4-asset optimization. Max-Sharpe: 2.619. Portfolio: return=37.60%, vol=12.83%. Weights: w_SPY=0.0000, w_ETH-USD=0.0000, w_HAUZ=0.8896, w_UNG=0.1104.

Question:
Assets: SPY, ETH-USD, HAUZ, UNG
Annualized mean returns: SPY:-0.3269, ETH-USD:-2.9067, HAUZ:0.2966, UNG:1.0156
Covariance matrix (annualized):
[[0.026696, 0.038493, 0.009212, -0.013491], [0.038493, 0.420296, 0.017986, -0.047047], [0.009212, 0.017986, 0.014109, 0.000191], [-0.013491, -0.047047, 0.000191, 0.431363]]
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_SPY=0.0000, w_ETH-USD=0.0000, w_HAUZ=0.8896, w_UNG=0.1104

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_SPY=0.0000, w_ETH-USD=0.0000, w_HAUZ=0.8896, w_UNG=0.1104
Portfolio annualized return: 37.60%, volatility: 12.83%
Sharpe ratio: (0.3760 - 0.0400) / 0.1283 = 2.6187


4-asset optimization. Max-Sharpe: 1.333. Portfolio: return=10.94%, vol=5.21%. Weights: w_XLU=0.0000, w_XRP-USD=0.0000, w_EMB=1.0000, w_CSHI=0.0000.

Question:
Assets: XLU, XRP-USD, EMB, CSHI
Annualized mean returns: XLU:0.0337, XRP-USD:-1.1689, EMB:0.1094, CSHI:0.0408
Covariance matrix (annualized):
[[0.028096, -0.018999, 0.002915, 0.000505], [-0.018999, 0.743566, 0.003946, 0.000637], [0.002915, 0.003946, 0.002711, 5.1e-05], [0.000505, 0.000637, 5.1e-05, 0.000111]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_XLU=0.0000, w_XRP-USD=0.0000, w_EMB=1.0000, w_CSHI=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLU=0.0000, w_XRP-USD=0.0000, w_EMB=1.0000, w_CSHI=0.0000
Portfolio annualized return: 10.94%, volatility: 5.21%
Sharpe ratio: (0.1094 - 0.0400) / 0.0521 = 1.3334


4-asset optimization. Max-Sharpe: -1.462. Portfolio: return=-130.01%, vol=91.65%. Weights: w_XLP=0.0000, w_AVAX-USD=1.0000, w_DBB=0.0000, w_IYR=0.0000.

Question:
Assets: XLP, AVAX-USD, DBB, IYR
Annualized mean returns: XLP:-0.2492, AVAX-USD:-1.3001, DBB:-0.1124, IYR:-0.1220
Covariance matrix (annualized):
[[0.014331, 0.017408, 0.003529, 0.0152], [0.017408, 0.839975, 0.011004, 0.045695], [0.003529, 0.011004, 0.01308, 0.002605], [0.0152, 0.045695, 0.002605, 0.037684]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_XLP=0.0000, w_AVAX-USD=1.0000, w_DBB=0.0000, w_IYR=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLP=0.0000, w_AVAX-USD=1.0000, w_DBB=0.0000, w_IYR=0.0000
Portfolio annualized return: -130.01%, volatility: 91.65%
Sharpe ratio: (-1.3001 - 0.0400) / 0.9165 = -1.4622


4-asset optimization. Max-Sharpe: 1.281. Portfolio: return=9.62%, vol=4.39%. Weights: w_XLB=0.0000, w_ETH-USD=0.0000, w_USO=0.0000, w_EMB=1.0000.

Question:
Assets: XLB, ETH-USD, USO, EMB
Annualized mean returns: XLB:-0.3721, ETH-USD:-2.5340, USO:-0.0784, EMB:0.0962
Covariance matrix (annualized):
[[0.019825, 0.040093, 0.002791, 0.002101], [0.040093, 0.363113, 0.037515, 0.006099], [0.002791, 0.037515, 0.063417, 0.001369], [0.002101, 0.006099, 0.001369, 0.001925]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: bull

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

Answer: w_XLB=0.0000, w_ETH-USD=0.0000, w_USO=0.0000, w_EMB=1.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLB=0.0000, w_ETH-USD=0.0000, w_USO=0.0000, w_EMB=1.0000
Portfolio annualized return: 9.62%, volatility: 4.39%
Sharpe ratio: (0.0962 - 0.0400) / 0.0439 = 1.2812


4-asset optimization. Max-Sharpe: 2.273. Portfolio: return=30.86%, vol=11.82%. Weights: w_EEM=0.0000, w_BNB-USD=0.0543, w_DBC=0.9457, w_HYG=0.0000.

Question:
Assets: EEM, BNB-USD, DBC, HYG
Annualized mean returns: EEM:-0.0288, BNB-USD:0.2841, DBC:0.3101, HYG:0.0255
Covariance matrix (annualized):
[[0.022944, 0.005923, 0.002002, 0.00377], [0.005923, 0.171107, 0.003604, 0.006011], [0.002002, 0.003604, 0.014645, 0.000679], [0.00377, 0.006011, 0.000679, 0.002481]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_EEM=0.0000, w_BNB-USD=0.0543, w_DBC=0.9457, w_HYG=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EEM=0.0000, w_BNB-USD=0.0543, w_DBC=0.9457, w_HYG=0.0000
Portfolio annualized return: 30.86%, volatility: 11.82%
Sharpe ratio: (0.3086 - 0.0400) / 0.1182 = 2.2727


4-asset optimization. Max-Sharpe: 8.105. Portfolio: return=70.38%, vol=8.19%. Weights: w_QUAL=0.4331, w_LINK-USD=0.0000, w_IAU=0.5669, w_TLH=0.0000.

Question:
Assets: QUAL, LINK-USD, IAU, TLH
Annualized mean returns: QUAL:0.3426, LINK-USD:0.0175, IAU:0.9798, TLH:0.1579
Covariance matrix (annualized):
[[0.006643, 0.02811, 0.000318, 0.001389], [0.02811, 0.677939, 0.027178, 0.006196], [0.000318, 0.027178, 0.016509, 0.0015], [0.001389, 0.006196, 0.0015, 0.005883]]
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=0.4331, w_LINK-USD=0.0000, w_IAU=0.5669, w_TLH=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_QUAL=0.4331, w_LINK-USD=0.0000, w_IAU=0.5669, w_TLH=0.0000
Portfolio annualized return: 70.38%, volatility: 8.19%
Sharpe ratio: (0.7038 - 0.0400) / 0.0819 = 8.1047


4-asset optimization. Max-Sharpe: 2.779. Portfolio: return=6.16%, vol=0.78%. Weights: w_VEA=0.0000, w_BNB-USD=0.0047, w_UNG=0.0070, w_ICSH=0.9883.

Question:
Assets: VEA, BNB-USD, UNG, ICSH
Annualized mean returns: VEA:-0.1583, BNB-USD:0.6323, UNG:1.3467, ICSH:0.0498
Covariance matrix (annualized):
[[0.011778, 0.029108, -0.004568, 0.000236], [0.029108, 0.354755, -0.041302, 0.000287], [-0.004568, -0.041302, 0.564367, -0.000114], [0.000236, 0.000287, -0.000114, 2.7e-05]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_VEA=0.0000, w_BNB-USD=0.0047, w_UNG=0.0070, w_ICSH=0.9883

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VEA=0.0000, w_BNB-USD=0.0047, w_UNG=0.0070, w_ICSH=0.9883
Portfolio annualized return: 6.16%, volatility: 0.78%
Sharpe ratio: (0.0616 - 0.0400) / 0.0078 = 2.7786


4-asset optimization. Max-Sharpe: 2.320. Portfolio: return=5.54%, vol=0.66%. Weights: w_EEM=0.0000, w_AVAX-USD=0.0000, w_CSHI=0.7602, w_TIP=0.2398.

Question:
Assets: EEM, AVAX-USD, CSHI, TIP
Annualized mean returns: EEM:0.0383, AVAX-USD:-1.5666, CSHI:0.0512, TIP:0.0686
Covariance matrix (annualized):
[[0.02149, 0.048485, 0.000463, 0.000686], [0.048485, 0.59301, 0.002392, 0.004366], [0.000463, 0.002392, 3.4e-05, 2.6e-05], [0.000686, 0.004366, 2.6e-05, 0.00026]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_EEM=0.0000, w_AVAX-USD=0.0000, w_CSHI=0.7602, w_TIP=0.2398

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EEM=0.0000, w_AVAX-USD=0.0000, w_CSHI=0.7602, w_TIP=0.2398
Portfolio annualized return: 5.54%, volatility: 0.66%
Sharpe ratio: (0.0554 - 0.0400) / 0.0066 = 2.3199


4-asset optimization. Max-Sharpe: 2.759. Portfolio: return=19.40%, vol=5.58%. Weights: w_XLV=0.2681, w_LINK-USD=0.0000, w_EMB=0.5114, w_DBC=0.2205.

Question:
Assets: XLV, LINK-USD, EMB, DBC
Annualized mean returns: XLV:0.2967, LINK-USD:-2.8145, EMB:0.1211, DBC:0.2384
Covariance matrix (annualized):
[[0.01784, 0.034779, 0.001396, -0.001363], [0.034779, 0.680033, 0.013233, 0.039005], [0.001396, 0.013233, 0.002044, 0.001006], [-0.001363, 0.039005, 0.001006, 0.017541]]
Risk-free rate: 4.00%
Constraints: weights 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=0.2681, w_LINK-USD=0.0000, w_EMB=0.5114, w_DBC=0.2205

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLV=0.2681, w_LINK-USD=0.0000, w_EMB=0.5114, w_DBC=0.2205
Portfolio annualized return: 19.40%, volatility: 5.58%
Sharpe ratio: (0.1940 - 0.0400) / 0.0558 = 2.7587


4-asset optimization. Max-Sharpe: 0.749. Portfolio: return=93.85%, vol=119.89%. Weights: w_^VIX=1.0000, w_AVAX-USD=0.0000, w_BIL=0.0000, w_IGOV=0.0000.

Question:
Assets: ^VIX, AVAX-USD, BIL, IGOV
Annualized mean returns: ^VIX:0.9385, AVAX-USD:-2.4897, BIL:0.0367, IGOV:-0.0980
Covariance matrix (annualized):
[[1.437473, -0.415861, -5.8e-05, 0.025022], [-0.415861, 0.800384, -8.7e-05, -0.003596], [-5.8e-05, -8.7e-05, 3e-06, 1e-06], [0.025022, -0.003596, 1e-06, 0.003693]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_^VIX=1.0000, w_AVAX-USD=0.0000, w_BIL=0.0000, w_IGOV=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_^VIX=1.0000, w_AVAX-USD=0.0000, w_BIL=0.0000, w_IGOV=0.0000
Portfolio annualized return: 93.85%, volatility: 119.89%
Sharpe ratio: (0.9385 - 0.0400) / 1.1989 = 0.7494


4-asset optimization. Max-Sharpe: 2.600. Portfolio: return=32.00%, vol=10.77%. Weights: w_XLP=0.2496, w_DOT-USD=0.0000, w_HAUZ=0.7504, w_CORN=0.0000.

Question:
Assets: XLP, DOT-USD, HAUZ, CORN
Annualized mean returns: XLP:0.2743, DOT-USD:-0.3393, HAUZ:0.3351, CORN:-0.0904
Covariance matrix (annualized):
[[0.024089, 0.003015, 0.004924, 0.001217], [0.003015, 0.530774, 0.012052, 0.028948], [0.004924, 0.012052, 0.014656, 0.00328], [0.001217, 0.028948, 0.00328, 0.030779]]
Risk-free rate: 4.00%
Constraints: weights 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=0.2496, w_DOT-USD=0.0000, w_HAUZ=0.7504, w_CORN=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLP=0.2496, w_DOT-USD=0.0000, w_HAUZ=0.7504, w_CORN=0.0000
Portfolio annualized return: 32.00%, volatility: 10.77%
Sharpe ratio: (0.3200 - 0.0400) / 0.1077 = 2.5996


4-asset optimization. Max-Sharpe: 3.412. Portfolio: return=119.83%, vol=33.95%. Weights: w_MTUM=0.0000, w_ADA-USD=0.0000, w_SLV=1.0000, w_HYG=0.0000.

Question:
Assets: MTUM, ADA-USD, SLV, HYG
Annualized mean returns: MTUM:-0.4352, ADA-USD:-4.2966, SLV:1.1983, HYG:-0.0256
Covariance matrix (annualized):
[[0.022129, 0.06464, 0.012714, 0.003753], [0.06464, 0.547082, 0.051142, 0.014546], [0.012714, 0.051142, 0.115267, 0.001262], [0.003753, 0.014546, 0.001262, 0.001327]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_MTUM=0.0000, w_ADA-USD=0.0000, w_SLV=1.0000, w_HYG=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_MTUM=0.0000, w_ADA-USD=0.0000, w_SLV=1.0000, w_HYG=0.0000
Portfolio annualized return: 119.83%, volatility: 33.95%
Sharpe ratio: (1.1983 - 0.0400) / 0.3395 = 3.4116


4-asset optimization. Max-Sharpe: 1.242. Portfolio: return=17.52%, vol=10.88%. Weights: w_QUAL=0.0000, w_ETH-USD=0.0000, w_VNQI=1.0000, w_DBC=0.0000.

Question:
Assets: QUAL, ETH-USD, VNQI, DBC
Annualized mean returns: QUAL:-0.3033, ETH-USD:-2.4971, VNQI:0.1752, DBC:-0.0051
Covariance matrix (annualized):
[[0.024598, 0.038766, 0.01071, 0.006894], [0.038766, 0.426526, 0.019056, 0.019085], [0.01071, 0.019056, 0.011833, 0.002572], [0.006894, 0.019085, 0.002572, 0.012124]]
Risk-free rate: 4.00%
Constraints: weights 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=0.0000, w_VNQI=1.0000, w_DBC=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_QUAL=0.0000, w_ETH-USD=0.0000, w_VNQI=1.0000, w_DBC=0.0000
Portfolio annualized return: 17.52%, volatility: 10.88%
Sharpe ratio: (0.1752 - 0.0400) / 0.1088 = 1.2424


4-asset optimization. Max-Sharpe: 1.863. Portfolio: return=122.54%, vol=63.63%. Weights: w_FXI=0.0000, w_DOT-USD=1.0000, w_WEAT=0.0000, w_CSHI=0.0000.

Question:
Assets: FXI, DOT-USD, WEAT, CSHI
Annualized mean returns: FXI:0.2166, DOT-USD:1.2254, WEAT:-0.1303, CSHI:0.0632
Covariance matrix (annualized):
[[0.090353, 0.063296, 0.015265, 0.008662], [0.063296, 0.404858, -0.003872, 0.010802], [0.015265, -0.003872, 0.036535, 0.002441], [0.008662, 0.010802, 0.002441, 0.002101]]
Risk-free rate: 4.00%
Constraints: weights 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_DOT-USD=1.0000, w_WEAT=0.0000, w_CSHI=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_FXI=0.0000, w_DOT-USD=1.0000, w_WEAT=0.0000, w_CSHI=0.0000
Portfolio annualized return: 122.54%, volatility: 63.63%
Sharpe ratio: (1.2254 - 0.0400) / 0.6363 = 1.8631


4-asset optimization. Max-Sharpe: 0.539. Portfolio: return=4.23%, vol=0.42%. Weights: w_QUAL=0.0254, w_SOL-USD=0.0000, w_TIP=0.0000, w_ICSH=0.9746.

Question:
Assets: QUAL, SOL-USD, TIP, ICSH
Annualized mean returns: QUAL:0.0832, SOL-USD:-3.1309, TIP:0.0195, ICSH:0.0412
Covariance matrix (annualized):
[[0.015993, 0.053957, -0.000217, -7.1e-05], [0.053957, 0.616487, -0.001537, -0.000204], [-0.000217, -0.001537, 0.00017, 1.4e-05], [-7.1e-05, -0.000204, 1.4e-05, 1.1e-05]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_QUAL=0.0254, w_SOL-USD=0.0000, w_TIP=0.0000, w_ICSH=0.9746

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_QUAL=0.0254, w_SOL-USD=0.0000, w_TIP=0.0000, w_ICSH=0.9746
Portfolio annualized return: 4.23%, volatility: 0.42%
Sharpe ratio: (0.0423 - 0.0400) / 0.0042 = 0.5388


4-asset optimization. Max-Sharpe: -1.906. Portfolio: return=-36.25%, vol=21.12%. Weights: w_IWM=0.2500, w_ADA-USD=0.2500, w_ICSH=0.2500, w_DBC=0.2500.

Question:
Assets: IWM, ADA-USD, ICSH, DBC
Annualized mean returns: IWM:0.2530, ADA-USD:-1.8883, ICSH:0.0431, DBC:0.1424
Covariance matrix (annualized):
[[0.033532, 0.065425, -2.6e-05, 0.003105], [0.065425, 0.450166, -0.000178, 0.037097], [-2.6e-05, -0.000178, 1.4e-05, -0.000149], [0.003105, 0.037097, -0.000149, 0.019097]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: bull

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

Answer: w_IWM=0.2500, w_ADA-USD=0.2500, w_ICSH=0.2500, w_DBC=0.2500

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_IWM=0.2500, w_ADA-USD=0.2500, w_ICSH=0.2500, w_DBC=0.2500
Portfolio annualized return: -36.25%, volatility: 21.12%
Sharpe ratio: (-0.3625 - 0.0400) / 0.2112 = -1.9061


4-asset optimization. Max-Sharpe: 4.271. Portfolio: return=10.70%, vol=1.57%. Weights: w_QQQ=0.0000, w_BTC-USD=0.0000, w_IAU=0.0860, w_ICSH=0.9140.

Question:
Assets: QQQ, BTC-USD, IAU, ICSH
Annualized mean returns: QQQ:-1.5392, BTC-USD:-0.3275, IAU:0.7774, ICSH:0.0439
Covariance matrix (annualized):
[[0.093322, 0.078618, 0.003627, 2.4e-05], [0.078618, 0.27454, 0.00916, 0.000281], [0.003627, 0.00916, 0.033731, -0.000213], [2.4e-05, 0.000281, -0.000213, 3.6e-05]]
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_QQQ=0.0000, w_BTC-USD=0.0000, w_IAU=0.0860, w_ICSH=0.9140

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_QQQ=0.0000, w_BTC-USD=0.0000, w_IAU=0.0860, w_ICSH=0.9140
Portfolio annualized return: 10.70%, volatility: 1.57%
Sharpe ratio: (0.1070 - 0.0400) / 0.0157 = 4.2715


4-asset optimization. Max-Sharpe: 2.385. Portfolio: return=4.96%, vol=0.40%. Weights: w_IVV=0.0058, w_ADA-USD=0.0034, w_SGOV=0.9908, w_IYR=0.0000.

Question:
Assets: IVV, ADA-USD, SGOV, IYR
Annualized mean returns: IVV:0.3700, ADA-USD:1.3101, SGOV:0.0434, IYR:0.0126
Covariance matrix (annualized):
[[0.051072, 0.057652, 6.6e-05, 0.038248], [0.057652, 0.479354, 0.000197, 0.025294], [6.6e-05, 0.000197, 5e-06, 9.6e-05], [0.038248, 0.025294, 9.6e-05, 0.050976]]
Risk-free rate: 4.00%
Constraints: weights 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=0.0058, w_ADA-USD=0.0034, w_SGOV=0.9908, w_IYR=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_IVV=0.0058, w_ADA-USD=0.0034, w_SGOV=0.9908, w_IYR=0.0000
Portfolio annualized return: 4.96%, volatility: 0.40%
Sharpe ratio: (0.0496 - 0.0400) / 0.0040 = 2.3852


4-asset optimization. Max-Sharpe: 0.744. Portfolio: return=69.85%, vol=88.48%. Weights: w_IWM=0.0000, w_SOL-USD=1.0000, w_BNDX=0.0000, w_CSHI=0.0000.

Question:
Assets: IWM, SOL-USD, BNDX, CSHI
Annualized mean returns: IWM:-0.5602, SOL-USD:0.6985, BNDX:0.0294, CSHI:0.0346
Covariance matrix (annualized):
[[0.081038, 0.143785, -0.001655, 0.009019], [0.143785, 0.782943, -0.002121, 0.011838], [-0.001655, -0.002121, 0.001644, -0.000473], [0.009019, 0.011838, -0.000473, 0.002106]]
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_IWM=0.0000, w_SOL-USD=1.0000, w_BNDX=0.0000, w_CSHI=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_IWM=0.0000, w_SOL-USD=1.0000, w_BNDX=0.0000, w_CSHI=0.0000
Portfolio annualized return: 69.85%, volatility: 88.48%
Sharpe ratio: (0.6985 - 0.0400) / 0.8848 = 0.7442


4-asset optimization. Max-Sharpe: -1.280. Portfolio: return=-23.34%, vol=21.35%. Weights: w_EEM=0.2500, w_MATIC-USD=0.2500, w_ITB=0.2500, w_ICSH=0.2500.

Question:
Assets: EEM, MATIC-USD, ITB, ICSH
Annualized mean returns: EEM:0.2113, MATIC-USD:-0.9450, ITB:-0.2570, ICSH:0.0573
Covariance matrix (annualized):
[[0.023475, 0.033078, 0.01179, 5.3e-05], [0.033078, 0.482683, 0.031737, 0.000121], [0.01179, 0.031737, 0.069131, 0.000176], [5.3e-05, 0.000121, 0.000176, 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_EEM=0.2500, w_MATIC-USD=0.2500, w_ITB=0.2500, w_ICSH=0.2500

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EEM=0.2500, w_MATIC-USD=0.2500, w_ITB=0.2500, w_ICSH=0.2500
Portfolio annualized return: -23.34%, volatility: 21.35%
Sharpe ratio: (-0.2334 - 0.0400) / 0.2135 = -1.2805


4-asset optimization. Max-Sharpe: 2.896. Portfolio: return=52.02%, vol=16.58%. Weights: w_ACWI=0.0000, w_SOL-USD=0.0000, w_INDS=1.0000, w_BIL=0.0000.

Question:
Assets: ACWI, SOL-USD, INDS, BIL
Annualized mean returns: ACWI:0.2030, SOL-USD:-0.0744, INDS:0.5202, BIL:0.0392
Covariance matrix (annualized):
[[0.011718, 0.055546, 0.009505, -2.6e-05], [0.055546, 0.691818, 0.031699, 0.000214], [0.009505, 0.031699, 0.027497, 1.8e-05], [-2.6e-05, 0.000214, 1.8e-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_ACWI=0.0000, w_SOL-USD=0.0000, w_INDS=1.0000, w_BIL=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_ACWI=0.0000, w_SOL-USD=0.0000, w_INDS=1.0000, w_BIL=0.0000
Portfolio annualized return: 52.02%, volatility: 16.58%
Sharpe ratio: (0.5202 - 0.0400) / 0.1658 = 2.8958


4-asset optimization. Max-Sharpe: 4.219. Portfolio: return=6.36%, vol=0.56%. Weights: w_QQQ=0.0413, w_ETH-USD=0.0000, w_ICSH=0.9587, w_XHB=0.0000.

Question:
Assets: QQQ, ETH-USD, ICSH, XHB
Annualized mean returns: QQQ:0.3803, ETH-USD:0.6951, ICSH:0.0500, XHB:-0.0190
Covariance matrix (annualized):
[[0.010448, 0.036125, 2.1e-05, 0.01028], [0.036125, 0.478384, 0.000464, 0.081014], [2.1e-05, 0.000464, 1.3e-05, 0.000323], [0.01028, 0.081014, 0.000323, 0.072189]]
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_QQQ=0.0413, w_ETH-USD=0.0000, w_ICSH=0.9587, w_XHB=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_QQQ=0.0413, w_ETH-USD=0.0000, w_ICSH=0.9587, w_XHB=0.0000
Portfolio annualized return: 6.36%, volatility: 0.56%
Sharpe ratio: (0.0636 - 0.0400) / 0.0056 = 4.2192


4-asset optimization. Max-Sharpe: 3.763. Portfolio: return=12.66%, vol=2.30%. Weights: w_XLY=0.0000, w_BNB-USD=0.0699, w_ICSH=0.9301, w_IYR=0.0000.

Question:
Assets: XLY, BNB-USD, ICSH, IYR
Annualized mean returns: XLY:-0.0264, BNB-USD:1.2233, ICSH:0.0442, IYR:-0.1865
Covariance matrix (annualized):
[[0.089447, 0.023042, 0.000365, 0.053099], [0.023042, 0.10399, -3e-05, 0.01076], [0.000365, -3e-05, 3e-05, 0.000563], [0.053099, 0.01076, 0.000563, 0.057073]]
Risk-free rate: 4.00%
Constraints: weights 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_BNB-USD=0.0699, w_ICSH=0.9301, w_IYR=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLY=0.0000, w_BNB-USD=0.0699, w_ICSH=0.9301, w_IYR=0.0000
Portfolio annualized return: 12.66%, volatility: 2.30%
Sharpe ratio: (0.1266 - 0.0400) / 0.0230 = 3.7627


4-asset optimization. Max-Sharpe: 5.349. Portfolio: return=26.20%, vol=4.15%. Weights: w_QUAL=0.0000, w_BTC-USD=0.1063, w_DBA=0.0000, w_ICSH=0.8937.

Question:
Assets: QUAL, BTC-USD, DBA, ICSH
Annualized mean returns: QUAL:-0.0132, BTC-USD:2.1079, DBA:0.1845, ICSH:0.0424
Covariance matrix (annualized):
[[0.0543, 0.031848, 0.017118, 0.000183], [0.031848, 0.15151, 0.025192, -6.9e-05], [0.017118, 0.025192, 0.025369, 6.8e-05], [0.000183, -6.9e-05, 6.8e-05, 2.9e-05]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_QUAL=0.0000, w_BTC-USD=0.1063, w_DBA=0.0000, w_ICSH=0.8937

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_QUAL=0.0000, w_BTC-USD=0.1063, w_DBA=0.0000, w_ICSH=0.8937
Portfolio annualized return: 26.20%, volatility: 4.15%
Sharpe ratio: (0.2620 - 0.0400) / 0.0415 = 5.3490


4-asset optimization. Max-Sharpe: -1.576. Portfolio: return=-16.91%, vol=13.27%. Weights: w_XLU=0.0000, w_BTC-USD=0.0000, w_INDS=1.0000, w_BIL=0.0000.

Question:
Assets: XLU, BTC-USD, INDS, BIL
Annualized mean returns: XLU:-0.3758, BTC-USD:-1.8014, INDS:-0.1691, BIL:0.0392
Covariance matrix (annualized):
[[0.016103, 0.015459, 0.007656, 1.3e-05], [0.015459, 0.15357, 0.017239, 5.1e-05], [0.007656, 0.017239, 0.017602, 8e-06], [1.3e-05, 5.1e-05, 8e-06, 4e-06]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_XLU=0.0000, w_BTC-USD=0.0000, w_INDS=1.0000, w_BIL=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLU=0.0000, w_BTC-USD=0.0000, w_INDS=1.0000, w_BIL=0.0000
Portfolio annualized return: -16.91%, volatility: 13.27%
Sharpe ratio: (-0.1691 - 0.0400) / 0.1327 = -1.5761


4-asset optimization. Max-Sharpe: 2.311. Portfolio: return=4.52%, vol=0.22%. Weights: w_XLE=0.0000, w_SOL-USD=0.0000, w_SGOV=1.0000, w_SOYB=0.0000.

Question:
Assets: XLE, SOL-USD, SGOV, SOYB
Annualized mean returns: XLE:-0.3440, SOL-USD:-0.0550, SGOV:0.0452, SOYB:-0.2774
Covariance matrix (annualized):
[[0.027554, 0.053614, -6e-06, 0.006835], [0.053614, 0.475731, -5.5e-05, 0.002003], [-6e-06, -5.5e-05, 5e-06, 1.1e-05], [0.006835, 0.002003, 1.1e-05, 0.022421]]
Risk-free rate: 4.00%
Constraints: weights 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_SOL-USD=0.0000, w_SGOV=1.0000, w_SOYB=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLE=0.0000, w_SOL-USD=0.0000, w_SGOV=1.0000, w_SOYB=0.0000
Portfolio annualized return: 4.52%, volatility: 0.22%
Sharpe ratio: (0.0452 - 0.0400) / 0.0022 = 2.3106


4-asset optimization. Max-Sharpe: -0.899. Portfolio: return=-14.59%, vol=20.67%. Weights: w_XLB=0.2500, w_DOT-USD=0.2500, w_PALL=0.2500, w_SGOV=0.2500.

Question:
Assets: XLB, DOT-USD, PALL, SGOV
Annualized mean returns: XLB:-0.1252, DOT-USD:-0.5504, PALL:0.0492, SGOV:0.0429
Covariance matrix (annualized):
[[0.022167, 0.045308, 0.003185, 2.9e-05], [0.045308, 0.445293, 0.012879, -9e-05], [0.003185, 0.012879, 0.093743, -7.1e-05], [2.9e-05, -9e-05, -7.1e-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_XLB=0.2500, w_DOT-USD=0.2500, w_PALL=0.2500, w_SGOV=0.2500

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLB=0.2500, w_DOT-USD=0.2500, w_PALL=0.2500, w_SGOV=0.2500
Portfolio annualized return: -14.59%, volatility: 20.67%
Sharpe ratio: (-0.1459 - 0.0400) / 0.2067 = -0.8991


4-asset optimization. Max-Sharpe: 2.233. Portfolio: return=21.46%, vol=7.82%. Weights: w_^VIX=0.0389, w_ETH-USD=0.0000, w_ITB=0.0000, w_LQD=0.9611.

Question:
Assets: ^VIX, ETH-USD, ITB, LQD
Annualized mean returns: ^VIX:1.9316, ETH-USD:-2.8125, ITB:-0.8075, LQD:0.1452
Covariance matrix (annualized):
[[1.569982, -0.314957, -0.074797, 0.005399], [-0.314957, 0.398186, 0.027801, -0.008481], [-0.074797, 0.027801, 0.063607, 0.006252], [0.005399, -0.008481, 0.006252, 0.00361]]
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=0.0389, w_ETH-USD=0.0000, w_ITB=0.0000, w_LQD=0.9611

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_^VIX=0.0389, w_ETH-USD=0.0000, w_ITB=0.0000, w_LQD=0.9611
Portfolio annualized return: 21.46%, volatility: 7.82%
Sharpe ratio: (0.2146 - 0.0400) / 0.0782 = 2.2334


4-asset optimization. Max-Sharpe: 4.032. Portfolio: return=5.44%, vol=0.36%. Weights: w_ACWI=0.0313, w_BTC-USD=0.0004, w_STIP=0.1605, w_BIL=0.8078.

Question:
Assets: ACWI, BTC-USD, STIP, BIL
Annualized mean returns: ACWI:0.2051, BTC-USD:0.4450, STIP:0.0782, BIL:0.0437
Covariance matrix (annualized):
[[0.009017, 0.011688, -0.000652, -4.4e-05], [0.011688, 0.084429, -0.000408, 3.5e-05], [-0.000652, -0.000408, 0.000313, 5e-06], [-4.4e-05, 3.5e-05, 5e-06, 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_ACWI=0.0313, w_BTC-USD=0.0004, w_STIP=0.1605, w_BIL=0.8078

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_ACWI=0.0313, w_BTC-USD=0.0004, w_STIP=0.1605, w_BIL=0.8078
Portfolio annualized return: 5.44%, volatility: 0.36%
Sharpe ratio: (0.0544 - 0.0400) / 0.0036 = 4.0321


4-asset optimization. Max-Sharpe: 3.252. Portfolio: return=5.34%, vol=0.41%. Weights: w_XLE=0.0132, w_BTC-USD=0.0000, w_TLH=0.0000, w_ICSH=0.9868.

Question:
Assets: XLE, BTC-USD, TLH, ICSH
Annualized mean returns: XLE:0.1850, BTC-USD:0.0224, TLH:0.0140, ICSH:0.0516
Covariance matrix (annualized):
[[0.025114, 0.015596, -0.000915, -0.000149], [0.015596, 0.081576, 0.003476, -9e-05], [-0.000915, 0.003476, 0.007801, 0.000147], [-0.000149, -9e-05, 0.000147, 1.7e-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_XLE=0.0132, w_BTC-USD=0.0000, w_TLH=0.0000, w_ICSH=0.9868

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLE=0.0132, w_BTC-USD=0.0000, w_TLH=0.0000, w_ICSH=0.9868
Portfolio annualized return: 5.34%, volatility: 0.41%
Sharpe ratio: (0.0534 - 0.0400) / 0.0041 = 3.2524


4-asset optimization. Max-Sharpe: 2.101. Portfolio: return=15.67%, vol=5.55%. Weights: w_EFA=0.4682, w_AVAX-USD=0.0000, w_IEF=0.5318, w_VNQI=0.0000.

Question:
Assets: EFA, AVAX-USD, IEF, VNQI
Annualized mean returns: EFA:0.2341, AVAX-USD:-1.0669, IEF:0.0886, VNQI:0.0721
Covariance matrix (annualized):
[[0.010264, 0.036257, 0.000614, 0.007919], [0.036257, 0.734868, -0.009664, 0.017999], [0.000614, -0.009664, 0.001875, 0.001568], [0.007919, 0.017999, 0.001568, 0.010072]]
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=0.4682, w_AVAX-USD=0.0000, w_IEF=0.5318, w_VNQI=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EFA=0.4682, w_AVAX-USD=0.0000, w_IEF=0.5318, w_VNQI=0.0000
Portfolio annualized return: 15.67%, volatility: 5.55%
Sharpe ratio: (0.1567 - 0.0400) / 0.0555 = 2.1011


4-asset optimization. Max-Sharpe: -1.986. Portfolio: return=-34.67%, vol=19.47%. Weights: w_IVV=0.2500, w_AVAX-USD=0.2500, w_VNQ=0.2500, w_BIL=0.2500.

Question:
Assets: IVV, AVAX-USD, VNQ, BIL
Annualized mean returns: IVV:0.5911, AVAX-USD:-2.0911, VNQ:0.0707, BIL:0.0425
Covariance matrix (annualized):
[[0.015876, 0.025684, 0.010577, -5.4e-05], [0.025684, 0.497235, -1.3e-05, 1.7e-05], [0.010577, -1.3e-05, 0.021232, 8e-06], [-5.4e-05, 1.7e-05, 8e-06, 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_IVV=0.2500, w_AVAX-USD=0.2500, w_VNQ=0.2500, w_BIL=0.2500

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_IVV=0.2500, w_AVAX-USD=0.2500, w_VNQ=0.2500, w_BIL=0.2500
Portfolio annualized return: -34.67%, volatility: 19.47%
Sharpe ratio: (-0.3467 - 0.0400) / 0.1947 = -1.9858


4-asset optimization. Max-Sharpe: 2.478. Portfolio: return=263.68%, vol=104.79%. Weights: w_EFA=0.0000, w_ADA-USD=1.0000, w_SLV=0.0000, w_SCHP=0.0000.

Question:
Assets: EFA, ADA-USD, SLV, SCHP
Annualized mean returns: EFA:0.0501, ADA-USD:2.6368, SLV:-0.0893, SCHP:-0.0148
Covariance matrix (annualized):
[[0.01297, 0.035445, 0.011697, 0.00285], [0.035445, 1.098176, 0.059438, 0.008317], [0.011697, 0.059438, 0.055848, 0.002607], [0.00285, 0.008317, 0.002607, 0.001775]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_EFA=0.0000, w_ADA-USD=1.0000, w_SLV=0.0000, w_SCHP=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EFA=0.0000, w_ADA-USD=1.0000, w_SLV=0.0000, w_SCHP=0.0000
Portfolio annualized return: 263.68%, volatility: 104.79%
Sharpe ratio: (2.6368 - 0.0400) / 1.0479 = 2.4780


4-asset optimization. Max-Sharpe: 2.000. Portfolio: return=8.30%, vol=2.15%. Weights: w_XLP=0.1311, w_ETH-USD=0.0000, w_DBC=0.1277, w_ICSH=0.7412.

Question:
Assets: XLP, ETH-USD, DBC, ICSH
Annualized mean returns: XLP:0.1846, ETH-USD:-1.9166, DBC:0.2125, ICSH:0.0427
Covariance matrix (annualized):
[[0.01112, -0.008077, 0.000352, 7e-05], [-0.008077, 0.396146, 0.010188, 9e-06], [0.000352, 0.010188, 0.013729, 7.5e-05], [7e-05, 9e-06, 7.5e-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_XLP=0.1311, w_ETH-USD=0.0000, w_DBC=0.1277, w_ICSH=0.7412

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLP=0.1311, w_ETH-USD=0.0000, w_DBC=0.1277, w_ICSH=0.7412
Portfolio annualized return: 8.30%, volatility: 2.15%
Sharpe ratio: (0.0830 - 0.0400) / 0.0215 = 1.9998


4-asset optimization. Max-Sharpe: 1.853. Portfolio: return=52.02%, vol=25.92%. Weights: w_XLE=0.0000, w_AVAX-USD=0.0000, w_PPLT=0.2661, w_ITB=0.7339.

Question:
Assets: XLE, AVAX-USD, PPLT, ITB
Annualized mean returns: XLE:-0.1216, AVAX-USD:0.0571, PPLT:0.4250, ITB:0.5547
Covariance matrix (annualized):
[[0.031441, -0.019572, -0.003288, -0.000248], [-0.019572, 0.444837, 0.065673, 0.050733], [-0.003288, 0.065673, 0.152126, 0.018233], [-0.000248, 0.050733, 0.018233, 0.0915]]
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=0.0000, w_AVAX-USD=0.0000, w_PPLT=0.2661, w_ITB=0.7339

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLE=0.0000, w_AVAX-USD=0.0000, w_PPLT=0.2661, w_ITB=0.7339
Portfolio annualized return: 52.02%, volatility: 25.92%
Sharpe ratio: (0.5202 - 0.0400) / 0.2592 = 1.8528


4-asset optimization. Max-Sharpe: 3.586. Portfolio: return=6.35%, vol=0.66%. Weights: w_EFA=0.0176, w_SOL-USD=0.0009, w_SLV=0.0221, w_BIL=0.9594.

Question:
Assets: EFA, SOL-USD, SLV, BIL
Annualized mean returns: EFA:0.3125, SOL-USD:1.7782, SLV:0.6861, BIL:0.0430
Covariance matrix (annualized):
[[0.016387, 0.035489, 0.007566, 1.1e-05], [0.035489, 0.589303, 0.086866, 0.000116], [0.007566, 0.086866, 0.041905, 4.7e-05], [1.1e-05, 0.000116, 4.7e-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_EFA=0.0176, w_SOL-USD=0.0009, w_SLV=0.0221, w_BIL=0.9594

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EFA=0.0176, w_SOL-USD=0.0009, w_SLV=0.0221, w_BIL=0.9594
Portfolio annualized return: 6.35%, volatility: 0.66%
Sharpe ratio: (0.0635 - 0.0400) / 0.0066 = 3.5858


4-asset optimization. Max-Sharpe: 4.079. Portfolio: return=5.42%, vol=0.35%. Weights: w_XLRE=0.0000, w_ADA-USD=0.0044, w_SGOV=0.9956, w_BNDX=0.0000.

Question:
Assets: XLRE, ADA-USD, SGOV, BNDX
Annualized mean returns: XLRE:-0.0783, ADA-USD:2.2361, SGOV:0.0446, BNDX:-0.0045
Covariance matrix (annualized):
[[0.021036, 0.035163, -1.9e-05, 0.00073], [0.035163, 0.485235, -0.000256, 0.00043], [-1.9e-05, -0.000256, 5e-06, 1e-06], [0.00073, 0.00043, 1e-06, 0.0008]]
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_ADA-USD=0.0044, w_SGOV=0.9956, w_BNDX=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLRE=0.0000, w_ADA-USD=0.0044, w_SGOV=0.9956, w_BNDX=0.0000
Portfolio annualized return: 5.42%, volatility: 0.35%
Sharpe ratio: (0.0542 - 0.0400) / 0.0035 = 4.0785


4-asset optimization. Max-Sharpe: 2.068. Portfolio: return=198.49%, vol=94.04%. Weights: w_SPY=0.0000, w_XRP-USD=1.0000, w_SHY=0.0000, w_SCHH=0.0000.

Question:
Assets: SPY, XRP-USD, SHY, SCHH
Annualized mean returns: SPY:0.0322, XRP-USD:1.9849, SHY:0.0359, SCHH:-0.4837
Covariance matrix (annualized):
[[0.019606, 0.055359, 0.000672, 0.01111], [0.055359, 0.884336, 0.003571, 0.01938], [0.000672, 0.003571, 0.00015, 0.001044], [0.01111, 0.01938, 0.001044, 0.035356]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_SPY=0.0000, w_XRP-USD=1.0000, w_SHY=0.0000, w_SCHH=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_SPY=0.0000, w_XRP-USD=1.0000, w_SHY=0.0000, w_SCHH=0.0000
Portfolio annualized return: 198.49%, volatility: 94.04%
Sharpe ratio: (1.9849 - 0.0400) / 0.9404 = 2.0681


4-asset optimization. Max-Sharpe: 2.557. Portfolio: return=42.53%, vol=15.07%. Weights: w_^VIX=0.0000, w_SOL-USD=0.0000, w_SLV=0.5487, w_INDS=0.4513.

Question:
Assets: ^VIX, SOL-USD, SLV, INDS
Annualized mean returns: ^VIX:-2.6108, SOL-USD:-0.2223, SLV:0.6209, INDS:0.1874
Covariance matrix (annualized):
[[1.230334, -0.151141, 0.092145, -0.080598], [-0.151141, 0.395197, 0.005955, 0.010118], [0.092145, 0.005955, 0.064517, -0.002599], [-0.080598, 0.010118, -0.002599, 0.022412]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_^VIX=0.0000, w_SOL-USD=0.0000, w_SLV=0.5487, w_INDS=0.4513

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_^VIX=0.0000, w_SOL-USD=0.0000, w_SLV=0.5487, w_INDS=0.4513
Portfolio annualized return: 42.53%, volatility: 15.07%
Sharpe ratio: (0.4253 - 0.0400) / 0.1507 = 2.5572


4-asset optimization. Max-Sharpe: 0.782. Portfolio: return=8.11%, vol=5.26%. Weights: w_XLU=0.0000, w_DOT-USD=0.0000, w_VNQI=0.2051, w_JNK=0.7949.

Question:
Assets: XLU, DOT-USD, VNQI, JNK
Annualized mean returns: XLU:-0.0964, DOT-USD:-0.7411, VNQI:0.1253, JNK:0.0697
Covariance matrix (annualized):
[[0.034007, 0.035134, 0.009754, 0.003362], [0.035134, 0.605586, 0.019617, 0.005737], [0.009754, 0.019617, 0.014442, 0.003488], [0.003362, 0.005737, 0.003488, 0.001613]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_XLU=0.0000, w_DOT-USD=0.0000, w_VNQI=0.2051, w_JNK=0.7949

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLU=0.0000, w_DOT-USD=0.0000, w_VNQI=0.2051, w_JNK=0.7949
Portfolio annualized return: 8.11%, volatility: 5.26%
Sharpe ratio: (0.0811 - 0.0400) / 0.0526 = 0.7823


4-asset optimization. Max-Sharpe: 3.142. Portfolio: return=79.40%, vol=24.00%. Weights: w_XLU=0.3013, w_ETH-USD=0.2932, w_INDS=0.0000, w_IEF=0.4055.

Question:
Assets: XLU, ETH-USD, INDS, IEF
Annualized mean returns: XLU:0.3556, ETH-USD:2.2775, INDS:-0.1040, IEF:0.0469
Covariance matrix (annualized):
[[0.035114, 0.044132, 0.036921, 0.001436], [0.044132, 0.547117, 0.086896, -0.007031], [0.036921, 0.086896, 0.07138, 0.000192], [0.001436, -0.007031, 0.000192, 0.005313]]
Risk-free rate: 4.00%
Constraints: weights 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=0.3013, w_ETH-USD=0.2932, w_INDS=0.0000, w_IEF=0.4055

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLU=0.3013, w_ETH-USD=0.2932, w_INDS=0.0000, w_IEF=0.4055
Portfolio annualized return: 79.40%, volatility: 24.00%
Sharpe ratio: (0.7940 - 0.0400) / 0.2400 = 3.1421


4-asset optimization. Max-Sharpe: 2.927. Portfolio: return=5.81%, vol=0.62%. Weights: w_FXI=0.0037, w_SOL-USD=0.0000, w_ICSH=0.9731, w_GLD=0.0233.

Question:
Assets: FXI, SOL-USD, ICSH, GLD
Annualized mean returns: FXI:0.2610, SOL-USD:0.3112, ICSH:0.0524, GLD:0.2629
Covariance matrix (annualized):
[[0.068437, 0.012563, 0.000234, -0.000566], [0.012563, 0.446386, 0.000293, 0.017755], [0.000234, 0.000293, 2.5e-05, 5.5e-05], [-0.000566, 0.017755, 5.5e-05, 0.017999]]
Risk-free rate: 4.00%
Constraints: weights 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=0.0037, w_SOL-USD=0.0000, w_ICSH=0.9731, w_GLD=0.0233

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_FXI=0.0037, w_SOL-USD=0.0000, w_ICSH=0.9731, w_GLD=0.0233
Portfolio annualized return: 5.81%, volatility: 0.62%
Sharpe ratio: (0.0581 - 0.0400) / 0.0062 = 2.9269


4-asset optimization. Max-Sharpe: 0.380. Portfolio: return=9.84%, vol=15.35%. Weights: w_XLK=0.0000, w_AVAX-USD=0.0000, w_IYR=1.0000, w_SOYB=0.0000.

Question:
Assets: XLK, AVAX-USD, IYR, SOYB
Annualized mean returns: XLK:-0.6246, AVAX-USD:-1.1396, IYR:0.0984, SOYB:-0.1054
Covariance matrix (annualized):
[[0.071407, 0.099138, 0.01896, 0.003333], [0.099138, 0.781754, 0.003679, 0.020847], [0.01896, 0.003679, 0.023563, -0.000729], [0.003333, 0.020847, -0.000729, 0.019253]]
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_XLK=0.0000, w_AVAX-USD=0.0000, w_IYR=1.0000, w_SOYB=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLK=0.0000, w_AVAX-USD=0.0000, w_IYR=1.0000, w_SOYB=0.0000
Portfolio annualized return: 9.84%, volatility: 15.35%
Sharpe ratio: (0.0984 - 0.0400) / 0.1535 = 0.3803


4-asset optimization. Max-Sharpe: 2.265. Portfolio: return=81.59%, vol=34.25%. Weights: w_EWJ=0.0000, w_XRP-USD=0.0000, w_PPLT=1.0000, w_STIP=0.0000.

Question:
Assets: EWJ, XRP-USD, PPLT, STIP
Annualized mean returns: EWJ:0.1161, XRP-USD:-2.9680, PPLT:0.8159, STIP:-0.0013
Covariance matrix (annualized):
[[0.026982, 0.050529, 0.014083, -0.000294], [0.050529, 0.462057, 0.045948, -0.001527], [0.014083, 0.045948, 0.117327, -0.000234], [-0.000294, -0.001527, -0.000234, 0.000184]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_EWJ=0.0000, w_XRP-USD=0.0000, w_PPLT=1.0000, w_STIP=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EWJ=0.0000, w_XRP-USD=0.0000, w_PPLT=1.0000, w_STIP=0.0000
Portfolio annualized return: 81.59%, volatility: 34.25%
Sharpe ratio: (0.8159 - 0.0400) / 0.3425 = 2.2651


4-asset optimization. Max-Sharpe: 2.804. Portfolio: return=6.37%, vol=0.84%. Weights: w_USMV=0.0329, w_DOT-USD=0.0006, w_CPER=0.0226, w_BIL=0.9439.

Question:
Assets: USMV, DOT-USD, CPER, BIL
Annualized mean returns: USMV:0.2670, DOT-USD:0.2754, CPER:0.6450, BIL:0.0425
Covariance matrix (annualized):
[[0.019256, 0.004487, 0.002042, -0.0], [0.004487, 0.395948, 0.008943, 0.000127], [0.002042, 0.008943, 0.072906, 0.000108], [-0.0, 0.000127, 0.000108, 5e-06]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_USMV=0.0329, w_DOT-USD=0.0006, w_CPER=0.0226, w_BIL=0.9439

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_USMV=0.0329, w_DOT-USD=0.0006, w_CPER=0.0226, w_BIL=0.9439
Portfolio annualized return: 6.37%, volatility: 0.84%
Sharpe ratio: (0.0637 - 0.0400) / 0.0084 = 2.8041


4-asset optimization. Max-Sharpe: 2.645. Portfolio: return=66.98%, vol=23.81%. Weights: w_FXI=0.7113, w_ETH-USD=0.1934, w_CSHI=0.0000, w_DBB=0.0953.

Question:
Assets: FXI, ETH-USD, CSHI, DBB
Annualized mean returns: FXI:0.4728, ETH-USD:1.6363, CSHI:0.0462, DBB:0.1787
Covariance matrix (annualized):
[[0.035925, 0.065372, 0.00037, 0.007867], [0.065372, 0.487996, 0.001775, 0.028951], [0.00037, 0.001775, 7.2e-05, 0.00013], [0.007867, 0.028951, 0.00013, 0.013529]]
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=0.7113, w_ETH-USD=0.1934, w_CSHI=0.0000, w_DBB=0.0953

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_FXI=0.7113, w_ETH-USD=0.1934, w_CSHI=0.0000, w_DBB=0.0953
Portfolio annualized return: 66.98%, volatility: 23.81%
Sharpe ratio: (0.6698 - 0.0400) / 0.2381 = 2.6455


4-asset optimization. Max-Sharpe: 2.756. Portfolio: return=46.55%, vol=15.44%. Weights: w_USMV=0.4284, w_BNB-USD=0.0000, w_STIP=0.0000, w_CPER=0.5716.

Question:
Assets: USMV, BNB-USD, STIP, CPER
Annualized mean returns: USMV:0.1446, BNB-USD:-1.6240, STIP:0.0199, CPER:0.7060
Covariance matrix (annualized):
[[0.00619, 0.0058, 0.000321, 0.005609], [0.0058, 0.227906, -0.000139, 0.029362], [0.000321, -0.000139, 0.000125, 0.000154], [0.005609, 0.029362, 0.000154, 0.061044]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_USMV=0.4284, w_BNB-USD=0.0000, w_STIP=0.0000, w_CPER=0.5716

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_USMV=0.4284, w_BNB-USD=0.0000, w_STIP=0.0000, w_CPER=0.5716
Portfolio annualized return: 46.55%, volatility: 15.44%
Sharpe ratio: (0.4655 - 0.0400) / 0.1544 = 2.7564


4-asset optimization. Max-Sharpe: 3.309. Portfolio: return=28.57%, vol=7.42%. Weights: w_XLK=0.3007, w_LINK-USD=0.0000, w_EMB=0.6993, w_SCHH=0.0000.

Question:
Assets: XLK, LINK-USD, EMB, SCHH
Annualized mean returns: XLK:0.5748, LINK-USD:-2.0582, EMB:0.1614, SCHH:0.0864
Covariance matrix (annualized):
[[0.030835, 0.085606, 0.003898, 0.003741], [0.085606, 0.668559, 0.013123, 0.007592], [0.003898, 0.013123, 0.002218, 0.002464], [0.003741, 0.007592, 0.002464, 0.012426]]
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=0.3007, w_LINK-USD=0.0000, w_EMB=0.6993, w_SCHH=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLK=0.3007, w_LINK-USD=0.0000, w_EMB=0.6993, w_SCHH=0.0000
Portfolio annualized return: 28.57%, volatility: 7.42%
Sharpe ratio: (0.2857 - 0.0400) / 0.0742 = 3.3092


4-asset optimization. Max-Sharpe: 4.481. Portfolio: return=58.22%, vol=12.10%. Weights: w_XLV=0.7995, w_DOT-USD=0.0000, w_VCIT=0.0000, w_CPER=0.2005.

Question:
Assets: XLV, DOT-USD, VCIT, CPER
Annualized mean returns: XLV:0.5847, DOT-USD:-2.1615, VCIT:0.0180, CPER:0.5722
Covariance matrix (annualized):
[[0.017914, 0.022386, 0.001219, 0.001908], [0.022386, 0.929583, -0.002485, 0.082598], [0.001219, -0.002485, 0.000986, -6.9e-05], [0.001908, 0.082598, -6.9e-05, 0.06404]]
Risk-free rate: 4.00%
Constraints: weights 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=0.7995, w_DOT-USD=0.0000, w_VCIT=0.0000, w_CPER=0.2005

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLV=0.7995, w_DOT-USD=0.0000, w_VCIT=0.0000, w_CPER=0.2005
Portfolio annualized return: 58.22%, volatility: 12.10%
Sharpe ratio: (0.5822 - 0.0400) / 0.1210 = 4.4814


4-asset optimization. Max-Sharpe: 5.122. Portfolio: return=185.22%, vol=35.38%. Weights: w_EWJ=0.1573, w_BTC-USD=0.8427, w_SGOV=0.0000, w_USO=0.0000.

Question:
Assets: EWJ, BTC-USD, SGOV, USO
Annualized mean returns: EWJ:0.4476, BTC-USD:2.1144, SGOV:0.0414, USO:-0.6282
Covariance matrix (annualized):
[[0.049611, 0.024157, 4.2e-05, 0.046063], [0.024157, 0.165541, 0.0002, 0.066641], [4.2e-05, 0.0002, 5e-06, 0.00013], [0.046063, 0.066641, 0.00013, 0.169675]]
Risk-free rate: 4.00%
Constraints: weights 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=0.1573, w_BTC-USD=0.8427, w_SGOV=0.0000, w_USO=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EWJ=0.1573, w_BTC-USD=0.8427, w_SGOV=0.0000, w_USO=0.0000
Portfolio annualized return: 185.22%, volatility: 35.38%
Sharpe ratio: (1.8522 - 0.0400) / 0.3538 = 5.1217


4-asset optimization. Max-Sharpe: 3.468. Portfolio: return=6.43%, vol=0.70%. Weights: w_IWM=0.0000, w_ETH-USD=0.0051, w_CSHI=0.9949, w_CPER=0.0000.

Question:
Assets: IWM, ETH-USD, CSHI, CPER
Annualized mean returns: IWM:-0.0076, ETH-USD:1.8806, CSHI:0.0551, CPER:-0.4967
Covariance matrix (annualized):
[[0.040293, 0.077799, 0.000496, -0.002188], [0.077799, 0.497882, 0.001207, -0.018009], [0.000496, 0.001207, 2.4e-05, 6.8e-05], [-0.002188, -0.018009, 6.8e-05, 0.04341]]
Risk-free rate: 4.00%
Constraints: weights 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=0.0051, w_CSHI=0.9949, w_CPER=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_IWM=0.0000, w_ETH-USD=0.0051, w_CSHI=0.9949, w_CPER=0.0000
Portfolio annualized return: 6.43%, volatility: 0.70%
Sharpe ratio: (0.0643 - 0.0400) / 0.0070 = 3.4683


4-asset optimization. Max-Sharpe: 0.543. Portfolio: return=4.63%, vol=1.17%. Weights: w_EEM=0.0000, w_ETH-USD=0.0000, w_VNQI=0.0000, w_SHY=1.0000.

Question:
Assets: EEM, ETH-USD, VNQI, SHY
Annualized mean returns: EEM:0.0186, ETH-USD:-3.7577, VNQI:-0.0450, SHY:0.0463
Covariance matrix (annualized):
[[0.030056, 0.061775, 0.008003, -0.000209], [0.061775, 0.365543, 0.025521, -0.000329], [0.008003, 0.025521, 0.009632, 0.00028], [-0.000209, -0.000329, 0.00028, 0.000136]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

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

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EEM=0.0000, w_ETH-USD=0.0000, w_VNQI=0.0000, w_SHY=1.0000
Portfolio annualized return: 4.63%, volatility: 1.17%
Sharpe ratio: (0.0463 - 0.0400) / 0.0117 = 0.5428


4-asset optimization. Max-Sharpe: 3.702. Portfolio: return=44.90%, vol=11.05%. Weights: w_XLU=0.7982, w_ADA-USD=0.0000, w_BIL=0.0000, w_INDS=0.2018.

Question:
Assets: XLU, ADA-USD, BIL, INDS
Annualized mean returns: XLU:0.4629, ADA-USD:-1.2896, BIL:0.0398, INDS:0.3941
Covariance matrix (annualized):
[[0.014211, 0.018397, 4.4e-05, 0.006317], [0.018397, 0.586304, 6.7e-05, 0.02892], [4.4e-05, 6.7e-05, 4e-06, 2.5e-05], [0.006317, 0.02892, 2.5e-05, 0.027368]]
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=0.7982, w_ADA-USD=0.0000, w_BIL=0.0000, w_INDS=0.2018

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLU=0.7982, w_ADA-USD=0.0000, w_BIL=0.0000, w_INDS=0.2018
Portfolio annualized return: 44.90%, volatility: 11.05%
Sharpe ratio: (0.4490 - 0.0400) / 0.1105 = 3.7025


4-asset optimization. Max-Sharpe: -0.338. Portfolio: return=-3.62%, vol=22.55%. Weights: w_XLI=0.2500, w_LINK-USD=0.2500, w_HAUZ=0.2500, w_BIL=0.2500.

Question:
Assets: XLI, LINK-USD, HAUZ, BIL
Annualized mean returns: XLI:0.0838, LINK-USD:-0.4606, HAUZ:0.1892, BIL:0.0428
Covariance matrix (annualized):
[[0.01802, 0.032985, 0.007286, -8.5e-05], [0.032985, 0.643928, 0.028858, 0.000222], [0.007286, 0.028858, 0.013614, -8.5e-05], [-8.5e-05, 0.000222, -8.5e-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_XLI=0.2500, w_LINK-USD=0.2500, w_HAUZ=0.2500, w_BIL=0.2500

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLI=0.2500, w_LINK-USD=0.2500, w_HAUZ=0.2500, w_BIL=0.2500
Portfolio annualized return: -3.62%, volatility: 22.55%
Sharpe ratio: (-0.0362 - 0.0400) / 0.2255 = -0.3379


4-asset optimization. Max-Sharpe: 7.313. Portfolio: return=74.49%, vol=9.64%. Weights: w_VTI=0.2179, w_BTC-USD=0.1417, w_HAUZ=0.6405, w_UNG=0.0000.

Question:
Assets: VTI, BTC-USD, HAUZ, UNG
Annualized mean returns: VTI:0.7210, BTC-USD:1.1475, HAUZ:0.6639, UNG:-0.7349
Covariance matrix (annualized):
[[0.028007, 0.00637, 0.003077, 0.015597], [0.00637, 0.114701, -0.004746, -0.001445], [0.003077, -0.004746, 0.012841, 0.01079], [0.015597, -0.001445, 0.01079, 0.311089]]
Risk-free rate: 4.00%
Constraints: weights 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=0.2179, w_BTC-USD=0.1417, w_HAUZ=0.6405, w_UNG=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VTI=0.2179, w_BTC-USD=0.1417, w_HAUZ=0.6405, w_UNG=0.0000
Portfolio annualized return: 74.49%, volatility: 9.64%
Sharpe ratio: (0.7449 - 0.0400) / 0.0964 = 7.3133


4-asset optimization. Max-Sharpe: 2.352. Portfolio: return=253.68%, vol=106.17%. Weights: w_ACWI=0.0000, w_ADA-USD=1.0000, w_JNK=0.0000, w_MORT=0.0000.

Question:
Assets: ACWI, ADA-USD, JNK, MORT
Annualized mean returns: ACWI:0.0363, ADA-USD:2.5368, JNK:0.0612, MORT:0.0520
Covariance matrix (annualized):
[[0.016396, 0.058067, 0.005288, 0.015742], [0.058067, 1.12713, 0.01807, 0.071542], [0.005288, 0.01807, 0.002678, 0.006585], [0.015742, 0.071542, 0.006585, 0.032753]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_ACWI=0.0000, w_ADA-USD=1.0000, w_JNK=0.0000, w_MORT=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_ACWI=0.0000, w_ADA-USD=1.0000, w_JNK=0.0000, w_MORT=0.0000
Portfolio annualized return: 253.68%, volatility: 106.17%
Sharpe ratio: (2.5368 - 0.0400) / 1.0617 = 2.3518


4-asset optimization. Max-Sharpe: 2.253. Portfolio: return=13.12%, vol=4.05%. Weights: w_XLE=0.1854, w_XRP-USD=0.0000, w_HYG=0.8146, w_CPER=0.0000.

Question:
Assets: XLE, XRP-USD, HYG, CPER
Annualized mean returns: XLE:0.3162, XRP-USD:-0.3326, HYG:0.0891, CPER:-0.1063
Covariance matrix (annualized):
[[0.025304, 0.0086, 0.000332, 0.00561], [0.0086, 0.343512, 0.008128, 0.035111], [0.000332, 0.008128, 0.001007, 0.000843], [0.00561, 0.035111, 0.000843, 0.04232]]
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=0.1854, w_XRP-USD=0.0000, w_HYG=0.8146, w_CPER=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLE=0.1854, w_XRP-USD=0.0000, w_HYG=0.8146, w_CPER=0.0000
Portfolio annualized return: 13.12%, volatility: 4.05%
Sharpe ratio: (0.1312 - 0.0400) / 0.0405 = 2.2528


4-asset optimization. Max-Sharpe: -3.192. Portfolio: return=-67.18%, vol=22.30%. Weights: w_VTI=0.2500, w_XRP-USD=0.2500, w_CSHI=0.2500, w_IYR=0.2500.

Question:
Assets: VTI, XRP-USD, CSHI, IYR
Annualized mean returns: VTI:0.1186, XRP-USD:-2.7904, CSHI:0.0536, IYR:-0.0692
Covariance matrix (annualized):
[[0.021869, 0.073198, 0.000453, 0.008363], [0.073198, 0.538924, 0.001538, 0.023495], [0.000453, 0.001538, 0.000136, 0.000468], [0.008363, 0.023495, 0.000468, 0.019978]]
Risk-free rate: 4.00%
Constraints: weights 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=0.2500, w_XRP-USD=0.2500, w_CSHI=0.2500, w_IYR=0.2500

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VTI=0.2500, w_XRP-USD=0.2500, w_CSHI=0.2500, w_IYR=0.2500
Portfolio annualized return: -67.18%, volatility: 22.30%
Sharpe ratio: (-0.6718 - 0.0400) / 0.2230 = -3.1915


4-asset optimization. Max-Sharpe: 1.289. Portfolio: return=17.71%, vol=10.63%. Weights: w_XLY=0.0000, w_MATIC-USD=0.0000, w_VNQI=1.0000, w_DBA=0.0000.

Question:
Assets: XLY, MATIC-USD, VNQI, DBA
Annualized mean returns: XLY:-0.7233, MATIC-USD:-2.5661, VNQI:0.1771, DBA:-0.1953
Covariance matrix (annualized):
[[0.051131, 0.040958, 0.013613, 0.003178], [0.040958, 0.470231, 0.013715, 0.02163], [0.013613, 0.013715, 0.01131, 0.003], [0.003178, 0.02163, 0.003, 0.014927]]
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_XLY=0.0000, w_MATIC-USD=0.0000, w_VNQI=1.0000, w_DBA=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLY=0.0000, w_MATIC-USD=0.0000, w_VNQI=1.0000, w_DBA=0.0000
Portfolio annualized return: 17.71%, volatility: 10.63%
Sharpe ratio: (0.1771 - 0.0400) / 0.1063 = 1.2888


4-asset optimization. Max-Sharpe: 2.651. Portfolio: return=32.71%, vol=10.83%. Weights: w_IVV=1.0000, w_DOT-USD=0.0000, w_SCHH=0.0000, w_BIL=0.0000.

Question:
Assets: IVV, DOT-USD, SCHH, BIL
Annualized mean returns: IVV:0.3271, DOT-USD:-2.5548, SCHH:-0.0475, BIL:0.0383
Covariance matrix (annualized):
[[0.011732, 0.051065, 0.003949, -2e-05], [0.051065, 0.600529, 0.010358, 2.2e-05], [0.003949, 0.010358, 0.016132, -4.4e-05], [-2e-05, 2.2e-05, -4.4e-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_IVV=1.0000, w_DOT-USD=0.0000, w_SCHH=0.0000, w_BIL=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_IVV=1.0000, w_DOT-USD=0.0000, w_SCHH=0.0000, w_BIL=0.0000
Portfolio annualized return: 32.71%, volatility: 10.83%
Sharpe ratio: (0.3271 - 0.0400) / 0.1083 = 2.6511


4-asset optimization. Max-Sharpe: 3.947. Portfolio: return=47.74%, vol=11.08%. Weights: w_XLRE=0.0000, w_ETH-USD=0.1784, w_IAU=0.0000, w_VCIT=0.8216.

Question:
Assets: XLRE, ETH-USD, IAU, VCIT
Annualized mean returns: XLRE:0.0078, ETH-USD:2.1305, IAU:-0.0157, VCIT:0.1184
Covariance matrix (annualized):
[[0.019014, 0.022154, 0.003306, 0.002262], [0.022154, 0.309365, 0.00355, 0.004268], [0.003306, 0.00355, 0.022568, 0.001592], [0.002262, 0.004268, 0.001592, 0.001751]]
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_ETH-USD=0.1784, w_IAU=0.0000, w_VCIT=0.8216

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLRE=0.0000, w_ETH-USD=0.1784, w_IAU=0.0000, w_VCIT=0.8216
Portfolio annualized return: 47.74%, volatility: 11.08%
Sharpe ratio: (0.4774 - 0.0400) / 0.1108 = 3.9465


4-asset optimization. Max-Sharpe: 0.959. Portfolio: return=4.22%, vol=0.23%. Weights: w_EWJ=0.0046, w_LINK-USD=0.0000, w_SHV=0.3867, w_SGOV=0.6087.

Question:
Assets: EWJ, LINK-USD, SHV, SGOV
Annualized mean returns: EWJ:0.0835, LINK-USD:-1.0190, SHV:0.0421, SGOV:0.0420
Covariance matrix (annualized):
[[0.028548, 0.082711, 1e-05, -4.8e-05], [0.082711, 0.811249, -0.000318, -0.000465], [1e-05, -0.000318, 6e-06, 4e-06], [-4.8e-05, -0.000465, 4e-06, 6e-06]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: bull

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

Answer: w_EWJ=0.0046, w_LINK-USD=0.0000, w_SHV=0.3867, w_SGOV=0.6087

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EWJ=0.0046, w_LINK-USD=0.0000, w_SHV=0.3867, w_SGOV=0.6087
Portfolio annualized return: 4.22%, volatility: 0.23%
Sharpe ratio: (0.0422 - 0.0400) / 0.0023 = 0.9591


4-asset optimization. Max-Sharpe: 5.327. Portfolio: return=32.36%, vol=5.32%. Weights: w_XLB=0.0000, w_BTC-USD=0.1304, w_IAU=0.0568, w_ICSH=0.8128.

Question:
Assets: XLB, BTC-USD, IAU, ICSH
Annualized mean returns: XLB:-0.0055, BTC-USD:2.0490, IAU:0.3876, ICSH:0.0422
Covariance matrix (annualized):
[[0.064947, 0.046721, 0.000717, 0.000334], [0.046721, 0.154598, -0.000537, -7.3e-05], [0.000717, -0.000537, 0.060489, 0.000133], [0.000334, -7.3e-05, 0.000133, 3e-05]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_XLB=0.0000, w_BTC-USD=0.1304, w_IAU=0.0568, w_ICSH=0.8128

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLB=0.0000, w_BTC-USD=0.1304, w_IAU=0.0568, w_ICSH=0.8128
Portfolio annualized return: 32.36%, volatility: 5.32%
Sharpe ratio: (0.3236 - 0.0400) / 0.0532 = 5.3273


4-asset optimization. Max-Sharpe: 3.422. Portfolio: return=5.22%, vol=0.36%. Weights: w_XLY=0.0000, w_BTC-USD=0.0000, w_CPER=0.0156, w_BIL=0.9844.

Question:
Assets: XLY, BTC-USD, CPER, BIL
Annualized mean returns: XLY:-0.8204, BTC-USD:-0.3902, CPER:0.7230, BIL:0.0416
Covariance matrix (annualized):
[[0.042634, 0.034003, 0.00633, -1.9e-05], [0.034003, 0.209074, 0.02767, -8e-06], [0.00633, 0.02767, 0.055084, -0.000148], [-1.9e-05, -8e-06, -0.000148, 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_XLY=0.0000, w_BTC-USD=0.0000, w_CPER=0.0156, w_BIL=0.9844

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLY=0.0000, w_BTC-USD=0.0000, w_CPER=0.0156, w_BIL=0.9844
Portfolio annualized return: 5.22%, volatility: 0.36%
Sharpe ratio: (0.0522 - 0.0400) / 0.0036 = 3.4221


4-asset optimization. Max-Sharpe: 4.547. Portfolio: return=5.34%, vol=0.30%. Weights: w_VTI=0.0111, w_BNB-USD=0.0040, w_BIL=0.9733, w_LQD=0.0116.

Question:
Assets: VTI, BNB-USD, BIL, LQD
Annualized mean returns: VTI:0.2949, BNB-USD:1.0342, BIL:0.0459, LQD:0.1176
Covariance matrix (annualized):
[[0.016437, -0.000997, -5.4e-05, 0.00345], [-0.000997, 0.191676, -5.7e-05, -0.005205], [-5.4e-05, -5.7e-05, 5e-06, -1.6e-05], [0.00345, -0.005205, -1.6e-05, 0.004193]]
Risk-free rate: 4.00%
Constraints: weights 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=0.0111, w_BNB-USD=0.0040, w_BIL=0.9733, w_LQD=0.0116

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VTI=0.0111, w_BNB-USD=0.0040, w_BIL=0.9733, w_LQD=0.0116
Portfolio annualized return: 5.34%, volatility: 0.30%
Sharpe ratio: (0.0534 - 0.0400) / 0.0030 = 4.5471


4-asset optimization. Max-Sharpe: 3.779. Portfolio: return=191.50%, vol=49.61%. Weights: w_MTUM=0.3797, w_SOL-USD=0.6203, w_JNK=0.0000, w_SLV=0.0000.

Question:
Assets: MTUM, SOL-USD, JNK, SLV
Annualized mean returns: MTUM:0.6562, SOL-USD:2.6856, JNK:0.0343, SLV:0.0277
Covariance matrix (annualized):
[[0.079325, 0.081843, 0.021665, 0.02181], [0.081843, 0.509755, 0.023573, 0.042667], [0.021665, 0.023573, 0.00876, 0.010328], [0.02181, 0.042667, 0.010328, 0.076004]]
Risk-free rate: 4.00%
Constraints: weights 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=0.3797, w_SOL-USD=0.6203, w_JNK=0.0000, w_SLV=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_MTUM=0.3797, w_SOL-USD=0.6203, w_JNK=0.0000, w_SLV=0.0000
Portfolio annualized return: 191.50%, volatility: 49.61%
Sharpe ratio: (1.9150 - 0.0400) / 0.4961 = 3.7795


4-asset optimization. Max-Sharpe: -0.029. Portfolio: return=3.97%, vol=1.03%. Weights: w_XLK=0.0000, w_AVAX-USD=0.0000, w_CSHI=1.0000, w_HYG=0.0000.

Question:
Assets: XLK, AVAX-USD, CSHI, HYG
Annualized mean returns: XLK:-0.6647, AVAX-USD:-1.1622, CSHI:0.0397, HYG:-0.0051
Covariance matrix (annualized):
[[0.079519, 0.08247, 0.001725, 0.007467], [0.08247, 0.743884, 0.003042, 0.006258], [0.001725, 0.003042, 0.000107, 0.000168], [0.007467, 0.006258, 0.000168, 0.001696]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_XLK=0.0000, w_AVAX-USD=0.0000, w_CSHI=1.0000, w_HYG=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLK=0.0000, w_AVAX-USD=0.0000, w_CSHI=1.0000, w_HYG=0.0000
Portfolio annualized return: 3.97%, volatility: 1.03%
Sharpe ratio: (0.0397 - 0.0400) / 0.0103 = -0.0289


4-asset optimization. Max-Sharpe: 4.470. Portfolio: return=5.53%, vol=0.34%. Weights: w_EEM=0.0272, w_BNB-USD=0.0000, w_VNQ=0.0000, w_SGOV=0.9728.

Question:
Assets: EEM, BNB-USD, VNQ, SGOV
Annualized mean returns: EEM:0.5179, BNB-USD:0.0915, VNQ:0.0738, SGOV:0.0423
Covariance matrix (annualized):
[[0.017067, 0.005084, 0.004431, -0.000103], [0.005084, 0.076652, -0.000423, -9e-05], [0.004431, -0.000423, 0.020689, -1.9e-05], [-0.000103, -9e-05, -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_EEM=0.0272, w_BNB-USD=0.0000, w_VNQ=0.0000, w_SGOV=0.9728

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EEM=0.0272, w_BNB-USD=0.0000, w_VNQ=0.0000, w_SGOV=0.9728
Portfolio annualized return: 5.53%, volatility: 0.34%
Sharpe ratio: (0.0553 - 0.0400) / 0.0034 = 4.4703


4-asset optimization. Max-Sharpe: 0.948. Portfolio: return=14.71%, vol=11.30%. Weights: w_QUAL=1.0000, w_LINK-USD=0.0000, w_SHY=0.0000, w_ICSH=0.0000.

Question:
Assets: QUAL, LINK-USD, SHY, ICSH
Annualized mean returns: QUAL:0.1471, LINK-USD:-2.1652, SHY:0.0320, ICSH:0.0389
Covariance matrix (annualized):
[[0.012772, 0.026492, 7.5e-05, 5.4e-05], [0.026492, 0.588689, -0.000192, 5.6e-05], [7.5e-05, -0.000192, 0.000104, 1.6e-05], [5.4e-05, 5.6e-05, 1.6e-05, 1.3e-05]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_QUAL=1.0000, w_LINK-USD=0.0000, w_SHY=0.0000, w_ICSH=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_QUAL=1.0000, w_LINK-USD=0.0000, w_SHY=0.0000, w_ICSH=0.0000
Portfolio annualized return: 14.71%, volatility: 11.30%
Sharpe ratio: (0.1471 - 0.0400) / 0.1130 = 0.9476


4-asset optimization. Max-Sharpe: 2.734. Portfolio: return=319.40%, vol=115.35%. Weights: w_IWM=0.0000, w_LINK-USD=1.0000, w_IGOV=0.0000, w_IYR=0.0000.

Question:
Assets: IWM, LINK-USD, IGOV, IYR
Annualized mean returns: IWM:-0.2604, LINK-USD:3.1940, IGOV:-0.2446, IYR:-0.2961
Covariance matrix (annualized):
[[0.031883, 0.070025, 0.006832, 0.018958], [0.070025, 1.330484, 0.006422, 0.056589], [0.006832, 0.006422, 0.006893, 0.00639], [0.018958, 0.056589, 0.00639, 0.026269]]
Risk-free rate: 4.00%
Constraints: weights 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=1.0000, w_IGOV=0.0000, w_IYR=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_IWM=0.0000, w_LINK-USD=1.0000, w_IGOV=0.0000, w_IYR=0.0000
Portfolio annualized return: 319.40%, volatility: 115.35%
Sharpe ratio: (3.1940 - 0.0400) / 1.1535 = 2.7344


4-asset optimization. Max-Sharpe: 4.031. Portfolio: return=30.08%, vol=6.47%. Weights: w_FXI=0.1515, w_SOL-USD=0.0000, w_IAU=0.3287, w_STIP=0.5198.

Question:
Assets: FXI, SOL-USD, IAU, STIP
Annualized mean returns: FXI:0.5365, SOL-USD:1.7216, IAU:0.5435, STIP:0.0786
Covariance matrix (annualized):
[[0.03769, 0.068143, 0.006675, 0.000119], [0.068143, 0.585675, 0.045767, 0.004551], [0.006675, 0.045767, 0.019448, 0.001297], [0.000119, 0.004551, 0.001297, 0.000335]]
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=0.1515, w_SOL-USD=0.0000, w_IAU=0.3287, w_STIP=0.5198

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_FXI=0.1515, w_SOL-USD=0.0000, w_IAU=0.3287, w_STIP=0.5198
Portfolio annualized return: 30.08%, volatility: 6.47%
Sharpe ratio: (0.3008 - 0.0400) / 0.0647 = 4.0315


4-asset optimization. Max-Sharpe: 3.975. Portfolio: return=5.46%, vol=0.37%. Weights: w_QQQ=0.0000, w_ADA-USD=0.0000, w_SHV=0.0000, w_ICSH=1.0000.

Question:
Assets: QQQ, ADA-USD, SHV, ICSH
Annualized mean returns: QQQ:-0.2046, ADA-USD:-1.4527, SHV:0.0423, ICSH:0.0546
Covariance matrix (annualized):
[[0.039745, 0.056084, -3e-06, -9e-06], [0.056084, 0.743925, -6.3e-05, -0.000141], [-3e-06, -6.3e-05, 4e-06, 2e-06], [-9e-06, -0.000141, 2e-06, 1.3e-05]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_QQQ=0.0000, w_ADA-USD=0.0000, w_SHV=0.0000, w_ICSH=1.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_QQQ=0.0000, w_ADA-USD=0.0000, w_SHV=0.0000, w_ICSH=1.0000
Portfolio annualized return: 5.46%, volatility: 0.37%
Sharpe ratio: (0.0546 - 0.0400) / 0.0037 = 3.9750


4-asset optimization. Max-Sharpe: -2.962. Portfolio: return=-70.78%, vol=25.25%. Weights: w_SPY=0.2500, w_SOL-USD=0.2500, w_SGOV=0.2500, w_INDS=0.2500.

Question:
Assets: SPY, SOL-USD, SGOV, INDS
Annualized mean returns: SPY:-0.4637, SOL-USD:-2.4363, SGOV:0.0420, INDS:0.0268
Covariance matrix (annualized):
[[0.029689, 0.07178, -5.6e-05, 0.011714], [0.07178, 0.810509, 0.000224, -0.006148], [-5.6e-05, 0.000224, 3e-06, -4.2e-05], [0.011714, -0.006148, -4.2e-05, 0.024847]]
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_SPY=0.2500, w_SOL-USD=0.2500, w_SGOV=0.2500, w_INDS=0.2500

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_SPY=0.2500, w_SOL-USD=0.2500, w_SGOV=0.2500, w_INDS=0.2500
Portfolio annualized return: -70.78%, volatility: 25.25%
Sharpe ratio: (-0.7078 - 0.0400) / 0.2525 = -2.9618


4-asset optimization. Max-Sharpe: 1.330. Portfolio: return=4.25%, vol=0.19%. Weights: w_QUAL=0.0000, w_MATIC-USD=0.0000, w_HAUZ=0.0001, w_SGOV=0.9999.

Question:
Assets: QUAL, MATIC-USD, HAUZ, SGOV
Annualized mean returns: QUAL:-0.4293, MATIC-USD:-2.2759, HAUZ:0.0343, SGOV:0.0425
Covariance matrix (annualized):
[[0.02667, 0.037379, 0.010654, -4.4e-05], [0.037379, 0.473125, 0.011126, -8.5e-05], [0.010654, 0.011126, 0.012663, -9e-06], [-4.4e-05, -8.5e-05, -9e-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_QUAL=0.0000, w_MATIC-USD=0.0000, w_HAUZ=0.0001, w_SGOV=0.9999

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_QUAL=0.0000, w_MATIC-USD=0.0000, w_HAUZ=0.0001, w_SGOV=0.9999
Portfolio annualized return: 4.25%, volatility: 0.19%
Sharpe ratio: (0.0425 - 0.0400) / 0.0019 = 1.3300


4-asset optimization. Max-Sharpe: 3.122. Portfolio: return=148.18%, vol=46.17%. Weights: w_XLI=0.2948, w_DOT-USD=0.7052, w_PPLT=0.0000, w_MORT=0.0000.

Question:
Assets: XLI, DOT-USD, PPLT, MORT
Annualized mean returns: XLI:0.4687, DOT-USD:1.9052, PPLT:-0.0038, MORT:-0.1854
Covariance matrix (annualized):
[[0.057679, 0.065796, 0.010021, 0.054473], [0.065796, 0.363632, 0.026457, 0.086063], [0.010021, 0.026457, 0.036609, 0.016002], [0.054473, 0.086063, 0.016002, 0.086743]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_XLI=0.2948, w_DOT-USD=0.7052, w_PPLT=0.0000, w_MORT=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLI=0.2948, w_DOT-USD=0.7052, w_PPLT=0.0000, w_MORT=0.0000
Portfolio annualized return: 148.18%, volatility: 46.17%
Sharpe ratio: (1.4818 - 0.0400) / 0.4617 = 3.1224


4-asset optimization. Max-Sharpe: 0.484. Portfolio: return=35.23%, vol=64.53%. Weights: w_VTI=0.0000, w_XRP-USD=1.0000, w_REZ=0.0000, w_USO=0.0000.

Question:
Assets: VTI, XRP-USD, REZ, USO
Annualized mean returns: VTI:-0.0092, XRP-USD:0.3523, REZ:-0.2583, USO:-0.6217
Covariance matrix (annualized):
[[0.059821, 0.060483, 0.036568, 0.05791], [0.060483, 0.416405, 0.018571, 0.102366], [0.036568, 0.018571, 0.056207, 0.048948], [0.05791, 0.102366, 0.048948, 0.169576]]
Risk-free rate: 4.00%
Constraints: weights 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=1.0000, w_REZ=0.0000, w_USO=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VTI=0.0000, w_XRP-USD=1.0000, w_REZ=0.0000, w_USO=0.0000
Portfolio annualized return: 35.23%, volatility: 64.53%
Sharpe ratio: (0.3523 - 0.0400) / 0.6453 = 0.4840


4-asset optimization. Max-Sharpe: 2.082. Portfolio: return=10.89%, vol=3.31%. Weights: w_VTI=0.1049, w_BTC-USD=0.0000, w_CSHI=0.7197, w_SOYB=0.1754.

Question:
Assets: VTI, BTC-USD, CSHI, SOYB
Annualized mean returns: VTI:0.2245, BTC-USD:-1.3345, CSHI:0.0500, SOYB:0.2813
Covariance matrix (annualized):
[[0.015008, 0.027483, 0.000123, 0.007225], [0.027483, 0.122739, 0.000505, 0.020451], [0.000123, 0.000505, 0.000124, 0.00032], [0.007225, 0.020451, 0.00032, 0.01622]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: bull

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

Answer: w_VTI=0.1049, w_BTC-USD=0.0000, w_CSHI=0.7197, w_SOYB=0.1754

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VTI=0.1049, w_BTC-USD=0.0000, w_CSHI=0.7197, w_SOYB=0.1754
Portfolio annualized return: 10.89%, volatility: 3.31%
Sharpe ratio: (0.1089 - 0.0400) / 0.0331 = 2.0822


4-asset optimization. Max-Sharpe: 2.451. Portfolio: return=4.84%, vol=0.34%. Weights: w_EFA=0.0323, w_SOL-USD=0.0000, w_SGOV=0.9677, w_DBA=0.0000.

Question:
Assets: EFA, SOL-USD, SGOV, DBA
Annualized mean returns: EFA:0.2410, SOL-USD:-0.6618, SGOV:0.0420, DBA:-0.2752
Covariance matrix (annualized):
[[0.010528, 0.032882, -6e-05, 0.003908], [0.032882, 0.5307, -0.000412, 0.001502], [-6e-05, -0.000412, 5e-06, 3e-06], [0.003908, 0.001502, 3e-06, 0.011542]]
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=0.0323, w_SOL-USD=0.0000, w_SGOV=0.9677, w_DBA=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EFA=0.0323, w_SOL-USD=0.0000, w_SGOV=0.9677, w_DBA=0.0000
Portfolio annualized return: 4.84%, volatility: 0.34%
Sharpe ratio: (0.0484 - 0.0400) / 0.0034 = 2.4513


4-asset optimization. Max-Sharpe: -1.018. Portfolio: return=-96.24%, vol=98.50%. Weights: w_XLE=0.0000, w_SOL-USD=1.0000, w_HYG=0.0000, w_DBB=0.0000.

Question:
Assets: XLE, SOL-USD, HYG, DBB
Annualized mean returns: XLE:-0.2599, SOL-USD:-0.9624, HYG:-0.1969, DBB:-0.3568
Covariance matrix (annualized):
[[0.096532, 0.126966, 0.020634, 0.030146], [0.126966, 0.970232, 0.025888, 0.054677], [0.020634, 0.025888, 0.006639, 0.007899], [0.030146, 0.054677, 0.007899, 0.034978]]
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=1.0000, w_HYG=0.0000, w_DBB=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLE=0.0000, w_SOL-USD=1.0000, w_HYG=0.0000, w_DBB=0.0000
Portfolio annualized return: -96.24%, volatility: 98.50%
Sharpe ratio: (-0.9624 - 0.0400) / 0.9850 = -1.0177


4-asset optimization. Max-Sharpe: 5.053. Portfolio: return=5.26%, vol=0.25%. Weights: w_SPY=0.0002, w_ETH-USD=0.0000, w_SHV=0.9866, w_SLV=0.0132.

Question:
Assets: SPY, ETH-USD, SHV, SLV
Annualized mean returns: SPY:0.2304, ETH-USD:0.2679, SHV:0.0434, SLV:0.7361
Covariance matrix (annualized):
[[0.015843, 0.022284, -2.2e-05, 0.008536], [0.022284, 0.291935, 0.000199, 0.023747], [-2.2e-05, 0.000199, 4e-06, -0.000142], [0.008536, 0.023747, -0.000142, 0.036585]]
Risk-free rate: 4.00%
Constraints: weights 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=0.0002, w_ETH-USD=0.0000, w_SHV=0.9866, w_SLV=0.0132

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_SPY=0.0002, w_ETH-USD=0.0000, w_SHV=0.9866, w_SLV=0.0132
Portfolio annualized return: 5.26%, volatility: 0.25%
Sharpe ratio: (0.0526 - 0.0400) / 0.0025 = 5.0527


4-asset optimization. Max-Sharpe: 3.416. Portfolio: return=4.69%, vol=0.20%. Weights: w_XLI=0.0000, w_DOT-USD=0.0000, w_SGOV=1.0000, w_TLT=0.0000.

Question:
Assets: XLI, DOT-USD, SGOV, TLT
Annualized mean returns: XLI:-0.1932, DOT-USD:0.4358, SGOV:0.0469, TLT:-0.3201
Covariance matrix (annualized):
[[0.017931, 0.051093, 1.9e-05, 0.005983], [0.051093, 0.985768, 0.000347, 0.028507], [1.9e-05, 0.000347, 4e-06, -2.4e-05], [0.005983, 0.028507, -2.4e-05, 0.015455]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_XLI=0.0000, w_DOT-USD=0.0000, w_SGOV=1.0000, w_TLT=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLI=0.0000, w_DOT-USD=0.0000, w_SGOV=1.0000, w_TLT=0.0000
Portfolio annualized return: 4.69%, volatility: 0.20%
Sharpe ratio: (0.0469 - 0.0400) / 0.0020 = 3.4165


4-asset optimization. Max-Sharpe: 2.456. Portfolio: return=5.66%, vol=0.68%. Weights: w_IWM=0.0296, w_BTC-USD=0.0000, w_LQD=0.0279, w_SGOV=0.9424.

Question:
Assets: IWM, BTC-USD, LQD, SGOV
Annualized mean returns: IWM:0.4924, BTC-USD:0.1087, LQD:0.1042, SGOV:0.0415
Covariance matrix (annualized):
[[0.038725, 0.033879, 0.003698, -4e-06], [0.033879, 0.082984, 0.004254, 7e-06], [0.003698, 0.004254, 0.003116, -2.1e-05], [-4e-06, 7e-06, -2.1e-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_IWM=0.0296, w_BTC-USD=0.0000, w_LQD=0.0279, w_SGOV=0.9424

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_IWM=0.0296, w_BTC-USD=0.0000, w_LQD=0.0279, w_SGOV=0.9424
Portfolio annualized return: 5.66%, volatility: 0.68%
Sharpe ratio: (0.0566 - 0.0400) / 0.0068 = 2.4562


4-asset optimization. Max-Sharpe: 5.482. Portfolio: return=6.32%, vol=0.42%. Weights: w_XLV=0.0267, w_LINK-USD=0.0000, w_SHV=0.9696, w_UNG=0.0037.

Question:
Assets: XLV, LINK-USD, SHV, UNG
Annualized mean returns: XLV:0.5389, LINK-USD:-1.5435, SHV:0.0434, UNG:1.8225
Covariance matrix (annualized):
[[0.016399, -0.00861, -2e-06, -0.014193], [-0.00861, 0.820715, 0.000348, -0.017465], [-2e-06, 0.000348, 4e-06, -0.000322], [-0.014193, -0.017465, -0.000322, 0.565408]]
Risk-free rate: 4.00%
Constraints: weights 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=0.0267, w_LINK-USD=0.0000, w_SHV=0.9696, w_UNG=0.0037

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLV=0.0267, w_LINK-USD=0.0000, w_SHV=0.9696, w_UNG=0.0037
Portfolio annualized return: 6.32%, volatility: 0.42%
Sharpe ratio: (0.0632 - 0.0400) / 0.0042 = 5.4823


4-asset optimization. Max-Sharpe: 0.551. Portfolio: return=11.85%, vol=14.24%. Weights: w_SPY=1.0000, w_LINK-USD=0.0000, w_SGOV=0.0000, w_BNO=0.0000.

Question:
Assets: SPY, LINK-USD, SGOV, BNO
Annualized mean returns: SPY:0.1185, LINK-USD:-3.7261, SGOV:0.0379, BNO:-0.5142
Covariance matrix (annualized):
[[0.020289, 0.066936, -5.1e-05, 0.00887], [0.066936, 0.704553, -0.000633, 0.057954], [-5.1e-05, -0.000633, 3e-06, -7e-05], [0.00887, 0.057954, -7e-05, 0.064893]]
Risk-free rate: 4.00%
Constraints: weights 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=1.0000, w_LINK-USD=0.0000, w_SGOV=0.0000, w_BNO=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_SPY=1.0000, w_LINK-USD=0.0000, w_SGOV=0.0000, w_BNO=0.0000
Portfolio annualized return: 11.85%, volatility: 14.24%
Sharpe ratio: (0.1185 - 0.0400) / 0.1424 = 0.5511


4-asset optimization. Max-Sharpe: 5.623. Portfolio: return=90.00%, vol=15.29%. Weights: w_SPY=0.8390, w_ETH-USD=0.1610, w_DBB=0.0000, w_CSHI=0.0000.

Question:
Assets: SPY, ETH-USD, DBB, CSHI
Annualized mean returns: SPY:0.4859, ETH-USD:3.0573, DBB:0.2347, CSHI:0.0490
Covariance matrix (annualized):
[[0.008677, 0.030101, 0.00539, 0.000245], [0.030101, 0.352783, 0.029215, 0.001295], [0.00539, 0.029215, 0.016233, -0.000129], [0.000245, 0.001295, -0.000129, 9.6e-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_SPY=0.8390, w_ETH-USD=0.1610, w_DBB=0.0000, w_CSHI=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_SPY=0.8390, w_ETH-USD=0.1610, w_DBB=0.0000, w_CSHI=0.0000
Portfolio annualized return: 90.00%, volatility: 15.29%
Sharpe ratio: (0.9000 - 0.0400) / 0.1529 = 5.6232


4-asset optimization. Max-Sharpe: 2.721. Portfolio: return=20.38%, vol=6.02%. Weights: w_XLE=0.0000, w_ETH-USD=0.0000, w_IEF=1.0000, w_BIL=0.0000.

Question:
Assets: XLE, ETH-USD, IEF, BIL
Annualized mean returns: XLE:-0.0744, ETH-USD:-2.3457, IEF:0.2038, BIL:0.0399
Covariance matrix (annualized):
[[0.051905, 0.032767, 0.000288, -2.2e-05], [0.032767, 0.423685, -0.012104, -0.00015], [0.000288, -0.012104, 0.003625, 4e-06], [-2.2e-05, -0.00015, 4e-06, 3e-06]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_XLE=0.0000, w_ETH-USD=0.0000, w_IEF=1.0000, w_BIL=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLE=0.0000, w_ETH-USD=0.0000, w_IEF=1.0000, w_BIL=0.0000
Portfolio annualized return: 20.38%, volatility: 6.02%
Sharpe ratio: (0.2038 - 0.0400) / 0.0602 = 2.7211


4-asset optimization. Max-Sharpe: 3.855. Portfolio: return=9.65%, vol=1.47%. Weights: w_XLU=0.0207, w_SOL-USD=0.0015, w_SHY=0.0000, w_CSHI=0.9778.

Question:
Assets: XLU, SOL-USD, SHY, CSHI
Annualized mean returns: XLU:0.3533, SOL-USD:0.5499, SHY:0.0169, CSHI:0.0904
Covariance matrix (annualized):
[[0.027033, -0.010993, 0.000653, 0.000663], [-0.010993, 0.356667, -0.002581, 0.001687], [0.000653, -0.002581, 0.000294, -1.2e-05], [0.000663, 0.001687, -1.2e-05, 0.00018]]
Risk-free rate: 4.00%
Constraints: weights 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=0.0207, w_SOL-USD=0.0015, w_SHY=0.0000, w_CSHI=0.9778

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLU=0.0207, w_SOL-USD=0.0015, w_SHY=0.0000, w_CSHI=0.9778
Portfolio annualized return: 9.65%, volatility: 1.47%
Sharpe ratio: (0.0965 - 0.0400) / 0.0147 = 3.8546


4-asset optimization. Max-Sharpe: 5.209. Portfolio: return=121.14%, vol=22.49%. Weights: w_XLK=0.8848, w_ADA-USD=0.0000, w_MORT=0.1152, w_SHY=0.0000.

Question:
Assets: XLK, ADA-USD, MORT, SHY
Annualized mean returns: XLK:1.2650, ADA-USD:0.7948, MORT:0.7995, SHY:0.0169
Covariance matrix (annualized):
[[0.055764, 0.041765, 0.030764, -0.001147], [0.041765, 0.401593, 0.020849, -0.003988], [0.030764, 0.020849, 0.04832, 0.000418], [-0.001147, -0.003988, 0.000418, 0.000333]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_XLK=0.8848, w_ADA-USD=0.0000, w_MORT=0.1152, w_SHY=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLK=0.8848, w_ADA-USD=0.0000, w_MORT=0.1152, w_SHY=0.0000
Portfolio annualized return: 121.14%, volatility: 22.49%
Sharpe ratio: (1.2114 - 0.0400) / 0.2249 = 5.2092


4-asset optimization. Max-Sharpe: 4.441. Portfolio: return=22.94%, vol=4.26%. Weights: w_USMV=0.0000, w_BTC-USD=0.0545, w_JNK=0.9073, w_SOYB=0.0383.

Question:
Assets: USMV, BTC-USD, JNK, SOYB
Annualized mean returns: USMV:0.1064, BTC-USD:0.5320, JNK:0.2147, SOYB:0.1466
Covariance matrix (annualized):
[[0.01134, -0.007448, 0.002339, -0.00307], [-0.007448, 0.104588, -0.001019, -0.001248], [0.002339, -0.001019, 0.001896, 0.000322], [-0.00307, -0.001248, 0.000322, 0.02088]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_USMV=0.0000, w_BTC-USD=0.0545, w_JNK=0.9073, w_SOYB=0.0383

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_USMV=0.0000, w_BTC-USD=0.0545, w_JNK=0.9073, w_SOYB=0.0383
Portfolio annualized return: 22.94%, volatility: 4.26%
Sharpe ratio: (0.2294 - 0.0400) / 0.0426 = 4.4412


4-asset optimization. Max-Sharpe: 3.082. Portfolio: return=54.29%, vol=16.32%. Weights: w_EEM=0.0000, w_SOL-USD=0.0000, w_GLD=1.0000, w_IYR=0.0000.

Question:
Assets: EEM, SOL-USD, GLD, IYR
Annualized mean returns: EEM:0.0107, SOL-USD:-2.4073, GLD:0.5429, IYR:-0.1834
Covariance matrix (annualized):
[[0.015502, 0.025504, 0.005096, 0.00102], [0.025504, 0.464799, 0.022479, 0.005404], [0.005096, 0.022479, 0.026625, 0.003815], [0.00102, 0.005404, 0.003815, 0.016888]]
Risk-free rate: 4.00%
Constraints: weights 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_GLD=1.0000, w_IYR=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EEM=0.0000, w_SOL-USD=0.0000, w_GLD=1.0000, w_IYR=0.0000
Portfolio annualized return: 54.29%, volatility: 16.32%
Sharpe ratio: (0.5429 - 0.0400) / 0.1632 = 3.0821


4-asset optimization. Max-Sharpe: 5.649. Portfolio: return=12.63%, vol=1.53%. Weights: w_^VIX=0.0101, w_BNB-USD=0.0195, w_CSHI=0.5502, w_JNK=0.4202.

Question:
Assets: ^VIX, BNB-USD, CSHI, JNK
Annualized mean returns: ^VIX:-2.4289, BNB-USD:0.8170, CSHI:0.0683, JNK:0.2317
Covariance matrix (annualized):
[[1.237936, -0.083325, -0.00361, -0.037138], [-0.083325, 0.106473, 0.000481, 0.001442], [-0.00361, 0.000481, 0.000149, 5.2e-05], [-0.037138, 0.001442, 5.2e-05, 0.001994]]
Risk-free rate: 4.00%
Constraints: weights 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=0.0101, w_BNB-USD=0.0195, w_CSHI=0.5502, w_JNK=0.4202

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_^VIX=0.0101, w_BNB-USD=0.0195, w_CSHI=0.5502, w_JNK=0.4202
Portfolio annualized return: 12.63%, volatility: 1.53%
Sharpe ratio: (0.1263 - 0.0400) / 0.0153 = 5.6486


4-asset optimization. Max-Sharpe: 1.501. Portfolio: return=4.87%, vol=0.58%. Weights: w_VTI=0.0000, w_AVAX-USD=0.0000, w_CSHI=1.0000, w_XHB=0.0000.

Question:
Assets: VTI, AVAX-USD, CSHI, XHB
Annualized mean returns: VTI:0.0611, AVAX-USD:-1.4710, CSHI:0.0487, XHB:-0.4207
Covariance matrix (annualized):
[[0.022144, 0.051218, 0.000455, 0.024468], [0.051218, 0.586145, 0.002141, 0.066358], [0.000455, 0.002141, 3.3e-05, 0.000401], [0.024468, 0.066358, 0.000401, 0.057503]]
Risk-free rate: 4.00%
Constraints: weights 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_AVAX-USD=0.0000, w_CSHI=1.0000, w_XHB=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VTI=0.0000, w_AVAX-USD=0.0000, w_CSHI=1.0000, w_XHB=0.0000
Portfolio annualized return: 4.87%, volatility: 0.58%
Sharpe ratio: (0.0487 - 0.0400) / 0.0058 = 1.5007


4-asset optimization. Max-Sharpe: 2.578. Portfolio: return=27.88%, vol=9.26%. Weights: w_SPY=0.5920, w_DOT-USD=0.0000, w_SOYB=0.1413, w_MORT=0.2668.

Question:
Assets: SPY, DOT-USD, SOYB, MORT
Annualized mean returns: SPY:0.2578, DOT-USD:-0.6258, SOYB:0.1662, MORT:0.3849
Covariance matrix (annualized):
[[0.009274, 0.029267, 0.002458, 0.007445], [0.029267, 0.463018, 0.016456, 0.045501], [0.002458, 0.016456, 0.016068, 0.003029], [0.007445, 0.045501, 0.003029, 0.028326]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: bull

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

Answer: w_SPY=0.5920, w_DOT-USD=0.0000, w_SOYB=0.1413, w_MORT=0.2668

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_SPY=0.5920, w_DOT-USD=0.0000, w_SOYB=0.1413, w_MORT=0.2668
Portfolio annualized return: 27.88%, volatility: 9.26%
Sharpe ratio: (0.2788 - 0.0400) / 0.0926 = 2.5780


4-asset optimization. Max-Sharpe: 6.695. Portfolio: return=12.01%, vol=1.20%. Weights: w_VLUE=0.0963, w_SOL-USD=0.0000, w_ICSH=0.9037, w_SCHP=0.0000.

Question:
Assets: VLUE, SOL-USD, ICSH, SCHP
Annualized mean returns: VLUE:0.7893, SOL-USD:2.0483, ICSH:0.0488, SCHP:0.0899
Covariance matrix (annualized):
[[0.013506, 0.038137, 4.3e-05, 0.001299], [0.038137, 0.600402, 0.000341, 0.009236], [4.3e-05, 0.000341, 1.3e-05, 2.1e-05], [0.001299, 0.009236, 2.1e-05, 0.001049]]
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=0.0963, w_SOL-USD=0.0000, w_ICSH=0.9037, w_SCHP=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VLUE=0.0963, w_SOL-USD=0.0000, w_ICSH=0.9037, w_SCHP=0.0000
Portfolio annualized return: 12.01%, volatility: 1.20%
Sharpe ratio: (0.1201 - 0.0400) / 0.0120 = 6.6948


4-asset optimization. Max-Sharpe: 1.957. Portfolio: return=44.57%, vol=20.74%. Weights: w_QUAL=0.1244, w_SOL-USD=0.2083, w_VNQI=0.1204, w_DBB=0.5468.

Question:
Assets: QUAL, SOL-USD, VNQI, DBB
Annualized mean returns: QUAL:0.1406, SOL-USD:1.4664, VNQI:0.1592, DBB:0.1894
Covariance matrix (annualized):
[[0.010087, 0.03358, 0.005894, 0.003115], [0.03358, 0.587627, 0.040099, 0.0361], [0.005894, 0.040099, 0.012249, 0.003785], [0.003115, 0.0361, 0.003785, 0.013652]]
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=0.1244, w_SOL-USD=0.2083, w_VNQI=0.1204, w_DBB=0.5468

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_QUAL=0.1244, w_SOL-USD=0.2083, w_VNQI=0.1204, w_DBB=0.5468
Portfolio annualized return: 44.57%, volatility: 20.74%
Sharpe ratio: (0.4457 - 0.0400) / 0.2074 = 1.9565


4-asset optimization. Max-Sharpe: 1.118. Portfolio: return=5.31%, vol=1.17%. Weights: w_XLY=0.0000, w_LINK-USD=0.0000, w_USO=0.0000, w_CSHI=1.0000.

Question:
Assets: XLY, LINK-USD, USO, CSHI
Annualized mean returns: XLY:-0.1205, LINK-USD:-3.9914, USO:-0.1406, CSHI:0.0531
Covariance matrix (annualized):
[[0.046721, 0.072722, 0.013629, 0.000396], [0.072722, 0.69822, 0.077015, 0.000682], [0.013629, 0.077015, 0.073082, 0.000432], [0.000396, 0.000682, 0.000432, 0.000136]]
Risk-free rate: 4.00%
Constraints: weights 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_USO=0.0000, w_CSHI=1.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLY=0.0000, w_LINK-USD=0.0000, w_USO=0.0000, w_CSHI=1.0000
Portfolio annualized return: 5.31%, volatility: 1.17%
Sharpe ratio: (0.0531 - 0.0400) / 0.0117 = 1.1178


4-asset optimization. Max-Sharpe: 3.919. Portfolio: return=86.57%, vol=21.07%. Weights: w_ACWI=0.6835, w_BTC-USD=0.3165, w_BNO=0.0000, w_REZ=0.0000.

Question:
Assets: ACWI, BTC-USD, BNO, REZ
Annualized mean returns: ACWI:0.6248, BTC-USD:1.3860, BNO:0.1360, REZ:0.0698
Covariance matrix (annualized):
[[0.032247, 0.029714, 0.024508, 0.02594], [0.029714, 0.16448, 0.064686, 0.020566], [0.024508, 0.064686, 0.106753, 0.023772], [0.02594, 0.020566, 0.023772, 0.04694]]
Risk-free rate: 4.00%
Constraints: weights 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=0.6835, w_BTC-USD=0.3165, w_BNO=0.0000, w_REZ=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_ACWI=0.6835, w_BTC-USD=0.3165, w_BNO=0.0000, w_REZ=0.0000
Portfolio annualized return: 86.57%, volatility: 21.07%
Sharpe ratio: (0.8657 - 0.0400) / 0.2107 = 3.9189


4-asset optimization. Max-Sharpe: 4.948. Portfolio: return=70.32%, vol=13.41%. Weights: w_XLF=0.0000, w_XRP-USD=0.0274, w_VNQI=0.6931, w_PALL=0.2794.

Question:
Assets: XLF, XRP-USD, VNQI, PALL
Annualized mean returns: XLF:0.0726, XRP-USD:0.8979, VNQI:0.3214, PALL:1.6314
Covariance matrix (annualized):
[[0.019838, 0.017356, 0.009512, 0.000716], [0.017356, 0.258311, 0.000703, 0.056098], [0.009512, 0.000703, 0.009019, 0.004841], [0.000716, 0.056098, 0.004841, 0.13679]]
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_XRP-USD=0.0274, w_VNQI=0.6931, w_PALL=0.2794

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLF=0.0000, w_XRP-USD=0.0274, w_VNQI=0.6931, w_PALL=0.2794
Portfolio annualized return: 70.32%, volatility: 13.41%
Sharpe ratio: (0.7032 - 0.0400) / 0.1341 = 4.9476


4-asset optimization. Max-Sharpe: 4.286. Portfolio: return=44.96%, vol=9.56%. Weights: w_FXI=0.2304, w_LINK-USD=0.0000, w_SCHP=0.0840, w_HAUZ=0.6856.

Question:
Assets: FXI, LINK-USD, SCHP, HAUZ
Annualized mean returns: FXI:0.6194, LINK-USD:-0.1147, SCHP:0.0351, HAUZ:0.4434
Covariance matrix (annualized):
[[0.04518, 0.043237, -0.004193, 0.004176], [0.043237, 0.543679, -0.009074, -0.00631], [-0.004193, -0.009074, 0.002409, 0.000954], [0.004176, -0.00631, 0.000954, 0.011598]]
Risk-free rate: 4.00%
Constraints: weights 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=0.2304, w_LINK-USD=0.0000, w_SCHP=0.0840, w_HAUZ=0.6856

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_FXI=0.2304, w_LINK-USD=0.0000, w_SCHP=0.0840, w_HAUZ=0.6856
Portfolio annualized return: 44.96%, volatility: 9.56%
Sharpe ratio: (0.4496 - 0.0400) / 0.0956 = 4.2861


4-asset optimization. Max-Sharpe: 4.776. Portfolio: return=7.39%, vol=0.71%. Weights: w_EEM=0.0523, w_DOT-USD=0.0000, w_MORT=0.0000, w_BIL=0.9477.

Question:
Assets: EEM, DOT-USD, MORT, BIL
Annualized mean returns: EEM:0.6903, DOT-USD:-0.6045, MORT:0.2982, BIL:0.0398
Covariance matrix (annualized):
[[0.019948, 0.010705, 0.008319, -8.2e-05], [0.010705, 0.413289, 0.011515, 0.000138], [0.008319, 0.011515, 0.033288, -4.5e-05], [-8.2e-05, 0.000138, -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_EEM=0.0523, w_DOT-USD=0.0000, w_MORT=0.0000, w_BIL=0.9477

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EEM=0.0523, w_DOT-USD=0.0000, w_MORT=0.0000, w_BIL=0.9477
Portfolio annualized return: 7.39%, volatility: 0.71%
Sharpe ratio: (0.0739 - 0.0400) / 0.0071 = 4.7756


4-asset optimization. Max-Sharpe: 2.409. Portfolio: return=31.40%, vol=11.37%. Weights: w_VLUE=0.0000, w_ETH-USD=0.0000, w_PPLT=0.0236, w_VNQI=0.9764.

Question:
Assets: VLUE, ETH-USD, PPLT, VNQI
Annualized mean returns: VLUE:-0.0012, ETH-USD:-2.4811, PPLT:0.2107, VNQI:0.3165
Covariance matrix (annualized):
[[0.021579, 0.032364, 0.001161, 0.009255], [0.032364, 0.456923, 0.024924, 0.027519], [0.001161, 0.024924, 0.027804, 0.007581], [0.009255, 0.027519, 0.007581, 0.013187]]
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_ETH-USD=0.0000, w_PPLT=0.0236, w_VNQI=0.9764

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VLUE=0.0000, w_ETH-USD=0.0000, w_PPLT=0.0236, w_VNQI=0.9764
Portfolio annualized return: 31.40%, volatility: 11.37%
Sharpe ratio: (0.3140 - 0.0400) / 0.1137 = 2.4091


4-asset optimization. Max-Sharpe: 5.944. Portfolio: return=42.04%, vol=6.40%. Weights: w_XLP=0.0000, w_XRP-USD=0.0000, w_TLH=0.5601, w_DBA=0.4399.

Question:
Assets: XLP, XRP-USD, TLH, DBA
Annualized mean returns: XLP:-0.1310, XRP-USD:-0.5560, TLH:0.3619, DBA:0.4949
Covariance matrix (annualized):
[[0.011283, 0.015324, 0.002016, 0.001139], [0.015324, 0.38458, 0.010419, 0.001156], [0.002016, 0.010419, 0.00751, -0.001685], [0.001139, 0.001156, -0.001685, 0.013278]]
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_XLP=0.0000, w_XRP-USD=0.0000, w_TLH=0.5601, w_DBA=0.4399

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLP=0.0000, w_XRP-USD=0.0000, w_TLH=0.5601, w_DBA=0.4399
Portfolio annualized return: 42.04%, volatility: 6.40%
Sharpe ratio: (0.4204 - 0.0400) / 0.0640 = 5.9445


4-asset optimization. Max-Sharpe: 4.315. Portfolio: return=65.67%, vol=14.29%. Weights: w_VLUE=0.9722, w_XRP-USD=0.0000, w_INDS=0.0000, w_UNG=0.0278.

Question:
Assets: VLUE, XRP-USD, INDS, UNG
Annualized mean returns: VLUE:0.6648, XRP-USD:-0.2720, INDS:0.3819, UNG:0.3743
Covariance matrix (annualized):
[[0.021223, 0.031811, 0.012776, 0.00207], [0.031811, 0.280689, 0.004805, 0.000277], [0.012776, 0.004805, 0.019745, -0.003089], [0.00207, 0.000277, -0.003089, 0.325947]]
Risk-free rate: 4.00%
Constraints: weights 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=0.9722, w_XRP-USD=0.0000, w_INDS=0.0000, w_UNG=0.0278

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VLUE=0.9722, w_XRP-USD=0.0000, w_INDS=0.0000, w_UNG=0.0278
Portfolio annualized return: 65.67%, volatility: 14.29%
Sharpe ratio: (0.6567 - 0.0400) / 0.1429 = 4.3154