset optimization. Max-Sharpe: -1.358. Portfolio: return=-112.43%, vol=85.73%. Weights: w_XLF=0.0000, w_XRP-USD=1.0000, w_CPER=0.0000, w_ITB=0.0000.

Question:
Assets: XLF, XRP-USD, CPER, ITB
Annualized mean returns: XLF:-0.6849, XRP-USD:-1.1243, CPER:-0.0475, ITB:-0.9146
Covariance matrix (annualized):
[[0.047901, 0.010553, 0.018673, 0.023649], [0.010553, 0.735002, 0.039725, 0.045639], [0.018673, 0.039725, 0.087112, 0.006686], [0.023649, 0.045639, 0.006686, 0.079659]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: bear

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

Answer: w_XLF=0.0000, w_XRP-USD=1.0000, w_CPER=0.0000, w_ITB=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLF=0.0000, w_XRP-USD=1.0000, w_CPER=0.0000, w_ITB=0.0000
Portfolio annualized return: -112.43%, volatility: 85.73%
Sharpe ratio: (-1.1243 - 0.0400) / 0.8573 = -1.3581


4-asset optimization. Max-Sharpe: 3.264. Portfolio: return=4.72%, vol=0.22%. Weights: w_EWJ=0.0000, w_AVAX-USD=0.0000, w_SGOV=1.0000, w_IYR=0.0000.

Question:
Assets: EWJ, AVAX-USD, SGOV, IYR
Annualized mean returns: EWJ:-0.2186, AVAX-USD:-0.4984, SGOV:0.0472, IYR:-0.2365
Covariance matrix (annualized):
[[0.025405, 0.038098, -3.6e-05, 0.013846], [0.038098, 0.84263, 9.3e-05, 0.050196], [-3.6e-05, 9.3e-05, 5e-06, -7e-05], [0.013846, 0.050196, -7e-05, 0.036969]]
Risk-free rate: 4.00%
Constraints: weights 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_AVAX-USD=0.0000, w_SGOV=1.0000, w_IYR=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EWJ=0.0000, w_AVAX-USD=0.0000, w_SGOV=1.0000, w_IYR=0.0000
Portfolio annualized return: 4.72%, volatility: 0.22%
Sharpe ratio: (0.0472 - 0.0400) / 0.0022 = 3.2640


4-asset optimization. Max-Sharpe: 5.213. Portfolio: return=61.92%, vol=11.11%. Weights: w_ACWI=0.7785, w_ETH-USD=0.1184, w_TLH=0.1031, w_SCHH=0.0000.

Question:
Assets: ACWI, ETH-USD, TLH, SCHH
Annualized mean returns: ACWI:0.4147, ETH-USD:2.3970, TLH:0.1213, SCHH:0.1395
Covariance matrix (annualized):
[[0.007642, 0.016437, 0.000857, 0.004523], [0.016437, 0.315607, 0.000535, 0.020147], [0.000857, 0.000535, 0.009714, 0.004232], [0.004523, 0.020147, 0.004232, 0.015966]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: bull

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

Answer: w_ACWI=0.7785, w_ETH-USD=0.1184, w_TLH=0.1031, w_SCHH=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_ACWI=0.7785, w_ETH-USD=0.1184, w_TLH=0.1031, w_SCHH=0.0000
Portfolio annualized return: 61.92%, volatility: 11.11%
Sharpe ratio: (0.6192 - 0.0400) / 0.1111 = 5.2132


4-asset optimization. Max-Sharpe: 2.222. Portfolio: return=37.91%, vol=15.26%. Weights: w_MTUM=0.4906, w_AVAX-USD=0.0196, w_TIP=0.0000, w_USO=0.4898.

Question:
Assets: MTUM, AVAX-USD, TIP, USO
Annualized mean returns: MTUM:0.2837, AVAX-USD:1.0645, TIP:0.0450, USO:0.4471
Covariance matrix (annualized):
[[0.033873, 0.090414, 0.001432, -0.003357], [0.090414, 0.975863, 0.004565, 0.014065], [0.001432, 0.004565, 0.000246, 0.000363], [-0.003357, 0.014065, 0.000363, 0.059906]]
Risk-free rate: 4.00%
Constraints: weights 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=0.4906, w_AVAX-USD=0.0196, w_TIP=0.0000, w_USO=0.4898

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_MTUM=0.4906, w_AVAX-USD=0.0196, w_TIP=0.0000, w_USO=0.4898
Portfolio annualized return: 37.91%, volatility: 15.26%
Sharpe ratio: (0.3791 - 0.0400) / 0.1526 = 2.2216


4-asset optimization. Max-Sharpe: -0.080. Portfolio: return=2.66%, vol=16.67%. Weights: w_SPY=0.2500, w_SOL-USD=0.2500, w_IEF=0.2500, w_BIL=0.2500.

Question:
Assets: SPY, SOL-USD, IEF, BIL
Annualized mean returns: SPY:0.4867, SOL-USD:-0.5033, IEF:0.0816, BIL:0.0414
Covariance matrix (annualized):
[[0.014578, 0.018567, 0.0002, -6.5e-05], [0.018567, 0.406085, -0.008865, 0.000185], [0.0002, -0.008865, 0.003785, -1.9e-05], [-6.5e-05, 0.000185, -1.9e-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_SPY=0.2500, w_SOL-USD=0.2500, w_IEF=0.2500, w_BIL=0.2500

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_SPY=0.2500, w_SOL-USD=0.2500, w_IEF=0.2500, w_BIL=0.2500
Portfolio annualized return: 2.66%, volatility: 16.67%
Sharpe ratio: (0.0266 - 0.0400) / 0.1667 = -0.0803


4-asset optimization. Max-Sharpe: 1.704. Portfolio: return=5.05%, vol=0.62%. Weights: w_QQQ=0.0000, w_BNB-USD=0.0000, w_MORT=0.0056, w_CSHI=0.9944.

Question:
Assets: QQQ, BNB-USD, MORT, CSHI
Annualized mean returns: QQQ:-0.0775, BNB-USD:0.1823, MORT:0.1866, CSHI:0.0498
Covariance matrix (annualized):
[[0.041338, 0.01994, 0.017218, 0.000707], [0.01994, 0.139241, 0.008647, 0.00051], [0.017218, 0.008647, 0.037803, 0.000323], [0.000707, 0.00051, 0.000323, 3.4e-05]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_QQQ=0.0000, w_BNB-USD=0.0000, w_MORT=0.0056, w_CSHI=0.9944

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_QQQ=0.0000, w_BNB-USD=0.0000, w_MORT=0.0056, w_CSHI=0.9944
Portfolio annualized return: 5.05%, volatility: 0.62%
Sharpe ratio: (0.0505 - 0.0400) / 0.0062 = 1.7041


4-asset optimization. Max-Sharpe: 0.218. Portfolio: return=8.58%, vol=21.02%. Weights: w_IWM=1.0000, w_AVAX-USD=0.0000, w_VCIT=0.0000, w_BIL=0.0000.

Question:
Assets: IWM, AVAX-USD, VCIT, BIL
Annualized mean returns: IWM:0.0858, AVAX-USD:-3.3857, VCIT:-0.0020, BIL:0.0399
Covariance matrix (annualized):
[[0.044168, 0.06757, 0.002404, 1.4e-05], [0.06757, 0.567768, 0.003437, 0.000349], [0.002404, 0.003437, 0.001185, -2.1e-05], [1.4e-05, 0.000349, -2.1e-05, 4e-06]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_IWM=1.0000, w_AVAX-USD=0.0000, w_VCIT=0.0000, w_BIL=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_IWM=1.0000, w_AVAX-USD=0.0000, w_VCIT=0.0000, w_BIL=0.0000
Portfolio annualized return: 8.58%, volatility: 21.02%
Sharpe ratio: (0.0858 - 0.0400) / 0.2102 = 0.2180


4-asset optimization. Max-Sharpe: 0.736. Portfolio: return=8.40%, vol=5.97%. Weights: w_IVV=0.0000, w_MATIC-USD=0.0000, w_XHB=0.0000, w_LQD=1.0000.

Question:
Assets: IVV, MATIC-USD, XHB, LQD
Annualized mean returns: IVV:-0.3917, MATIC-USD:-2.5661, XHB:-0.6429, LQD:0.0840
Covariance matrix (annualized):
[[0.027255, 0.030914, 0.023276, 0.000291], [0.030914, 0.470231, 0.041091, -0.008805], [0.023276, 0.041091, 0.061161, 0.004442], [0.000291, -0.008805, 0.004442, 0.003565]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: bear

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

Answer: w_IVV=0.0000, w_MATIC-USD=0.0000, w_XHB=0.0000, w_LQD=1.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_IVV=0.0000, w_MATIC-USD=0.0000, w_XHB=0.0000, w_LQD=1.0000
Portfolio annualized return: 8.40%, volatility: 5.97%
Sharpe ratio: (0.0840 - 0.0400) / 0.0597 = 0.7361


4-asset optimization. Max-Sharpe: 3.455. Portfolio: return=15.02%, vol=3.19%. Weights: w_XLF=0.0000, w_ETH-USD=0.0000, w_SGOV=0.0000, w_VCIT=1.0000.

Question:
Assets: XLF, ETH-USD, SGOV, VCIT
Annualized mean returns: XLF:-0.0947, ETH-USD:-1.4060, SGOV:0.0390, VCIT:0.1502
Covariance matrix (annualized):
[[0.01972, 0.023344, -1.6e-05, -0.000105], [0.023344, 0.289267, -0.00018, 0.000559], [-1.6e-05, -0.00018, 4e-06, 5e-06], [-0.000105, 0.000559, 5e-06, 0.001017]]
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_ETH-USD=0.0000, w_SGOV=0.0000, w_VCIT=1.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLF=0.0000, w_ETH-USD=0.0000, w_SGOV=0.0000, w_VCIT=1.0000
Portfolio annualized return: 15.02%, volatility: 3.19%
Sharpe ratio: (0.1502 - 0.0400) / 0.0319 = 3.4548


4-asset optimization. Max-Sharpe: 1.707. Portfolio: return=51.47%, vol=27.81%. Weights: w_EWJ=0.0000, w_XRP-USD=0.0000, w_SLV=1.0000, w_JNK=0.0000.

Question:
Assets: EWJ, XRP-USD, SLV, JNK
Annualized mean returns: EWJ:0.2030, XRP-USD:-0.4265, SLV:0.5147, JNK:-0.1349
Covariance matrix (annualized):
[[0.055514, 0.048835, 0.033072, 0.017124], [0.048835, 0.708553, 0.032439, 0.023231], [0.033072, 0.032439, 0.077341, 0.009706], [0.017124, 0.023231, 0.009706, 0.008588]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: bear

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

Answer: w_EWJ=0.0000, w_XRP-USD=0.0000, w_SLV=1.0000, w_JNK=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EWJ=0.0000, w_XRP-USD=0.0000, w_SLV=1.0000, w_JNK=0.0000
Portfolio annualized return: 51.47%, volatility: 27.81%
Sharpe ratio: (0.5147 - 0.0400) / 0.2781 = 1.7071


4-asset optimization. Max-Sharpe: 0.313. Portfolio: return=23.02%, vol=60.82%. Weights: w_QUAL=0.0000, w_ETH-USD=1.0000, w_VCIT=0.0000, w_XHB=0.0000.

Question:
Assets: QUAL, ETH-USD, VCIT, XHB
Annualized mean returns: QUAL:0.0148, ETH-USD:0.2302, VCIT:-0.0624, XHB:-0.6086
Covariance matrix (annualized):
[[0.015497, 0.040105, 0.004381, 0.018877], [0.040105, 0.369894, 0.014836, 0.046693], [0.004381, 0.014836, 0.002883, 0.006883], [0.018877, 0.046693, 0.006883, 0.045749]]
Risk-free rate: 4.00%
Constraints: weights 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_ETH-USD=1.0000, w_VCIT=0.0000, w_XHB=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_QUAL=0.0000, w_ETH-USD=1.0000, w_VCIT=0.0000, w_XHB=0.0000
Portfolio annualized return: 23.02%, volatility: 60.82%
Sharpe ratio: (0.2302 - 0.0400) / 0.6082 = 0.3127


4-asset optimization. Max-Sharpe: 1.690. Portfolio: return=31.87%, vol=16.49%. Weights: w_EWJ=1.0000, w_MATIC-USD=0.0000, w_USO=0.0000, w_VNQI=0.0000.

Question:
Assets: EWJ, MATIC-USD, USO, VNQI
Annualized mean returns: EWJ:0.3187, MATIC-USD:-2.9907, USO:-0.0693, VNQI:0.1074
Covariance matrix (annualized):
[[0.027185, 0.015227, 0.0003, 0.015003], [0.015227, 0.475762, 0.03592, 0.017797], [0.0003, 0.03592, 0.048574, 0.0022], [0.015003, 0.017797, 0.0022, 0.01287]]
Risk-free rate: 4.00%
Constraints: weights 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=1.0000, w_MATIC-USD=0.0000, w_USO=0.0000, w_VNQI=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EWJ=1.0000, w_MATIC-USD=0.0000, w_USO=0.0000, w_VNQI=0.0000
Portfolio annualized return: 31.87%, volatility: 16.49%
Sharpe ratio: (0.3187 - 0.0400) / 0.1649 = 1.6901


4-asset optimization. Max-Sharpe: 2.509. Portfolio: return=4.93%, vol=0.37%. Weights: w_XLP=0.0000, w_BTC-USD=0.0056, w_BNO=0.0000, w_SGOV=0.9944.

Question:
Assets: XLP, BTC-USD, BNO, SGOV
Annualized mean returns: XLP:-0.0402, BTC-USD:1.1046, BNO:-0.3024, SGOV:0.0434
Covariance matrix (annualized):
[[0.033738, 0.020002, 0.027173, 8.2e-05], [0.020002, 0.259349, 0.065212, 0.000121], [0.027173, 0.065212, 0.121058, 8.5e-05], [8.2e-05, 0.000121, 8.5e-05, 4e-06]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: bear

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

Answer: w_XLP=0.0000, w_BTC-USD=0.0056, w_BNO=0.0000, w_SGOV=0.9944

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLP=0.0000, w_BTC-USD=0.0056, w_BNO=0.0000, w_SGOV=0.9944
Portfolio annualized return: 4.93%, volatility: 0.37%
Sharpe ratio: (0.0493 - 0.0400) / 0.0037 = 2.5095


4-asset optimization. Max-Sharpe: 1.602. Portfolio: return=5.19%, vol=0.75%. Weights: w_XLRE=0.0129, w_BTC-USD=0.0000, w_SGOV=0.9382, w_GLD=0.0488.

Question:
Assets: XLRE, BTC-USD, SGOV, GLD
Annualized mean returns: XLRE:0.1541, BTC-USD:0.0750, SGOV:0.0411, GLD:0.2327
Covariance matrix (annualized):
[[0.018872, 0.01447, -2.9e-05, 0.006436], [0.01447, 0.08115, 9e-06, 0.010323], [-2.9e-05, 9e-06, 5e-06, 1.8e-05], [0.006436, 0.010323, 1.8e-05, 0.016332]]
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=0.0129, w_BTC-USD=0.0000, w_SGOV=0.9382, w_GLD=0.0488

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLRE=0.0129, w_BTC-USD=0.0000, w_SGOV=0.9382, w_GLD=0.0488
Portfolio annualized return: 5.19%, volatility: 0.75%
Sharpe ratio: (0.0519 - 0.0400) / 0.0075 = 1.6016


4-asset optimization. Max-Sharpe: 1.745. Portfolio: return=93.86%, vol=51.49%. Weights: w_XLRE=0.0000, w_XRP-USD=0.0000, w_UNG=1.0000, w_ICSH=0.0000.

Question:
Assets: XLRE, XRP-USD, UNG, ICSH
Annualized mean returns: XLRE:-0.0273, XRP-USD:-1.8095, UNG:0.9386, ICSH:0.0371
Covariance matrix (annualized):
[[0.019565, 0.012909, 0.016682, 8.5e-05], [0.012909, 0.416582, -0.070207, -5.6e-05], [0.016682, -0.070207, 0.265077, 0.000265], [8.5e-05, -5.6e-05, 0.000265, 1.3e-05]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_XLRE=0.0000, w_XRP-USD=0.0000, w_UNG=1.0000, w_ICSH=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLRE=0.0000, w_XRP-USD=0.0000, w_UNG=1.0000, w_ICSH=0.0000
Portfolio annualized return: 93.86%, volatility: 51.49%
Sharpe ratio: (0.9386 - 0.0400) / 0.5149 = 1.7453


4-asset optimization. Max-Sharpe: 3.710. Portfolio: return=15.83%, vol=3.19%. Weights: w_FXI=0.1379, w_ETH-USD=0.0000, w_CSHI=0.7704, w_SCHH=0.0916.

Question:
Assets: FXI, ETH-USD, CSHI, SCHH
Annualized mean returns: FXI:0.6989, ETH-USD:1.2899, CSHI:0.0511, SCHH:0.2457
Covariance matrix (annualized):
[[0.037108, 0.057873, 0.000338, 0.003096], [0.057873, 0.500777, 0.001157, 0.0242], [0.000338, 0.001157, 6.1e-05, 2.1e-05], [0.003096, 0.0242, 2.1e-05, 0.014461]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: bull

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

Answer: w_FXI=0.1379, w_ETH-USD=0.0000, w_CSHI=0.7704, w_SCHH=0.0916

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_FXI=0.1379, w_ETH-USD=0.0000, w_CSHI=0.7704, w_SCHH=0.0916
Portfolio annualized return: 15.83%, volatility: 3.19%
Sharpe ratio: (0.1583 - 0.0400) / 0.0319 = 3.7104